Add Elmar Peise's ReLAPACK

relapack/LICENSE

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+The MIT License (MIT)
+
+Copyright (c) 2016 Elmar Peise
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+

relapack/Makefile

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+TOPDIR  = ..
+include $(TOPDIR)/Makefile.system
+
+
+
+SRC = $(wildcard src/*.c)
+OBJS = $(SRC:%.c=%.o)
+
+TEST_SUITS = \
+	slauum dlauum clauum zlauum \
+	spotrf dpotrf cpotrf zpotrf \
+	spbtrf dpbtrf cpbtrf zpbtrf \
+	ssygst dsygst chegst zhegst \
+	ssytrf dsytrf csytrf chetrf zsytrf zhetrf \
+	sgetrf dgetrf cgetrf zgetrf \
+	sgbtrf dgbtrf cgbtrf zgbtrf \
+	strsyl dtrsyl ctrsyl ztrsyl \
+	stgsyl dtgsyl ctgsyl ztgsyl \
+	sgemmt dgemmt cgemmt zgemmt
+TESTS = $(TEST_SUITS:%=test/%.pass)  # dummies
+TEST_EXES = $(TEST_SUITS:%=test/%.x)
+
+LINK_TEST = -L$(TOPDIR) -lopenblas -lgfortran -lm
+
+.SECONDARY: $(TEST_EXES)
+.PHONY: test
+
+# ReLAPACK compilation
+
+libs:	$(OBJS)
+	@echo "Building ReLAPACK library $(LIBNAME)"
+	$(AR) -r  $(TOPDIR)/$(LIBNAME) $(OBJS)
+	$(RANLIB) $(TOPDIR)/$(LIBNAME)
+
+%.o: %.c config.h
+	$(CC) $(CFLAGS) -c $< -o $@
+
+
+# ReLAPACK testing
+
+test: $(TEST_EXES) $(TESTS)
+	@echo "passed all tests"
+
+test/%.pass: test/%.x
+	@echo -n $*:
+	@./$< > /dev/null && echo " pass" || (echo " FAIL" && ./$<)
+
+test/s%.x: test/x%.c test/util.o $(TOPDIR)/$(LIBNAME) test/config.h test/test.h
+	$(CC) $(CFLAGS) -DDT_PREFIX=s $< test/util.o -o $@ $(LINK_TEST) $(TOPDIR)/$(LIBNAME) $(LINK_TEST)
+
+test/d%.x: test/x%.c test/util.o $(TOPDIR)/$(LIBNAME) test/config.h test/test.h
+	$(CC) $(CFLAGS) -DDT_PREFIX=d $< test/util.o -o $@ $(LINK_TEST) $(TOPDIR)/$(LIBNAME) $(LINK_TEST)
+
+test/c%.x: test/x%.c test/util.o $(TOPDIR)/$(LIBNAME) test/config.h test/test.h
+	$(CC) $(CFLAGS) -DDT_PREFIX=c $< test/util.o -o $@ $(LINK_TEST) $(TOPDIR)/$(LIBNAME) $(LINK_TEST)
+
+test/z%.x: test/x%.c test/util.o $(TOPDIR)/$(LIBNAME) test/config.h test/test.h
+	$(CC) $(CFLAGS) -DDT_PREFIX=z $< test/util.o -o $@ $(LINK_TEST) $(TOPDIR)/$(LIBNAME) $(LINK_TEST)
+
+
+# cleaning up
+
+clean:
+	rm -f  $(OBJS) test/util.o test/*.x

relapack/README.md

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+ReLAPACK
+========
+
+[![Build Status](https://travis-ci.org/HPAC/ReLAPACK.svg?branch=master)](https://travis-ci.org/HPAC/ReLAPACK)
+
+[Recursive LAPACK Collection](https://github.com/HPAC/ReLAPACK)
+
+ReLAPACK offers a collection of recursive algorithms for many of LAPACK's
+compute kernels.  Since it preserves LAPACK's established interfaces, ReLAPACK
+integrates effortlessly into existing application codes.  ReLAPACK's routines
+not only outperform the reference LAPACK but also improve upon the performance
+of tuned implementations, such as OpenBLAS and MKL.
+
+
+Coverage
+--------
+For a detailed list of covered operations and an overview of operations to which
+recursion is not efficiently applicable, see [coverage.md](coverage.md).
+
+
+Installation
+------------
+To compile with the default configuration, simply run `make` to create the
+library `librelapack.a`.
+
+### Linking with MKL
+Note that to link with MKL, you currently need to set the flag
+`COMPLEX_FUNCTIONS_AS_ROUTINES` to `1` to avoid problems in `ctrsyl` and
+`ztrsyl`.  For further configuration options see [config.md](config.md).
+
+
+### Dependencies
+ReLAPACK builds on top of [BLAS](http://www.netlib.org/blas/) and unblocked
+kernels from [LAPACK](http://www.netlib.org/lapack/).  There are many optimized
+and machine specific implementations of these libraries, which are commonly
+provided by hardware vendors or available as open source (e.g.,
+[OpenBLAS](http://www.openblas.net/)).
+
+
+Testing
+-------
+ReLAPACK's test suite compares its routines numerically with LAPACK's
+counterparts.  To set up the tests (located int `test/`) you need to specify
+link flags for BLAS and LAPACK (version 3.5.0 or newer) in `make.inc`; then
+`make test` runs the tests.  For details on the performed tests, see
+[test/README.md](test/README.md).
+
+
+Examples
+--------
+Since ReLAPACK replaces parts of LAPACK, any LAPACK example involving the
+covered routines applies directly to ReLAPACK.  A few separate examples are
+given in `examples/`. For details, see [examples/README.md](examples/README.md).
+
+
+Citing
+------
+When referencing ReLAPACK, please cite the preprint of the paper
+[Recursive Algorithms for Dense Linear Algebra: The ReLAPACK Collection](http://arxiv.org/abs/1602.06763):
+
+    @article{relapack,
+      author    = {Elmar Peise and Paolo Bientinesi},
+      title     = {Recursive Algorithms for Dense Linear Algebra: The ReLAPACK Collection},
+      journal   = {CoRR},
+      volume    = {abs/1602.06763},
+      year      = {2016},
+      url       = {http://arxiv.org/abs/1602.06763},
+    }

relapack/config.h

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+#ifndef RELAPACK_CONFIG_H
+#define RELAPACK_CONFIG_H
+
+// ReLAPACK configuration file.
+// See also config.md
+
+
+///////////////////////////////
+// BLAS/LAPACK obect symbols //
+///////////////////////////////
+
+// BLAS routines linked against have a trailing underscore
+#define BLAS_UNDERSCORE 1
+// LAPACK routines linked against have a trailing underscore
+#define LAPACK_UNDERSCORE BLAS_UNDERSCORE
+
+// Complex BLAS/LAPACK routines return their result in the first argument
+// This option must be enabled when linking to MKL for ctrsyl and ztrsyl to
+// work.
+#define COMPLEX_FUNCTIONS_AS_ROUTINES 0
+#ifdef F_INTERFACE_INTEL
+#define COMPLEX_FUNCTIONS_AS_ROUTINES 1
+#endif
+#define BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES COMPLEX_FUNCTIONS_AS_ROUTINES
+#define LAPACK_BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES COMPLEX_FUNCTIONS_AS_ROUTINES
+
+// The BLAS-like extension xgemmt is provided by an external library.
+#define HAVE_XGEMMT 0
+
+
+////////////////////////////
+// Use malloc in ReLAPACK //
+////////////////////////////
+
+#define ALLOW_MALLOC 1
+// allow malloc in xsygst for improved performance
+#define XSYGST_ALLOW_MALLOC ALLOW_MALLOC
+// allow malloc in xsytrf if the passed work buffer is too small
+#define XSYTRF_ALLOW_MALLOC ALLOW_MALLOC
+
+
+////////////////////////////////
+// LAPACK routine replacement //
+////////////////////////////////
+// The following macros specify which routines are included in the library under
+// LAPACK's symbol names: 1 included, 0 not included
+
+#define INCLUDE_ALL 1
+
+#define INCLUDE_XLAUUM INCLUDE_ALL
+#define INCLUDE_SLAUUM INCLUDE_XLAUUM
+#define INCLUDE_DLAUUM INCLUDE_XLAUUM
+#define INCLUDE_CLAUUM INCLUDE_XLAUUM
+#define INCLUDE_ZLAUUM INCLUDE_XLAUUM
+
+#define INCLUDE_XSYGST INCLUDE_ALL
+#define INCLUDE_SSYGST INCLUDE_XSYGST
+#define INCLUDE_DSYGST INCLUDE_XSYGST
+#define INCLUDE_CHEGST INCLUDE_XSYGST
+#define INCLUDE_ZHEGST INCLUDE_XSYGST
+
+#define INCLUDE_XTRTRI INCLUDE_ALL
+#define INCLUDE_STRTRI INCLUDE_XTRTRI
+#define INCLUDE_DTRTRI INCLUDE_XTRTRI
+#define INCLUDE_CTRTRI INCLUDE_XTRTRI
+#define INCLUDE_ZTRTRI INCLUDE_XTRTRI
+
+#define INCLUDE_XPOTRF INCLUDE_ALL
+#define INCLUDE_SPOTRF INCLUDE_XPOTRF
+#define INCLUDE_DPOTRF INCLUDE_XPOTRF
+#define INCLUDE_CPOTRF INCLUDE_XPOTRF
+#define INCLUDE_ZPOTRF INCLUDE_XPOTRF
+
+#define INCLUDE_XPBTRF INCLUDE_ALL
+#define INCLUDE_SPBTRF INCLUDE_XPBTRF
+#define INCLUDE_DPBTRF INCLUDE_XPBTRF
+#define INCLUDE_CPBTRF INCLUDE_XPBTRF
+#define INCLUDE_ZPBTRF INCLUDE_XPBTRF
+
+#define INCLUDE_XSYTRF INCLUDE_ALL
+#define INCLUDE_SSYTRF INCLUDE_XSYTRF
+#define INCLUDE_DSYTRF INCLUDE_XSYTRF
+#define INCLUDE_CSYTRF INCLUDE_XSYTRF
+#define INCLUDE_CHETRF INCLUDE_XSYTRF
+#define INCLUDE_ZSYTRF INCLUDE_XSYTRF
+#define INCLUDE_ZHETRF INCLUDE_XSYTRF
+#define INCLUDE_SSYTRF_ROOK INCLUDE_SSYTRF
+#define INCLUDE_DSYTRF_ROOK INCLUDE_DSYTRF
+#define INCLUDE_CSYTRF_ROOK INCLUDE_CSYTRF
+#define INCLUDE_CHETRF_ROOK INCLUDE_CHETRF
+#define INCLUDE_ZSYTRF_ROOK INCLUDE_ZSYTRF
+#define INCLUDE_ZHETRF_ROOK INCLUDE_ZHETRF
+
+#define INCLUDE_XGETRF INCLUDE_ALL
+#define INCLUDE_SGETRF INCLUDE_XGETRF
+#define INCLUDE_DGETRF INCLUDE_XGETRF
+#define INCLUDE_CGETRF INCLUDE_XGETRF
+#define INCLUDE_ZGETRF INCLUDE_XGETRF
+
+#define INCLUDE_XGBTRF INCLUDE_ALL
+#define INCLUDE_SGBTRF INCLUDE_XGBTRF
+#define INCLUDE_DGBTRF INCLUDE_XGBTRF
+#define INCLUDE_CGBTRF INCLUDE_XGBTRF
+#define INCLUDE_ZGBTRF INCLUDE_XGBTRF
+
+#define INCLUDE_XTRSYL INCLUDE_ALL
+#define INCLUDE_STRSYL INCLUDE_XTRSYL
+#define INCLUDE_DTRSYL INCLUDE_XTRSYL
+#define INCLUDE_CTRSYL INCLUDE_XTRSYL
+#define INCLUDE_ZTRSYL INCLUDE_XTRSYL
+
+#define INCLUDE_XTGSYL INCLUDE_ALL
+#define INCLUDE_STGSYL INCLUDE_XTGSYL
+#define INCLUDE_DTGSYL INCLUDE_XTGSYL
+#define INCLUDE_CTGSYL INCLUDE_XTGSYL
+#define INCLUDE_ZTGSYL INCLUDE_XTGSYL
+
+#define INCLUDE_XGEMMT 0
+#define INCLUDE_SGEMMT INCLUDE_XGEMMT
+#define INCLUDE_DGEMMT INCLUDE_XGEMMT
+#define INCLUDE_CGEMMT INCLUDE_XGEMMT
+#define INCLUDE_ZGEMMT INCLUDE_XGEMMT
+
+
+/////////////////////
+// crossover sizes //
+/////////////////////
+
+// default crossover size
+#define CROSSOVER 24
+
+// individual crossover sizes
+#define CROSSOVER_XLAUUM CROSSOVER
+#define CROSSOVER_SLAUUM CROSSOVER_XLAUUM
+#define CROSSOVER_DLAUUM CROSSOVER_XLAUUM
+#define CROSSOVER_CLAUUM CROSSOVER_XLAUUM
+#define CROSSOVER_ZLAUUM CROSSOVER_XLAUUM
+
+#define CROSSOVER_XSYGST CROSSOVER
+#define CROSSOVER_SSYGST CROSSOVER_XSYGST
+#define CROSSOVER_DSYGST CROSSOVER_XSYGST
+#define CROSSOVER_CHEGST CROSSOVER_XSYGST
+#define CROSSOVER_ZHEGST CROSSOVER_XSYGST
+
+#define CROSSOVER_XTRTRI CROSSOVER
+#define CROSSOVER_STRTRI CROSSOVER_XTRTRI
+#define CROSSOVER_DTRTRI CROSSOVER_XTRTRI
+#define CROSSOVER_CTRTRI CROSSOVER_XTRTRI
+#define CROSSOVER_ZTRTRI CROSSOVER_XTRTRI
+
+#define CROSSOVER_XPOTRF CROSSOVER
+#define CROSSOVER_SPOTRF CROSSOVER_XPOTRF
+#define CROSSOVER_DPOTRF CROSSOVER_XPOTRF
+#define CROSSOVER_CPOTRF CROSSOVER_XPOTRF
+#define CROSSOVER_ZPOTRF CROSSOVER_XPOTRF
+
+#define CROSSOVER_XPBTRF CROSSOVER
+#define CROSSOVER_SPBTRF CROSSOVER_XPBTRF
+#define CROSSOVER_DPBTRF CROSSOVER_XPBTRF
+#define CROSSOVER_CPBTRF CROSSOVER_XPBTRF
+#define CROSSOVER_ZPBTRF CROSSOVER_XPBTRF
+
+#define CROSSOVER_XSYTRF CROSSOVER
+#define CROSSOVER_SSYTRF CROSSOVER_XSYTRF
+#define CROSSOVER_DSYTRF CROSSOVER_XSYTRF
+#define CROSSOVER_CSYTRF CROSSOVER_XSYTRF
+#define CROSSOVER_CHETRF CROSSOVER_XSYTRF
+#define CROSSOVER_ZSYTRF CROSSOVER_XSYTRF
+#define CROSSOVER_ZHETRF CROSSOVER_XSYTRF
+#define CROSSOVER_SSYTRF_ROOK CROSSOVER_SSYTRF
+#define CROSSOVER_DSYTRF_ROOK CROSSOVER_DSYTRF
+#define CROSSOVER_CSYTRF_ROOK CROSSOVER_CSYTRF
+#define CROSSOVER_CHETRF_ROOK CROSSOVER_CHETRF
+#define CROSSOVER_ZSYTRF_ROOK CROSSOVER_ZSYTRF
+#define CROSSOVER_ZHETRF_ROOK CROSSOVER_ZHETRF
+
+#define CROSSOVER_XGETRF CROSSOVER
+#define CROSSOVER_SGETRF CROSSOVER_XGETRF
+#define CROSSOVER_DGETRF CROSSOVER_XGETRF
+#define CROSSOVER_CGETRF CROSSOVER_XGETRF
+#define CROSSOVER_ZGETRF CROSSOVER_XGETRF
+
+#define CROSSOVER_XGBTRF CROSSOVER
+#define CROSSOVER_SGBTRF CROSSOVER_XGBTRF
+#define CROSSOVER_DGBTRF CROSSOVER_XGBTRF
+#define CROSSOVER_CGBTRF CROSSOVER_XGBTRF
+#define CROSSOVER_ZGBTRF CROSSOVER_XGBTRF
+
+#define CROSSOVER_XTRSYL CROSSOVER
+#define CROSSOVER_STRSYL CROSSOVER_XTRSYL
+#define CROSSOVER_DTRSYL CROSSOVER_XTRSYL
+#define CROSSOVER_CTRSYL CROSSOVER_XTRSYL
+#define CROSSOVER_ZTRSYL CROSSOVER_XTRSYL
+
+#define CROSSOVER_XTGSYL CROSSOVER
+#define CROSSOVER_STGSYL CROSSOVER_XTGSYL
+#define CROSSOVER_DTGSYL CROSSOVER_XTGSYL
+#define CROSSOVER_CTGSYL CROSSOVER_XTGSYL
+#define CROSSOVER_ZTGSYL CROSSOVER_XTGSYL
+
+// sytrf helper routine
+#define CROSSOVER_XGEMMT CROSSOVER_XSYTRF
+#define CROSSOVER_SGEMMT CROSSOVER_XGEMMT
+#define CROSSOVER_DGEMMT CROSSOVER_XGEMMT
+#define CROSSOVER_CGEMMT CROSSOVER_XGEMMT
+#define CROSSOVER_ZGEMMT CROSSOVER_XGEMMT
+
+#endif /* RELAPACK_CONFIG_H */

relapack/config.md

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+RELAPACK Configuration
+======================
+
+ReLAPACK has two configuration files: `make.inc`, which is included by the
+Makefile, and `config.h` which is included in the source files.
+
+
+Build and Testing Environment
+-----------------------------
+The build environment (compiler and flags) and the test configuration (linker
+flags for BLAS and LAPACK) are specified in `make.inc`.  The test matrix size
+and error bounds are defined in `test/config.h`.
+
+The library `librelapack.a` is compiled by invoking `make`.  The tests are
+performed by either `make test` or calling `make` in the test folder.
+
+
+BLAS/LAPACK complex function interfaces
+---------------------------------------
+For BLAS and LAPACK functions that return a complex number, there exist two
+conflicting (FORTRAN compiler dependent) calling conventions: either the result
+is returned as a `struct` of two floating point numbers or an additional first
+argument with a pointer to such a `struct` is used.  By default ReLAPACK uses
+the former (which is what gfortran uses), but it can switch to the latter by
+setting `COMPLEX_FUNCTIONS_AS_ROUTINES` (or explicitly the BLAS and LAPACK
+specific counterparts) to `1` in `config.h`.
+
+**For MKL, `COMPLEX_FUNCTIONS_AS_ROUTINES` must be set to `1`.**
+
+(Using the wrong convention will break `ctrsyl` and `ztrsyl` and the test cases
+will segfault or return errors on the order of 1 or larger.)
+
+
+BLAS extension `xgemmt`
+-----------------------
+The LDL decompositions require a general matrix-matrix product that updates only
+a triangular matrix called `xgemmt`.  If the BLAS implementation linked against
+provides such a routine, set the flag `HAVE_XGEMMT` to `1` in `config.h`;
+otherwise, ReLAPACK uses its own recursive implementation of these kernels.
+
+`xgemmt` is provided by MKL.
+
+
+Routine Selection
+-----------------
+ReLAPACK's routines are named `RELAPACK_X` (e.g., `RELAPACK_dgetrf`).  If the
+corresponding `INCLUDE_X` flag in `config.h` (e.g., `INCLUDE_DGETRF`) is set to
+`1`, ReLAPACK additionally provides a wrapper under the LAPACK name (e.g.,
+`dgetrf_`).  By default, wrappers for all routines are enabled.
+
+
+Crossover Size
+--------------
+The crossover size determines below which matrix sizes ReLAPACK's recursive
+algorithms switch to LAPACK's unblocked routines to avoid tiny BLAS Level 3
+routines.  The crossover size is set in `config.h` and can be chosen either
+globally for the entire library, by operation, or individually by routine.
+
+
+Allowing Temporary Buffers
+--------------------------
+Two of ReLAPACK's routines make use of temporary buffers, which are allocated
+and freed within ReLAPACK.  Setting `ALLOW_MALLOC` (or one of the routine
+specific counterparts) to 0 in `config.h` will disable these buffers.  The
+affected routines are:
+
+ * `xsytrf`: The LDL decomposition requires a buffer of size n^2 / 2.  As in
+   LAPACK, this size can be queried by setting `lWork = -1` and the passed
+   buffer will be used if it is large enough; only if it is not, a local buffer
+   will be allocated.
+
+   The advantage of this mechanism is that ReLAPACK will seamlessly work even
+   with codes that statically provide too little memory instead of breaking
+   them.
+
+ * `xsygst`: The reduction of a real symmetric-definite generalized eigenproblem
+   to standard form can use an auxiliary buffer of size n^2 / 2 to avoid
+   redundant computations.  It thereby performs about 30% less FLOPs than
+   LAPACK.
+
+
+FORTRAN symbol names
+--------------------
+ReLAPACK is commonly linked to BLAS and LAPACK with standard FORTRAN interfaces.
+Since these libraries usually have an underscore to their symbol names, ReLAPACK
+has configuration switches in `config.h` to adjust the corresponding routine
+names.

relapack/coverage.md

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+Coverage of ReLAPACK
+====================
+
+This file lists all LAPACK compute routines that are covered by recursive
+algorithms in ReLAPACK, it also lists all of LAPACK's blocked algorithms which
+are not (yet) part of ReLAPACK.
+
+<!-- START doctoc generated TOC please keep comment here to allow auto update -->
+<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
+**Table of Contents**  *generated with [DocToc](https://github.com/thlorenz/doctoc)*
+
+- [List of covered LAPACK routines](#list-of-covered-lapack-routines)
+  - [`xlauum`](#xlauum)
+  - [`xsygst`](#xsygst)
+  - [`xtrtri`](#xtrtri)
+  - [`xpotrf`](#xpotrf)
+  - [`xpbtrf`](#xpbtrf)
+  - [`xsytrf`](#xsytrf)
+  - [`xgetrf`](#xgetrf)
+  - [`xgbtrf`](#xgbtrf)
+  - [`xtrsyl`](#xtrsyl)
+  - [`xtgsyl`](#xtgsyl)
+- [Covered BLAS extension](#covered-blas-extension)
+  - [`xgemmt`](#xgemmt)
+- [Not covered yet](#not-covered-yet)
+  - [`xpstrf`](#xpstrf)
+- [Not covered: extra FLOPs](#not-covered-extra-flops)
+  - [QR decomposition (and related)](#qr-decomposition-and-related)
+  - [Symmetric reduction to tridiagonal](#symmetric-reduction-to-tridiagonal)
+  - [Symmetric reduction to bidiagonal](#symmetric-reduction-to-bidiagonal)
+  - [Reduction to upper Hessenberg](#reduction-to-upper-hessenberg)
+
+<!-- END doctoc generated TOC please keep comment here to allow auto update -->
+
+
+List of covered LAPACK routines
+-------------------------------
+
+### `xlauum`
+Multiplication of a triangular matrix with its (complex conjugate) transpose,
+resulting in a symmetric (Hermitian) matrix.
+
+Routines: `slauum`, `dlauum`, `clauum`, `zlauum`
+
+Operations:
+* A = L^T L
+* A = U U^T
+
+### `xsygst`
+Simultaneous two-sided multiplication of a symmetric matrix with a triangular
+matrix and its transpose
+
+Routines: `ssygst`, `dsygst`, `chegst`, `zhegst`
+
+Operations:
+* A = inv(L) A inv(L^T)
+* A = inv(U^T) A inv(U)
+* A = L^T A L
+* A = U A U^T
+
+### `xtrtri`
+Inversion of a triangular matrix
+
+Routines: `strtri`, `dtrtri`, `ctrtri`, `ztrtri`
+
+Operations:
+* L = inv(L)
+* U = inv(U)
+
+### `xpotrf`
+Cholesky decomposition of a symmetric (Hermitian) positive definite matrix
+
+Routines: `spotrf`, `dpotrf`, `cpotrf`, `zpotrf`
+
+Operations:
+* L L^T = A
+* U^T U = A
+
+### `xpbtrf`
+Cholesky decomposition of a banded symmetric (Hermitian) positive definite matrix
+
+Routines: `spbtrf`, `dpbtrf`, `cpbtrf`, `zpbtrf`
+
+Operations:
+* L L^T = A
+* U^T U = A
+
+### `xsytrf`
+LDL decomposition of a symmetric (or Hermitian) matrix
+
+Routines:
+* `ssytrf`, `dsytrf`, `csytrf`, `chetrf`, `zsytrf`, `zhetrf`,
+* `ssytrf_rook`, `dsytrf_rook`, `csytrf_rook`, `chetrf_rook`, `zsytrf_rook`,
+  `zhetrf_rook`
+
+Operations:
+* L D L^T = A
+* U^T D U = A
+
+### `xgetrf`
+LU decomposition of a general matrix with pivoting
+
+Routines: `sgetrf`, `dgetrf`, `cgetrf`, `zgetrf`
+
+Operation: P L U = A
+
+### `xgbtrf`
+LU decomposition of a general banded matrix with pivoting
+
+Routines: `sgbtrf`, `dgbtrf`, `cgbtrf`, `zgbtrf`
+
+Operation: L U = A
+
+### `xtrsyl`
+Solution of the quasi-triangular Sylvester equation
+
+Routines: `strsyl`, `dtrsyl`, `ctrsyl`, `ztrsyl`
+
+Operations:
+* A X + B Y = C -> X
+* A^T X + B Y = C -> X
+* A X + B^T Y = C -> X
+* A^T X + B^T Y = C -> X
+* A X - B Y = C -> X
+* A^T X - B Y = C -> X
+* A X - B^T Y = C -> X
+* A^T X - B^T Y = C -> X
+
+### `xtgsyl`
+Solution of the generalized Sylvester equations
+
+Routines: `stgsyl`, `dtgsyl`, `ctgsyl`, `ztgsyl`
+
+Operations:
+* A R - L B = C, D R - L E = F -> L, R
+* A^T R + D^T L = C, R B^T - L E^T = -F -> L, R
+
+
+Covered BLAS extension
+----------------------
+
+### `xgemmt`
+Matrix-matrix product updating only a triangular part of the result
+
+Routines: `sgemmt`, `dgemmt`, `cgemmt`, `zgemmt`
+
+Operations:
+* C = alpha A B + beta C
+* C = alpha A B^T + beta C
+* C = alpha A^T B + beta C
+* C = alpha A^T B^T + beta C
+
+
+Not covered yet
+---------------
+The following operation is implemented as a blocked algorithm in LAPACK but
+currently not yet covered in ReLAPACK as a recursive algorithm
+
+### `xpstrf`
+Cholesky decomposition of a positive semi-definite matrix with complete pivoting.
+
+Routines: `spstrf`, `dpstrf`, `cpstrf`, `zpstrf`
+
+Operations:
+* P L L^T P^T = A
+* P U^T U P^T = A
+
+
+Not covered: extra FLOPs
+------------------------
+The following routines are not covered because recursive variants would require
+considerably more FLOPs or operate on banded matrices.
+
+### QR decomposition (and related)
+Routines:
+* `sgeqrf`, `dgeqrf`, `cgeqrf`, `zgeqrf`
+* `sgerqf`, `dgerqf`, `cgerqf`, `zgerqf`
+* `sgeqlf`, `dgeqlf`, `cgeqlf`, `zgeqlf`
+* `sgelqf`, `dgelqf`, `cgelqf`, `zgelqf`
+* `stzrzf`, `dtzrzf`, `ctzrzf`, `ztzrzf`
+
+Operations: Q R = A, R Q = A, Q L = A, L Q = A, R Z = A
+
+Routines for multiplication with Q:
+* `sormqr`, `dormqr`, `cunmqr`, `zunmqr`
+* `sormrq`, `dormrq`, `cunmrq`, `zunmrq`
+* `sormql`, `dormql`, `cunmql`, `zunmql`
+* `sormlq`, `dormlq`, `cunmlq`, `zunmlq`
+* `sormrz`, `dormrz`, `cunmrz`, `zunmrz`
+
+Operations: C = Q C, C = C Q, C = Q^T C, C = C Q^T
+
+Routines for construction of Q:
+* `sorgqr`, `dorgqr`, `cungqr`, `zungqr`
+* `sorgrq`, `dorgrq`, `cungrq`, `zungrq`
+* `sorgql`, `dorgql`, `cungql`, `zungql`
+* `sorglq`, `dorglq`, `cunglq`, `zunglq`
+
+### Symmetric reduction to tridiagonal
+Routines: `ssytrd`, `dsytrd`, `csytrd`, `zsytrd`
+
+Operation: Q T Q^T = A
+
+### Symmetric reduction to bidiagonal
+Routines: `ssybrd`, `dsybrd`, `csybrd`, `zsybrd`
+
+Operation: Q T P^T = A
+
+### Reduction to upper Hessenberg
+Routines: `sgehrd`, `dgehrd`, `cgehrd`, `zgehrd`
+
+Operation: Q H Q^T = A

relapack/inc/relapack.h

@@ -0,0 +1,67 @@
+#ifndef RELAPACK_H
+#define RELAPACK_H
+
+void RELAPACK_slauum(const char *, const int *, float *, const int *, int *);
+void RELAPACK_dlauum(const char *, const int *, double *, const int *, int *);
+void RELAPACK_clauum(const char *, const int *, float *, const int *, int *);
+void RELAPACK_zlauum(const char *, const int *, double *, const int *, int *);
+
+void RELAPACK_strtri(const char *, const char *, const int *, float *, const int *, int *);
+void RELAPACK_dtrtri(const char *, const char *, const int *, double *, const int *, int *);
+void RELAPACK_ctrtri(const char *, const char *, const int *, float *, const int *, int *);
+void RELAPACK_ztrtri(const char *, const char *, const int *, double *, const int *, int *);
+
+void RELAPACK_spotrf(const char *, const int *, float *, const int *, int *);
+void RELAPACK_dpotrf(const char *, const int *, double *, const int *, int *);
+void RELAPACK_cpotrf(const char *, const int *, float *, const int *, int *);
+void RELAPACK_zpotrf(const char *, const int *, double *, const int *, int *);
+
+void RELAPACK_spbtrf(const char *, const int *, const int *, float *, const int *, int *);
+void RELAPACK_dpbtrf(const char *, const int *, const int *, double *, const int *, int *);
+void RELAPACK_cpbtrf(const char *, const int *, const int *, float *, const int *, int *);
+void RELAPACK_zpbtrf(const char *, const int *, const int *, double *, const int *, int *);
+
+void RELAPACK_ssytrf(const char *, const int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_dsytrf(const char *, const int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_csytrf(const char *, const int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_chetrf(const char *, const int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_zsytrf(const char *, const int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_zhetrf(const char *, const int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_ssytrf_rook(const char *, const int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_dsytrf_rook(const char *, const int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_csytrf_rook(const char *, const int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_chetrf_rook(const char *, const int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_zsytrf_rook(const char *, const int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_zhetrf_rook(const char *, const int *, double *, const int *, int *, double *, const int *, int *);
+
+void RELAPACK_sgetrf(const int *, const int *, float *, const int *, int *, int *);
+void RELAPACK_dgetrf(const int *, const int *, double *, const int *, int *, int *);
+void RELAPACK_cgetrf(const int *, const int *, float *, const int *, int *, int *);
+void RELAPACK_zgetrf(const int *, const int *, double *, const int *, int *, int *);
+
+void RELAPACK_sgbtrf(const int *, const int *, const int *, const int *, float *, const int *, int *, int *);
+void RELAPACK_dgbtrf(const int *, const int *, const int *, const int *, double *, const int *, int *, int *);
+void RELAPACK_cgbtrf(const int *, const int *, const int *, const int *, float *, const int *, int *, int *);
+void RELAPACK_zgbtrf(const int *, const int *, const int *, const int *, double *, const int *, int *, int *);
+
+void RELAPACK_ssygst(const int *, const char *, const int *, float *, const int *, const float *, const int *, int *);
+void RELAPACK_dsygst(const int *, const char *, const int *, double *, const int *, const double *, const int *, int *);
+void RELAPACK_chegst(const int *, const char *, const int *, float *, const int *, const float *, const int *, int *);
+void RELAPACK_zhegst(const int *, const char *, const int *, double *, const int *, const double *, const int *, int *);
+
+void RELAPACK_strsyl(const char *, const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, int *);
+void RELAPACK_dtrsyl(const char *, const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, int *);
+void RELAPACK_ctrsyl(const char *, const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, int *);
+void RELAPACK_ztrsyl(const char *, const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, int *);
+
+void RELAPACK_stgsyl(const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, float *, float *, const int *, int *, int *);
+void RELAPACK_dtgsyl(const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, double *, double *, const int *, int *, int *);
+void RELAPACK_ctgsyl(const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, float *, float *, const int *, int *, int *);
+void RELAPACK_ztgsyl(const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, double *, double *, const int *, int *, int *);
+
+void RELAPACK_sgemmt(const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+void RELAPACK_dgemmt(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+void RELAPACK_cgemmt(const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+void RELAPACK_zgemmt(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+#endif /*  RELAPACK_H */

relapack/src/blas.h

@@ -0,0 +1,61 @@
+#ifndef BLAS_H
+#define BLAS_H
+
+extern void BLAS(sswap)(const int *, float *, const int *, float *, const int *);
+extern void BLAS(dswap)(const int *, double *, const int *, double *, const int *);
+extern void BLAS(cswap)(const int *, float *, const int *, float *, const int *);
+extern void BLAS(zswap)(const int *, double *, const int *, double *, const int *);
+
+extern void BLAS(sscal)(const int *, const float *, float *, const int *);
+extern void BLAS(dscal)(const int *, const double *, double *, const int *);
+extern void BLAS(cscal)(const int *, const float *, float *, const int *);
+extern void BLAS(zscal)(const int *, const double *, double *, const int *);
+
+extern void BLAS(saxpy)(const int *, const float *, const float *, const int *, float *, const int *);
+extern void BLAS(daxpy)(const int *, const double *, const double *, const int *, double *, const int *);
+extern void BLAS(caxpy)(const int *, const float *, const float *, const int *, float *, const int *);
+extern void BLAS(zaxpy)(const int *, const double *, const double *, const int *, double *, const int *);
+
+extern void BLAS(sgemv)(const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, const float *, const int*);
+extern void BLAS(dgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, const double *, const int*);
+extern void BLAS(cgemv)(const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, const float *, const int*);
+extern void BLAS(zgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, const double *, const int*);
+
+extern void BLAS(sgemm)(const char *, const char *, const int *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, const float *, const int*);
+extern void BLAS(dgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, const double *, const int*);
+extern void BLAS(cgemm)(const char *, const char *, const int *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, const float *, const int*);
+extern void BLAS(zgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, const double *, const int*);
+
+extern void BLAS(strsm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+extern void BLAS(dtrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+extern void BLAS(ctrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+extern void BLAS(ztrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+
+extern void BLAS(strmm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+extern void BLAS(dtrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+extern void BLAS(ctrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+extern void BLAS(ztrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+
+extern void BLAS(ssyrk)(const char *, const char *, const int *, const int *, const float *, float *, const int *, const float *, float *, const int *);
+extern void BLAS(dsyrk)(const char *, const char *, const int *, const int *, const double *, double *, const int *, const double *, double *, const int *);
+extern void BLAS(cherk)(const char *, const char *, const int *, const int *, const float *, float *, const int *, const float *, float *, const int *);
+extern void BLAS(zherk)(const char *, const char *, const int *, const int *, const double *, double *, const int *, const double *, double *, const int *);
+
+extern void BLAS(ssymm)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+extern void BLAS(dsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+extern void BLAS(chemm)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+extern void BLAS(zhemm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+extern void BLAS(ssyr2k)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+extern void BLAS(dsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+extern void BLAS(cher2k)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+extern void BLAS(zher2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+#if HAVE_XGEMMT
+extern void BLAS(sgemmt)(const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, const float *, const int*);
+extern void BLAS(dgemmt)(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, const double *, const int*);
+extern void BLAS(cgemmt)(const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, const float *, const int*);
+extern void BLAS(zgemmt)(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, const double *, const int*);
+#endif
+
+#endif /* BLAS_H */

relapack/src/cgbtrf.c

@@ -0,0 +1,230 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_cgbtrf_rec(const int *, const int *, const int *,
+    const int *, float *, const int *, int *, float *, const int *, float *,
+    const int *, int *);
+
+
+/** CGBTRF computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's cgbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d0/d3a/cgbtrf_8f.html
+ * */
+void RELAPACK_cgbtrf(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kl < 0)
+        *info = -3;
+    else if (*ku < 0)
+        *info = -4;
+    else if (*ldAb < 2 * *kl + *ku + 1)
+        *info = -6;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CGBTRF", &minfo);
+        return;
+    }
+
+    // Constant
+    const float ZERO[] = { 0., 0. };
+
+    // Result upper band width
+    const int kv = *ku + *kl;
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    float *const A = Ab + 2 * kv;
+
+    // Zero upper diagonal fill-in elements
+    int i, j;
+    for (j = 0; j < *n; j++) {
+        float *const A_j = A + 2 * *ldA * j;
+        for (i = MAX(0, j - kv); i < j - *ku; i++)
+            A_j[2 * i] = A_j[2 * i + 1] = 0.;
+    }
+
+    // Allocate work space
+    const int n1 = CREC_SPLIT(*n);
+    const int mWorkl = (kv > n1) ? MAX(1, *m - *kl) : kv;
+    const int nWorkl = (kv > n1) ? n1 : kv;
+    const int mWorku = (*kl > n1) ? n1 : *kl;
+    const int nWorku = (*kl > n1) ? MAX(0, *n - *kl) : *kl;
+    float *Workl = malloc(mWorkl * nWorkl * 2 * sizeof(float));
+    float *Worku = malloc(mWorku * nWorku * 2 * sizeof(float));
+    LAPACK(claset)("L", &mWorkl, &nWorkl, ZERO, ZERO, Workl, &mWorkl);
+    LAPACK(claset)("U", &mWorku, &nWorku, ZERO, ZERO, Worku, &mWorku);
+
+    // Recursive kernel
+    RELAPACK_cgbtrf_rec(m, n, kl, ku, Ab, ldAb, ipiv, Workl, &mWorkl, Worku, &mWorku, info);
+
+    // Free work space
+    free(Workl);
+    free(Worku);
+}
+
+
+/** cgbtrf's recursive compute kernel */
+static void RELAPACK_cgbtrf_rec(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    float *Workl, const int *ldWorkl, float *Worku, const int *ldWorku,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_CGBTRF, 1)) {
+        // Unblocked
+        LAPACK(cgbtf2)(m, n, kl, ku, Ab, ldAb, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const int   iONE[] = { 1 };
+
+    // Loop iterators
+    int i, j;
+
+    // Output upper band width
+    const int kv = *ku + *kl;
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    float *const A = Ab + 2 * kv;
+
+    // Splitting
+    const int n1  = MIN(CREC_SPLIT(*n), *kl);
+    const int n2  = *n - n1;
+    const int m1  = MIN(n1, *m);
+    const int m2  = *m - m1;
+    const int mn1 = MIN(m1, n1);
+    const int mn2 = MIN(m2, n2);
+
+    // Ab_L *
+    //      Ab_BR
+    float *const Ab_L  = Ab;
+    float *const Ab_BR = Ab + 2 * *ldAb * n1;
+
+    // A_L A_R
+    float *const A_L = A;
+    float *const A_R = A + 2 * *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + 2 * *ldA * n1;
+    float *const A_BL = A                 + 2 * m1;
+    float *const A_BR = A + 2 * *ldA * n1 + 2 * m1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // Banded splitting
+    const int n21 = MIN(n2, kv - n1);
+    const int n22 = MIN(n2 - n21, n1);
+    const int m21 = MIN(m2, *kl - m1);
+    const int m22 = MIN(m2 - m21, m1);
+
+    //   n1 n21  n22
+    // m *  A_Rl ARr
+    float *const A_Rl = A_R;
+    float *const A_Rr = A_R + 2 * *ldA * n21;
+
+    //     n1    n21    n22
+    // m1  *     A_TRl  A_TRr
+    // m21 A_BLt A_BRtl A_BRtr
+    // m22 A_BLb A_BRbl A_BRbr
+    float *const A_TRl  = A_TR;
+    float *const A_TRr  = A_TR + 2 * *ldA * n21;
+    float *const A_BLt  = A_BL;
+    float *const A_BLb  = A_BL                  + 2 * m21;
+    float *const A_BRtl = A_BR;
+    float *const A_BRtr = A_BR + 2 * *ldA * n21;
+    float *const A_BRbl = A_BR                  + 2 * m21;
+    float *const A_BRbr = A_BR + 2 * *ldA * n21 + 2 * m21;
+
+    // recursion(Ab_L, ipiv_T)
+    RELAPACK_cgbtrf_rec(m, &n1, kl, ku, Ab_L, ldAb, ipiv_T, Workl, ldWorkl, Worku, ldWorku, info);
+
+    // Workl = A_BLb
+    LAPACK(clacpy)("U", &m22, &n1, A_BLb, ldA, Workl, ldWorkl);
+
+    // partially redo swaps in A_L
+    for (i = 0; i < mn1; i++) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(cswap)(&i, A_L + 2 * i, ldA, A_L + 2 * ip, ldA);
+            else
+                BLAS(cswap)(&i, A_L + 2 * i, ldA, Workl + 2 * (ip - *kl), ldWorkl);
+        }
+    }
+
+    // apply pivots to A_Rl
+    LAPACK(claswp)(&n21, A_Rl, ldA, iONE, &mn1, ipiv_T, iONE);
+
+    // apply pivots to A_Rr columnwise
+    for (j = 0; j < n22; j++) {
+        float *const A_Rrj = A_Rr + 2 * *ldA * j;
+        for (i = j; i < mn1; i++) {
+            const int ip = ipiv_T[i] - 1;
+            if (ip != i) {
+                const float tmpr = A_Rrj[2 * i];
+                const float tmpc = A_Rrj[2 * i + 1];
+                A_Rrj[2 * i]     = A_Rrj[2 * ip];
+                A_Rrj[2 * i + 1] = A_Rr[2 * ip + 1];
+                A_Rrj[2 * ip]     = tmpr;
+                A_Rrj[2 * ip + 1] = tmpc;
+            }
+        }
+    }
+
+    // A_TRl = A_TL \ A_TRl
+    BLAS(ctrsm)("L", "L", "N", "U", &m1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+    // Worku = A_TRr
+    LAPACK(clacpy)("L", &m1, &n22, A_TRr, ldA, Worku, ldWorku);
+    // Worku = A_TL \ Worku
+    BLAS(ctrsm)("L", "L", "N", "U", &m1, &n22, ONE, A_TL, ldA, Worku, ldWorku);
+    // A_TRr = Worku
+    LAPACK(clacpy)("L", &m1, &n22, Worku, ldWorku, A_TRr, ldA);
+    // A_BRtl = A_BRtl - A_BLt * A_TRl
+    BLAS(cgemm)("N", "N", &m21, &n21, &n1, MONE, A_BLt, ldA, A_TRl, ldA, ONE, A_BRtl, ldA);
+    // A_BRbl = A_BRbl - Workl * A_TRl
+    BLAS(cgemm)("N", "N", &m22, &n21, &n1, MONE, Workl, ldWorkl, A_TRl, ldA, ONE, A_BRbl, ldA);
+    // A_BRtr = A_BRtr - A_BLt * Worku
+    BLAS(cgemm)("N", "N", &m21, &n22, &n1, MONE, A_BLt, ldA, Worku, ldWorku, ONE, A_BRtr, ldA);
+    // A_BRbr = A_BRbr - Workl * Worku
+    BLAS(cgemm)("N", "N", &m22, &n22, &n1, MONE, Workl, ldWorkl, Worku, ldWorku, ONE, A_BRbr, ldA);
+
+    // partially undo swaps in A_L
+    for (i = mn1 - 1; i >= 0; i--) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(cswap)(&i, A_L + 2 * i, ldA, A_L + 2 * ip, ldA);
+            else
+                BLAS(cswap)(&i, A_L + 2 * i, ldA, Workl + 2 * (ip - *kl), ldWorkl);
+        }
+    }
+
+    // recursion(Ab_BR, ipiv_B)
+    RELAPACK_cgbtrf_rec(&m2, &n2, kl, ku, Ab_BR, ldAb, ipiv_B, Workl, ldWorkl, Worku, ldWorku, info);
+    if (*info)
+        *info += n1;
+    // shift pivots
+    for (i = 0; i < mn2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/cgemmt.c

@@ -0,0 +1,167 @@
+#include "relapack.h"
+
+static void RELAPACK_cgemmt_rec(const char *, const char *, const char *,
+    const int *, const int *, const float *, const float *, const int *,
+    const float *, const int *, const float *, float *, const int *);
+
+static void RELAPACK_cgemmt_rec2(const char *, const char *, const char *,
+    const int *, const int *, const float *, const float *, const int *,
+    const float *, const int *, const float *, float *, const int *);
+
+
+/** CGEMMT computes a matrix-matrix product with general matrices but updates
+ * only the upper or lower triangular part of the result matrix.
+ *
+ * This routine performs the same operation as the BLAS routine
+ * cgemm(transA, transB, n, n, k, alpha, A, ldA, B, ldB, beta, C, ldC)
+ * but only updates the triangular part of C specified by uplo:
+ * If (*uplo == 'L'), only the lower triangular part of C is updated,
+ * otherwise the upper triangular part is updated.
+ * */
+void RELAPACK_cgemmt(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+
+#if HAVE_XGEMMT
+    BLAS(cgemmt)(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+    return;
+#else
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int notransA = LAPACK(lsame)(transA, "N");
+    const int tranA = LAPACK(lsame)(transA, "T");
+    const int ctransA = LAPACK(lsame)(transA, "C");
+    const int notransB = LAPACK(lsame)(transB, "N");
+    const int tranB = LAPACK(lsame)(transB, "T");
+    const int ctransB = LAPACK(lsame)(transB, "C");
+    int info = 0;
+    if (!lower && !upper)
+        info = 1;
+    else if (!tranA && !ctransA && !notransA)
+        info = 2;
+    else if (!tranB && !ctransB && !notransB)
+        info = 3;
+    else if (*n < 0)
+        info = 4;
+    else if (*k < 0)
+        info = 5;
+    else if (*ldA < MAX(1, notransA ? *n : *k))
+        info = 8;
+    else if (*ldB < MAX(1, notransB ? *k : *n))
+        info = 10;
+    else if (*ldC < MAX(1, *n))
+        info = 13;
+    if (info) {
+        LAPACK(xerbla)("CGEMMT", &info);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+    const char cleantransA = notransA ? 'N' : (tranA ? 'T' : 'C');
+    const char cleantransB = notransB ? 'N' : (tranB ? 'T' : 'C');
+
+    // Recursive kernel
+    RELAPACK_cgemmt_rec(&cleanuplo, &cleantransA, &cleantransB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+#endif
+}
+
+
+/** cgemmt's recursive compute kernel */
+static void RELAPACK_cgemmt_rec(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+
+    if (*n <= MAX(CROSSOVER_CGEMMT, 1)) {
+        // Unblocked
+        RELAPACK_cgemmt_rec2(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+        return;
+    }
+
+    // Splitting
+    const int n1 = CREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_T
+    // A_B
+    const float *const A_T = A;
+    const float *const A_B = A + 2 * ((*transA == 'N') ? n1 : *ldA * n1);
+
+    // B_L B_R
+    const float *const B_L = B;
+    const float *const B_R = B + 2 * ((*transB == 'N') ? *ldB * n1 : n1);
+
+    // C_TL C_TR
+    // C_BL C_BR
+    float *const C_TL = C;
+    float *const C_TR = C + 2 * *ldC * n1;
+    float *const C_BL = C                 + 2 * n1;
+    float *const C_BR = C + 2 * *ldC * n1 + 2 * n1;
+
+    // recursion(C_TL)
+    RELAPACK_cgemmt_rec(uplo, transA, transB, &n1, k, alpha, A_T, ldA, B_L, ldB, beta, C_TL, ldC);
+
+    if (*uplo == 'L')
+        // C_BL = alpha A_B B_L + beta C_BL
+        BLAS(cgemm)(transA, transB, &n2, &n1, k, alpha, A_B, ldA, B_L, ldB, beta, C_BL, ldC);
+    else
+        // C_TR = alpha A_T B_R + beta C_TR
+        BLAS(cgemm)(transA, transB, &n1, &n2, k, alpha, A_T, ldA, B_R, ldB, beta, C_TR, ldC);
+
+    // recursion(C_BR)
+    RELAPACK_cgemmt_rec(uplo, transA, transB, &n2, k, alpha, A_B, ldA, B_R, ldB, beta, C_BR, ldC);
+}
+
+
+/** cgemmt's unblocked compute kernel */
+static void RELAPACK_cgemmt_rec2(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+
+    const int incB = (*transB == 'N') ? 1 : *ldB;
+    const int incC = 1;
+
+    int i;
+    for (i = 0; i < *n; i++) {
+        // A_0
+        // A_i
+        const float *const A_0 = A;
+        const float *const A_i = A + 2 * ((*transA == 'N') ? i : *ldA * i);
+
+        // * B_i *
+        const float *const B_i = B + 2 * ((*transB == 'N') ? *ldB * i : i);
+
+        // * C_0i *
+        // * C_ii *
+        float *const C_0i = C + 2 * *ldC * i;
+        float *const C_ii = C + 2 * *ldC * i + 2 * i;
+
+        if (*uplo == 'L') {
+            const int nmi = *n - i;
+            if (*transA == 'N')
+                BLAS(cgemv)(transA, &nmi, k, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+            else
+                BLAS(cgemv)(transA, k, &nmi, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+        } else {
+            const int ip1 = i + 1;
+            if (*transA == 'N')
+                BLAS(cgemv)(transA, &ip1, k, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+            else
+                BLAS(cgemv)(transA, k, &ip1, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+        }
+    }
+}

relapack/src/cgetrf.c

@@ -0,0 +1,117 @@
+#include "relapack.h"
+
+static void RELAPACK_cgetrf_rec(const int *, const int *, float *,
+    const int *, int *, int *);
+
+
+/** CGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's cgetrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d9/dfb/cgetrf_8f.html
+ */
+void RELAPACK_cgetrf(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CGETRF", &minfo);
+        return;
+    }
+
+    const int sn = MIN(*m, *n);
+
+    RELAPACK_cgetrf_rec(m, &sn, A, ldA, ipiv, info);
+
+    // Right remainder
+    if (*m < *n) {
+        // Constants
+        const float ONE[]  = { 1., 0. };
+        const int   iONE[] = { 1 };
+
+        // Splitting
+        const int rn = *n - *m;
+
+        // A_L A_R
+        const float *const A_L = A;
+        float *const       A_R = A + 2 * *ldA * *m;
+
+        // A_R = apply(ipiv, A_R)
+        LAPACK(claswp)(&rn, A_R, ldA, iONE, m, ipiv, iONE);
+        // A_R = A_L \ A_R
+        BLAS(ctrsm)("L", "L", "N", "U", m, &rn, ONE, A_L, ldA, A_R, ldA);
+    }
+}
+
+
+/** cgetrf's recursive compute kernel */
+static void RELAPACK_cgetrf_rec(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_CGETRF, 1)) {
+        // Unblocked
+        LAPACK(cgetf2)(m, n, A, ldA, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const int   iONE[] = { 1 };
+
+    // Splitting
+    const int n1 = CREC_SPLIT(*n);
+    const int n2 = *n - n1;
+    const int m2 = *m - n1;
+
+    // A_L A_R
+    float *const A_L = A;
+    float *const A_R = A + 2 * *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + 2 * *ldA * n1;
+    float *const A_BL = A                 + 2 * n1;
+    float *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // recursion(A_L, ipiv_T)
+    RELAPACK_cgetrf_rec(m, &n1, A_L, ldA, ipiv_T, info);
+    // apply pivots to A_R
+    LAPACK(claswp)(&n2, A_R, ldA, iONE, &n1, ipiv_T, iONE);
+
+    // A_TR = A_TL \ A_TR
+    BLAS(ctrsm)("L", "L", "N", "U", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+    // A_BR = A_BR - A_BL * A_TR
+    BLAS(cgemm)("N", "N", &m2, &n2, &n1, MONE, A_BL, ldA, A_TR, ldA, ONE, A_BR, ldA);
+
+    // recursion(A_BR, ipiv_B)
+    RELAPACK_cgetrf_rec(&m2, &n2, A_BR, ldA, ipiv_B, info);
+    if (*info)
+        *info += n1;
+    // apply pivots to A_BL
+    LAPACK(claswp)(&n1, A_BL, ldA, iONE, &n2, ipiv_B, iONE);
+    // shift pivots
+    int i;
+    for (i = 0; i < n2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/chegst.c

@@ -0,0 +1,212 @@
+#include "relapack.h"
+#if XSYGST_ALLOW_MALLOC
+#include "stdlib.h"
+#endif
+
+static void RELAPACK_chegst_rec(const int *, const char *, const int *,
+    float *, const int *, const float *, const int *,
+    float *, const int *, int *);
+
+
+/** CHEGST reduces a complex Hermitian-definite generalized eigenproblem to standard form.
+ *
+ * This routine is functionally equivalent to LAPACK's chegst.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d7/d2a/chegst_8f.html
+ * */
+void RELAPACK_chegst(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (*itype < 1 || *itype > 3)
+        *info = -1;
+    else if (!lower && !upper)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    else if (*ldB < MAX(1, *n))
+        *info = -7;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CHEGST", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Allocate work space
+    float *Work = NULL;
+    int   lWork = 0;
+#if XSYGST_ALLOW_MALLOC
+    const int n1 = CREC_SPLIT(*n);
+    lWork = n1 * (*n - n1);
+    Work  = malloc(lWork * 2 * sizeof(float));
+    if (!Work)
+        lWork = 0;
+#endif
+
+    // recursive kernel
+    RELAPACK_chegst_rec(itype, &cleanuplo, n, A, ldA, B, ldB, Work, &lWork, info);
+
+    // Free work space
+#if XSYGST_ALLOW_MALLOC
+    if (Work)
+        free(Work);
+#endif
+}
+
+
+/** chegst's recursive compute kernel */
+static void RELAPACK_chegst_rec(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    float *Work, const int *lWork, int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_CHEGST, 1)) {
+        // Unblocked
+        LAPACK(chegs2)(itype, uplo, n, A, ldA, B, ldB, info);
+        return;
+    }
+
+    // Constants
+    const float ZERO[]  = { 0., 0. };
+    const float ONE[]   = { 1., 0. };
+    const float MONE[]  = { -1., 0. };
+    const float HALF[]  = { .5, 0. };
+    const float MHALF[] = { -.5, 0. };
+    const int   iONE[]  = { 1 };
+
+    // Loop iterator
+    int i;
+
+    // Splitting
+    const int n1 = CREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + 2 * *ldA * n1;
+    float *const A_BL = A                 + 2 * n1;
+    float *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // B_TL B_TR
+    // B_BL B_BR
+    const float *const B_TL = B;
+    const float *const B_TR = B + 2 * *ldB * n1;
+    const float *const B_BL = B                 + 2 * n1;
+    const float *const B_BR = B + 2 * *ldB * n1 + 2 * n1;
+
+    // recursion(A_TL, B_TL)
+    RELAPACK_chegst_rec(itype, uplo, &n1, A_TL, ldA, B_TL, ldB, Work, lWork, info);
+
+    if (*itype == 1)
+        if (*uplo == 'L') {
+            // A_BL = A_BL / B_TL'
+            BLAS(ctrsm)("R", "L", "C", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork > n2 * n1) {
+                // T = -1/2 * B_BL * A_TL
+                BLAS(chemm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(caxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            } else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(chemm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BR = A_BR - A_BL * B_BL' - B_BL * A_BL'
+            BLAS(cher2k)("L", "N", &n2, &n1, MONE, A_BL, ldA, B_BL, ldB, ONE, A_BR, ldA);
+            if (*lWork > n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(caxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(chemm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR \ A_BL
+            BLAS(ctrsm)("L", "L", "N", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL' \ A_TR
+            BLAS(ctrsm)("L", "U", "C", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork > n2 * n1) {
+                // T = -1/2 * A_TL * B_TR
+                BLAS(chemm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(caxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            } else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(chemm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_BR = A_BR - A_TR' * B_TR - B_TR' * A_TR
+            BLAS(cher2k)("U", "C", &n2, &n1, MONE, A_TR, ldA, B_TR, ldB, ONE, A_BR, ldA);
+            if (*lWork > n2 * n1)
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(caxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(chemm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR / B_BR
+            BLAS(ctrsm)("R", "U", "N", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+    else
+        if (*uplo == 'L') {
+            // A_BL = A_BL * B_TL
+            BLAS(ctrmm)("R", "L", "N", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork > n2 * n1) {
+                // T = 1/2 * A_BR * B_BL
+                BLAS(chemm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(caxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            } else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(chemm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_TL = A_TL + A_BL' * B_BL + B_BL' * A_BL
+            BLAS(cher2k)("L", "C", &n1, &n2, ONE, A_BL, ldA, B_BL, ldB, ONE, A_TL, ldA);
+            if (*lWork > n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(caxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(chemm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR * A_BL
+            BLAS(ctrmm)("L", "L", "C", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL * A_TR
+            BLAS(ctrmm)("L", "U", "N", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork > n2 * n1) {
+                // T = 1/2 * B_TR * A_BR
+                BLAS(chemm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(caxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            } else
+                // A_TR = A_TR + 1/2 B_TR A_BR
+                BLAS(chemm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TL = A_TL + A_TR * B_TR' + B_TR * A_TR'
+            BLAS(cher2k)("U", "N", &n1, &n2, ONE, A_TR, ldA, B_TR, ldB, ONE, A_TL, ldA);
+            if (*lWork > n2 * n1)
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(caxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            else
+                // A_TR = A_TR + 1/2 B_TR * A_BR
+                BLAS(chemm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR * B_BR
+            BLAS(ctrmm)("R", "U", "C", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+
+    // recursion(A_BR, B_BR)
+    RELAPACK_chegst_rec(itype, uplo, &n2, A_BR, ldA, B_BR, ldB, Work, lWork, info);
+}

relapack/src/chetrf.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_chetrf_rec(const char *, const int *, const int *, int *,
+    float *, const int *, int *, float *, const int *, int *);
+
+
+/** CHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's chetrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/da/dc1/chetrf_8f.html
+ * */
+void RELAPACK_chetrf(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    float *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(float));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CHETRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_chetrf_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** chetrf's recursive compute kernel */
+static void RELAPACK_chetrf_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_CHETRF, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(chetf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_chetrf_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const int   iONE[] = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = CREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        float *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_chetrf_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        float *const A_BL   = A                 + 2 * n1;
+        float *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        float *const A_BL_B = A                 + 2 * *n;
+        float *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        float *const Work_BL =              Work                    + 2 * n1;
+        float *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_cgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_chetrf_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            float *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            float *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            float *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(cgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = CREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        float *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_chetrf_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        float *const A_TL_T = A + 2 * *ldA * n_rest;
+        float *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        float *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        float *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        float *const Work_L  = Work;
+        float *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_cgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_chetrf_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(cgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/chetrf_rec2.c

@@ -0,0 +1,520 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static int c__1 = 1;
+
+/** CHETRF_REC2 computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kau fman diagonal pivoting method
+ *
+ * This routine is a minor modification of LAPACK's clahef.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_chetrf_rec2(char *uplo, int *n, int *
+	nb, int *kb, complex *a, int *lda, int *ipiv, complex *w,
+	int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    float r__1, r__2, r__3, r__4;
+    complex q__1, q__2, q__3, q__4;
+
+    /* Builtin functions */
+    double sqrt(double), r_imag(complex *);
+    void r_cnjg(complex *, complex *), c_div(complex *, complex *, complex *);
+
+    /* Local variables */
+    static int j, k;
+    static float t, r1;
+    static complex d11, d21, d22;
+    static int jj, kk, jp, kp, kw, kkw, imax, jmax;
+    static float alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int cgemv_(char *, int *, int *, complex *
+	    , complex *, int *, complex *, int *, complex *, complex *
+	    , int *, ftnlen), ccopy_(int *, complex *, int *,
+	    complex *, int *), cswap_(int *, complex *, int *,
+	    complex *, int *);
+    static int kstep;
+    static float absakk;
+    extern /* Subroutine */ int clacgv_(int *, complex *, int *);
+    extern int icamax_(int *, complex *, int *);
+    extern /* Subroutine */ int csscal_(int *, float *, complex *, int
+	    *);
+    static float colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.f) + 1.f) / 8.f;
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	i__1 = k - 1;
+	ccopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	i__1 = k + kw * w_dim1;
+	i__2 = k + k * a_dim1;
+	r__1 = a[i__2].r;
+	w[i__1].r = r__1, w[i__1].i = 0.f;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    q__1.r = -1.f, q__1.i = -0.f;
+	    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	    i__1 = k + kw * w_dim1;
+	    i__2 = k + kw * w_dim1;
+	    r__1 = w[i__2].r;
+	    w[i__1].r = r__1, w[i__1].i = 0.f;
+	}
+	i__1 = k + kw * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = icamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + kw * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + k * a_dim1;
+	    r__1 = a[i__2].r;
+	    a[i__1].r = r__1, a[i__1].i = 0.f;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - 1;
+		ccopy_(&i__1, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = imax + (kw - 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		r__1 = a[i__2].r;
+		w[i__1].r = r__1, w[i__1].i = 0.f;
+		i__1 = k - imax;
+		ccopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		i__1 = k - imax;
+		clacgv_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    q__1.r = -1.f, q__1.i = -0.f;
+		    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    i__2 = imax + (kw - 1) * w_dim1;
+		    r__1 = w[i__2].r;
+		    w[i__1].r = r__1, w[i__1].i = 0.f;
+		}
+		i__1 = k - imax;
+		jmax = imax + icamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
+			 &c__1);
+		i__1 = jmax + (kw - 1) * w_dim1;
+		rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			jmax + (kw - 1) * w_dim1]), dabs(r__2));
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    jmax = icamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + (
+			    r__2 = r_imag(&w[jmax + (kw - 1) * w_dim1]), dabs(
+			    r__2));
+		    rowmax = dmax(r__3,r__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    if ((r__1 = w[i__1].r, dabs(r__1)) >= alpha * rowmax) {
+			kp = imax;
+			ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+				w_dim1 + 1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		r__1 = a[i__2].r;
+		a[i__1].r = r__1, a[i__1].i = 0.f;
+		i__1 = kk - 1 - kp;
+		ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		i__1 = kk - 1 - kp;
+		clacgv_(&i__1, &a[kp + (kp + 1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    ccopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    cswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		cswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    i__1 = k + k * a_dim1;
+		    r1 = 1.f / a[i__1].r;
+		    i__1 = k - 1;
+		    csscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    i__1 = k - 1;
+		    clacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		}
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    r_cnjg(&q__2, &d21);
+		    c_div(&q__1, &w[k + kw * w_dim1], &q__2);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    c_div(&q__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__1.r = d11.r * d22.r - d11.i * d22.i, q__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1.f / (q__1.r - 1.f);
+		    q__2.r = t, q__2.i = 0.f;
+		    c_div(&q__1, &q__2, &d21);
+		    d21.r = q__1.r, d21.i = q__1.i;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			q__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
+				.i;
+			q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
+				d21.r * q__2.i + d21.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + k * a_dim1;
+			r_cnjg(&q__2, &d21);
+			i__3 = j + kw * w_dim1;
+			q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			q__1.r = q__2.r * q__3.r - q__2.i * q__3.i, q__1.i =
+				q__2.r * q__3.i + q__2.i * q__3.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1;
+		clacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		i__1 = k - 2;
+		clacgv_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    ++j;
+	}
+	++j;
+	if (jp != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    cswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
+	}
+	if (j <= *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	i__1 = k + k * w_dim1;
+	i__2 = k + k * a_dim1;
+	r__1 = a[i__2].r;
+	w[i__1].r = r__1, w[i__1].i = 0.f;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    ccopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &w[k + 1 + k *
+		    w_dim1], &c__1);
+	}
+	i__1 = *n - k + 1;
+	i__2 = k - 1;
+	q__1.r = -1.f, q__1.i = -0.f;
+	cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, &w[k
+		+ w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (ftnlen)12);
+	i__1 = k + k * w_dim1;
+	i__2 = k + k * w_dim1;
+	r__1 = w[i__2].r;
+	w[i__1].r = r__1, w[i__1].i = 0.f;
+	i__1 = k + k * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + icamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + k * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + k * a_dim1;
+	    r__1 = a[i__2].r;
+	    a[i__1].r = r__1, a[i__1].i = 0.f;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - k;
+		ccopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = imax - k;
+		clacgv_(&i__1, &w[k + (k + 1) * w_dim1], &c__1);
+		i__1 = imax + (k + 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		r__1 = a[i__2].r;
+		w[i__1].r = r__1, w[i__1].i = 0.f;
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    ccopy_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1, &w[
+			    imax + 1 + (k + 1) * w_dim1], &c__1);
+		}
+		i__1 = *n - k + 1;
+		i__2 = k - 1;
+		q__1.r = -1.f, q__1.i = -0.f;
+		cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1],
+			lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) *
+			w_dim1], &c__1, (ftnlen)12);
+		i__1 = imax + (k + 1) * w_dim1;
+		i__2 = imax + (k + 1) * w_dim1;
+		r__1 = w[i__2].r;
+		w[i__1].r = r__1, w[i__1].i = 0.f;
+		i__1 = imax - k;
+		jmax = k - 1 + icamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
+			;
+		i__1 = jmax + (k + 1) * w_dim1;
+		rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			jmax + (k + 1) * w_dim1]), dabs(r__2));
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    jmax = imax + icamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + (
+			    r__2 = r_imag(&w[jmax + (k + 1) * w_dim1]), dabs(
+			    r__2));
+		    rowmax = dmax(r__3,r__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (k + 1) * w_dim1;
+		    if ((r__1 = w[i__1].r, dabs(r__1)) >= alpha * rowmax) {
+			kp = imax;
+			i__1 = *n - k + 1;
+			ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k +
+				k * w_dim1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		r__1 = a[i__2].r;
+		a[i__1].r = r__1, a[i__1].i = 0.f;
+		i__1 = kp - kk - 1;
+		ccopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		i__1 = kp - kk - 1;
+		clacgv_(&i__1, &a[kp + (kk + 1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    cswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		cswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    i__1 = k + k * a_dim1;
+		    r1 = 1.f / a[i__1].r;
+		    i__1 = *n - k;
+		    csscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    i__1 = *n - k;
+		    clacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    c_div(&q__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    r_cnjg(&q__2, &d21);
+		    c_div(&q__1, &w[k + k * w_dim1], &q__2);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__1.r = d11.r * d22.r - d11.i * d22.i, q__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1.f / (q__1.r - 1.f);
+		    q__2.r = t, q__2.i = 0.f;
+		    c_div(&q__1, &q__2, &d21);
+		    d21.r = q__1.r, d21.i = q__1.i;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			r_cnjg(&q__2, &d21);
+			i__3 = j + k * w_dim1;
+			q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			q__1.r = q__2.r * q__3.r - q__2.i * q__3.i, q__1.i =
+				q__2.r * q__3.i + q__2.i * q__3.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			q__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
+				.i;
+			q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
+				d21.r * q__2.i + d21.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = *n - k;
+		clacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		i__1 = *n - k - 1;
+		clacgv_(&i__1, &w[k + 2 + (k + 1) * w_dim1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    --j;
+	}
+	--j;
+	if (jp != jj && j >= 1) {
+	    cswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j >= 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/chetrf_rook.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_chetrf_rook_rec(const char *, const int *, const int *, int *,
+    float *, const int *, int *, float *, const int *, int *);
+
+
+/** CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's chetrf_rook.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d0/d5e/chetrf__rook_8f.html
+ * */
+void RELAPACK_chetrf_rook(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    float *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(float));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CHETRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_chetrf_rook_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** chetrf_rook's recursive compute kernel */
+static void RELAPACK_chetrf_rook_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_CHETRF, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(chetf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_chetrf_rook_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const int   iONE[] = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = CREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        float *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_chetrf_rook_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        float *const A_BL   = A                 + 2 * n1;
+        float *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        float *const A_BL_B = A                 + 2 * *n;
+        float *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        float *const Work_BL =              Work                    + 2 * n1;
+        float *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_cgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_chetrf_rook_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            float *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            float *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            float *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(cgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = CREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        float *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_chetrf_rook_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        float *const A_TL_T = A + 2 * *ldA * n_rest;
+        float *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        float *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        float *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        float *const Work_L  = Work;
+        float *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_cgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_chetrf_rook_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(cgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/chetrf_rook_rec2.c

@@ -0,0 +1,661 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static int c__1 = 1;
+
+/** CHETRF_ROOK_REC2 computes a partial factorization of a complex Hermitian indefinite matrix using the boun ded Bunch-Kaufman ("rook") diagonal pivoting method
+ *
+ * This routine is a minor modification of LAPACK's clahef_rook.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_chetrf_rook_rec2(char *uplo, int *n,
+	int *nb, int *kb, complex *a, int *lda, int *ipiv,
+	complex *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    float r__1, r__2;
+    complex q__1, q__2, q__3, q__4, q__5;
+
+    /* Builtin functions */
+    double sqrt(double), r_imag(complex *);
+    void r_cnjg(complex *, complex *), c_div(complex *, complex *, complex *);
+
+    /* Local variables */
+    static int j, k, p;
+    static float t, r1;
+    static complex d11, d21, d22;
+    static int ii, jj, kk, kp, kw, jp1, jp2, kkw;
+    static logical done;
+    static int imax, jmax;
+    static float alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int cgemv_(char *, int *, int *, complex *
+	    , complex *, int *, complex *, int *, complex *, complex *
+	    , int *, ftnlen);
+    static float sfmin;
+    extern /* Subroutine */ int ccopy_(int *, complex *, int *,
+	    complex *, int *);
+    static int itemp;
+    extern /* Subroutine */ int cswap_(int *, complex *, int *,
+	    complex *, int *);
+    static int kstep;
+    static float stemp, absakk;
+    extern /* Subroutine */ int clacgv_(int *, complex *, int *);
+    extern int icamax_(int *, complex *, int *);
+    extern double slamch_(char *, ftnlen);
+    extern /* Subroutine */ int csscal_(int *, float *, complex *, int
+	    *);
+    static float colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.f) + 1.f) / 8.f;
+    sfmin = slamch_("S", (ftnlen)1);
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	p = k;
+	if (k > 1) {
+	    i__1 = k - 1;
+	    ccopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &
+		    c__1);
+	}
+	i__1 = k + kw * w_dim1;
+	i__2 = k + k * a_dim1;
+	r__1 = a[i__2].r;
+	w[i__1].r = r__1, w[i__1].i = 0.f;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    q__1.r = -1.f, q__1.i = -0.f;
+	    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	    i__1 = k + kw * w_dim1;
+	    i__2 = k + kw * w_dim1;
+	    r__1 = w[i__2].r;
+	    w[i__1].r = r__1, w[i__1].i = 0.f;
+	}
+	i__1 = k + kw * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = icamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + kw * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + kw * w_dim1;
+	    r__1 = w[i__2].r;
+	    a[i__1].r = r__1, a[i__1].i = 0.f;
+	    if (k > 1) {
+		i__1 = k - 1;
+		ccopy_(&i__1, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1],
+			&c__1);
+	    }
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L12:
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    ccopy_(&i__1, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			    w_dim1 + 1], &c__1);
+		}
+		i__1 = imax + (kw - 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		r__1 = a[i__2].r;
+		w[i__1].r = r__1, w[i__1].i = 0.f;
+		i__1 = k - imax;
+		ccopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		i__1 = k - imax;
+		clacgv_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    q__1.r = -1.f, q__1.i = -0.f;
+		    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    i__2 = imax + (kw - 1) * w_dim1;
+		    r__1 = w[i__2].r;
+		    w[i__1].r = r__1, w[i__1].i = 0.f;
+		}
+		if (imax != k) {
+		    i__1 = k - imax;
+		    jmax = imax + icamax_(&i__1, &w[imax + 1 + (kw - 1) *
+			    w_dim1], &c__1);
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[jmax + (kw - 1) * w_dim1]), dabs(r__2));
+		} else {
+		    rowmax = 0.f;
+		}
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    itemp = icamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+		    i__1 = itemp + (kw - 1) * w_dim1;
+		    stemp = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[itemp + (kw - 1) * w_dim1]), dabs(r__2));
+		    if (stemp > rowmax) {
+			rowmax = stemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (kw - 1) * w_dim1;
+		if (! ((r__1 = w[i__1].r, dabs(r__1)) < alpha * rowmax)) {
+		    kp = imax;
+		    ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		}
+		if (! done) {
+		    goto L12;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kstep == 2 && p != k) {
+		i__1 = p + p * a_dim1;
+		i__2 = k + k * a_dim1;
+		r__1 = a[i__2].r;
+		a[i__1].r = r__1, a[i__1].i = 0.f;
+		i__1 = k - 1 - p;
+		ccopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
+			a_dim1], lda);
+		i__1 = k - 1 - p;
+		clacgv_(&i__1, &a[p + (p + 1) * a_dim1], lda);
+		if (p > 1) {
+		    i__1 = p - 1;
+		    ccopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 +
+			    1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    cswap_(&i__1, &a[k + (k + 1) * a_dim1], lda, &a[p + (k +
+			    1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		cswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
+			 ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		r__1 = a[i__2].r;
+		a[i__1].r = r__1, a[i__1].i = 0.f;
+		i__1 = kk - 1 - kp;
+		ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		i__1 = kk - 1 - kp;
+		clacgv_(&i__1, &a[kp + (kp + 1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    ccopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    cswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		cswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    i__1 = k + k * a_dim1;
+		    t = a[i__1].r;
+		    if (dabs(t) >= sfmin) {
+			r1 = 1.f / t;
+			i__1 = k - 1;
+			csscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    } else {
+			i__1 = k - 1;
+			for (ii = 1; ii <= i__1; ++ii) {
+			    i__2 = ii + k * a_dim1;
+			    i__3 = ii + k * a_dim1;
+			    q__1.r = a[i__3].r / t, q__1.i = a[i__3].i / t;
+			    a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L14: */
+			}
+		    }
+		    i__1 = k - 1;
+		    clacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		}
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    r_cnjg(&q__2, &d21);
+		    c_div(&q__1, &w[k + kw * w_dim1], &q__2);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    c_div(&q__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__1.r = d11.r * d22.r - d11.i * d22.i, q__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1.f / (q__1.r - 1.f);
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			c_div(&q__2, &q__3, &d21);
+			q__1.r = t * q__2.r, q__1.i = t * q__2.i;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + k * a_dim1;
+			i__3 = j + kw * w_dim1;
+			q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			r_cnjg(&q__5, &d21);
+			c_div(&q__2, &q__3, &q__5);
+			q__1.r = t * q__2.r, q__1.i = t * q__2.i;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1;
+		clacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		i__1 = k - 2;
+		clacgv_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    ++j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	++j;
+	if (jp2 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    cswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	++jj;
+	if (kstep == 2 && jp1 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    cswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	if (j < *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	p = k;
+	i__1 = k + k * w_dim1;
+	i__2 = k + k * a_dim1;
+	r__1 = a[i__2].r;
+	w[i__1].r = r__1, w[i__1].i = 0.f;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    ccopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &w[k + 1 + k *
+		    w_dim1], &c__1);
+	}
+	if (k > 1) {
+	    i__1 = *n - k + 1;
+	    i__2 = k - 1;
+	    q__1.r = -1.f, q__1.i = -0.f;
+	    cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, &
+		    w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (
+		    ftnlen)12);
+	    i__1 = k + k * w_dim1;
+	    i__2 = k + k * w_dim1;
+	    r__1 = w[i__2].r;
+	    w[i__1].r = r__1, w[i__1].i = 0.f;
+	}
+	i__1 = k + k * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + icamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + k * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + k * w_dim1;
+	    r__1 = w[i__2].r;
+	    a[i__1].r = r__1, a[i__1].i = 0.f;
+	    if (k < *n) {
+		i__1 = *n - k;
+		ccopy_(&i__1, &w[k + 1 + k * w_dim1], &c__1, &a[k + 1 + k *
+			a_dim1], &c__1);
+	    }
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L72:
+		i__1 = imax - k;
+		ccopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = imax - k;
+		clacgv_(&i__1, &w[k + (k + 1) * w_dim1], &c__1);
+		i__1 = imax + (k + 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		r__1 = a[i__2].r;
+		w[i__1].r = r__1, w[i__1].i = 0.f;
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    ccopy_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1, &w[
+			    imax + 1 + (k + 1) * w_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = *n - k + 1;
+		    i__2 = k - 1;
+		    q__1.r = -1.f, q__1.i = -0.f;
+		    cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1]
+			    , lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k +
+			    1) * w_dim1], &c__1, (ftnlen)12);
+		    i__1 = imax + (k + 1) * w_dim1;
+		    i__2 = imax + (k + 1) * w_dim1;
+		    r__1 = w[i__2].r;
+		    w[i__1].r = r__1, w[i__1].i = 0.f;
+		}
+		if (imax != k) {
+		    i__1 = imax - k;
+		    jmax = k - 1 + icamax_(&i__1, &w[k + (k + 1) * w_dim1], &
+			    c__1);
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[jmax + (k + 1) * w_dim1]), dabs(r__2));
+		} else {
+		    rowmax = 0.f;
+		}
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    itemp = imax + icamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+		    i__1 = itemp + (k + 1) * w_dim1;
+		    stemp = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[itemp + (k + 1) * w_dim1]), dabs(r__2));
+		    if (stemp > rowmax) {
+			rowmax = stemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (k + 1) * w_dim1;
+		if (! ((r__1 = w[i__1].r, dabs(r__1)) < alpha * rowmax)) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    i__1 = *n - k + 1;
+		    ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		}
+		if (! done) {
+		    goto L72;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kstep == 2 && p != k) {
+		i__1 = p + p * a_dim1;
+		i__2 = k + k * a_dim1;
+		r__1 = a[i__2].r;
+		a[i__1].r = r__1, a[i__1].i = 0.f;
+		i__1 = p - k - 1;
+		ccopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[p + (k + 1) *
+			a_dim1], lda);
+		i__1 = p - k - 1;
+		clacgv_(&i__1, &a[p + (k + 1) * a_dim1], lda);
+		if (p < *n) {
+		    i__1 = *n - p;
+		    ccopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + 1 + p
+			    * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    cswap_(&i__1, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
+		}
+		cswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		r__1 = a[i__2].r;
+		a[i__1].r = r__1, a[i__1].i = 0.f;
+		i__1 = kp - kk - 1;
+		ccopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		i__1 = kp - kk - 1;
+		clacgv_(&i__1, &a[kp + (kk + 1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    cswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		cswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    i__1 = k + k * a_dim1;
+		    t = a[i__1].r;
+		    if (dabs(t) >= sfmin) {
+			r1 = 1.f / t;
+			i__1 = *n - k;
+			csscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    } else {
+			i__1 = *n;
+			for (ii = k + 1; ii <= i__1; ++ii) {
+			    i__2 = ii + k * a_dim1;
+			    i__3 = ii + k * a_dim1;
+			    q__1.r = a[i__3].r / t, q__1.i = a[i__3].i / t;
+			    a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L74: */
+			}
+		    }
+		    i__1 = *n - k;
+		    clacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    c_div(&q__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    r_cnjg(&q__2, &d21);
+		    c_div(&q__1, &w[k + k * w_dim1], &q__2);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__1.r = d11.r * d22.r - d11.i * d22.i, q__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1.f / (q__1.r - 1.f);
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			i__3 = j + k * w_dim1;
+			q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			r_cnjg(&q__5, &d21);
+			c_div(&q__2, &q__3, &q__5);
+			q__1.r = t * q__2.r, q__1.i = t * q__2.i;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			c_div(&q__2, &q__3, &d21);
+			q__1.r = t * q__2.r, q__1.i = t * q__2.i;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = *n - k;
+		clacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		i__1 = *n - k - 1;
+		clacgv_(&i__1, &w[k + 2 + (k + 1) * w_dim1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    --j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	--j;
+	if (jp2 != jj && j >= 1) {
+	    cswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	--jj;
+	if (kstep == 2 && jp1 != jj && j >= 1) {
+	    cswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j > 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/clauum.c

@@ -0,0 +1,87 @@
+#include "relapack.h"
+
+static void RELAPACK_clauum_rec(const char *, const int *, float *,
+    const int *, int *);
+
+
+/** CLAUUM computes the product U * U**H or L**H * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A.
+ *
+ * This routine is functionally equivalent to LAPACK's clauum.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d2/d36/clauum_8f.html
+ * */
+void RELAPACK_clauum(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CLAUUM", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_clauum_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** clauum's recursive compute kernel */
+static void RELAPACK_clauum_rec(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_CLAUUM, 1)) {
+        // Unblocked
+        LAPACK(clauu2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[] = { 1., 0. };
+
+    // Splitting
+    const int n1 = CREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + 2 * *ldA * n1;
+    float *const A_BL = A                 + 2 * n1;
+    float *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_clauum_rec(uplo, &n1, A_TL, ldA, info);
+
+    if (*uplo == 'L') {
+        // A_TL = A_TL + A_BL' * A_BL
+        BLAS(cherk)("L", "C", &n1, &n2, ONE, A_BL, ldA, ONE, A_TL, ldA);
+        // A_BL = A_BR' * A_BL
+        BLAS(ctrmm)("L", "L", "C", "N", &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TL = A_TL + A_TR * A_TR'
+        BLAS(cherk)("U", "N", &n1, &n2, ONE, A_TR, ldA, ONE, A_TL, ldA);
+        // A_TR = A_TR * A_BR'
+        BLAS(ctrmm)("R", "U", "C", "N", &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_clauum_rec(uplo, &n2, A_BR, ldA, info);
+}

relapack/src/cpbtrf.c

@@ -0,0 +1,157 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_cpbtrf_rec(const char *, const int *, const int *,
+    float *, const int *, float *, const int *, int *);
+
+
+/** CPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's cpbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/de/d2d/cpbtrf_8f.html
+ * */
+void RELAPACK_cpbtrf(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kd < 0)
+        *info = -3;
+    else if (*ldAb < *kd + 1)
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CPBTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Constant
+    const float ZERO[] = { 0., 0. };
+
+    // Allocate work space
+    const int n1 = CREC_SPLIT(*n);
+    const int mWork = (*kd > n1) ? (lower ? *n - *kd : n1) : *kd;
+    const int nWork = (*kd > n1) ? (lower ? n1 : *n - *kd) : *kd;
+    float *Work = malloc(mWork * nWork * 2 * sizeof(float));
+    LAPACK(claset)(uplo, &mWork, &nWork, ZERO, ZERO, Work, &mWork);
+
+    // Recursive kernel
+    RELAPACK_cpbtrf_rec(&cleanuplo, n, kd, Ab, ldAb, Work, &mWork, info);
+
+    // Free work space
+    free(Work);
+}
+
+
+/** cpbtrf's recursive compute kernel */
+static void RELAPACK_cpbtrf_rec(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    float *Work, const int *ldWork,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_CPBTRF, 1)) {
+        // Unblocked
+        LAPACK(cpbtf2)(uplo, n, kd, Ab, ldAb, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    float *const A = Ab + 2 * ((*uplo == 'L') ? 0 : *kd);
+
+    // Splitting
+    const int n1 = MIN(CREC_SPLIT(*n), *kd);
+    const int n2 = *n - n1;
+
+    // * *
+    // * Ab_BR
+    float *const Ab_BR = Ab + 2 * *ldAb * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + 2 * *ldA * n1;
+    float *const A_BL = A                 + 2 * n1;
+    float *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_cpotrf(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    // Banded splitting
+    const int n21 = MIN(n2, *kd - n1);
+    const int n22 = MIN(n2 - n21, *kd);
+
+    //     n1    n21    n22
+    // n1  *     A_TRl  A_TRr
+    // n21 A_BLt A_BRtl A_BRtr
+    // n22 A_BLb A_BRbl A_BRbr
+    float *const A_TRl  = A_TR;
+    float *const A_TRr  = A_TR + 2 * *ldA * n21;
+    float *const A_BLt  = A_BL;
+    float *const A_BLb  = A_BL                   + 2 * n21;
+    float *const A_BRtl = A_BR;
+    float *const A_BRtr = A_BR + 2 * *ldA * n21;
+    float *const A_BRbl = A_BR                   + 2 * n21;
+    float *const A_BRbr = A_BR + 2 * *ldA * n21  + 2 * n21;
+
+    if (*uplo == 'L') {
+        // A_BLt = ABLt / A_TL'
+        BLAS(ctrsm)("R", "L", "C", "N", &n21, &n1, ONE, A_TL, ldA, A_BLt, ldA);
+        // A_BRtl = A_BRtl - A_BLt * A_BLt'
+        BLAS(cherk)("L", "N", &n21, &n1, MONE, A_BLt, ldA, ONE, A_BRtl, ldA);
+        // Work = A_BLb
+        LAPACK(clacpy)("U", &n22, &n1, A_BLb, ldA, Work, ldWork);
+        // Work = Work / A_TL'
+        BLAS(ctrsm)("R", "L", "C", "N", &n22, &n1, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRbl = A_BRbl - Work * A_BLt'
+        BLAS(cgemm)("N", "C", &n22, &n21, &n1, MONE, Work, ldWork, A_BLt, ldA, ONE, A_BRbl, ldA);
+        // A_BRbr = A_BRbr - Work * Work'
+        BLAS(cherk)("L", "N", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_BLb = Work
+        LAPACK(clacpy)("U", &n22, &n1, Work, ldWork, A_BLb, ldA);
+    } else {
+        // A_TRl = A_TL' \ A_TRl
+        BLAS(ctrsm)("L", "U", "C", "N", &n1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+        // A_BRtl = A_BRtl - A_TRl' * A_TRl
+        BLAS(cherk)("U", "C", &n21, &n1, MONE, A_TRl, ldA, ONE, A_BRtl, ldA);
+        // Work = A_TRr
+        LAPACK(clacpy)("L", &n1, &n22, A_TRr, ldA, Work, ldWork);
+        // Work = A_TL' \ Work
+        BLAS(ctrsm)("L", "U", "C", "N", &n1, &n22, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRtr = A_BRtr - A_TRl' * Work
+        BLAS(cgemm)("C", "N", &n21, &n22, &n1, MONE, A_TRl, ldA, Work, ldWork, ONE, A_BRtr, ldA);
+        // A_BRbr = A_BRbr - Work' * Work
+        BLAS(cherk)("U", "C", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_TRr = Work
+        LAPACK(clacpy)("L", &n1, &n22, Work, ldWork, A_TRr, ldA);
+    }
+
+    // recursion(A_BR)
+    if (*kd > n1)
+        RELAPACK_cpotrf(uplo, &n2, A_BR, ldA, info);
+    else
+        RELAPACK_cpbtrf_rec(uplo, &n2, kd, Ab_BR, ldAb, Work, ldWork, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/cpotrf.c

@@ -0,0 +1,92 @@
+#include "relapack.h"
+
+static void RELAPACK_cpotrf_rec(const char *, const int *, float *,
+        const int *, int *);
+
+
+/** CPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's cpotrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dd/dce/cpotrf_8f.html
+ * */
+void RELAPACK_cpotrf(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CPOTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_cpotrf_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** cpotrf's recursive compute kernel */
+static void RELAPACK_cpotrf_rec(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_CPOTRF, 1)) {
+        // Unblocked
+        LAPACK(cpotf2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+
+    // Splitting
+    const int n1 = CREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + 2 * *ldA * n1;
+    float *const A_BL = A                 + 2 * n1;
+    float *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_cpotrf_rec(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = A_BL / A_TL'
+        BLAS(ctrsm)("R", "L", "C", "N", &n2, &n1, ONE, A_TL, ldA, A_BL, ldA);
+        // A_BR = A_BR - A_BL * A_BL'
+        BLAS(cherk)("L", "N", &n2, &n1, MONE, A_BL, ldA, ONE, A_BR, ldA);
+    } else {
+        // A_TR = A_TL' \ A_TR
+        BLAS(ctrsm)("L", "U", "C", "N", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+        // A_BR = A_BR - A_TR' * A_TR
+        BLAS(cherk)("U", "C", &n2, &n1, MONE, A_TR, ldA, ONE, A_BR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_cpotrf_rec(uplo, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/csytrf.c

@@ -0,0 +1,238 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_csytrf_rec(const char *, const int *, const int *, int *,
+    float *, const int *, int *, float *, const int *, int *);
+
+
+/** CSYTRF computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's csytrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d5/d21/csytrf_8f.html
+ * */
+void RELAPACK_csytrf(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    float *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(float));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy arguments
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_csytrf_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** csytrf's recursive compute kernel */
+static void RELAPACK_csytrf_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_CSYTRF, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(csytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_csytrf_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const int   iONE[] = { 1 };
+
+    // Loop iterator
+    int i;
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = CREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        float *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_csytrf_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        float *const A_BL   = A                 + 2 * n1;
+        float *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        float *const A_BL_B = A                 + 2 * *n;
+        float *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        float *const Work_BL =              Work                    + 2 * n1;
+        float *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_cgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_csytrf_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            float *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            float *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            float *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(cgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = CREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        float *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_csytrf_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1  = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        float *const A_TL_T = A + 2 * *ldA * n_rest;
+        float *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        float *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        float *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        float *const Work_L  = Work;
+        float *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_cgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_csytrf_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(cgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/csytrf_rec2.c

@@ -0,0 +1,451 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static int c__1 = 1;
+
+/** CSYTRF_REC2 computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagon al pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's clasyf.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_csytrf_rec2(char *uplo, int *n, int *
+	nb, int *kb, complex *a, int *lda, int *ipiv, complex *w,
+	int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    float r__1, r__2, r__3, r__4;
+    complex q__1, q__2, q__3;
+
+    /* Builtin functions */
+    double sqrt(double), r_imag(complex *);
+    void c_div(complex *, complex *, complex *);
+
+    /* Local variables */
+    static int j, k;
+    static complex t, r1, d11, d21, d22;
+    static int jj, kk, jp, kp, kw, kkw, imax, jmax;
+    static float alpha;
+    extern /* Subroutine */ int cscal_(int *, complex *, complex *,
+	    int *);
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int cgemv_(char *, int *, int *, complex *
+	    , complex *, int *, complex *, int *, complex *, complex *
+	    , int *, ftnlen), ccopy_(int *, complex *, int *,
+	    complex *, int *), cswap_(int *, complex *, int *,
+	    complex *, int *);
+    static int kstep;
+    static float absakk;
+    extern int icamax_(int *, complex *, int *);
+    static float colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.f) + 1.f) / 8.f;
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	ccopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    q__1.r = -1.f, q__1.i = -0.f;
+	    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	kstep = 1;
+	i__1 = k + kw * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + kw *
+		w_dim1]), dabs(r__2));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = icamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + kw * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		ccopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		ccopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    q__1.r = -1.f, q__1.i = -0.f;
+		    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		i__1 = k - imax;
+		jmax = imax + icamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
+			 &c__1);
+		i__1 = jmax + (kw - 1) * w_dim1;
+		rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			jmax + (kw - 1) * w_dim1]), dabs(r__2));
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    jmax = icamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + (
+			    r__2 = r_imag(&w[jmax + (kw - 1) * w_dim1]), dabs(
+			    r__2));
+		    rowmax = dmax(r__3,r__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    if ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			    imax + (kw - 1) * w_dim1]), dabs(r__2)) >= alpha *
+			     rowmax) {
+			kp = imax;
+			ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+				w_dim1 + 1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = kk - 1 - kp;
+		ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    ccopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    cswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		cswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
+		r1.r = q__1.r, r1.i = q__1.i;
+		i__1 = k - 1;
+		cscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    c_div(&q__1, &w[k + kw * w_dim1], &d21);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    c_div(&q__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
+		    c_div(&q__1, &c_b1, &q__2);
+		    t.r = q__1.r, t.i = q__1.i;
+		    c_div(&q__1, &t, &d21);
+		    d21.r = q__1.r, d21.i = q__1.i;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			q__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
+				.i;
+			q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
+				d21.r * q__2.i + d21.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + k * a_dim1;
+			i__3 = j + kw * w_dim1;
+			q__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
+				.i;
+			q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
+				d21.r * q__2.i + d21.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    ++j;
+	}
+	++j;
+	if (jp != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    cswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
+	}
+	if (j < *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	i__1 = *n - k + 1;
+	ccopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	i__1 = *n - k + 1;
+	i__2 = k - 1;
+	q__1.r = -1.f, q__1.i = -0.f;
+	cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, &w[k
+		+ w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (ftnlen)12);
+	kstep = 1;
+	i__1 = k + k * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + k *
+		w_dim1]), dabs(r__2));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + icamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + k * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - k;
+		ccopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		ccopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		i__1 = *n - k + 1;
+		i__2 = k - 1;
+		q__1.r = -1.f, q__1.i = -0.f;
+		cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1],
+			lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) *
+			w_dim1], &c__1, (ftnlen)12);
+		i__1 = imax - k;
+		jmax = k - 1 + icamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
+			;
+		i__1 = jmax + (k + 1) * w_dim1;
+		rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			jmax + (k + 1) * w_dim1]), dabs(r__2));
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    jmax = imax + icamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + (
+			    r__2 = r_imag(&w[jmax + (k + 1) * w_dim1]), dabs(
+			    r__2));
+		    rowmax = dmax(r__3,r__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (k + 1) * w_dim1;
+		    if ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			    imax + (k + 1) * w_dim1]), dabs(r__2)) >= alpha *
+			    rowmax) {
+			kp = imax;
+			i__1 = *n - k + 1;
+			ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k +
+				k * w_dim1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = kp - kk - 1;
+		ccopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    cswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		cswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
+		    r1.r = q__1.r, r1.i = q__1.i;
+		    i__1 = *n - k;
+		    cscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    c_div(&q__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    c_div(&q__1, &w[k + k * w_dim1], &d21);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
+		    c_div(&q__1, &c_b1, &q__2);
+		    t.r = q__1.r, t.i = q__1.i;
+		    c_div(&q__1, &t, &d21);
+		    d21.r = q__1.r, d21.i = q__1.i;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			i__3 = j + k * w_dim1;
+			q__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
+				.i;
+			q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
+				d21.r * q__2.i + d21.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			q__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
+				.i;
+			q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
+				d21.r * q__2.i + d21.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    --j;
+	}
+	--j;
+	if (jp != jj && j >= 1) {
+	    cswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j > 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/csytrf_rook.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_csytrf_rook_rec(const char *, const int *, const int *, int *,
+    float *, const int *, int *, float *, const int *, int *);
+
+
+/** CSYTRF_ROOK computes the factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's csytrf_rook.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d8/dc8/csytrf__rook_8f.html
+ * */
+void RELAPACK_csytrf_rook(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    float *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(float));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_csytrf_rook_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** csytrf_rook's recursive compute kernel */
+static void RELAPACK_csytrf_rook_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_CSYTRF_ROOK, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(csytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_csytrf_rook_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const int   iONE[] = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = CREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        float *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_csytrf_rook_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2   = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        float *const A_BL   = A                 + 2 * n1;
+        float *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        float *const A_BL_B = A                 + 2 * *n;
+        float *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        float *const Work_BL =              Work                    + 2 * n1;
+        float *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_cgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_csytrf_rook_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            float *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            float *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            float *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(cgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = CREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        float *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_csytrf_rook_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        float *const A_TL_T = A + 2 * *ldA * n_rest;
+        float *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        float *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        float *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        float *const Work_L  = Work;
+        float *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_cgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(cgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_csytrf_rook_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(cgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/csytrf_rook_rec2.c

@@ -0,0 +1,565 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static int c__1 = 1;
+
+/** CSYTRF_ROOK_REC2 computes a partial factorization of a complex symmetric matrix using the bounded Bunch-K aufman ("rook") diagonal pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's clasyf_rook.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_csytrf_rook_rec2(char *uplo, int *n,
+	int *nb, int *kb, complex *a, int *lda, int *ipiv,
+	complex *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    float r__1, r__2;
+    complex q__1, q__2, q__3, q__4;
+
+    /* Builtin functions */
+    double sqrt(double), r_imag(complex *);
+    void c_div(complex *, complex *, complex *);
+
+    /* Local variables */
+    static int j, k, p;
+    static complex t, r1, d11, d12, d21, d22;
+    static int ii, jj, kk, kp, kw, jp1, jp2, kkw;
+    static logical done;
+    static int imax, jmax;
+    static float alpha;
+    extern /* Subroutine */ int cscal_(int *, complex *, complex *,
+	    int *);
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int cgemv_(char *, int *, int *, complex *
+	    , complex *, int *, complex *, int *, complex *, complex *
+	    , int *, ftnlen);
+    static float sfmin;
+    extern /* Subroutine */ int ccopy_(int *, complex *, int *,
+	    complex *, int *);
+    static int itemp;
+    extern /* Subroutine */ int cswap_(int *, complex *, int *,
+	    complex *, int *);
+    static int kstep;
+    static float stemp, absakk;
+    extern int icamax_(int *, complex *, int *);
+    extern double slamch_(char *, ftnlen);
+    static float colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.f) + 1.f) / 8.f;
+    sfmin = slamch_("S", (ftnlen)1);
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	p = k;
+	ccopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    q__1.r = -1.f, q__1.i = -0.f;
+	    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	i__1 = k + kw * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + kw *
+		w_dim1]), dabs(r__2));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = icamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + kw * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L12:
+		ccopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		ccopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    q__1.r = -1.f, q__1.i = -0.f;
+		    cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = k - imax;
+		    jmax = imax + icamax_(&i__1, &w[imax + 1 + (kw - 1) *
+			    w_dim1], &c__1);
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[jmax + (kw - 1) * w_dim1]), dabs(r__2));
+		} else {
+		    rowmax = 0.f;
+		}
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    itemp = icamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+		    i__1 = itemp + (kw - 1) * w_dim1;
+		    stemp = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[itemp + (kw - 1) * w_dim1]), dabs(r__2));
+		    if (stemp > rowmax) {
+			rowmax = stemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (kw - 1) * w_dim1;
+		if (! ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			imax + (kw - 1) * w_dim1]), dabs(r__2)) < alpha *
+			rowmax)) {
+		    kp = imax;
+		    ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		}
+		if (! done) {
+		    goto L12;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kstep == 2 && p != k) {
+		i__1 = k - p;
+		ccopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
+			a_dim1], lda);
+		ccopy_(&p, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - k + 1;
+		cswap_(&i__1, &a[k + k * a_dim1], lda, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - kk + 1;
+		cswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
+			 ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + k * a_dim1;
+		i__2 = kk + k * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = k - 1 - kp;
+		ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		ccopy_(&kp, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - kk + 1;
+		cswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1],
+			 lda);
+		i__1 = *n - kk + 1;
+		cswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    i__1 = k + k * a_dim1;
+		    if ((r__1 = a[i__1].r, dabs(r__1)) + (r__2 = r_imag(&a[k
+			    + k * a_dim1]), dabs(r__2)) >= sfmin) {
+			c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
+			r1.r = q__1.r, r1.i = q__1.i;
+			i__1 = k - 1;
+			cscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    } else /* if(complicated condition) */ {
+			i__1 = k + k * a_dim1;
+			if (a[i__1].r != 0.f || a[i__1].i != 0.f) {
+			    i__1 = k - 1;
+			    for (ii = 1; ii <= i__1; ++ii) {
+				i__2 = ii + k * a_dim1;
+				c_div(&q__1, &a[ii + k * a_dim1], &a[k + k *
+					a_dim1]);
+				a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L14: */
+			    }
+			}
+		    }
+		}
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d12.r = w[i__1].r, d12.i = w[i__1].i;
+		    c_div(&q__1, &w[k + kw * w_dim1], &d12);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    c_div(&q__1, &w[k - 1 + (kw - 1) * w_dim1], &d12);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
+		    c_div(&q__1, &c_b1, &q__2);
+		    t.r = q__1.r, t.i = q__1.i;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			c_div(&q__2, &q__3, &d12);
+			q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r *
+				q__2.i + t.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + k * a_dim1;
+			i__3 = j + kw * w_dim1;
+			q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			c_div(&q__2, &q__3, &d12);
+			q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r *
+				q__2.i + t.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    ++j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	++j;
+	if (jp2 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    cswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	jj = j - 1;
+	if (jp1 != jj && kstep == 2) {
+	    i__1 = *n - j + 1;
+	    cswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	if (j <= *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	p = k;
+	i__1 = *n - k + 1;
+	ccopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	if (k > 1) {
+	    i__1 = *n - k + 1;
+	    i__2 = k - 1;
+	    q__1.r = -1.f, q__1.i = -0.f;
+	    cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, &
+		    w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (
+		    ftnlen)12);
+	}
+	i__1 = k + k * w_dim1;
+	absakk = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + k *
+		w_dim1]), dabs(r__2));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + icamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
+		    + k * w_dim1]), dabs(r__2));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = *n - k + 1;
+	    ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+		    c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L72:
+		i__1 = imax - k;
+		ccopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		ccopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		if (k > 1) {
+		    i__1 = *n - k + 1;
+		    i__2 = k - 1;
+		    q__1.r = -1.f, q__1.i = -0.f;
+		    cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1]
+			    , lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k +
+			    1) * w_dim1], &c__1, (ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = imax - k;
+		    jmax = k - 1 + icamax_(&i__1, &w[k + (k + 1) * w_dim1], &
+			    c__1);
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[jmax + (k + 1) * w_dim1]), dabs(r__2));
+		} else {
+		    rowmax = 0.f;
+		}
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    itemp = imax + icamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+		    i__1 = itemp + (k + 1) * w_dim1;
+		    stemp = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
+			    w[itemp + (k + 1) * w_dim1]), dabs(r__2));
+		    if (stemp > rowmax) {
+			rowmax = stemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (k + 1) * w_dim1;
+		if (! ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
+			imax + (k + 1) * w_dim1]), dabs(r__2)) < alpha *
+			rowmax)) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    i__1 = *n - k + 1;
+		    ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		}
+		if (! done) {
+		    goto L72;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kstep == 2 && p != k) {
+		i__1 = p - k;
+		ccopy_(&i__1, &a[k + k * a_dim1], &c__1, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - p + 1;
+		ccopy_(&i__1, &a[p + k * a_dim1], &c__1, &a[p + p * a_dim1], &
+			c__1);
+		cswap_(&k, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
+		cswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + k * a_dim1;
+		i__2 = kk + k * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = kp - k - 1;
+		ccopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1)
+			* a_dim1], lda);
+		i__1 = *n - kp + 1;
+		ccopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp *
+			a_dim1], &c__1);
+		cswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		cswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    i__1 = k + k * a_dim1;
+		    if ((r__1 = a[i__1].r, dabs(r__1)) + (r__2 = r_imag(&a[k
+			    + k * a_dim1]), dabs(r__2)) >= sfmin) {
+			c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
+			r1.r = q__1.r, r1.i = q__1.i;
+			i__1 = *n - k;
+			cscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    } else /* if(complicated condition) */ {
+			i__1 = k + k * a_dim1;
+			if (a[i__1].r != 0.f || a[i__1].i != 0.f) {
+			    i__1 = *n;
+			    for (ii = k + 1; ii <= i__1; ++ii) {
+				i__2 = ii + k * a_dim1;
+				c_div(&q__1, &a[ii + k * a_dim1], &a[k + k *
+					a_dim1]);
+				a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L74: */
+			    }
+			}
+		    }
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    c_div(&q__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = q__1.r, d11.i = q__1.i;
+		    c_div(&q__1, &w[k + k * w_dim1], &d21);
+		    d22.r = q__1.r, d22.i = q__1.i;
+		    q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
+		    c_div(&q__1, &c_b1, &q__2);
+		    t.r = q__1.r, t.i = q__1.i;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			i__3 = j + k * w_dim1;
+			q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				q__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			c_div(&q__2, &q__3, &d21);
+			q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r *
+				q__2.i + t.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				q__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
+				.i;
+			c_div(&q__2, &q__3, &d21);
+			q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r *
+				q__2.i + t.i * q__2.r;
+			a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    --j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	--j;
+	if (jp2 != jj && j >= 1) {
+	    cswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	jj = j + 1;
+	if (jp1 != jj && kstep == 2) {
+	    cswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j >= 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/ctgsyl.c

@@ -0,0 +1,268 @@
+#include "relapack.h"
+#include <math.h>
+
+static void RELAPACK_ctgsyl_rec(const char *, const int *, const int *,
+    const int *, const float *, const int *, const float *, const int *,
+    float *, const int *, const float *, const int *, const float *,
+    const int *, float *, const int *, float *, float *, float *, int *);
+
+
+/** CTGSYL solves the generalized Sylvester equation.
+ *
+ * This routine is functionally equivalent to LAPACK's ctgsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d7/de7/ctgsyl_8f.html
+ * */
+void RELAPACK_ctgsyl(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dif,
+    float *Work, const int *lWork, int *iWork, int *info
+) {
+
+    // Parse arguments
+    const int notran = LAPACK(lsame)(trans, "N");
+    const int tran = LAPACK(lsame)(trans, "C");
+
+    // Compute work buffer size
+    int lwmin = 1;
+    if (notran && (*ijob == 1 || *ijob == 2))
+        lwmin = MAX(1, 2 * *m * *n);
+    *info = 0;
+
+    // Check arguments
+    if (!tran && !notran)
+        *info = -1;
+    else if (notran && (*ijob < 0 || *ijob > 4))
+        *info = -2;
+    else if (*m <= 0)
+        *info = -3;
+    else if (*n <= 0)
+        *info = -4;
+    else if (*ldA < MAX(1, *m))
+        *info = -6;
+    else if (*ldB < MAX(1, *n))
+        *info = -8;
+    else if (*ldC < MAX(1, *m))
+        *info = -10;
+    else if (*ldD < MAX(1, *m))
+        *info = -12;
+    else if (*ldE < MAX(1, *n))
+        *info = -14;
+    else if (*ldF < MAX(1, *m))
+        *info = -16;
+    else if (*lWork < lwmin && *lWork != -1)
+        *info = -20;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CTGSYL", &minfo);
+        return;
+    }
+
+    if (*lWork == -1) {
+        // Work size query
+        *Work = lwmin;
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantrans = notran ? 'N' : 'C';
+
+    // Constant
+    const float ZERO[] = { 0., 0. };
+
+    int isolve = 1;
+    int ifunc  = 0;
+    if (notran) {
+        if (*ijob >= 3) {
+            ifunc = *ijob - 2;
+            LAPACK(claset)("F", m, n, ZERO, ZERO, C, ldC);
+            LAPACK(claset)("F", m, n, ZERO, ZERO, F, ldF);
+        } else if (*ijob >= 1)
+            isolve = 2;
+    }
+
+    float scale2;
+    int iround;
+    for (iround = 1; iround <= isolve; iround++) {
+        *scale = 1;
+        float dscale = 0;
+        float dsum   = 1;
+        RELAPACK_ctgsyl_rec(&cleantrans, &ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, &dsum, &dscale, info);
+        if (dscale != 0) {
+            if (*ijob == 1 || *ijob == 3)
+                *dif = sqrt(2 * *m * *n) / (dscale * sqrt(dsum));
+            else
+                *dif = sqrt(*m * *n) / (dscale * sqrt(dsum));
+        }
+        if (isolve == 2) {
+            if (iround == 1) {
+                if (notran)
+                    ifunc = *ijob;
+                scale2 = *scale;
+                LAPACK(clacpy)("F", m, n, C, ldC, Work, m);
+                LAPACK(clacpy)("F", m, n, F, ldF, Work + 2 * *m * *n, m);
+                LAPACK(claset)("F", m, n, ZERO, ZERO, C, ldC);
+                LAPACK(claset)("F", m, n, ZERO, ZERO, F, ldF);
+            } else {
+                LAPACK(clacpy)("F", m, n, Work, m, C, ldC);
+                LAPACK(clacpy)("F", m, n, Work + 2 * *m * *n, m, F, ldF);
+                *scale = scale2;
+            }
+        }
+    }
+}
+
+
+/** ctgsyl's recursive vompute kernel */
+static void RELAPACK_ctgsyl_rec(
+    const char *trans, const int *ifunc, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dsum, float *dscale,
+    int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_CTGSYL, 1) && *n <= MAX(CROSSOVER_CTGSYL, 1)) {
+        // Unblocked
+        LAPACK(ctgsy2)(trans, ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dsum, dscale, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const int   iONE[] = { 1 };
+
+    // Outputs
+    float scale1[] = { 1., 0. };
+    float scale2[] = { 1., 0. };
+    int   info1[]  = { 0 };
+    int   info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        const int m1 = CREC_SPLIT(*m);
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const float *const A_TL = A;
+        const float *const A_TR = A + 2 * *ldA * m1;
+        const float *const A_BR = A + 2 * *ldA * m1 + 2 * m1;
+
+        // C_T
+        // C_B
+        float *const C_T = C;
+        float *const C_B = C + 2 * m1;
+
+        // D_TL D_TR
+        // 0    D_BR
+        const float *const D_TL = D;
+        const float *const D_TR = D + 2 * *ldD * m1;
+        const float *const D_BR = D + 2 * *ldD * m1 + 2 * m1;
+
+        // F_T
+        // F_B
+        float *const F_T = F;
+        float *const F_B = F + 2 * m1;
+
+        if (*trans == 'N') {
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_ctgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale1, dsum, dscale, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(cgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // F_T = F_T - D_TR * C_B
+            BLAS(cgemm)("N", "N", &m1, n, &m2, MONE, D_TR, ldD, C_B, ldC, scale1, F_T, ldF);
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_ctgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m2, n, F_B, ldF, info);
+            }
+        } else {
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_ctgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale1, dsum, dscale, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale1, &m2, n, F_B, ldF, info);
+            // C_B = C_B - A_TR^H * C_T
+            BLAS(cgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // C_B = C_B - D_TR^H * F_T
+            BLAS(cgemm)("C", "N", &m2, n, &m1, MONE, D_TR, ldD, F_T, ldC, ONE, C_B, ldC);
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_ctgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_T, ldC, info);
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m1, n, F_T, ldF, info);
+            }
+        }
+    } else {
+        // Splitting
+        const int n1 = CREC_SPLIT(*n);
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const float *const B_TL = B;
+        const float *const B_TR = B + 2 * *ldB * n1;
+        const float *const B_BR = B + 2 * *ldB * n1 + 2 * n1;
+
+        // C_L C_R
+        float *const C_L = C;
+        float *const C_R = C + 2 * *ldC * n1;
+
+        // E_TL E_TR
+        // 0    E_BR
+        const float *const E_TL = E;
+        const float *const E_TR = E + 2 * *ldE * n1;
+        const float *const E_BR = E + 2 * *ldE * n1 + 2 * n1;
+
+        // F_L F_R
+        float *const F_L = F;
+        float *const F_R = F + 2 * *ldF * n1;
+
+        if (*trans == 'N') {
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_ctgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale1, dsum, dscale, info1);
+            // C_R = C_R + F_L * B_TR
+            BLAS(cgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, B_TR, ldB, scale1, C_R, ldC);
+            // F_R = F_R + F_L * E_TR
+            BLAS(cgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, E_TR, ldE, scale1, F_R, ldF);
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_ctgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n1, F_L, ldF, info);
+            }
+        } else {
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_ctgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale1, dsum, dscale, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale1, m, &n1, C_L, ldC, info);
+            // F_L = F_L + C_R * B_TR
+            BLAS(cgemm)("N", "C", m, &n1, &n2, ONE, C_R, ldC, B_TR, ldB, scale1, F_L, ldF);
+            // F_L = F_L + F_R * E_TR
+            BLAS(cgemm)("N", "C", m, &n1, &n2, ONE, F_R, ldF, E_TR, ldB, ONE, F_L, ldF);
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_ctgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n2, F_R, ldF, info);
+            }
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/ctrsyl.c

@@ -0,0 +1,163 @@
+#include "relapack.h"
+
+static void RELAPACK_ctrsyl_rec(const char *, const char *, const int *,
+    const int *, const int *, const float *, const int *, const float *,
+    const int *, float *, const int *, float *, int *);
+
+
+/** CTRSYL solves the complex Sylvester matrix equation.
+ *
+ * This routine is functionally equivalent to LAPACK's ctrsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d8/df4/ctrsyl_8f.html
+ * */
+void RELAPACK_ctrsyl(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+
+    // Check arguments
+    const int notransA = LAPACK(lsame)(tranA, "N");
+    const int ctransA = LAPACK(lsame)(tranA, "C");
+    const int notransB = LAPACK(lsame)(tranB, "N");
+    const int ctransB = LAPACK(lsame)(tranB, "C");
+    *info = 0;
+    if (!ctransA && !notransA)
+        *info = -1;
+    else if (!ctransB && !notransB)
+        *info = -2;
+    else if (*isgn != 1 && *isgn != -1)
+        *info = -3;
+    else if (*m < 0)
+        *info = -4;
+    else if (*n < 0)
+        *info = -5;
+    else if (*ldA < MAX(1, *m))
+        *info = -7;
+    else if (*ldB < MAX(1, *n))
+        *info = -9;
+    else if (*ldC < MAX(1, *m))
+        *info = -11;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CTRSYL", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantranA = notransA ? 'N' : 'C';
+    const char cleantranB = notransB ? 'N' : 'C';
+
+    // Recursive kernel
+    RELAPACK_ctrsyl_rec(&cleantranA, &cleantranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+
+
+/** ctrsyl's recursive compute kernel */
+static void RELAPACK_ctrsyl_rec(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_CTRSYL, 1) && *n <= MAX(CROSSOVER_CTRSYL, 1)) {
+        // Unblocked
+        RELAPACK_ctrsyl_rec2(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+    const float MSGN[] = { -*isgn, 0. };
+    const int   iONE[] = { 1 };
+
+    // Outputs
+    float scale1[] = { 1., 0. };
+    float scale2[] = { 1., 0. };
+    int   info1[]  = { 0 };
+    int   info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        const int m1 = CREC_SPLIT(*m);
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const float *const A_TL = A;
+        const float *const A_TR = A + 2 * *ldA * m1;
+        const float *const A_BR = A + 2 * *ldA * m1 + 2 * m1;
+
+        // C_T
+        // C_B
+        float *const C_T = C;
+        float *const C_B = C + 2 * m1;
+
+        if (*tranA == 'N') {
+            // recusion(A_BR, B, C_B)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale1, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(cgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // recusion(A_TL, B, C_T)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+        } else {
+            // recusion(A_TL, B, C_T)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale1, info1);
+            // C_B = C_B - A_TR' * C_T
+            BLAS(cgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // recusion(A_BR, B, C_B)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_B, ldC, info);
+        }
+    } else {
+        // Splitting
+        const int n1 = CREC_SPLIT(*n);
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const float *const B_TL = B;
+        const float *const B_TR = B + 2 * *ldB * n1;
+        const float *const B_BR = B + 2 * *ldB * n1 + 2 * n1;
+
+        // C_L C_R
+        float *const C_L = C;
+        float *const C_R = C + 2 * *ldC * n1;
+
+        if (*tranB == 'N') {
+            // recusion(A, B_TL, C_L)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale1, info1);
+            // C_R = C_R -/+ C_L * B_TR
+            BLAS(cgemm)("N", "N", m, &n2, &n1, MSGN, C_L, ldC, B_TR, ldB, scale1, C_R, ldC);
+            // recusion(A, B_BR, C_R)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+        } else {
+            // recusion(A, B_BR, C_R)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale1, info1);
+            // C_L = C_L -/+ C_R * B_TR'
+            BLAS(cgemm)("N", "C", m, &n1, &n2, MSGN, C_R, ldC, B_TR, ldB, scale1, C_L, ldC);
+            // recusion(A, B_TL, C_L)
+            RELAPACK_ctrsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/ctrsyl_rec2.c

@@ -0,0 +1,392 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "../config.h"
+#include "f2c.h"
+
+#if BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES
+complex cdotu_fun(int *n, complex *x, int *incx, complex *y, int *incy) {
+    extern void cdotu_(complex *, int *, complex *, int *, complex *, int *);
+    complex result;
+    cdotu_(&result, n, x, incx, y, incy);
+    return result;
+}
+#define cdotu_ cdotu_fun
+
+complex cdotc_fun(int *n, complex *x, int *incx, complex *y, int *incy) {
+    extern void cdotc_(complex *, int *, complex *, int *, complex *, int *);
+    complex result;
+    cdotc_(&result, n, x, incx, y, incy);
+    return result;
+}
+#define cdotc_ cdotc_fun
+#endif
+
+#if LAPACK_BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES
+complex cladiv_fun(complex *a, complex *b) {
+    extern void cladiv_(complex *, complex *, complex *);
+    complex result;
+    cladiv_(&result, a, b);
+    return result;
+}
+#define cladiv_ cladiv_fun
+#endif
+
+/* Table of constant values */
+
+static int c__1 = 1;
+
+/** RELAPACK_CTRSYL_REC2 solves the complex Sylvester matrix equation (unblocked algorithm)
+ *
+ * This routine is an exact copy of LAPACK's ctrsyl.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * */
+/* Subroutine */ void RELAPACK_ctrsyl_rec2(char *trana, char *tranb, int
+	*isgn, int *m, int *n, complex *a, int *lda, complex *b,
+	int *ldb, complex *c__, int *ldc, float *scale, int *info,
+	ftnlen trana_len, ftnlen tranb_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
+	    i__3, i__4;
+    float r__1, r__2;
+    complex q__1, q__2, q__3, q__4;
+
+    /* Builtin functions */
+    float r_imag(complex *);
+    void r_cnjg(complex *, complex *);
+
+    /* Local variables */
+    static int j, k, l;
+    static complex a11;
+    static float db;
+    static complex x11;
+    static float da11;
+    static complex vec;
+    static float dum[1], eps, sgn, smin;
+    static complex suml, sumr;
+    /* Complex */ complex cdotc_(int *, complex *, int
+	    *, complex *, int *);
+    extern int lsame_(char *, char *, ftnlen, ftnlen);
+    /* Complex */ complex cdotu_(int *, complex *, int
+	    *, complex *, int *);
+    extern /* Subroutine */ int slabad_(float *, float *);
+    extern float clange_(char *, int *, int *, complex *,
+	    int *, float *, ftnlen);
+    /* Complex */ complex cladiv_(complex *, complex *);
+    static float scaloc;
+    extern float slamch_(char *, ftnlen);
+    extern /* Subroutine */ int csscal_(int *, float *, complex *, int
+	    *), xerbla_(char *, int *, ftnlen);
+    static float bignum;
+    static int notrna, notrnb;
+    static float smlnum;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+
+    /* Function Body */
+    notrna = lsame_(trana, "N", (ftnlen)1, (ftnlen)1);
+    notrnb = lsame_(tranb, "N", (ftnlen)1, (ftnlen)1);
+    *info = 0;
+    if (! notrna && ! lsame_(trana, "C", (ftnlen)1, (ftnlen)1)) {
+	*info = -1;
+    } else if (! notrnb && ! lsame_(tranb, "C", (ftnlen)1, (ftnlen)1)) {
+	*info = -2;
+    } else if (*isgn != 1 && *isgn != -1) {
+	*info = -3;
+    } else if (*m < 0) {
+	*info = -4;
+    } else if (*n < 0) {
+	*info = -5;
+    } else if (*lda < max(1,*m)) {
+	*info = -7;
+    } else if (*ldb < max(1,*n)) {
+	*info = -9;
+    } else if (*ldc < max(1,*m)) {
+	*info = -11;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CTRSY2", &i__1, (ftnlen)6);
+	return;
+    }
+    *scale = 1.f;
+    if (*m == 0 || *n == 0) {
+	return;
+    }
+    eps = slamch_("P", (ftnlen)1);
+    smlnum = slamch_("S", (ftnlen)1);
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+    smlnum = smlnum * (float) (*m * *n) / eps;
+    bignum = 1.f / smlnum;
+/* Computing MAX */
+    r__1 = smlnum, r__2 = eps * clange_("M", m, m, &a[a_offset], lda, dum, (
+	    ftnlen)1), r__1 = max(r__1,r__2), r__2 = eps * clange_("M", n, n,
+	    &b[b_offset], ldb, dum, (ftnlen)1);
+    smin = dmax(r__1,r__2);
+    sgn = (float) (*isgn);
+    if (notrna && notrnb) {
+	i__1 = *n;
+	for (l = 1; l <= i__1; ++l) {
+	    for (k = *m; k >= 1; --k) {
+		i__2 = *m - k;
+/* Computing MIN */
+		i__3 = k + 1;
+/* Computing MIN */
+		i__4 = k + 1;
+		q__1 = cdotu_(&i__2, &a[k + min(i__3,*m) * a_dim1], lda, &c__[
+			min(i__4,*m) + l * c_dim1], &c__1);
+		suml.r = q__1.r, suml.i = q__1.i;
+		i__2 = l - 1;
+		q__1 = cdotu_(&i__2, &c__[k + c_dim1], ldc, &b[l * b_dim1 + 1]
+			, &c__1);
+		sumr.r = q__1.r, sumr.i = q__1.i;
+		i__2 = k + l * c_dim1;
+		q__3.r = sgn * sumr.r, q__3.i = sgn * sumr.i;
+		q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
+		q__1.r = c__[i__2].r - q__2.r, q__1.i = c__[i__2].i - q__2.i;
+		vec.r = q__1.r, vec.i = q__1.i;
+		scaloc = 1.f;
+		i__2 = k + k * a_dim1;
+		i__3 = l + l * b_dim1;
+		q__2.r = sgn * b[i__3].r, q__2.i = sgn * b[i__3].i;
+		q__1.r = a[i__2].r + q__2.r, q__1.i = a[i__2].i + q__2.i;
+		a11.r = q__1.r, a11.i = q__1.i;
+		da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
+			dabs(r__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.f;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
+			r__2));
+		if (da11 < 1.f && db > 1.f) {
+		    if (db > bignum * da11) {
+			scaloc = 1.f / db;
+		    }
+		}
+		q__3.r = scaloc, q__3.i = 0.f;
+		q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
+			q__3.i + vec.i * q__3.r;
+		q__1 = cladiv_(&q__2, &a11);
+		x11.r = q__1.r, x11.i = q__1.i;
+		if (scaloc != 1.f) {
+		    i__2 = *n;
+		    for (j = 1; j <= i__2; ++j) {
+			csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L10: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__2 = k + l * c_dim1;
+		c__[i__2].r = x11.r, c__[i__2].i = x11.i;
+/* L20: */
+	    }
+/* L30: */
+	}
+    } else if (! notrna && notrnb) {
+	i__1 = *n;
+	for (l = 1; l <= i__1; ++l) {
+	    i__2 = *m;
+	    for (k = 1; k <= i__2; ++k) {
+		i__3 = k - 1;
+		q__1 = cdotc_(&i__3, &a[k * a_dim1 + 1], &c__1, &c__[l *
+			c_dim1 + 1], &c__1);
+		suml.r = q__1.r, suml.i = q__1.i;
+		i__3 = l - 1;
+		q__1 = cdotu_(&i__3, &c__[k + c_dim1], ldc, &b[l * b_dim1 + 1]
+			, &c__1);
+		sumr.r = q__1.r, sumr.i = q__1.i;
+		i__3 = k + l * c_dim1;
+		q__3.r = sgn * sumr.r, q__3.i = sgn * sumr.i;
+		q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
+		q__1.r = c__[i__3].r - q__2.r, q__1.i = c__[i__3].i - q__2.i;
+		vec.r = q__1.r, vec.i = q__1.i;
+		scaloc = 1.f;
+		r_cnjg(&q__2, &a[k + k * a_dim1]);
+		i__3 = l + l * b_dim1;
+		q__3.r = sgn * b[i__3].r, q__3.i = sgn * b[i__3].i;
+		q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
+		a11.r = q__1.r, a11.i = q__1.i;
+		da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
+			dabs(r__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.f;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
+			r__2));
+		if (da11 < 1.f && db > 1.f) {
+		    if (db > bignum * da11) {
+			scaloc = 1.f / db;
+		    }
+		}
+		q__3.r = scaloc, q__3.i = 0.f;
+		q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
+			q__3.i + vec.i * q__3.r;
+		q__1 = cladiv_(&q__2, &a11);
+		x11.r = q__1.r, x11.i = q__1.i;
+		if (scaloc != 1.f) {
+		    i__3 = *n;
+		    for (j = 1; j <= i__3; ++j) {
+			csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L40: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__3 = k + l * c_dim1;
+		c__[i__3].r = x11.r, c__[i__3].i = x11.i;
+/* L50: */
+	    }
+/* L60: */
+	}
+    } else if (! notrna && ! notrnb) {
+	for (l = *n; l >= 1; --l) {
+	    i__1 = *m;
+	    for (k = 1; k <= i__1; ++k) {
+		i__2 = k - 1;
+		q__1 = cdotc_(&i__2, &a[k * a_dim1 + 1], &c__1, &c__[l *
+			c_dim1 + 1], &c__1);
+		suml.r = q__1.r, suml.i = q__1.i;
+		i__2 = *n - l;
+/* Computing MIN */
+		i__3 = l + 1;
+/* Computing MIN */
+		i__4 = l + 1;
+		q__1 = cdotc_(&i__2, &c__[k + min(i__3,*n) * c_dim1], ldc, &b[
+			l + min(i__4,*n) * b_dim1], ldb);
+		sumr.r = q__1.r, sumr.i = q__1.i;
+		i__2 = k + l * c_dim1;
+		r_cnjg(&q__4, &sumr);
+		q__3.r = sgn * q__4.r, q__3.i = sgn * q__4.i;
+		q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
+		q__1.r = c__[i__2].r - q__2.r, q__1.i = c__[i__2].i - q__2.i;
+		vec.r = q__1.r, vec.i = q__1.i;
+		scaloc = 1.f;
+		i__2 = k + k * a_dim1;
+		i__3 = l + l * b_dim1;
+		q__3.r = sgn * b[i__3].r, q__3.i = sgn * b[i__3].i;
+		q__2.r = a[i__2].r + q__3.r, q__2.i = a[i__2].i + q__3.i;
+		r_cnjg(&q__1, &q__2);
+		a11.r = q__1.r, a11.i = q__1.i;
+		da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
+			dabs(r__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.f;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
+			r__2));
+		if (da11 < 1.f && db > 1.f) {
+		    if (db > bignum * da11) {
+			scaloc = 1.f / db;
+		    }
+		}
+		q__3.r = scaloc, q__3.i = 0.f;
+		q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
+			q__3.i + vec.i * q__3.r;
+		q__1 = cladiv_(&q__2, &a11);
+		x11.r = q__1.r, x11.i = q__1.i;
+		if (scaloc != 1.f) {
+		    i__2 = *n;
+		    for (j = 1; j <= i__2; ++j) {
+			csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L70: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__2 = k + l * c_dim1;
+		c__[i__2].r = x11.r, c__[i__2].i = x11.i;
+/* L80: */
+	    }
+/* L90: */
+	}
+    } else if (notrna && ! notrnb) {
+	for (l = *n; l >= 1; --l) {
+	    for (k = *m; k >= 1; --k) {
+		i__1 = *m - k;
+/* Computing MIN */
+		i__2 = k + 1;
+/* Computing MIN */
+		i__3 = k + 1;
+		q__1 = cdotu_(&i__1, &a[k + min(i__2,*m) * a_dim1], lda, &c__[
+			min(i__3,*m) + l * c_dim1], &c__1);
+		suml.r = q__1.r, suml.i = q__1.i;
+		i__1 = *n - l;
+/* Computing MIN */
+		i__2 = l + 1;
+/* Computing MIN */
+		i__3 = l + 1;
+		q__1 = cdotc_(&i__1, &c__[k + min(i__2,*n) * c_dim1], ldc, &b[
+			l + min(i__3,*n) * b_dim1], ldb);
+		sumr.r = q__1.r, sumr.i = q__1.i;
+		i__1 = k + l * c_dim1;
+		r_cnjg(&q__4, &sumr);
+		q__3.r = sgn * q__4.r, q__3.i = sgn * q__4.i;
+		q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
+		q__1.r = c__[i__1].r - q__2.r, q__1.i = c__[i__1].i - q__2.i;
+		vec.r = q__1.r, vec.i = q__1.i;
+		scaloc = 1.f;
+		i__1 = k + k * a_dim1;
+		r_cnjg(&q__3, &b[l + l * b_dim1]);
+		q__2.r = sgn * q__3.r, q__2.i = sgn * q__3.i;
+		q__1.r = a[i__1].r + q__2.r, q__1.i = a[i__1].i + q__2.i;
+		a11.r = q__1.r, a11.i = q__1.i;
+		da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
+			dabs(r__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.f;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
+			r__2));
+		if (da11 < 1.f && db > 1.f) {
+		    if (db > bignum * da11) {
+			scaloc = 1.f / db;
+		    }
+		}
+		q__3.r = scaloc, q__3.i = 0.f;
+		q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
+			q__3.i + vec.i * q__3.r;
+		q__1 = cladiv_(&q__2, &a11);
+		x11.r = q__1.r, x11.i = q__1.i;
+		if (scaloc != 1.f) {
+		    i__1 = *n;
+		    for (j = 1; j <= i__1; ++j) {
+			csscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L100: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__1 = k + l * c_dim1;
+		c__[i__1].r = x11.r, c__[i__1].i = x11.i;
+/* L110: */
+	    }
+/* L120: */
+	}
+    }
+    return;
+}

relapack/src/ctrtri.c

@@ -0,0 +1,107 @@
+#include "relapack.h"
+
+static void RELAPACK_ctrtri_rec(const char *, const char *, const int *,
+    float *, const int *, int *);
+
+
+/** CTRTRI computes the inverse of a complex upper or lower triangular matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's ctrtri.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/df/df8/ctrtri_8f.html
+ * */
+void RELAPACK_ctrtri(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int nounit = LAPACK(lsame)(diag, "N");
+    const int unit = LAPACK(lsame)(diag, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (!nounit && !unit)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("CTRTRI", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower  ? 'L' : 'U';
+    const char cleandiag = nounit ? 'N' : 'U';
+
+    // check for singularity
+    if (nounit) {
+        int i;
+        for (i = 0; i < *n; i++)
+            if (A[2 * (i + *ldA * i)] == 0 && A[2 * (i + *ldA * i) + 1] == 0) {
+                *info = i;
+                return;
+            }
+    }
+
+    // Recursive kernel
+    RELAPACK_ctrtri_rec(&cleanuplo, &cleandiag, n, A, ldA, info);
+}
+
+
+/** ctrtri's recursive compute kernel */
+static void RELAPACK_ctrtri_rec(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_CTRTRI, 1)) {
+        // Unblocked
+        LAPACK(ctrti2)(uplo, diag, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1., 0. };
+    const float MONE[] = { -1., 0. };
+
+    // Splitting
+    const int n1 = CREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + 2 * *ldA * n1;
+    float *const A_BL = A                 + 2 * n1;
+    float *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_ctrtri_rec(uplo, diag, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = - A_BL * A_TL
+        BLAS(ctrmm)("R", "L", "N", diag, &n2, &n1, MONE, A_TL, ldA, A_BL, ldA);
+        // A_BL = A_BR \ A_BL
+        BLAS(ctrsm)("L", "L", "N", diag, &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TR = - A_TL * A_TR
+        BLAS(ctrmm)("L", "U", "N", diag, &n1, &n2, MONE, A_TL, ldA, A_TR, ldA);
+        // A_TR = A_TR / A_BR
+        BLAS(ctrsm)("R", "U", "N", diag, &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_ctrtri_rec(uplo, diag, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/dgbtrf.c

@@ -0,0 +1,227 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_dgbtrf_rec(const int *, const int *, const int *,
+    const int *, double *, const int *, int *, double *, const int *, double *,
+    const int *, int *);
+
+
+/** DGBTRF computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's dgbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/da/d87/dgbtrf_8f.html
+ * */
+void RELAPACK_dgbtrf(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kl < 0)
+        *info = -3;
+    else if (*ku < 0)
+        *info = -4;
+    else if (*ldAb < 2 * *kl + *ku + 1)
+        *info = -6;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DGBTRF", &minfo);
+        return;
+    }
+
+    // Constant
+    const double ZERO[] = { 0. };
+
+    // Result upper band width
+    const int kv = *ku + *kl;
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    double *const A = Ab + kv;
+
+    // Zero upper diagonal fill-in elements
+    int i, j;
+    for (j = 0; j < *n; j++) {
+        double *const A_j = A + *ldA * j;
+        for (i = MAX(0, j - kv); i < j - *ku; i++)
+            A_j[i] = 0.;
+    }
+
+    // Allocate work space
+    const int n1 = DREC_SPLIT(*n);
+    const int mWorkl = (kv > n1) ? MAX(1, *m - *kl) : kv;
+    const int nWorkl = (kv > n1) ? n1 : kv;
+    const int mWorku = (*kl > n1) ? n1 : *kl;
+    const int nWorku = (*kl > n1) ? MAX(0, *n - *kl) : *kl;
+    double *Workl = malloc(mWorkl * nWorkl * sizeof(double));
+    double *Worku = malloc(mWorku * nWorku * sizeof(double));
+    LAPACK(dlaset)("L", &mWorkl, &nWorkl, ZERO, ZERO, Workl, &mWorkl);
+    LAPACK(dlaset)("U", &mWorku, &nWorku, ZERO, ZERO, Worku, &mWorku);
+
+    // Recursive kernel
+    RELAPACK_dgbtrf_rec(m, n, kl, ku, Ab, ldAb, ipiv, Workl, &mWorkl, Worku, &mWorku, info);
+
+    // Free work space
+    free(Workl);
+    free(Worku);
+}
+
+
+/** dgbtrf's recursive compute kernel */
+static void RELAPACK_dgbtrf_rec(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    double *Workl, const int *ldWorkl, double *Worku, const int *ldWorku,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_DGBTRF, 1)) {
+        // Unblocked
+        LAPACK(dgbtf2)(m, n, kl, ku, Ab, ldAb, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+    const int    iONE[] = { 1 };
+
+    // Loop iterators
+    int i, j;
+
+    // Output upper band width
+    const int kv = *ku + *kl;
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    double *const A = Ab + kv;
+
+    // Splitting
+    const int n1  = MIN(DREC_SPLIT(*n), *kl);
+    const int n2  = *n - n1;
+    const int m1  = MIN(n1, *m);
+    const int m2  = *m - m1;
+    const int mn1 = MIN(m1, n1);
+    const int mn2 = MIN(m2, n2);
+
+    // Ab_L *
+    //      Ab_BR
+    double *const Ab_L  = Ab;
+    double *const Ab_BR = Ab + *ldAb * n1;
+
+    // A_L A_R
+    double *const A_L = A;
+    double *const A_R = A + *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + *ldA * n1;
+    double *const A_BL = A             + m1;
+    double *const A_BR = A + *ldA * n1 + m1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // Banded splitting
+    const int n21 = MIN(n2, kv - n1);
+    const int n22 = MIN(n2 - n21, n1);
+    const int m21 = MIN(m2, *kl - m1);
+    const int m22 = MIN(m2 - m21, m1);
+
+    //   n1 n21  n22
+    // m *  A_Rl ARr
+    double *const A_Rl = A_R;
+    double *const A_Rr = A_R + *ldA * n21;
+
+    //     n1    n21    n22
+    // m1  *     A_TRl  A_TRr
+    // m21 A_BLt A_BRtl A_BRtr
+    // m22 A_BLb A_BRbl A_BRbr
+    double *const A_TRl  = A_TR;
+    double *const A_TRr  = A_TR + *ldA * n21;
+    double *const A_BLt  = A_BL;
+    double *const A_BLb  = A_BL              + m21;
+    double *const A_BRtl = A_BR;
+    double *const A_BRtr = A_BR + *ldA * n21;
+    double *const A_BRbl = A_BR              + m21;
+    double *const A_BRbr = A_BR + *ldA * n21 + m21;
+
+    // recursion(Ab_L, ipiv_T)
+    RELAPACK_dgbtrf_rec(m, &n1, kl, ku, Ab_L, ldAb, ipiv_T, Workl, ldWorkl, Worku, ldWorku, info);
+
+    // Workl = A_BLb
+    LAPACK(dlacpy)("U", &m22, &n1, A_BLb, ldA, Workl, ldWorkl);
+
+    // partially redo swaps in A_L
+    for (i = 0; i < mn1; i++) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(dswap)(&i, A_L + i, ldA, A_L + ip, ldA);
+            else
+                BLAS(dswap)(&i, A_L + i, ldA, Workl + ip - *kl, ldWorkl);
+        }
+    }
+
+    // apply pivots to A_Rl
+    LAPACK(dlaswp)(&n21, A_Rl, ldA, iONE, &mn1, ipiv_T, iONE);
+
+    // apply pivots to A_Rr columnwise
+    for (j = 0; j < n22; j++) {
+        double *const A_Rrj = A_Rr + *ldA * j;
+        for (i = j; i < mn1; i++) {
+            const int ip = ipiv_T[i] - 1;
+            if (ip != i) {
+                const double tmp = A_Rrj[i];
+                A_Rrj[i] = A_Rr[ip];
+                A_Rrj[ip] = tmp;
+            }
+        }
+    }
+
+    // A_TRl = A_TL \ A_TRl
+    BLAS(dtrsm)("L", "L", "N", "U", &m1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+    // Worku = A_TRr
+    LAPACK(dlacpy)("L", &m1, &n22, A_TRr, ldA, Worku, ldWorku);
+    // Worku = A_TL \ Worku
+    BLAS(dtrsm)("L", "L", "N", "U", &m1, &n22, ONE, A_TL, ldA, Worku, ldWorku);
+    // A_TRr = Worku
+    LAPACK(dlacpy)("L", &m1, &n22, Worku, ldWorku, A_TRr, ldA);
+    // A_BRtl = A_BRtl - A_BLt * A_TRl
+    BLAS(dgemm)("N", "N", &m21, &n21, &n1, MONE, A_BLt, ldA, A_TRl, ldA, ONE, A_BRtl, ldA);
+    // A_BRbl = A_BRbl - Workl * A_TRl
+    BLAS(dgemm)("N", "N", &m22, &n21, &n1, MONE, Workl, ldWorkl, A_TRl, ldA, ONE, A_BRbl, ldA);
+    // A_BRtr = A_BRtr - A_BLt * Worku
+    BLAS(dgemm)("N", "N", &m21, &n22, &n1, MONE, A_BLt, ldA, Worku, ldWorku, ONE, A_BRtr, ldA);
+    // A_BRbr = A_BRbr - Workl * Worku
+    BLAS(dgemm)("N", "N", &m22, &n22, &n1, MONE, Workl, ldWorkl, Worku, ldWorku, ONE, A_BRbr, ldA);
+
+    // partially undo swaps in A_L
+    for (i = mn1 - 1; i >= 0; i--) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(dswap)(&i, A_L + i, ldA, A_L + ip, ldA);
+            else
+                BLAS(dswap)(&i, A_L + i, ldA, Workl + ip - *kl, ldWorkl);
+        }
+    }
+
+    // recursion(Ab_BR, ipiv_B)
+    RELAPACK_dgbtrf_rec(&m2, &n2, kl, ku, Ab_BR, ldAb, ipiv_B, Workl, ldWorkl, Worku, ldWorku, info);
+    if (*info)
+        *info += n1;
+    // shift pivots
+    for (i = 0; i < mn2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/dgemmt.c

@@ -0,0 +1,165 @@
+#include "relapack.h"
+
+static void RELAPACK_dgemmt_rec(const char *, const char *, const char *,
+    const int *, const int *, const double *, const double *, const int *,
+    const double *, const int *, const double *, double *, const int *);
+
+static void RELAPACK_dgemmt_rec2(const char *, const char *, const char *,
+    const int *, const int *, const double *, const double *, const int *,
+    const double *, const int *, const double *, double *, const int *);
+
+
+/** DGEMMT computes a matrix-matrix product with general matrices but updates
+ * only the upper or lower triangular part of the result matrix.
+ *
+ * This routine performs the same operation as the BLAS routine
+ * dgemm(transA, transB, n, n, k, alpha, A, ldA, B, ldB, beta, C, ldC)
+ * but only updates the triangular part of C specified by uplo:
+ * If (*uplo == 'L'), only the lower triangular part of C is updated,
+ * otherwise the upper triangular part is updated.
+ * */
+void RELAPACK_dgemmt(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+
+#if HAVE_XGEMMT
+    BLAS(dgemmt)(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+    return;
+#else
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int notransA = LAPACK(lsame)(transA, "N");
+    const int tranA = LAPACK(lsame)(transA, "T");
+    const int notransB = LAPACK(lsame)(transB, "N");
+    const int tranB = LAPACK(lsame)(transB, "T");
+    int info = 0;
+    if (!lower && !upper)
+        info = 1;
+    else if (!tranA && !notransA)
+        info = 2;
+    else if (!tranB && !notransB)
+        info = 3;
+    else if (*n < 0)
+        info = 4;
+    else if (*k < 0)
+        info = 5;
+    else if (*ldA < MAX(1, notransA ? *n : *k))
+        info = 8;
+    else if (*ldB < MAX(1, notransB ? *k : *n))
+        info = 10;
+    else if (*ldC < MAX(1, *n))
+        info = 13;
+    if (info) {
+        LAPACK(xerbla)("DGEMMT", &info);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+    const char cleantransA = notransA ? 'N' : 'T';
+    const char cleantransB = notransB ? 'N' : 'T';
+
+    // Recursive kernel
+    RELAPACK_dgemmt_rec(&cleanuplo, &cleantransA, &cleantransB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+#endif
+}
+
+
+/** dgemmt's recursive compute kernel */
+static void RELAPACK_dgemmt_rec(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+
+    if (*n <= MAX(CROSSOVER_DGEMMT, 1)) {
+        // Unblocked
+        RELAPACK_dgemmt_rec2(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+        return;
+    }
+
+    // Splitting
+    const int n1 = DREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_T
+    // A_B
+    const double *const A_T = A;
+    const double *const A_B = A + ((*transA == 'N') ? n1 : *ldA * n1);
+
+    // B_L B_R
+    const double *const B_L = B;
+    const double *const B_R = B + ((*transB == 'N') ? *ldB * n1 : n1);
+
+    // C_TL C_TR
+    // C_BL C_BR
+    double *const C_TL = C;
+    double *const C_TR = C + *ldC * n1;
+    double *const C_BL = C             + n1;
+    double *const C_BR = C + *ldC * n1 + n1;
+
+    // recursion(C_TL)
+    RELAPACK_dgemmt_rec(uplo, transA, transB, &n1, k, alpha, A_T, ldA, B_L, ldB, beta, C_TL, ldC);
+
+    if (*uplo == 'L')
+        // C_BL = alpha A_B B_L + beta C_BL
+        BLAS(dgemm)(transA, transB, &n2, &n1, k, alpha, A_B, ldA, B_L, ldB, beta, C_BL, ldC);
+    else
+        // C_TR = alpha A_T B_R + beta C_TR
+        BLAS(dgemm)(transA, transB, &n1, &n2, k, alpha, A_T, ldA, B_R, ldB, beta, C_TR, ldC);
+
+    // recursion(C_BR)
+    RELAPACK_dgemmt_rec(uplo, transA, transB, &n2, k, alpha, A_B, ldA, B_R, ldB, beta, C_BR, ldC);
+}
+
+
+/** dgemmt's unblocked compute kernel */
+static void RELAPACK_dgemmt_rec2(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+
+    const int incB = (*transB == 'N') ? 1 : *ldB;
+    const int incC = 1;
+
+    int i;
+    for (i = 0; i < *n; i++) {
+        // A_0
+        // A_i
+        const double *const A_0 = A;
+        const double *const A_i = A + ((*transA == 'N') ? i : *ldA * i);
+
+        // * B_i *
+        const double *const B_i = B + ((*transB == 'N') ? *ldB * i : i);
+
+        // * C_0i *
+        // * C_ii *
+        double *const C_0i = C + *ldC * i;
+        double *const C_ii = C + *ldC * i + i;
+
+        if (*uplo == 'L') {
+            const int nmi = *n - i;
+            if (*transA == 'N')
+                BLAS(dgemv)(transA, &nmi, k, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+            else
+                BLAS(dgemv)(transA, k, &nmi, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+        } else {
+            const int ip1 = i + 1;
+            if (*transA == 'N')
+                BLAS(dgemv)(transA, &ip1, k, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+            else
+                BLAS(dgemv)(transA, k, &ip1, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+        }
+    }
+}

relapack/src/dgetrf.c

@@ -0,0 +1,117 @@
+#include "relapack.h"
+
+static void RELAPACK_dgetrf_rec(const int *, const int *, double *,
+    const int *, int *, int *);
+
+
+/** DGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's dgetrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d3/d6a/dgetrf_8f.html
+ * */
+void RELAPACK_dgetrf(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DGETRF", &minfo);
+        return;
+    }
+
+    const int sn = MIN(*m, *n);
+
+    RELAPACK_dgetrf_rec(m, &sn, A, ldA, ipiv, info);
+
+    // Right remainder
+    if (*m < *n) {
+        // Constants
+        const double ONE[] = { 1. };
+        const int   iONE[] = { 1. };
+
+        // Splitting
+        const int rn = *n - *m;
+
+        // A_L A_R
+        const double *const A_L = A;
+        double *const       A_R = A + *ldA * *m;
+
+        // A_R = apply(ipiv, A_R)
+        LAPACK(dlaswp)(&rn, A_R, ldA, iONE, m, ipiv, iONE);
+        // A_R = A_S \ A_R
+        BLAS(dtrsm)("L", "L", "N", "U", m, &rn, ONE, A_L, ldA, A_R, ldA);
+    }
+}
+
+
+/** dgetrf's recursive compute kernel */
+static void RELAPACK_dgetrf_rec(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_DGETRF, 1)) {
+        // Unblocked
+        LAPACK(dgetf2)(m, n, A, ldA, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+    const int    iONE[] = { 1 };
+
+    // Splitting
+    const int n1 = DREC_SPLIT(*n);
+    const int n2 = *n - n1;
+    const int m2 = *m - n1;
+
+    // A_L A_R
+    double *const A_L = A;
+    double *const A_R = A + *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + *ldA * n1;
+    double *const A_BL = A             + n1;
+    double *const A_BR = A + *ldA * n1 + n1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // recursion(A_L, ipiv_T)
+    RELAPACK_dgetrf_rec(m, &n1, A_L, ldA, ipiv_T, info);
+    // apply pivots to A_R
+    LAPACK(dlaswp)(&n2, A_R, ldA, iONE, &n1, ipiv_T, iONE);
+
+    // A_TR = A_TL \ A_TR
+    BLAS(dtrsm)("L", "L", "N", "U", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+    // A_BR = A_BR - A_BL * A_TR
+    BLAS(dgemm)("N", "N", &m2, &n2, &n1, MONE, A_BL, ldA, A_TR, ldA, ONE, A_BR, ldA);
+
+    // recursion(A_BR, ipiv_B)
+    RELAPACK_dgetrf_rec(&m2, &n2, A_BR, ldA, ipiv_B, info);
+    if (*info)
+        *info += n1;
+    // apply pivots to A_BL
+    LAPACK(dlaswp)(&n1, A_BL, ldA, iONE, &n2, ipiv_B, iONE);
+    // shift pivots
+    int i;
+    for (i = 0; i < n2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/dlauum.c

@@ -0,0 +1,87 @@
+#include "relapack.h"
+
+static void RELAPACK_dlauum_rec(const char *, const int *, double *,
+    const int *, int *);
+
+
+/** DLAUUM computes the product U * U**T or L**T * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A.
+ *
+ * This routine is functionally equivalent to LAPACK's dlauum.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d0/dc2/dlauum_8f.html
+ * */
+void RELAPACK_dlauum(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DLAUUM", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_dlauum_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** dlauum's recursive compute kernel */
+static void RELAPACK_dlauum_rec(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_DLAUUM, 1)) {
+        // Unblocked
+        LAPACK(dlauu2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[] = { 1. };
+
+    // Splitting
+    const int n1 = DREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + *ldA * n1;
+    double *const A_BL = A             + n1;
+    double *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_dlauum_rec(uplo, &n1, A_TL, ldA, info);
+
+    if (*uplo == 'L') {
+        // A_TL = A_TL + A_BL' * A_BL
+        BLAS(dsyrk)("L", "T", &n1, &n2, ONE, A_BL, ldA, ONE, A_TL, ldA);
+        // A_BL = A_BR' * A_BL
+        BLAS(dtrmm)("L", "L", "T", "N", &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TL = A_TL + A_TR * A_TR'
+        BLAS(dsyrk)("U", "N", &n1, &n2, ONE, A_TR, ldA, ONE, A_TL, ldA);
+        // A_TR = A_TR * A_BR'
+        BLAS(dtrmm)("R", "U", "T", "N", &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_dlauum_rec(uplo, &n2, A_BR, ldA, info);
+}

relapack/src/dpbtrf.c

@@ -0,0 +1,157 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_dpbtrf_rec(const char *, const int *, const int *,
+    double *, const int *, double *, const int *, int *);
+
+
+/** DPBTRF computes the Cholesky factorization of a real symmetric positive definite band matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's dpbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/df/da9/dpbtrf_8f.html
+ * */
+void RELAPACK_dpbtrf(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kd < 0)
+        *info = -3;
+    else if (*ldAb < *kd + 1)
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DPBTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Constant
+    const double ZERO[] = { 0. };
+
+    // Allocate work space
+    const int n1 = DREC_SPLIT(*n);
+    const int mWork = (*kd > n1) ? (lower ? *n - *kd : n1) : *kd;
+    const int nWork = (*kd > n1) ? (lower ? n1 : *n - *kd) : *kd;
+    double *Work = malloc(mWork * nWork * sizeof(double));
+    LAPACK(dlaset)(uplo, &mWork, &nWork, ZERO, ZERO, Work, &mWork);
+
+    // Recursive kernel
+    RELAPACK_dpbtrf_rec(&cleanuplo, n, kd, Ab, ldAb, Work, &mWork, info);
+
+    // Free work space
+    free(Work);
+}
+
+
+/** dpbtrf's recursive compute kernel */
+static void RELAPACK_dpbtrf_rec(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    double *Work, const int *ldWork,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_DPBTRF, 1)) {
+        // Unblocked
+        LAPACK(dpbtf2)(uplo, n, kd, Ab, ldAb, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    double *const A = Ab + ((*uplo == 'L') ? 0 : *kd);
+
+    // Splitting
+    const int n1 = MIN(DREC_SPLIT(*n), *kd);
+    const int n2 = *n - n1;
+
+    // * *
+    // * Ab_BR
+    double *const Ab_BR = Ab + *ldAb * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + *ldA * n1;
+    double *const A_BL = A             + n1;
+    double *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_dpotrf(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    // Banded splitting
+    const int n21 = MIN(n2, *kd - n1);
+    const int n22 = MIN(n2 - n21, n1);
+
+    //     n1    n21    n22
+    // n1  *     A_TRl  A_TRr
+    // n21 A_BLt A_BRtl A_BRtr
+    // n22 A_BLb A_BRbl A_BRbr
+    double *const A_TRl  = A_TR;
+    double *const A_TRr  = A_TR + *ldA * n21;
+    double *const A_BLt  = A_BL;
+    double *const A_BLb  = A_BL               + n21;
+    double *const A_BRtl = A_BR;
+    double *const A_BRtr = A_BR + *ldA * n21;
+    double *const A_BRbl = A_BR               + n21;
+    double *const A_BRbr = A_BR + *ldA * n21  + n21;
+
+    if (*uplo == 'L') {
+        // A_BLt = ABLt / A_TL'
+        BLAS(dtrsm)("R", "L", "T", "N", &n21, &n1, ONE, A_TL, ldA, A_BLt, ldA);
+        // A_BRtl = A_BRtl - A_BLt * A_BLt'
+        BLAS(dsyrk)("L", "N", &n21, &n1, MONE, A_BLt, ldA, ONE, A_BRtl, ldA);
+        // Work = A_BLb
+        LAPACK(dlacpy)("U", &n22, &n1, A_BLb, ldA, Work, ldWork);
+        // Work = Work / A_TL'
+        BLAS(dtrsm)("R", "L", "T", "N", &n22, &n1, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRbl = A_BRbl - Work * A_BLt'
+        BLAS(dgemm)("N", "T", &n22, &n21, &n1, MONE, Work, ldWork, A_BLt, ldA, ONE, A_BRbl, ldA);
+        // A_BRbr = A_BRbr - Work * Work'
+        BLAS(dsyrk)("L", "N", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_BLb = Work
+        LAPACK(dlacpy)("U", &n22, &n1, Work, ldWork, A_BLb, ldA);
+    } else {
+        // A_TRl = A_TL' \ A_TRl
+        BLAS(dtrsm)("L", "U", "T", "N", &n1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+        // A_BRtl = A_BRtl - A_TRl' * A_TRl
+        BLAS(dsyrk)("U", "T", &n21, &n1, MONE, A_TRl, ldA, ONE, A_BRtl, ldA);
+        // Work = A_TRr
+        LAPACK(dlacpy)("L", &n1, &n22, A_TRr, ldA, Work, ldWork);
+        // Work = A_TL' \ Work
+        BLAS(dtrsm)("L", "U", "T", "N", &n1, &n22, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRtr = A_BRtr - A_TRl' * Work
+        BLAS(dgemm)("T", "N", &n21, &n22, &n1, MONE, A_TRl, ldA, Work, ldWork, ONE, A_BRtr, ldA);
+        // A_BRbr = A_BRbr - Work' * Work
+        BLAS(dsyrk)("U", "T", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_TRr = Work
+        LAPACK(dlacpy)("L", &n1, &n22, Work, ldWork, A_TRr, ldA);
+    }
+
+    // recursion(A_BR)
+    if (*kd > n1)
+        RELAPACK_dpotrf(uplo, &n2, A_BR, ldA, info);
+    else
+        RELAPACK_dpbtrf_rec(uplo, &n2, kd, Ab_BR, ldAb, Work, ldWork, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/dpotrf.c

@@ -0,0 +1,92 @@
+#include "relapack.h"
+
+static void RELAPACK_dpotrf_rec(const char *, const int *, double *,
+        const int *, int *);
+
+
+/** DPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's dpotrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d0/d8a/dpotrf_8f.html
+ * */
+void RELAPACK_dpotrf(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DPOTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_dpotrf_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** dpotrf's recursive compute kernel */
+static void RELAPACK_dpotrf_rec(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_DPOTRF, 1)) {
+        // Unblocked
+        LAPACK(dpotf2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+
+    // Splitting
+    const int n1 = DREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + *ldA * n1;
+    double *const A_BL = A             + n1;
+    double *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_dpotrf_rec(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = A_BL / A_TL'
+        BLAS(dtrsm)("R", "L", "T", "N", &n2, &n1, ONE, A_TL, ldA, A_BL, ldA);
+        // A_BR = A_BR - A_BL * A_BL'
+        BLAS(dsyrk)("L", "N", &n2, &n1, MONE, A_BL, ldA, ONE, A_BR, ldA);
+    } else {
+        // A_TR = A_TL' \ A_TR
+        BLAS(dtrsm)("L", "U", "T", "N", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+        // A_BR = A_BR - A_TR' * A_TR
+        BLAS(dsyrk)("U", "T", &n2, &n1, MONE, A_TR, ldA, ONE, A_BR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_dpotrf_rec(uplo, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/dsygst.c

@@ -0,0 +1,212 @@
+#include "relapack.h"
+#if XSYGST_ALLOW_MALLOC
+#include "stdlib.h"
+#endif
+
+static void RELAPACK_dsygst_rec(const int *, const char *, const int *,
+    double *, const int *, const double *, const int *,
+    double *, const int *, int *);
+
+
+/** DSYGST reduces a real symmetric-definite generalized eigenproblem to standard form.
+ *
+ * This routine is functionally equivalent to LAPACK's dsygst.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dc/d04/dsygst_8f.html
+ * */
+void RELAPACK_dsygst(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (*itype < 1 || *itype > 3)
+        *info = -1;
+    else if (!lower && !upper)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    else if (*ldB < MAX(1, *n))
+        *info = -7;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DSYGST", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Allocate work space
+    double *Work = NULL;
+    int    lWork = 0;
+#if XSYGST_ALLOW_MALLOC
+    const int n1 = DREC_SPLIT(*n);
+    lWork = n1 * (*n - n1);
+    Work  = malloc(lWork * sizeof(double));
+    if (!Work)
+        lWork = 0;
+#endif
+
+    // recursive kernel
+    RELAPACK_dsygst_rec(itype, &cleanuplo, n, A, ldA, B, ldB, Work, &lWork, info);
+
+    // Free work space
+#if XSYGST_ALLOW_MALLOC
+    if (Work)
+        free(Work);
+#endif
+}
+
+
+/** dsygst's recursive compute kernel */
+static void RELAPACK_dsygst_rec(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    double *Work, const int *lWork, int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_SSYGST, 1)) {
+        // Unblocked
+        LAPACK(dsygs2)(itype, uplo, n, A, ldA, B, ldB, info);
+        return;
+    }
+
+    // Constants
+    const double ZERO[]  = { 0. };
+    const double ONE[]   = { 1. };
+    const double MONE[]  = { -1. };
+    const double HALF[]  = { .5 };
+    const double MHALF[] = { -.5 };
+    const int    iONE[]  = { 1 };
+
+    // Loop iterator
+    int i;
+
+    // Splitting
+    const int n1 = DREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + *ldA * n1;
+    double *const A_BL = A             + n1;
+    double *const A_BR = A + *ldA * n1 + n1;
+
+    // B_TL B_TR
+    // B_BL B_BR
+    const double *const B_TL = B;
+    const double *const B_TR = B + *ldB * n1;
+    const double *const B_BL = B             + n1;
+    const double *const B_BR = B + *ldB * n1 + n1;
+
+    // recursion(A_TL, B_TL)
+    RELAPACK_dsygst_rec(itype, uplo, &n1, A_TL, ldA, B_TL, ldB, Work, lWork, info);
+
+    if (*itype == 1)
+        if (*uplo == 'L') {
+            // A_BL = A_BL / B_TL'
+            BLAS(dtrsm)("R", "L", "T", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork > n2 * n1) {
+                // T = -1/2 * B_BL * A_TL
+                BLAS(dsymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            } else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(dsymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BR = A_BR - A_BL * B_BL' - B_BL * A_BL'
+            BLAS(dsyr2k)("L", "N", &n2, &n1, MONE, A_BL, ldA, B_BL, ldB, ONE, A_BR, ldA);
+            if (*lWork > n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(dsymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR \ A_BL
+            BLAS(dtrsm)("L", "L", "N", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL' \ A_TR
+            BLAS(dtrsm)("L", "U", "T", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork > n2 * n1) {
+                // T = -1/2 * A_TL * B_TR
+                BLAS(dsymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            } else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(dsymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_BR = A_BR - A_TR' * B_TR - B_TR' * A_TR
+            BLAS(dsyr2k)("U", "T", &n2, &n1, MONE, A_TR, ldA, B_TR, ldB, ONE, A_BR, ldA);
+            if (*lWork > n2 * n1)
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(dsymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR / B_BR
+            BLAS(dtrsm)("R", "U", "N", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+    else
+        if (*uplo == 'L') {
+            // A_BL = A_BL * B_TL
+            BLAS(dtrmm)("R", "L", "N", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork > n2 * n1) {
+                // T = 1/2 * A_BR * B_BL
+                BLAS(dsymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            } else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(dsymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_TL = A_TL + A_BL' * B_BL + B_BL' * A_BL
+            BLAS(dsyr2k)("L", "T", &n1, &n2, ONE, A_BL, ldA, B_BL, ldB, ONE, A_TL, ldA);
+            if (*lWork > n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(dsymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR * A_BL
+            BLAS(dtrmm)("L", "L", "T", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL * A_TR
+            BLAS(dtrmm)("L", "U", "N", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork > n2 * n1) {
+                // T = 1/2 * B_TR * A_BR
+                BLAS(dsymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            } else
+                // A_TR = A_TR + 1/2 B_TR A_BR
+                BLAS(dsymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TL = A_TL + A_TR * B_TR' + B_TR * A_TR'
+            BLAS(dsyr2k)("U", "N", &n1, &n2, ONE, A_TR, ldA, B_TR, ldB, ONE, A_TL, ldA);
+            if (*lWork > n2 * n1)
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            else
+                // A_TR = A_TR + 1/2 B_TR * A_BR
+                BLAS(dsymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR * B_BR
+            BLAS(dtrmm)("R", "U", "T", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+
+    // recursion(A_BR, B_BR)
+    RELAPACK_dsygst_rec(itype, uplo, &n2, A_BR, ldA, B_BR, ldB, Work, lWork, info);
+}

relapack/src/dsytrf.c

@@ -0,0 +1,238 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_dsytrf_rec(const char *, const int *, const int *, int *,
+    double *, const int *, int *, double *, const int *, int *);
+
+
+/** DSYTRF computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's dsytrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dd/df4/dsytrf_8f.html
+ * */
+void RELAPACK_dsytrf(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    double *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * sizeof(double));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy arguments
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_dsytrf_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** dsytrf's recursive compute kernel */
+static void RELAPACK_dsytrf_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_DSYTRF, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(dsytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_dsytrf_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+    const int    iONE[] = { 1 };
+
+    // Loop iterator
+    int i;
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = DREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        double *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_dsytrf_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        double *const A_BL   = A             + n1;
+        double *const A_BR   = A + *ldA * n1 + n1;
+        double *const A_BL_B = A             + *n;
+        double *const A_BR_B = A + *ldA * n1 + *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        double *const Work_BL =              Work                + n1;
+        double *const Work_BR = top ? Work : Work + *ldWork * n1 + n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_dgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(dgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_dsytrf_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            double *const A_BR_r = A_BR + *ldA * n2_out + n2_out;
+
+            // last row of A_BL
+            double *const A_BL_b = A_BL + n2_out;
+
+            // last row of Work_BL
+            double *const Work_BL_b = Work_BL + n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(dgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = DREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        double *const Work_R = top ? Work : Work + *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_dsytrf_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1  = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        double *const A_TL_T = A + *ldA * n_rest;
+        double *const A_TR_T = A + *ldA * (n_rest + n1);
+        double *const A_TL   = A + *ldA * n_rest        + n_rest;
+        double *const A_TR   = A + *ldA * (n_rest + n1) + n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        double *const Work_L  = Work;
+        double *const Work_TR = Work + *ldWork * (top ? n2_diff : n1) + n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_dgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(dgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_dsytrf_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(dgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/dsytrf_rec2.c

@@ -0,0 +1,352 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static int c__1 = 1;
+static double c_b8 = -1.;
+static double c_b9 = 1.;
+
+/** DSYTRF_REC2 computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagon al pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's dlasyf.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_dsytrf_rec2(char *uplo, int *n, int *
+	nb, int *kb, double *a, int *lda, int *ipiv,
+	double *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2;
+    double d__1, d__2, d__3;
+
+    /* Builtin functions */
+    double sqrt(double);
+
+    /* Local variables */
+    static int j, k;
+    static double t, r1, d11, d21, d22;
+    static int jj, kk, jp, kp, kw, kkw, imax, jmax;
+    static double alpha;
+    extern /* Subroutine */ int dscal_(int *, double *, double *,
+	    int *);
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int dgemv_(char *, int *, int *,
+	    double *, double *, int *, double *, int *,
+	    double *, double *, int *, ftnlen), dcopy_(int *,
+	    double *, int *, double *, int *), dswap_(int
+	    *, double *, int *, double *, int *);
+    static int kstep;
+    static double absakk;
+    extern int idamax_(int *, double *, int *);
+    static double colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.) + 1.) / 8.;
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	dcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    dgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b9, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	kstep = 1;
+	absakk = (d__1 = w[k + kw * w_dim1], abs(d__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = idamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    colmax = (d__1 = w[imax + kw * w_dim1], abs(d__1));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		dcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		dcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    dgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b9, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		i__1 = k - imax;
+		jmax = imax + idamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
+			 &c__1);
+		rowmax = (d__1 = w[jmax + (kw - 1) * w_dim1], abs(d__1));
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    jmax = idamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+/* Computing MAX */
+		    d__2 = rowmax, d__3 = (d__1 = w[jmax + (kw - 1) * w_dim1],
+			     abs(d__1));
+		    rowmax = max(d__2,d__3);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else if ((d__1 = w[imax + (kw - 1) * w_dim1], abs(d__1)) >=
+			alpha * rowmax) {
+		    kp = imax;
+		    dcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		} else {
+		    kp = imax;
+		    kstep = 2;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kp != kk) {
+		a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
+		i__1 = kk - 1 - kp;
+		dcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    dcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    dswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		dswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		dcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		r1 = 1. / a[k + k * a_dim1];
+		i__1 = k - 1;
+		dscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+	    } else {
+		if (k > 2) {
+		    d21 = w[k - 1 + kw * w_dim1];
+		    d11 = w[k + kw * w_dim1] / d21;
+		    d22 = w[k - 1 + (kw - 1) * w_dim1] / d21;
+		    t = 1. / (d11 * d22 - 1.);
+		    d21 = t / d21;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			a[j + (k - 1) * a_dim1] = d21 * (d11 * w[j + (kw - 1)
+				* w_dim1] - w[j + kw * w_dim1]);
+			a[j + k * a_dim1] = d21 * (d22 * w[j + kw * w_dim1] -
+				w[j + (kw - 1) * w_dim1]);
+/* L20: */
+		    }
+		}
+		a[k - 1 + (k - 1) * a_dim1] = w[k - 1 + (kw - 1) * w_dim1];
+		a[k - 1 + k * a_dim1] = w[k - 1 + kw * w_dim1];
+		a[k + k * a_dim1] = w[k + kw * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    ++j;
+	}
+	++j;
+	if (jp != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    dswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
+	}
+	if (j < *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	i__1 = *n - k + 1;
+	dcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	i__1 = *n - k + 1;
+	i__2 = k - 1;
+	dgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1], lda, &w[k
+		+ w_dim1], ldw, &c_b9, &w[k + k * w_dim1], &c__1, (ftnlen)12);
+	kstep = 1;
+	absakk = (d__1 = w[k + k * w_dim1], abs(d__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + idamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    colmax = (d__1 = w[imax + k * w_dim1], abs(d__1));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - k;
+		dcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		dcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		i__1 = *n - k + 1;
+		i__2 = k - 1;
+		dgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1],
+			lda, &w[imax + w_dim1], ldw, &c_b9, &w[k + (k + 1) *
+			w_dim1], &c__1, (ftnlen)12);
+		i__1 = imax - k;
+		jmax = k - 1 + idamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
+			;
+		rowmax = (d__1 = w[jmax + (k + 1) * w_dim1], abs(d__1));
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    jmax = imax + idamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+/* Computing MAX */
+		    d__2 = rowmax, d__3 = (d__1 = w[jmax + (k + 1) * w_dim1],
+			    abs(d__1));
+		    rowmax = max(d__2,d__3);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else if ((d__1 = w[imax + (k + 1) * w_dim1], abs(d__1)) >=
+			alpha * rowmax) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    dcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		} else {
+		    kp = imax;
+		    kstep = 2;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kp != kk) {
+		a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
+		i__1 = kp - kk - 1;
+		dcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    dcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    dswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		dswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		dcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    r1 = 1. / a[k + k * a_dim1];
+		    i__1 = *n - k;
+		    dscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    d21 = w[k + 1 + k * w_dim1];
+		    d11 = w[k + 1 + (k + 1) * w_dim1] / d21;
+		    d22 = w[k + k * w_dim1] / d21;
+		    t = 1. / (d11 * d22 - 1.);
+		    d21 = t / d21;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			a[j + k * a_dim1] = d21 * (d11 * w[j + k * w_dim1] -
+				w[j + (k + 1) * w_dim1]);
+			a[j + (k + 1) * a_dim1] = d21 * (d22 * w[j + (k + 1) *
+				 w_dim1] - w[j + k * w_dim1]);
+/* L80: */
+		    }
+		}
+		a[k + k * a_dim1] = w[k + k * w_dim1];
+		a[k + 1 + k * a_dim1] = w[k + 1 + k * w_dim1];
+		a[k + 1 + (k + 1) * a_dim1] = w[k + 1 + (k + 1) * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    --j;
+	}
+	--j;
+	if (jp != jj && j >= 1) {
+	    dswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j > 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/dsytrf_rook.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_dsytrf_rook_rec(const char *, const int *, const int *, int *,
+    double *, const int *, int *, double *, const int *, int *);
+
+
+/** DSYTRF_ROOK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's dsytrf_rook.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/db/df4/dsytrf__rook_8f.html
+ * */
+void RELAPACK_dsytrf_rook(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    double *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * sizeof(double));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_dsytrf_rook_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** dsytrf_rook's recursive compute kernel */
+static void RELAPACK_dsytrf_rook_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_DSYTRF_ROOK, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(dsytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_dsytrf_rook_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+    const int    iONE[] = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = DREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        double *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_dsytrf_rook_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2   = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        double *const A_BL   = A             + n1;
+        double *const A_BR   = A + *ldA * n1 + n1;
+        double *const A_BL_B = A             + *n;
+        double *const A_BR_B = A + *ldA * n1 + *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        double *const Work_BL =              Work                + n1;
+        double *const Work_BR = top ? Work : Work + *ldWork * n1 + n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_dgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(dgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_dsytrf_rook_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            double *const A_BR_r = A_BR + *ldA * n2_out + n2_out;
+
+            // last row of A_BL
+            double *const A_BL_b = A_BL + n2_out;
+
+            // last row of Work_BL
+            double *const Work_BL_b = Work_BL + n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(dgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = DREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        double *const Work_R = top ? Work : Work + *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_dsytrf_rook_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        double *const A_TL_T = A + *ldA * n_rest;
+        double *const A_TR_T = A + *ldA * (n_rest + n1);
+        double *const A_TL   = A + *ldA * n_rest        + n_rest;
+        double *const A_TR   = A + *ldA * (n_rest + n1) + n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        double *const Work_L  = Work;
+        double *const Work_TR = Work + *ldWork * (top ? n2_diff : n1) + n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_dgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(dgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_dsytrf_rook_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(dgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/dsytrf_rook_rec2.c

@@ -0,0 +1,451 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static int c__1 = 1;
+static double c_b9 = -1.;
+static double c_b10 = 1.;
+
+/** DSYTRF_ROOK_REC2 computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufma n ("rook") diagonal pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's dlasyf.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_dsytrf_rook_rec2(char *uplo, int *n,
+	int *nb, int *kb, double *a, int *lda, int *ipiv,
+	double *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2;
+    double d__1;
+
+    /* Builtin functions */
+    double sqrt(double);
+
+    /* Local variables */
+    static int j, k, p;
+    static double t, r1, d11, d12, d21, d22;
+    static int ii, jj, kk, kp, kw, jp1, jp2, kkw;
+    static logical done;
+    static int imax, jmax;
+    static double alpha;
+    extern /* Subroutine */ int dscal_(int *, double *, double *,
+	    int *);
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int dgemv_(char *, int *, int *,
+	    double *, double *, int *, double *, int *,
+	    double *, double *, int *, ftnlen);
+    static double dtemp, sfmin;
+    static int itemp;
+    extern /* Subroutine */ int dcopy_(int *, double *, int *,
+	    double *, int *), dswap_(int *, double *, int
+	    *, double *, int *);
+    static int kstep;
+    extern double dlamch_(char *, ftnlen);
+    static double absakk;
+    extern int idamax_(int *, double *, int *);
+    static double colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.) + 1.) / 8.;
+    sfmin = dlamch_("S", (ftnlen)1);
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	p = k;
+	dcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    dgemv_("No transpose", &k, &i__1, &c_b9, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b10, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	absakk = (d__1 = w[k + kw * w_dim1], abs(d__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = idamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    colmax = (d__1 = w[imax + kw * w_dim1], abs(d__1));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    dcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L12:
+		dcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		dcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    dgemv_("No transpose", &k, &i__1, &c_b9, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b10, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = k - imax;
+		    jmax = imax + idamax_(&i__1, &w[imax + 1 + (kw - 1) *
+			    w_dim1], &c__1);
+		    rowmax = (d__1 = w[jmax + (kw - 1) * w_dim1], abs(d__1));
+		} else {
+		    rowmax = 0.;
+		}
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    itemp = idamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+		    dtemp = (d__1 = w[itemp + (kw - 1) * w_dim1], abs(d__1));
+		    if (dtemp > rowmax) {
+			rowmax = dtemp;
+			jmax = itemp;
+		    }
+		}
+		if (! ((d__1 = w[imax + (kw - 1) * w_dim1], abs(d__1)) <
+			alpha * rowmax)) {
+		    kp = imax;
+		    dcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    dcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		}
+		if (! done) {
+		    goto L12;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kstep == 2 && p != k) {
+		i__1 = k - p;
+		dcopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
+			a_dim1], lda);
+		dcopy_(&p, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - k + 1;
+		dswap_(&i__1, &a[k + k * a_dim1], lda, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - kk + 1;
+		dswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
+			 ldw);
+	    }
+	    if (kp != kk) {
+		a[kp + k * a_dim1] = a[kk + k * a_dim1];
+		i__1 = k - 1 - kp;
+		dcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		dcopy_(&kp, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - kk + 1;
+		dswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1],
+			 lda);
+		i__1 = *n - kk + 1;
+		dswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		dcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    if ((d__1 = a[k + k * a_dim1], abs(d__1)) >= sfmin) {
+			r1 = 1. / a[k + k * a_dim1];
+			i__1 = k - 1;
+			dscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    } else if (a[k + k * a_dim1] != 0.) {
+			i__1 = k - 1;
+			for (ii = 1; ii <= i__1; ++ii) {
+			    a[ii + k * a_dim1] /= a[k + k * a_dim1];
+/* L14: */
+			}
+		    }
+		}
+	    } else {
+		if (k > 2) {
+		    d12 = w[k - 1 + kw * w_dim1];
+		    d11 = w[k + kw * w_dim1] / d12;
+		    d22 = w[k - 1 + (kw - 1) * w_dim1] / d12;
+		    t = 1. / (d11 * d22 - 1.);
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			a[j + (k - 1) * a_dim1] = t * ((d11 * w[j + (kw - 1) *
+				 w_dim1] - w[j + kw * w_dim1]) / d12);
+			a[j + k * a_dim1] = t * ((d22 * w[j + kw * w_dim1] -
+				w[j + (kw - 1) * w_dim1]) / d12);
+/* L20: */
+		    }
+		}
+		a[k - 1 + (k - 1) * a_dim1] = w[k - 1 + (kw - 1) * w_dim1];
+		a[k - 1 + k * a_dim1] = w[k - 1 + kw * w_dim1];
+		a[k + k * a_dim1] = w[k + kw * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    ++j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	++j;
+	if (jp2 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    dswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	jj = j - 1;
+	if (jp1 != jj && kstep == 2) {
+	    i__1 = *n - j + 1;
+	    dswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	if (j <= *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	p = k;
+	i__1 = *n - k + 1;
+	dcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	if (k > 1) {
+	    i__1 = *n - k + 1;
+	    i__2 = k - 1;
+	    dgemv_("No transpose", &i__1, &i__2, &c_b9, &a[k + a_dim1], lda, &
+		    w[k + w_dim1], ldw, &c_b10, &w[k + k * w_dim1], &c__1, (
+		    ftnlen)12);
+	}
+	absakk = (d__1 = w[k + k * w_dim1], abs(d__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + idamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    colmax = (d__1 = w[imax + k * w_dim1], abs(d__1));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = *n - k + 1;
+	    dcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+		    c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L72:
+		i__1 = imax - k;
+		dcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		dcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		if (k > 1) {
+		    i__1 = *n - k + 1;
+		    i__2 = k - 1;
+		    dgemv_("No transpose", &i__1, &i__2, &c_b9, &a[k + a_dim1]
+			    , lda, &w[imax + w_dim1], ldw, &c_b10, &w[k + (k
+			    + 1) * w_dim1], &c__1, (ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = imax - k;
+		    jmax = k - 1 + idamax_(&i__1, &w[k + (k + 1) * w_dim1], &
+			    c__1);
+		    rowmax = (d__1 = w[jmax + (k + 1) * w_dim1], abs(d__1));
+		} else {
+		    rowmax = 0.;
+		}
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    itemp = imax + idamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+		    dtemp = (d__1 = w[itemp + (k + 1) * w_dim1], abs(d__1));
+		    if (dtemp > rowmax) {
+			rowmax = dtemp;
+			jmax = itemp;
+		    }
+		}
+		if (! ((d__1 = w[imax + (k + 1) * w_dim1], abs(d__1)) < alpha
+			* rowmax)) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    dcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    i__1 = *n - k + 1;
+		    dcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		}
+		if (! done) {
+		    goto L72;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kstep == 2 && p != k) {
+		i__1 = p - k;
+		dcopy_(&i__1, &a[k + k * a_dim1], &c__1, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - p + 1;
+		dcopy_(&i__1, &a[p + k * a_dim1], &c__1, &a[p + p * a_dim1], &
+			c__1);
+		dswap_(&k, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
+		dswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
+	    }
+	    if (kp != kk) {
+		a[kp + k * a_dim1] = a[kk + k * a_dim1];
+		i__1 = kp - k - 1;
+		dcopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1)
+			* a_dim1], lda);
+		i__1 = *n - kp + 1;
+		dcopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp *
+			a_dim1], &c__1);
+		dswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		dswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		dcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    if ((d__1 = a[k + k * a_dim1], abs(d__1)) >= sfmin) {
+			r1 = 1. / a[k + k * a_dim1];
+			i__1 = *n - k;
+			dscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    } else if (a[k + k * a_dim1] != 0.) {
+			i__1 = *n;
+			for (ii = k + 1; ii <= i__1; ++ii) {
+			    a[ii + k * a_dim1] /= a[k + k * a_dim1];
+/* L74: */
+			}
+		    }
+		}
+	    } else {
+		if (k < *n - 1) {
+		    d21 = w[k + 1 + k * w_dim1];
+		    d11 = w[k + 1 + (k + 1) * w_dim1] / d21;
+		    d22 = w[k + k * w_dim1] / d21;
+		    t = 1. / (d11 * d22 - 1.);
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			a[j + k * a_dim1] = t * ((d11 * w[j + k * w_dim1] - w[
+				j + (k + 1) * w_dim1]) / d21);
+			a[j + (k + 1) * a_dim1] = t * ((d22 * w[j + (k + 1) *
+				w_dim1] - w[j + k * w_dim1]) / d21);
+/* L80: */
+		    }
+		}
+		a[k + k * a_dim1] = w[k + k * w_dim1];
+		a[k + 1 + k * a_dim1] = w[k + 1 + k * w_dim1];
+		a[k + 1 + (k + 1) * a_dim1] = w[k + 1 + (k + 1) * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    --j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	--j;
+	if (jp2 != jj && j >= 1) {
+	    dswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	jj = j + 1;
+	if (jp1 != jj && kstep == 2) {
+	    dswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j >= 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/dtgsyl.c

@@ -0,0 +1,274 @@
+#include "relapack.h"
+#include <math.h>
+
+static void RELAPACK_dtgsyl_rec(const char *, const int *, const int *,
+    const int *, const double *, const int *, const double *, const int *,
+    double *, const int *, const double *, const int *, const double *,
+    const int *, double *, const int *, double *, double *, double *, int *,
+    int *, int *);
+
+
+/** DTGSYL solves the generalized Sylvester equation.
+ *
+ * This routine is functionally equivalent to LAPACK's dtgsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/db/d88/dtgsyl_8f.html
+ * */
+void RELAPACK_dtgsyl(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dif,
+    double *Work, const int *lWork, int *iWork, int *info
+) {
+
+    // Parse arguments
+    const int notran = LAPACK(lsame)(trans, "N");
+    const int tran = LAPACK(lsame)(trans, "T");
+
+    // Compute work buffer size
+    int lwmin = 1;
+    if (notran && (*ijob == 1 || *ijob == 2))
+        lwmin = MAX(1, 2 * *m * *n);
+    *info = 0;
+
+    // Check arguments
+    if (!tran && !notran)
+        *info = -1;
+    else if (notran && (*ijob < 0 || *ijob > 4))
+        *info = -2;
+    else if (*m <= 0)
+        *info = -3;
+    else if (*n <= 0)
+        *info = -4;
+    else if (*ldA < MAX(1, *m))
+        *info = -6;
+    else if (*ldB < MAX(1, *n))
+        *info = -8;
+    else if (*ldC < MAX(1, *m))
+        *info = -10;
+    else if (*ldD < MAX(1, *m))
+        *info = -12;
+    else if (*ldE < MAX(1, *n))
+        *info = -14;
+    else if (*ldF < MAX(1, *m))
+        *info = -16;
+    else if (*lWork < lwmin && *lWork != -1)
+        *info = -20;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DTGSYL", &minfo);
+        return;
+    }
+
+    if (*lWork == -1) {
+        // Work size query
+        *Work = lwmin;
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantrans = notran ? 'N' : 'T';
+
+    // Constant
+    const double ZERO[] = { 0. };
+
+    int isolve = 1;
+    int ifunc  = 0;
+    if (notran) {
+        if (*ijob >= 3) {
+            ifunc = *ijob - 2;
+            LAPACK(dlaset)("F", m, n, ZERO, ZERO, C, ldC);
+            LAPACK(dlaset)("F", m, n, ZERO, ZERO, F, ldF);
+        } else if (*ijob >= 1)
+            isolve = 2;
+    }
+
+    double scale2;
+    int iround;
+    for (iround = 1; iround <= isolve; iround++) {
+        *scale = 1;
+        double dscale = 0;
+        double dsum   = 1;
+        int pq;
+        RELAPACK_dtgsyl_rec(&cleantrans, &ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, &dsum, &dscale, iWork, &pq, info);
+        if (dscale != 0) {
+            if (*ijob == 1 || *ijob == 3)
+                *dif = sqrt(2 * *m * *n) / (dscale * sqrt(dsum));
+            else
+                *dif = sqrt(pq) / (dscale * sqrt(dsum));
+        }
+        if (isolve == 2) {
+            if (iround == 1) {
+                if (notran)
+                    ifunc = *ijob;
+                scale2 = *scale;
+                LAPACK(dlacpy)("F", m, n, C, ldC, Work, m);
+                LAPACK(dlacpy)("F", m, n, F, ldF, Work + *m * *n, m);
+                LAPACK(dlaset)("F", m, n, ZERO, ZERO, C, ldC);
+                LAPACK(dlaset)("F", m, n, ZERO, ZERO, F, ldF);
+            } else {
+                LAPACK(dlacpy)("F", m, n, Work, m, C, ldC);
+                LAPACK(dlacpy)("F", m, n, Work + *m * *n, m, F, ldF);
+                *scale = scale2;
+            }
+        }
+    }
+}
+
+
+/** dtgsyl's recursive vompute kernel */
+static void RELAPACK_dtgsyl_rec(
+    const char *trans, const int *ifunc, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dsum, double *dscale,
+    int *iWork, int *pq, int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_DTGSYL, 1) && *n <= MAX(CROSSOVER_DTGSYL, 1)) {
+        // Unblocked
+        LAPACK(dtgsy2)(trans, ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dsum, dscale, iWork, pq, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+    const int    iONE[] = { 1 };
+
+    // Outputs
+    double scale1[] = { 1. };
+    double scale2[] = { 1. };
+    int    info1[]  = { 0 };
+    int    info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        int m1 = DREC_SPLIT(*m);
+        if (A[m1 + *ldA * (m1 - 1)])
+            m1++;
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const double *const A_TL = A;
+        const double *const A_TR = A + *ldA * m1;
+        const double *const A_BR = A + *ldA * m1 + m1;
+
+        // C_T
+        // C_B
+        double *const C_T = C;
+        double *const C_B = C + m1;
+
+        // D_TL D_TR
+        // 0    D_BR
+        const double *const D_TL = D;
+        const double *const D_TR = D + *ldD * m1;
+        const double *const D_BR = D + *ldD * m1 + m1;
+
+        // F_T
+        // F_B
+        double *const F_T = F;
+        double *const F_B = F + m1;
+
+        if (*trans == 'N') {
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_dtgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(dgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // F_T = F_T - D_TR * C_B
+            BLAS(dgemm)("N", "N", &m1, n, &m2, MONE, D_TR, ldD, C_B, ldC, scale1, F_T, ldF);
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_dtgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, &m2, n, F_B, ldF, info);
+            }
+        } else {
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_dtgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale1, &m2, n, F_B, ldF, info);
+            // C_B = C_B - A_TR^H * C_T
+            BLAS(dgemm)("T", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // C_B = C_B - D_TR^H * F_T
+            BLAS(dgemm)("T", "N", &m2, n, &m1, MONE, D_TR, ldD, F_T, ldC, ONE, C_B, ldC);
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_dtgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_T, ldC, info);
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, &m1, n, F_T, ldF, info);
+            }
+        }
+    } else {
+        // Splitting
+        int n1 = DREC_SPLIT(*n);
+        if (B[n1 + *ldB * (n1 - 1)])
+            n1++;
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const double *const B_TL = B;
+        const double *const B_TR = B + *ldB * n1;
+        const double *const B_BR = B + *ldB * n1 + n1;
+
+        // C_L C_R
+        double *const C_L = C;
+        double *const C_R = C + *ldC * n1;
+
+        // E_TL E_TR
+        // 0    E_BR
+        const double *const E_TL = E;
+        const double *const E_TR = E + *ldE * n1;
+        const double *const E_BR = E + *ldE * n1 + n1;
+
+        // F_L F_R
+        double *const F_L = F;
+        double *const F_R = F + *ldF * n1;
+
+        if (*trans == 'N') {
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_dtgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // C_R = C_R + F_L * B_TR
+            BLAS(dgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, B_TR, ldB, scale1, C_R, ldC);
+            // F_R = F_R + F_L * E_TR
+            BLAS(dgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, E_TR, ldE, scale1, F_R, ldF);
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_dtgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, m, &n1, F_L, ldF, info);
+            }
+        } else {
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_dtgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale1, m, &n1, C_L, ldC, info);
+            // F_L = F_L + C_R * B_TR
+            BLAS(dgemm)("N", "T", m, &n1, &n2, ONE, C_R, ldC, B_TR, ldB, scale1, F_L, ldF);
+            // F_L = F_L + F_R * E_TR
+            BLAS(dgemm)("N", "T", m, &n1, &n2, ONE, F_R, ldF, E_TR, ldB, ONE, F_L, ldF);
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_dtgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, m, &n2, F_R, ldF, info);
+            }
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/dtrsyl.c

@@ -0,0 +1,169 @@
+#include "relapack.h"
+
+static void RELAPACK_dtrsyl_rec(const char *, const char *, const int *,
+    const int *, const int *, const double *, const int *, const double *,
+    const int *, double *, const int *, double *, int *);
+
+
+/** DTRSYL solves the real Sylvester matrix equation.
+ *
+ * This routine is functionally equivalent to LAPACK's dtrsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d6/d43/dtrsyl_8f.html
+ * */
+void RELAPACK_dtrsyl(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+
+    // Check arguments
+    const int notransA = LAPACK(lsame)(tranA, "N");
+    const int transA = LAPACK(lsame)(tranA, "T");
+    const int ctransA = LAPACK(lsame)(tranA, "C");
+    const int notransB = LAPACK(lsame)(tranB, "N");
+    const int transB = LAPACK(lsame)(tranB, "T");
+    const int ctransB = LAPACK(lsame)(tranB, "C");
+    *info = 0;
+    if (!transA && !ctransA && !notransA)
+        *info = -1;
+    else if (!transB && !ctransB && !notransB)
+        *info = -2;
+    else if (*isgn != 1 && *isgn != -1)
+        *info = -3;
+    else if (*m < 0)
+        *info = -4;
+    else if (*n < 0)
+        *info = -5;
+    else if (*ldA < MAX(1, *m))
+        *info = -7;
+    else if (*ldB < MAX(1, *n))
+        *info = -9;
+    else if (*ldC < MAX(1, *m))
+        *info = -11;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DTRSYL", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantranA = notransA ? 'N' : (transA ? 'T' : 'C');
+    const char cleantranB = notransB ? 'N' : (transB ? 'T' : 'C');
+
+    // Recursive kernel
+    RELAPACK_dtrsyl_rec(&cleantranA, &cleantranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+
+
+/** dtrsyl's recursive compute kernel */
+static void RELAPACK_dtrsyl_rec(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_DTRSYL, 1) && *n <= MAX(CROSSOVER_DTRSYL, 1)) {
+        // Unblocked
+        RELAPACK_dtrsyl_rec2(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+    const double MSGN[] = { -*isgn };
+    const int    iONE[] = { 1 };
+
+    // Outputs
+    double scale1[] = { 1. };
+    double scale2[] = { 1. };
+    int    info1[]  = { 0 };
+    int    info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        int m1 = DREC_SPLIT(*m);
+        if (A[m1 + *ldA * (m1 - 1)])
+            m1++;
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const double *const A_TL = A;
+        const double *const A_TR = A + *ldA * m1;
+        const double *const A_BR = A + *ldA * m1 + m1;
+
+        // C_T
+        // C_B
+        double *const C_T = C;
+        double *const C_B = C + m1;
+
+        if (*tranA == 'N') {
+            // recusion(A_BR, B, C_B)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale1, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(dgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // recusion(A_TL, B, C_T)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+        } else {
+            // recusion(A_TL, B, C_T)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale1, info1);
+            // C_B = C_B - A_TR' * C_T
+            BLAS(dgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // recusion(A_BR, B, C_B)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_B, ldC, info);
+        }
+    } else {
+        // Splitting
+        int n1 = DREC_SPLIT(*n);
+        if (B[n1 + *ldB * (n1 - 1)])
+            n1++;
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const double *const B_TL = B;
+        const double *const B_TR = B + *ldB * n1;
+        const double *const B_BR = B + *ldB * n1 + n1;
+
+        // C_L C_R
+        double *const C_L = C;
+        double *const C_R = C + *ldC * n1;
+
+        if (*tranB == 'N') {
+            // recusion(A, B_TL, C_L)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale1, info1);
+            // C_R = C_R -/+ C_L * B_TR
+            BLAS(dgemm)("N", "N", m, &n2, &n1, MSGN, C_L, ldC, B_TR, ldB, scale1, C_R, ldC);
+            // recusion(A, B_BR, C_R)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+        } else {
+            // recusion(A, B_BR, C_R)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale1, info1);
+            // C_L = C_L -/+ C_R * B_TR'
+            BLAS(dgemm)("N", "C", m, &n1, &n2, MSGN, C_R, ldC, B_TR, ldB, scale1, C_L, ldC);
+            // recusion(A, B_TL, C_L)
+            RELAPACK_dtrsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(dlascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/dtrtri.c

@@ -0,0 +1,107 @@
+#include "relapack.h"
+
+static void RELAPACK_dtrtri_rec(const char *, const char *, const int *,
+    double *, const int *, int *);
+
+
+/** DTRTRI computes the inverse of a real upper or lower triangular matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's dtrtri.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d5/dba/dtrtri_8f.html
+ * */
+void RELAPACK_dtrtri(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int nounit = LAPACK(lsame)(diag, "N");
+    const int unit = LAPACK(lsame)(diag, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (!nounit && !unit)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("DTRTRI", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower  ? 'L' : 'U';
+    const char cleandiag = nounit ? 'N' : 'U';
+
+    // check for singularity
+    if (nounit) {
+        int i;
+        for (i = 0; i < *n; i++)
+            if (A[i + *ldA * i] == 0) {
+                *info = i;
+                return;
+            }
+    }
+
+    // Recursive kernel
+    RELAPACK_dtrtri_rec(&cleanuplo, &cleandiag, n, A, ldA, info);
+}
+
+
+/** dtrtri's recursive compute kernel */
+static void RELAPACK_dtrtri_rec(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_DTRTRI, 1)) {
+        // Unblocked
+        LAPACK(dtrti2)(uplo, diag, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+
+    // Splitting
+    const int n1 = DREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + *ldA * n1;
+    double *const A_BL = A             + n1;
+    double *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_dtrtri_rec(uplo, diag, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = - A_BL * A_TL
+        BLAS(dtrmm)("R", "L", "N", diag, &n2, &n1, MONE, A_TL, ldA, A_BL, ldA);
+        // A_BL = A_BR \ A_BL
+        BLAS(dtrsm)("L", "L", "N", diag, &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TR = - A_TL * A_TR
+        BLAS(dtrmm)("L", "U", "N", diag, &n1, &n2, MONE, A_TL, ldA, A_TR, ldA);
+        // A_TR = A_TR / A_BR
+        BLAS(dtrsm)("R", "U", "N", diag, &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_dtrtri_rec(uplo, diag, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/f2c.c

@@ -0,0 +1,109 @@
+#include "stdlib.h"
+#include "stdio.h"
+#include "signal.h"
+#include "f2c.h"
+
+#ifndef SIGIOT
+#ifdef SIGABRT
+#define SIGIOT SIGABRT
+#endif
+#endif
+
+void sig_die(const char *s, int kill) {
+	/* print error message, then clear buffers */
+	fprintf(stderr, "%s\n", s);
+
+	if(kill) {
+		fflush(stderr);
+		/* now get a core */
+		signal(SIGIOT, SIG_DFL);
+		abort();
+	} else
+		exit(1);
+}
+
+void c_div(complex *c, complex *a, complex *b) {
+	double ratio, den;
+	double abr, abi, cr;
+
+	if( (abr = b->r) < 0.)
+		abr = - abr;
+	if( (abi = b->i) < 0.)
+		abi = - abi;
+	if( abr <= abi ) {
+		if(abi == 0) {
+#ifdef IEEE_COMPLEX_DIVIDE
+			float af, bf;
+			af = bf = abr;
+			if (a->i != 0 || a->r != 0)
+				af = 1.;
+			c->i = c->r = af / bf;
+			return;
+#else
+			sig_die("complex division by zero", 1);
+#endif
+		}
+		ratio = (double)b->r / b->i ;
+		den = b->i * (1 + ratio*ratio);
+		cr = (a->r*ratio + a->i) / den;
+		c->i = (a->i*ratio - a->r) / den;
+	} else {
+		ratio = (double)b->i / b->r ;
+		den = b->r * (1 + ratio*ratio);
+		cr = (a->r + a->i*ratio) / den;
+		c->i = (a->i - a->r*ratio) / den;
+    }
+	c->r = cr;
+}
+
+void z_div(doublecomplex *c, doublecomplex *a, doublecomplex *b) {
+	double ratio, den;
+	double abr, abi, cr;
+
+	if( (abr = b->r) < 0.)
+		abr = - abr;
+	if( (abi = b->i) < 0.)
+		abi = - abi;
+	if( abr <= abi ) {
+		if(abi == 0) {
+#ifdef IEEE_COMPLEX_DIVIDE
+			if (a->i != 0 || a->r != 0)
+				abi = 1.;
+			c->i = c->r = abi / abr;
+			return;
+#else
+			sig_die("complex division by zero", 1);
+#endif
+        }
+		ratio = b->r / b->i ;
+		den = b->i * (1 + ratio*ratio);
+		cr = (a->r*ratio + a->i) / den;
+		c->i = (a->i*ratio - a->r) / den;
+	} else {
+		ratio = b->i / b->r ;
+		den = b->r * (1 + ratio*ratio);
+		cr = (a->r + a->i*ratio) / den;
+		c->i = (a->i - a->r*ratio) / den;
+    }
+	c->r = cr;
+}
+
+float r_imag(complex *z) {
+    return z->i;
+}
+
+void r_cnjg(complex *r, complex *z) {
+	float zi = z->i;
+	r->r = z->r;
+	r->i = -zi;
+}
+
+double d_imag(doublecomplex *z) {
+    return z->i;
+}
+
+void d_cnjg(doublecomplex *r, doublecomplex *z) {
+	double zi = z->i;
+	r->r = z->r;
+	r->i = -zi;
+}

relapack/src/f2c.h

@@ -0,0 +1,223 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+typedef long int integer;
+typedef unsigned long int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+typedef long int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+#ifdef INTEGER_STAR_8	/* Adjust for integer*8. */
+typedef long long longint;		/* system-dependent */
+typedef unsigned long long ulongint;	/* system-dependent */
+#define qbit_clear(a,b)	((a) & ~((ulongint)1 << (b)))
+#define qbit_set(a,b)	((a) |  ((ulongint)1 << (b)))
+#endif
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+#ifdef f2c_i2
+/* for -i2 */
+typedef short flag;
+typedef short ftnlen;
+typedef short ftnint;
+#else
+typedef long int flag;
+typedef long int ftnlen;
+typedef long int ftnint;
+#endif
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+/*typedef long int Long;*/	/* No longer used; formerly in Namelist */
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (doublereal)abs(x)
+#define min(a,b) ((a) <= (b) ? (a) : (b))
+#define max(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (doublereal)min(a,b)
+#define dmax(a,b) (doublereal)max(a,b)
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef int /* Unknown procedure type */ (*U_fp)(...);
+typedef shortint (*J_fp)(...);
+typedef integer (*I_fp)(...);
+typedef real (*R_fp)(...);
+typedef doublereal (*D_fp)(...), (*E_fp)(...);
+typedef /* Complex */ VOID (*C_fp)(...);
+typedef /* Double Complex */ VOID (*Z_fp)(...);
+typedef logical (*L_fp)(...);
+typedef shortlogical (*K_fp)(...);
+typedef /* Character */ VOID (*H_fp)(...);
+typedef /* Subroutine */ int (*S_fp)(...);
+#else
+typedef int /* Unknown procedure type */ (*U_fp)();
+typedef shortint (*J_fp)();
+typedef integer (*I_fp)();
+typedef real (*R_fp)();
+typedef doublereal (*D_fp)(), (*E_fp)();
+typedef /* Complex */ VOID (*C_fp)();
+typedef /* Double Complex */ VOID (*Z_fp)();
+typedef logical (*L_fp)();
+typedef shortlogical (*K_fp)();
+typedef /* Character */ VOID (*H_fp)();
+typedef /* Subroutine */ int (*S_fp)();
+#endif
+/* E_fp is for real functions when -R is not specified */
+typedef VOID C_f;	/* complex function */
+typedef VOID H_f;	/* character function */
+typedef VOID Z_f;	/* double complex function */
+typedef doublereal E_f;	/* real function with -R not specified */
+
+/* undef any lower-case symbols that your C compiler predefines, e.g.: */
+
+#ifndef Skip_f2c_Undefs
+#undef cray
+#undef gcos
+#undef mc68010
+#undef mc68020
+#undef mips
+#undef pdp11
+#undef sgi
+#undef sparc
+#undef sun
+#undef sun2
+#undef sun3
+#undef sun4
+#undef u370
+#undef u3b
+#undef u3b2
+#undef u3b5
+#undef unix
+#undef vax
+#endif
+#endif

relapack/src/lapack.h

@@ -0,0 +1,80 @@
+#ifndef LAPACK_H
+#define LAPACK_H
+
+extern int LAPACK(lsame)(const char *, const char *);
+extern int LAPACK(xerbla)(const char *, const int *);
+
+extern void LAPACK(slaswp)(const int *, float *, const int *, const int *, const int *, const int *, const int *);
+extern void LAPACK(dlaswp)(const int *, double *, const int *, const int *, const int *, const int *, const int *);
+extern void LAPACK(claswp)(const int *, float *, const int *, const int *, const int *, const int *, const int *);
+extern void LAPACK(zlaswp)(const int *, double *, const int *, const int *, const int *, const int *, const int *);
+
+extern void LAPACK(slaset)(const char *, const int *, const int *, const float *, const float *, float *, const int *);
+extern void LAPACK(dlaset)(const char *, const int *, const int *, const double *, const double *, double *, const int *);
+extern void LAPACK(claset)(const char *, const int *, const int *, const float *, const float *, float *, const int *);
+extern void LAPACK(zlaset)(const char *, const int *, const int *, const double *, const double *, double *, const int *);
+
+extern void LAPACK(slacpy)(const char *, const int *, const int *, const float *, const int *, float *, const int *);
+extern void LAPACK(dlacpy)(const char *, const int *, const int *, const double *, const int *, double *, const int *);
+extern void LAPACK(clacpy)(const char *, const int *, const int *, const float *, const int *, float *, const int *);
+extern void LAPACK(zlacpy)(const char *, const int *, const int *, const double *, const int *, double *, const int *);
+
+extern void LAPACK(slascl)(const char *, const int *, const int *, const float *, const float *, const int *, const int *, float *, const int *, int *);
+extern void LAPACK(dlascl)(const char *, const int *, const int *, const double *, const double *, const int *, const int *, double *, const int *, int *);
+extern void LAPACK(clascl)(const char *, const int *, const int *, const float *, const float *, const int *, const int *, float *, const int *, int *);
+extern void LAPACK(zlascl)(const char *, const int *, const int *, const double *, const double *, const int *, const int *, double *, const int *, int *);
+
+extern void LAPACK(slauu2)(const char *, const int *, float *, const int *, int *);
+extern void LAPACK(dlauu2)(const char *, const int *, double *, const int *, int *);
+extern void LAPACK(clauu2)(const char *, const int *, float *, const int *, int *);
+extern void LAPACK(zlauu2)(const char *, const int *, double *, const int *, int *);
+
+extern void LAPACK(ssygs2)(const int *, const char *, const int *, float *, const int *, const float *, const int *, int *);
+extern void LAPACK(dsygs2)(const int *, const char *, const int *, double *, const int *, const double *, const int *, int *);
+extern void LAPACK(chegs2)(const int *, const char *, const int *, float *, const int *, const float *, const int *, int *);
+extern void LAPACK(zhegs2)(const int *, const char *, const int *, double *, const int *, const double *, const int *, int *);
+
+extern void LAPACK(strti2)(const char *, const char *, const int *, float *, const int *, int *);
+extern void LAPACK(dtrti2)(const char *, const char *, const int *, double *, const int *, int *);
+extern void LAPACK(ctrti2)(const char *, const char *, const int *, float *, const int *, int *);
+extern void LAPACK(ztrti2)(const char *, const char *, const int *, double *, const int *, int *);
+
+extern void LAPACK(spotf2)(const char *, const int *, float *, const int *, int *);
+extern void LAPACK(dpotf2)(const char *, const int *, double *, const int *, int *);
+extern void LAPACK(cpotf2)(const char *, const int *, float *, const int *, int *);
+extern void LAPACK(zpotf2)(const char *, const int *, double *, const int *, int *);
+
+extern void LAPACK(spbtf2)(const char *, const int *, const int *, float *, const int *, int *);
+extern void LAPACK(dpbtf2)(const char *, const int *, const int *, double *, const int *, int *);
+extern void LAPACK(cpbtf2)(const char *, const int *, const int *, float *, const int *, int *);
+extern void LAPACK(zpbtf2)(const char *, const int *, const int *, double *, const int *, int *);
+
+extern void LAPACK(ssytf2)(const char *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(dsytf2)(const char *, const int *, double *, const int *, int *, int *);
+extern void LAPACK(csytf2)(const char *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(chetf2)(const char *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(zsytf2)(const char *, const int *, double *, const int *, int *, int *);
+extern void LAPACK(zhetf2)(const char *, const int *, double *, const int *, int *, int *);
+extern void LAPACK(ssytf2_rook)(const char *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(dsytf2_rook)(const char *, const int *, double *, const int *, int *, int *);
+extern void LAPACK(csytf2_rook)(const char *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(chetf2_rook)(const char *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(zsytf2_rook)(const char *, const int *, double *, const int *, int *, int *);
+extern void LAPACK(zhetf2_rook)(const char *, const int *, double *, const int *, int *, int *);
+
+extern void LAPACK(sgetf2)(const int *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(dgetf2)(const int *, const int *, double *, const int *, int *, int *);
+extern void LAPACK(cgetf2)(const int *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(zgetf2)(const int *, const int *, double *, const int *, int *, int *);
+
+extern void LAPACK(sgbtf2)(const int *, const int *, const int *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(dgbtf2)(const int *, const int *, const int *, const int *, double *, const int *, int *, int *);
+extern void LAPACK(cgbtf2)(const int *, const int *, const int *, const int *, float *, const int *, int *, int *);
+extern void LAPACK(zgbtf2)(const int *, const int *, const int *, const int *, double *, const int *, int *, int *);
+
+extern void LAPACK(stgsy2)(const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, float *, float *, int *, int *, int *);
+extern void LAPACK(dtgsy2)(const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, double *, double *, int *, int *, int *);
+extern void LAPACK(ctgsy2)(const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, float *, float *, int *);
+extern void LAPACK(ztgsy2)(const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, double *, double *, int *);
+
+#endif /* LAPACK_H */

relapack/src/lapack_wrappers.c

@@ -0,0 +1,607 @@
+#include "relapack.h"
+
+////////////
+// XLAUUM //
+////////////
+
+#if INCLUDE_SLAUUM
+void LAPACK(slauum)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_slauum(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DLAUUM
+void LAPACK(dlauum)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_dlauum(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CLAUUM
+void LAPACK(clauum)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_clauum(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZLAUUM
+void LAPACK(zlauum)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_zlauum(uplo, n, A, ldA, info);
+}
+#endif
+
+
+////////////
+// XSYGST //
+////////////
+
+#if INCLUDE_SSYGST
+void LAPACK(ssygst)(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_ssygst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+#if INCLUDE_DSYGST
+void LAPACK(dsygst)(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_dsygst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+#if INCLUDE_CHEGST
+void LAPACK(chegst)(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_chegst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+#if INCLUDE_ZHEGST
+void LAPACK(zhegst)(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_zhegst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+
+////////////
+// XTRTRI //
+////////////
+
+#if INCLUDE_STRTRI
+void LAPACK(strtri)(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_strtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DTRTRI
+void LAPACK(dtrtri)(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_dtrtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CTRTRI
+void LAPACK(ctrtri)(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_ctrtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZTRTRI
+void LAPACK(ztrtri)(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_ztrtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+
+////////////
+// XPOTRF //
+////////////
+
+#if INCLUDE_SPOTRF
+void LAPACK(spotrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_spotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DPOTRF
+void LAPACK(dpotrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_dpotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CPOTRF
+void LAPACK(cpotrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_cpotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZPOTRF
+void LAPACK(zpotrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_zpotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+
+////////////
+// XPBTRF //
+////////////
+
+#if INCLUDE_SPBTRF
+void LAPACK(spbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_spbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+#if INCLUDE_DPBTRF
+void LAPACK(dpbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_dpbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+#if INCLUDE_CPBTRF
+void LAPACK(cpbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_cpbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+#if INCLUDE_ZPBTRF
+void LAPACK(zpbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_zpbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+
+////////////
+// XSYTRF //
+////////////
+
+#if INCLUDE_SSYTRF
+void LAPACK(ssytrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_ssytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_DSYTRF
+void LAPACK(dsytrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_dsytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CSYTRF
+void LAPACK(csytrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_csytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZSYTRF
+void LAPACK(zsytrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zsytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CHETRF
+void LAPACK(chetrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_chetrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZHETRF
+void LAPACK(zhetrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zhetrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_SSYTRF_ROOK
+void LAPACK(ssytrf_rook)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_ssytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_DSYTRF_ROOK
+void LAPACK(dsytrf_rook)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_dsytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CSYTRF_ROOK
+void LAPACK(csytrf_rook)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_csytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZSYTRF_ROOK
+void LAPACK(zsytrf_rook)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zsytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CHETRF_ROOK
+void LAPACK(chetrf_rook)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_chetrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZHETRF_ROOK
+void LAPACK(zhetrf_rook)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zhetrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+
+////////////
+// XGETRF //
+////////////
+
+#if INCLUDE_SGETRF
+void LAPACK(sgetrf)(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_sgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+#if INCLUDE_DGETRF
+void LAPACK(dgetrf)(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_dgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+#if INCLUDE_CGETRF
+void LAPACK(cgetrf)(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_cgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+#if INCLUDE_ZGETRF
+void LAPACK(zgetrf)(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_zgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+
+////////////
+// XGBTRF //
+////////////
+
+#if INCLUDE_SGBTRF
+void LAPACK(sgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_sgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+#if INCLUDE_DGBTRF
+void LAPACK(dgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_dgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+#if INCLUDE_CGBTRF
+void LAPACK(cgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_cgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+#if INCLUDE_ZGBTRF
+void LAPACK(zgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_zgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+
+////////////
+// XTRSYL //
+////////////
+
+#if INCLUDE_STRSYL
+void LAPACK(strsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+    RELAPACK_strsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+#if INCLUDE_DTRSYL
+void LAPACK(dtrsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+    RELAPACK_dtrsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+#if INCLUDE_CTRSYL
+void LAPACK(ctrsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+    RELAPACK_ctrsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+#if INCLUDE_ZTRSYL
+void LAPACK(ztrsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+    RELAPACK_ztrsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+
+////////////
+// XTGSYL //
+////////////
+
+#if INCLUDE_STGSYL
+void LAPACK(stgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dif,
+    float *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_stgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+#if INCLUDE_DTGSYL
+void LAPACK(dtgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dif,
+    double *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_dtgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+#if INCLUDE_CTGSYL
+void LAPACK(ctgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dif,
+    float *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_ctgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+#if INCLUDE_ZTGSYL
+void LAPACK(ztgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dif,
+    double *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_ztgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+
+////////////
+// XGEMMT //
+////////////
+
+#if INCLUDE_SGEMMT
+void LAPACK(sgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+    RELAPACK_sgemmt(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DGEMMT
+void LAPACK(dgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+    RELAPACK_dgemmt(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CGEMMT
+void LAPACK(cgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+    RELAPACK_cgemmt(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZGEMMT
+void LAPACK(zgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+    RELAPACK_zgemmt(uplo, n, A, ldA, info);
+}
+#endif

relapack/src/lapack_wrappers.c.orig

@@ -0,0 +1,607 @@
+#include "relapack.h"
+
+////////////
+// XLAUUM //
+////////////
+
+#if INCLUDE_SLAUUM
+void LAPACK(slauum)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_slauum(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DLAUUM
+void LAPACK(dlauum)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_dlauum(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CLAUUM
+void LAPACK(clauum)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_clauum(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZLAUUM
+void LAPACK(zlauum)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_zlauum(uplo, n, A, ldA, info);
+}
+#endif
+
+
+////////////
+// XSYGST //
+////////////
+
+#if INCLUDE_SSYGST
+void LAPACK(ssygst)(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_ssygst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+#if INCLUDE_DSYGST
+void LAPACK(dsygst)(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_dsygst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+#if INCLUDE_CSYGST
+void LAPACK(csygst)(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_csygst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+#if INCLUDE_ZSYGST
+void LAPACK(zsygst)(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    int *info
+) {
+    RELAPACK_zsygst(itype, uplo, n, A, ldA, B, ldB, info);
+}
+#endif
+
+
+////////////
+// XTRTRI //
+////////////
+
+#if INCLUDE_STRTRI
+void LAPACK(strtri)(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_strtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DTRTRI
+void LAPACK(dtrtri)(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_dtrtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CTRTRI
+void LAPACK(ctrtri)(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_ctrtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZTRTRI
+void LAPACK(ztrtri)(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_ztrtri(uplo, diag, n, A, ldA, info);
+}
+#endif
+
+
+////////////
+// XPOTRF //
+////////////
+
+#if INCLUDE_SPOTRF
+void LAPACK(spotrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_spotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DPOTRF
+void LAPACK(dpotrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_dpotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CPOTRF
+void LAPACK(cpotrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_cpotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZPOTRF
+void LAPACK(zpotrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+    RELAPACK_zpotrf(uplo, n, A, ldA, info);
+}
+#endif
+
+
+////////////
+// XPBTRF //
+////////////
+
+#if INCLUDE_SPBTRF
+void LAPACK(spbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_spbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+#if INCLUDE_DPBTRF
+void LAPACK(dpbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_dpbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+#if INCLUDE_CPBTRF
+void LAPACK(cpbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_cpbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+#if INCLUDE_ZPBTRF
+void LAPACK(zpbtrf)(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    int *info
+) {
+    RELAPACK_zpbtrf(uplo, n, kd, Ab, ldAb, info);
+}
+#endif
+
+
+////////////
+// XSYTRF //
+////////////
+
+#if INCLUDE_SSYTRF
+void LAPACK(ssytrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_ssytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_DSYTRF
+void LAPACK(dsytrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_dsytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CSYTRF
+void LAPACK(csytrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_csytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZSYTRF
+void LAPACK(zsytrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zsytrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CHETRF
+void LAPACK(chetrf)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_chetrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZHETRF
+void LAPACK(zhetrf)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zhetrf(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_SSYTRF_ROOK
+void LAPACK(ssytrf_rook)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_ssytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_DSYTRF_ROOK
+void LAPACK(dsytrf_rook)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_dsytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CSYTRF_ROOK
+void LAPACK(csytrf_rook)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_csytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZSYTRF_ROOK
+void LAPACK(zsytrf_rook)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zsytrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_CHETRF_ROOK
+void LAPACK(chetrf_rook)(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+    RELAPACK_chetrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+#if INCLUDE_ZHETRF_ROOK
+void LAPACK(zhetrf_rook)(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+    RELAPACK_zhetrf_rook(uplo, n, A, ldA, ipiv, Work, lWork, info);
+}
+#endif
+
+
+////////////
+// XGETRF //
+////////////
+
+#if INCLUDE_SGETRF
+void LAPACK(sgetrf)(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_sgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+#if INCLUDE_DGETRF
+void LAPACK(dgetrf)(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_dgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+#if INCLUDE_CGETRF
+void LAPACK(cgetrf)(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_cgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+#if INCLUDE_ZGETRF
+void LAPACK(zgetrf)(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+    RELAPACK_zgetrf(m, n, A, ldA, ipiv, info);
+}
+#endif
+
+
+////////////
+// XGBTRF //
+////////////
+
+#if INCLUDE_SGBTRF
+void LAPACK(sgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_sgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+#if INCLUDE_DGBTRF
+void LAPACK(dgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_dgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+#if INCLUDE_CGBTRF
+void LAPACK(cgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_cgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+#if INCLUDE_ZGBTRF
+void LAPACK(zgbtrf)(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+    RELAPACK_zgbtrf(m, n, kl, ku, Ab, ldAb, ipiv, info);
+}
+#endif
+
+
+////////////
+// XTRSYL //
+////////////
+
+#if INCLUDE_STRSYL
+void LAPACK(strsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+    RELAPACK_strsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+#if INCLUDE_DTRSYL
+void LAPACK(dtrsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+    RELAPACK_dtrsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+#if INCLUDE_CTRSYL
+void LAPACK(ctrsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+    RELAPACK_ctrsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+#if INCLUDE_ZTRSYL
+void LAPACK(ztrsyl)(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+    RELAPACK_ztrsyl(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+#endif
+
+
+////////////
+// XTGSYL //
+////////////
+
+#if INCLUDE_STGSYL
+void LAPACK(stgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dif,
+    float *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_stgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+#if INCLUDE_DTGSYL
+void LAPACK(dtgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dif,
+    double *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_dtgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+#if INCLUDE_CTGSYL
+void LAPACK(ctgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dif,
+    float *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_ctgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+#if INCLUDE_ZTGSYL
+void LAPACK(ztgsyl)(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dif,
+    double *Work, const int *lWork, int *iWork, int *info
+) {
+    RELAPACK_ztgsyl(trans, ijob, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dif, Work, lWork, iWork, info);
+}
+#endif
+
+
+////////////
+// XGEMMT //
+////////////
+
+#if INCLUDE_SGEMMT
+void LAPACK(sgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+    RELAPACK_sgemmt(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_DGEMMT
+void LAPACK(dgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+    RELAPACK_dgemmt(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_CGEMMT
+void LAPACK(cgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+    RELAPACK_cgemmt(uplo, n, A, ldA, info);
+}
+#endif
+
+#if INCLUDE_ZGEMMT
+void LAPACK(zgemmt)(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+    RELAPACK_zgemmt(uplo, n, A, ldA, info);
+}
+#endif

relapack/src/relapack.h

@@ -0,0 +1,60 @@
+#ifndef RELAPACK_INT_H
+#define RELAPACK_INT_H
+
+#include "../config.h"
+
+#include "../inc/relapack.h"
+
+// add an underscore to BLAS routines (or not)
+#if BLAS_UNDERSCORE
+#define BLAS(routine) routine ## _
+#else
+#define BLAS(routine) routine
+#endif
+
+// add an underscore to LAPACK routines (or not)
+#if LAPACK_UNDERSCORE
+#define LAPACK(routine) routine ## _
+#else
+#define LAPACK(routine) routine
+#endif
+
+// minimum and maximum macros
+#define MAX(a, b) ((a) > (b) ? (a) : (b))
+#define MIN(a, b) ((a) < (b) ? (a) : (b))
+
+// REC_SPLIT(n) returns how a problem of size n is split recursively.
+// If n >= 16, we ensure that the size of at least one of the halves is
+// divisible by 8 (the cache line size in most CPUs), while both halves are
+// still as close as possible in size.
+// If n < 16 the problem is simply split in the middle. (Note that the
+// crossoversize is usually larger than 16.)
+#define SREC_SPLIT(n) ((n >= 32) ? ((n + 16) / 32) * 16 : n / 2)
+#define DREC_SPLIT(n) ((n >= 16) ? ((n + 8) / 16) * 8 : n / 2)
+#define CREC_SPLIT(n) ((n >= 16) ? ((n + 8) / 16) * 8 : n / 2)
+#define ZREC_SPLIT(n) ((n >= 8) ? ((n + 4) / 8) * 4 : n / 2)
+
+#include "lapack.h"
+#include "blas.h"
+
+// sytrf helper routines
+void RELAPACK_ssytrf_rec2(const char *, const int *, const int *, int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_dsytrf_rec2(const char *, const int *, const int *, int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_csytrf_rec2(const char *, const int *, const int *, int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_chetrf_rec2(const char *, const int *, const int *, int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_zsytrf_rec2(const char *, const int *, const int *, int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_zhetrf_rec2(const char *, const int *, const int *, int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_ssytrf_rook_rec2(const char *, const int *, const int *, int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_dsytrf_rook_rec2(const char *, const int *, const int *, int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_csytrf_rook_rec2(const char *, const int *, const int *, int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_chetrf_rook_rec2(const char *, const int *, const int *, int *, float *, const int *, int *, float *, const int *, int *);
+void RELAPACK_zsytrf_rook_rec2(const char *, const int *, const int *, int *, double *, const int *, int *, double *, const int *, int *);
+void RELAPACK_zhetrf_rook_rec2(const char *, const int *, const int *, int *, double *, const int *, int *, double *, const int *, int *);
+
+// trsyl helper routines
+void RELAPACK_strsyl_rec2(const char *, const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, int *);
+void RELAPACK_dtrsyl_rec2(const char *, const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, int *);
+void RELAPACK_ctrsyl_rec2(const char *, const char *, const int *, const int *, const int *, const float *, const int *, const float *, const int *, float *, const int *, float *, int *);
+void RELAPACK_ztrsyl_rec2(const char *, const char *, const int *, const int *, const int *, const double *, const int *, const double *, const int *, double *, const int *, double *, int *);
+
+#endif /*  RELAPACK_INT_H */

relapack/src/sgbtrf.c

@@ -0,0 +1,227 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_sgbtrf_rec(const int *, const int *, const int *,
+    const int *, float *, const int *, int *, float *, const int *, float *,
+    const int *, int *);
+
+
+/** SGBTRF computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's sgbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d5/d72/sgbtrf_8f.html
+ * */
+void RELAPACK_sgbtrf(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kl < 0)
+        *info = -3;
+    else if (*ku < 0)
+        *info = -4;
+    else if (*ldAb < 2 * *kl + *ku + 1)
+        *info = -6;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SGBTRF", &minfo);
+        return;
+    }
+
+    // Constant
+    const float ZERO[] = { 0. };
+
+    // Result upper band width
+    const int kv = *ku + *kl;
+
+    // Unskewg A
+    const int ldA[] = { *ldAb - 1 };
+    float *const A = Ab + kv;
+
+    // Zero upper diagonal fill-in elements
+    int i, j;
+    for (j = 0; j < *n; j++) {
+        float *const A_j = A + *ldA * j;
+        for (i = MAX(0, j - kv); i < j - *ku; i++)
+            A_j[i] = 0.;
+    }
+
+    // Allocate work space
+    const int n1 = SREC_SPLIT(*n);
+    const int mWorkl = (kv > n1) ? MAX(1, *m - *kl) : kv;
+    const int nWorkl = (kv > n1) ? n1 : kv;
+    const int mWorku = (*kl > n1) ? n1 : *kl;
+    const int nWorku = (*kl > n1) ? MAX(0, *n - *kl) : *kl;
+    float *Workl = malloc(mWorkl * nWorkl * sizeof(float));
+    float *Worku = malloc(mWorku * nWorku * sizeof(float));
+    LAPACK(slaset)("L", &mWorkl, &nWorkl, ZERO, ZERO, Workl, &mWorkl);
+    LAPACK(slaset)("U", &mWorku, &nWorku, ZERO, ZERO, Worku, &mWorku);
+
+    // Recursive kernel
+    RELAPACK_sgbtrf_rec(m, n, kl, ku, Ab, ldAb, ipiv, Workl, &mWorkl, Worku, &mWorku, info);
+
+    // Free work space
+    free(Workl);
+    free(Worku);
+}
+
+
+/** sgbtrf's recursive compute kernel */
+static void RELAPACK_sgbtrf_rec(
+    const int *m, const int *n, const int *kl, const int *ku,
+    float *Ab, const int *ldAb, int *ipiv,
+    float *Workl, const int *ldWorkl, float *Worku, const int *ldWorku,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_SGBTRF, 1)) {
+        // Unblocked
+        LAPACK(sgbtf2)(m, n, kl, ku, Ab, ldAb, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+    const int    iONE[] = { 1 };
+
+    // Loop iterators
+    int i, j;
+
+    // Output upper band width
+    const int kv = *ku + *kl;
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    float *const A = Ab + kv;
+
+    // Splitting
+    const int n1  = MIN(SREC_SPLIT(*n), *kl);
+    const int n2  = *n - n1;
+    const int m1  = MIN(n1, *m);
+    const int m2  = *m - m1;
+    const int mn1 = MIN(m1, n1);
+    const int mn2 = MIN(m2, n2);
+
+    // Ab_L *
+    //      Ab_BR
+    float *const Ab_L  = Ab;
+    float *const Ab_BR = Ab + *ldAb * n1;
+
+    // A_L A_R
+    float *const A_L = A;
+    float *const A_R = A + *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + *ldA * n1;
+    float *const A_BL = A             + m1;
+    float *const A_BR = A + *ldA * n1 + m1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // Banded splitting
+    const int n21 = MIN(n2, kv - n1);
+    const int n22 = MIN(n2 - n21, n1);
+    const int m21 = MIN(m2, *kl - m1);
+    const int m22 = MIN(m2 - m21, m1);
+
+    //   n1 n21  n22
+    // m *  A_Rl ARr
+    float *const A_Rl = A_R;
+    float *const A_Rr = A_R + *ldA * n21;
+
+    //     n1    n21    n22
+    // m1  *     A_TRl  A_TRr
+    // m21 A_BLt A_BRtl A_BRtr
+    // m22 A_BLb A_BRbl A_BRbr
+    float *const A_TRl  = A_TR;
+    float *const A_TRr  = A_TR + *ldA * n21;
+    float *const A_BLt  = A_BL;
+    float *const A_BLb  = A_BL              + m21;
+    float *const A_BRtl = A_BR;
+    float *const A_BRtr = A_BR + *ldA * n21;
+    float *const A_BRbl = A_BR              + m21;
+    float *const A_BRbr = A_BR + *ldA * n21 + m21;
+
+    // recursion(Ab_L, ipiv_T)
+    RELAPACK_sgbtrf_rec(m, &n1, kl, ku, Ab_L, ldAb, ipiv_T, Workl, ldWorkl, Worku, ldWorku, info);
+
+    // Workl = A_BLb
+    LAPACK(slacpy)("U", &m22, &n1, A_BLb, ldA, Workl, ldWorkl);
+
+    // partially redo swaps in A_L
+    for (i = 0; i < mn1; i++) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(sswap)(&i, A_L + i, ldA, A_L + ip, ldA);
+            else
+                BLAS(sswap)(&i, A_L + i, ldA, Workl + ip - *kl, ldWorkl);
+        }
+    }
+
+    // apply pivots to A_Rl
+    LAPACK(slaswp)(&n21, A_Rl, ldA, iONE, &mn1, ipiv_T, iONE);
+
+    // apply pivots to A_Rr columnwise
+    for (j = 0; j < n22; j++) {
+        float *const A_Rrj = A_Rr + *ldA * j;
+        for (i = j; i < mn1; i++) {
+            const int ip = ipiv_T[i] - 1;
+            if (ip != i) {
+                const float tmp = A_Rrj[i];
+                A_Rrj[i] = A_Rr[ip];
+                A_Rrj[ip] = tmp;
+            }
+        }
+    }
+
+    // A_TRl = A_TL \ A_TRl
+    BLAS(strsm)("L", "L", "N", "U", &m1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+    // Worku = A_TRr
+    LAPACK(slacpy)("L", &m1, &n22, A_TRr, ldA, Worku, ldWorku);
+    // Worku = A_TL \ Worku
+    BLAS(strsm)("L", "L", "N", "U", &m1, &n22, ONE, A_TL, ldA, Worku, ldWorku);
+    // A_TRr = Worku
+    LAPACK(slacpy)("L", &m1, &n22, Worku, ldWorku, A_TRr, ldA);
+    // A_BRtl = A_BRtl - A_BLt * A_TRl
+    BLAS(sgemm)("N", "N", &m21, &n21, &n1, MONE, A_BLt, ldA, A_TRl, ldA, ONE, A_BRtl, ldA);
+    // A_BRbl = A_BRbl - Workl * A_TRl
+    BLAS(sgemm)("N", "N", &m22, &n21, &n1, MONE, Workl, ldWorkl, A_TRl, ldA, ONE, A_BRbl, ldA);
+    // A_BRtr = A_BRtr - A_BLt * Worku
+    BLAS(sgemm)("N", "N", &m21, &n22, &n1, MONE, A_BLt, ldA, Worku, ldWorku, ONE, A_BRtr, ldA);
+    // A_BRbr = A_BRbr - Workl * Worku
+    BLAS(sgemm)("N", "N", &m22, &n22, &n1, MONE, Workl, ldWorkl, Worku, ldWorku, ONE, A_BRbr, ldA);
+
+    // partially undo swaps in A_L
+    for (i = mn1 - 1; i >= 0; i--) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(sswap)(&i, A_L + i, ldA, A_L + ip, ldA);
+            else
+                BLAS(sswap)(&i, A_L + i, ldA, Workl + ip - *kl, ldWorkl);
+        }
+    }
+
+    // recursion(Ab_BR, ipiv_B)
+    RELAPACK_sgbtrf_rec(&m2, &n2, kl, ku, Ab_BR, ldAb, ipiv_B, Workl, ldWorkl, Worku, ldWorku, info);
+    if (*info)
+        *info += n1;
+    // shift pivots
+    for (i = 0; i < mn2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/sgemmt.c

@@ -0,0 +1,165 @@
+#include "relapack.h"
+
+static void RELAPACK_sgemmt_rec(const char *, const char *, const char *,
+    const int *, const int *, const float *, const float *, const int *,
+    const float *, const int *, const float *, float *, const int *);
+
+static void RELAPACK_sgemmt_rec2(const char *, const char *, const char *,
+    const int *, const int *, const float *, const float *, const int *,
+    const float *, const int *, const float *, float *, const int *);
+
+
+/** SGEMMT computes a matrix-matrix product with general matrices but updates
+ * only the upper or lower triangular part of the result matrix.
+ *
+ * This routine performs the same operation as the BLAS routine
+ * sgemm(transA, transB, n, n, k, alpha, A, ldA, B, ldB, beta, C, ldC)
+ * but only updates the triangular part of C specified by uplo:
+ * If (*uplo == 'L'), only the lower triangular part of C is updated,
+ * otherwise the upper triangular part is updated.
+ * */
+void RELAPACK_sgemmt(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+
+#if HAVE_XGEMMT
+    BLAS(sgemmt)(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+    return;
+#else
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int notransA = LAPACK(lsame)(transA, "N");
+    const int tranA = LAPACK(lsame)(transA, "T");
+    const int notransB = LAPACK(lsame)(transB, "N");
+    const int tranB = LAPACK(lsame)(transB, "T");
+    int info = 0;
+    if (!lower && !upper)
+        info = 1;
+    else if (!tranA && !notransA)
+        info = 2;
+    else if (!tranB && !notransB)
+        info = 3;
+    else if (*n < 0)
+        info = 4;
+    else if (*k < 0)
+        info = 5;
+    else if (*ldA < MAX(1, notransA ? *n : *k))
+        info = 8;
+    else if (*ldB < MAX(1, notransB ? *k : *n))
+        info = 10;
+    else if (*ldC < MAX(1, *n))
+        info = 13;
+    if (info) {
+        LAPACK(xerbla)("SGEMMT", &info);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+    const char cleantransA = notransA ? 'N' : 'T';
+    const char cleantransB = notransB ? 'N' : 'T';
+
+    // Recursive kernel
+    RELAPACK_sgemmt_rec(&cleanuplo, &cleantransA, &cleantransB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+#endif
+}
+
+
+/** sgemmt's recursive compute kernel */
+static void RELAPACK_sgemmt_rec(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+
+    if (*n <= MAX(CROSSOVER_SGEMMT, 1)) {
+        // Unblocked
+        RELAPACK_sgemmt_rec2(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+        return;
+    }
+
+    // Splitting
+    const int n1 = SREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_T
+    // A_B
+    const float *const A_T = A;
+    const float *const A_B = A + ((*transA == 'N') ? n1 : *ldA * n1);
+
+    // B_L B_R
+    const float *const B_L = B;
+    const float *const B_R = B + ((*transB == 'N') ? *ldB * n1 : n1);
+
+    // C_TL C_TR
+    // C_BL C_BR
+    float *const C_TL = C;
+    float *const C_TR = C + *ldC * n1;
+    float *const C_BL = C             + n1;
+    float *const C_BR = C + *ldC * n1 + n1;
+
+    // recursion(C_TL)
+    RELAPACK_sgemmt_rec(uplo, transA, transB, &n1, k, alpha, A_T, ldA, B_L, ldB, beta, C_TL, ldC);
+
+    if (*uplo == 'L')
+        // C_BL = alpha A_B B_L + beta C_BL
+        BLAS(sgemm)(transA, transB, &n2, &n1, k, alpha, A_B, ldA, B_L, ldB, beta, C_BL, ldC);
+    else
+        // C_TR = alpha A_T B_R + beta C_TR
+        BLAS(sgemm)(transA, transB, &n1, &n2, k, alpha, A_T, ldA, B_R, ldB, beta, C_TR, ldC);
+
+    // recursion(C_BR)
+    RELAPACK_sgemmt_rec(uplo, transA, transB, &n2, k, alpha, A_B, ldA, B_R, ldB, beta, C_BR, ldC);
+}
+
+
+/** sgemmt's unblocked compute kernel */
+static void RELAPACK_sgemmt_rec2(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const float *alpha, const float *A, const int *ldA,
+    const float *B, const int *ldB,
+    const float *beta, float *C, const int *ldC
+) {
+
+    const int incB = (*transB == 'N') ? 1 : *ldB;
+    const int incC = 1;
+
+    int i;
+    for (i = 0; i < *n; i++) {
+        // A_0
+        // A_i
+        const float *const A_0 = A;
+        const float *const A_i = A + ((*transA == 'N') ? i : *ldA * i);
+
+        // * B_i *
+        const float *const B_i = B + ((*transB == 'N') ? *ldB * i : i);
+
+        // * C_0i *
+        // * C_ii *
+        float *const C_0i = C + *ldC * i;
+        float *const C_ii = C + *ldC * i + i;
+
+        if (*uplo == 'L') {
+            const int nmi = *n - i;
+            if (*transA == 'N')
+                BLAS(sgemv)(transA, &nmi, k, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+            else
+                BLAS(sgemv)(transA, k, &nmi, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+        } else {
+            const int ip1 = i + 1;
+            if (*transA == 'N')
+                BLAS(sgemv)(transA, &ip1, k, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+            else
+                BLAS(sgemv)(transA, k, &ip1, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+        }
+    }
+}

relapack/src/sgetrf.c

@@ -0,0 +1,117 @@
+#include "relapack.h"
+
+static void RELAPACK_sgetrf_rec(const int *, const int *, float *, const int *,
+    int *, int *);
+
+
+/** SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's sgetrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/de/de2/sgetrf_8f.html
+ * */
+void RELAPACK_sgetrf(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SGETRF", &minfo);
+        return;
+    }
+
+    const int sn = MIN(*m, *n);
+
+    RELAPACK_sgetrf_rec(m, &sn, A, ldA, ipiv, info);
+
+    // Right remainder
+    if (*m < *n) {
+        // Constants
+        const float ONE[] = { 1. };
+        const int  iONE[] = { 1. };
+
+        // Splitting
+        const int rn = *n - *m;
+
+        // A_L A_R
+        const float *const A_L = A;
+        float *const       A_R = A + *ldA * *m;
+
+        // A_R = apply(ipiv, A_R)
+        LAPACK(slaswp)(&rn, A_R, ldA, iONE, m, ipiv, iONE);
+        // A_R = A_L \ A_R
+        BLAS(strsm)("L", "L", "N", "U", m, &rn, ONE, A_L, ldA, A_R, ldA);
+    }
+}
+
+
+/** sgetrf's recursive compute kernel */
+static void RELAPACK_sgetrf_rec(
+    const int *m, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_SGETRF, 1)) {
+        // Unblocked
+        LAPACK(sgetf2)(m, n, A, ldA, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+    const int   iONE[] = { 1 };
+
+    // Splitting
+    const int n1 = SREC_SPLIT(*n);
+    const int n2 = *n - n1;
+    const int m2 = *m - n1;
+
+    // A_L A_R
+    float *const A_L = A;
+    float *const A_R = A + *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + *ldA * n1;
+    float *const A_BL = A             + n1;
+    float *const A_BR = A + *ldA * n1 + n1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // recursion(A_L, ipiv_T)
+    RELAPACK_sgetrf_rec(m, &n1, A_L, ldA, ipiv_T, info);
+    // apply pivots to A_R
+    LAPACK(slaswp)(&n2, A_R, ldA, iONE, &n1, ipiv_T, iONE);
+
+    // A_TR = A_TL \ A_TR
+    BLAS(strsm)("L", "L", "N", "U", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+    // A_BR = A_BR - A_BL * A_TR
+    BLAS(sgemm)("N", "N", &m2, &n2, &n1, MONE, A_BL, ldA, A_TR, ldA, ONE, A_BR, ldA);
+
+    // recursion(A_BR, ipiv_B)
+    RELAPACK_sgetrf_rec(&m2, &n2, A_BR, ldA, ipiv_B, info);
+    if (*info)
+        *info += n1;
+    // apply pivots to A_BL
+    LAPACK(slaswp)(&n1, A_BL, ldA, iONE, &n2, ipiv_B, iONE);
+    // shift pivots
+    int i;
+    for (i = 0; i < n2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/slauum.c

@@ -0,0 +1,87 @@
+#include "relapack.h"
+
+static void RELAPACK_slauum_rec(const char *, const int *, float *,
+    const int *, int *);
+
+
+/** SLAUUM computes the product U * U**T or L**T * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A.
+ *
+ * This routine is functionally equivalent to LAPACK's slauum.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dd/d5a/slauum_8f.html
+ * */
+void RELAPACK_slauum(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SLAUUM", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_slauum_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** slauum's recursive compute kernel */
+static void RELAPACK_slauum_rec(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_SLAUUM, 1)) {
+        // Unblocked
+        LAPACK(slauu2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[] = { 1. };
+
+    // Splitting
+    const int n1 = SREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + *ldA * n1;
+    float *const A_BL = A             + n1;
+    float *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_slauum_rec(uplo, &n1, A_TL, ldA, info);
+
+    if (*uplo == 'L') {
+        // A_TL = A_TL + A_BL' * A_BL
+        BLAS(ssyrk)("L", "T", &n1, &n2, ONE, A_BL, ldA, ONE, A_TL, ldA);
+        // A_BL = A_BR' * A_BL
+        BLAS(strmm)("L", "L", "T", "N", &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TL = A_TL + A_TR * A_TR'
+        BLAS(ssyrk)("U", "N", &n1, &n2, ONE, A_TR, ldA, ONE, A_TL, ldA);
+        // A_TR = A_TR * A_BR'
+        BLAS(strmm)("R", "U", "T", "N", &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_slauum_rec(uplo, &n2, A_BR, ldA, info);
+}

relapack/src/spbtrf.c

@@ -0,0 +1,157 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_spbtrf_rec(const char *, const int *, const int *,
+    float *, const int *, float *, const int *, int *);
+
+
+/** SPBTRF computes the Cholesky factorization of a real symmetric positive definite band matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's spbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d1/d22/spbtrf_8f.html
+ * */
+void RELAPACK_spbtrf(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kd < 0)
+        *info = -3;
+    else if (*ldAb < *kd + 1)
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SPBTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Constant
+    const float ZERO[] = { 0. };
+
+    // Allocate work space
+    const int n1 = SREC_SPLIT(*n);
+    const int mWork = (*kd > n1) ? (lower ? *n - *kd : n1) : *kd;
+    const int nWork = (*kd > n1) ? (lower ? n1 : *n - *kd) : *kd;
+    float *Work = malloc(mWork * nWork * sizeof(float));
+    LAPACK(slaset)(uplo, &mWork, &nWork, ZERO, ZERO, Work, &mWork);
+
+    // Recursive kernel
+    RELAPACK_spbtrf_rec(&cleanuplo, n, kd, Ab, ldAb, Work, &mWork, info);
+
+    // Free work space
+    free(Work);
+}
+
+
+/** spbtrf's recursive compute kernel */
+static void RELAPACK_spbtrf_rec(
+    const char *uplo, const int *n, const int *kd,
+    float *Ab, const int *ldAb,
+    float *Work, const int *ldWork,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_SPBTRF, 1)) {
+        // Unblocked
+        LAPACK(spbtf2)(uplo, n, kd, Ab, ldAb, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    float *const A = Ab + ((*uplo == 'L') ? 0 : *kd);
+
+    // Splitting
+    const int n1 = MIN(SREC_SPLIT(*n), *kd);
+    const int n2 = *n - n1;
+
+    // * *
+    // * Ab_BR
+    float *const Ab_BR = Ab + *ldAb * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + *ldA * n1;
+    float *const A_BL = A             + n1;
+    float *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_spotrf(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    // Banded splitting
+    const int n21 = MIN(n2, *kd - n1);
+    const int n22 = MIN(n2 - n21, *kd);
+
+    //     n1    n21    n22
+    // n1  *     A_TRl  A_TRr
+    // n21 A_BLt A_BRtl A_BRtr
+    // n22 A_BLb A_BRbl A_BRbr
+    float *const A_TRl  = A_TR;
+    float *const A_TRr  = A_TR + *ldA * n21;
+    float *const A_BLt  = A_BL;
+    float *const A_BLb  = A_BL               + n21;
+    float *const A_BRtl = A_BR;
+    float *const A_BRtr = A_BR + *ldA * n21;
+    float *const A_BRbl = A_BR               + n21;
+    float *const A_BRbr = A_BR + *ldA * n21  + n21;
+
+    if (*uplo == 'L') {
+        // A_BLt = ABLt / A_TL'
+        BLAS(strsm)("R", "L", "T", "N", &n21, &n1, ONE, A_TL, ldA, A_BLt, ldA);
+        // A_BRtl = A_BRtl - A_BLt * A_BLt'
+        BLAS(ssyrk)("L", "N", &n21, &n1, MONE, A_BLt, ldA, ONE, A_BRtl, ldA);
+        // Work = A_BLb
+        LAPACK(slacpy)("U", &n22, &n1, A_BLb, ldA, Work, ldWork);
+        // Work = Work / A_TL'
+        BLAS(strsm)("R", "L", "T", "N", &n22, &n1, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRbl = A_BRbl - Work * A_BLt'
+        BLAS(sgemm)("N", "T", &n22, &n21, &n1, MONE, Work, ldWork, A_BLt, ldA, ONE, A_BRbl, ldA);
+        // A_BRbr = A_BRbr - Work * Work'
+        BLAS(ssyrk)("L", "N", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_BLb = Work
+        LAPACK(slacpy)("U", &n22, &n1, Work, ldWork, A_BLb, ldA);
+    } else {
+        // A_TRl = A_TL' \ A_TRl
+        BLAS(strsm)("L", "U", "T", "N", &n1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+        // A_BRtl = A_BRtl - A_TRl' * A_TRl
+        BLAS(ssyrk)("U", "T", &n21, &n1, MONE, A_TRl, ldA, ONE, A_BRtl, ldA);
+        // Work = A_TRr
+        LAPACK(slacpy)("L", &n1, &n22, A_TRr, ldA, Work, ldWork);
+        // Work = A_TL' \ Work
+        BLAS(strsm)("L", "U", "T", "N", &n1, &n22, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRtr = A_BRtr - A_TRl' * Work
+        BLAS(sgemm)("T", "N", &n21, &n22, &n1, MONE, A_TRl, ldA, Work, ldWork, ONE, A_BRtr, ldA);
+        // A_BRbr = A_BRbr - Work' * Work
+        BLAS(ssyrk)("U", "T", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_TRr = Work
+        LAPACK(slacpy)("L", &n1, &n22, Work, ldWork, A_TRr, ldA);
+    }
+
+    // recursion(A_BR)
+    if (*kd > n1)
+        RELAPACK_spotrf(uplo, &n2, A_BR, ldA, info);
+    else
+        RELAPACK_spbtrf_rec(uplo, &n2, kd, Ab_BR, ldAb, Work, ldWork, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/spotrf.c

@@ -0,0 +1,92 @@
+#include "relapack.h"
+
+static void RELAPACK_spotrf_rec(const char *, const int *, float *, 
+        const int *, int *);
+
+
+/** SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's spotrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d0/da2/spotrf_8f.html
+ * */
+void RELAPACK_spotrf(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SPOTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_spotrf_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** spotrf's recursive compute kernel */
+static void RELAPACK_spotrf_rec(
+    const char *uplo, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_SPOTRF, 1)) {
+        // Unblocked
+        LAPACK(spotf2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+
+    // Splitting
+    const int n1 = SREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + *ldA * n1;
+    float *const A_BL = A             + n1;
+    float *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_spotrf_rec(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = A_BL / A_TL'
+        BLAS(strsm)("R", "L", "T", "N", &n2, &n1, ONE, A_TL, ldA, A_BL, ldA);
+        // A_BR = A_BR - A_BL * A_BL'
+        BLAS(ssyrk)("L", "N", &n2, &n1, MONE, A_BL, ldA, ONE, A_BR, ldA);
+    } else {
+        // A_TR = A_TL' \ A_TR
+        BLAS(strsm)("L", "U", "T", "N", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+        // A_BR = A_BR - A_TR' * A_TR
+        BLAS(ssyrk)("U", "T", &n2, &n1, MONE, A_TR, ldA, ONE, A_BR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_spotrf_rec(uplo, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/ssygst.c

@@ -0,0 +1,212 @@
+#include "relapack.h"
+#if XSYGST_ALLOW_MALLOC
+#include "stdlib.h"
+#endif
+
+static void RELAPACK_ssygst_rec(const int *, const char *, const int *,
+    float *, const int *, const float *, const int *,
+    float *, const int *, int *);
+
+
+/** SSYGST reduces a real symmetric-definite generalized eigenproblem to standard form.
+ *
+ * This routine is functionally equivalent to LAPACK's ssygst.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d8/d78/ssygst_8f.html
+ * */
+void RELAPACK_ssygst(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (*itype < 1 || *itype > 3)
+        *info = -1;
+    else if (!lower && !upper)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    else if (*ldB < MAX(1, *n))
+        *info = -7;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SSYGST", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Allocate work space
+    float *Work = NULL;
+    int   lWork = 0;
+#if XSYGST_ALLOW_MALLOC
+    const int n1 = SREC_SPLIT(*n);
+    lWork = n1 * (*n - n1);
+    Work  = malloc(lWork * sizeof(float));
+    if (!Work)
+        lWork = 0;
+#endif
+
+    // Recursive kernel
+    RELAPACK_ssygst_rec(itype, &cleanuplo, n, A, ldA, B, ldB, Work, &lWork, info);
+
+    // Free work space
+#if XSYGST_ALLOW_MALLOC
+    if (Work)
+        free(Work);
+#endif
+}
+
+
+/** ssygst's recursive compute kernel */
+static void RELAPACK_ssygst_rec(
+    const int *itype, const char *uplo, const int *n,
+    float *A, const int *ldA, const float *B, const int *ldB,
+    float *Work, const int *lWork, int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_SSYGST, 1)) {
+        // Unblocked
+        LAPACK(ssygs2)(itype, uplo, n, A, ldA, B, ldB, info);
+        return;
+    }
+
+    // Constants
+    const float ZERO[]  = { 0. };
+    const float ONE[]   = { 1. };
+    const float MONE[]  = { -1. };
+    const float HALF[]  = { .5 };
+    const float MHALF[] = { -.5 };
+    const int   iONE[]  = { 1 };
+
+    // Loop iterator
+    int i;
+
+    // Splitting
+    const int n1 = SREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + *ldA * n1;
+    float *const A_BL = A             + n1;
+    float *const A_BR = A + *ldA * n1 + n1;
+
+    // B_TL B_TR
+    // B_BL B_BR
+    const float *const B_TL = B;
+    const float *const B_TR = B + *ldB * n1;
+    const float *const B_BL = B             + n1;
+    const float *const B_BR = B + *ldB * n1 + n1;
+
+    // recursion(A_TL, B_TL)
+    RELAPACK_ssygst_rec(itype, uplo, &n1, A_TL, ldA, B_TL, ldB, Work, lWork, info);
+
+    if (*itype == 1)
+        if (*uplo == 'L') {
+            // A_BL = A_BL / B_TL'
+            BLAS(strsm)("R", "L", "T", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork > n2 * n1) {
+                // T = -1/2 * B_BL * A_TL
+                BLAS(ssymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(saxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            } else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(ssymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BR = A_BR - A_BL * B_BL' - B_BL * A_BL'
+            BLAS(ssyr2k)("L", "N", &n2, &n1, MONE, A_BL, ldA, B_BL, ldB, ONE, A_BR, ldA);
+            if (*lWork > n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(saxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(ssymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR \ A_BL
+            BLAS(strsm)("L", "L", "N", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL' \ A_TR
+            BLAS(strsm)("L", "U", "T", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork > n2 * n1) {
+                // T = -1/2 * A_TL * B_TR
+                BLAS(ssymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(saxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            } else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(ssymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_BR = A_BR - A_TR' * B_TR - B_TR' * A_TR
+            BLAS(ssyr2k)("U", "T", &n2, &n1, MONE, A_TR, ldA, B_TR, ldB, ONE, A_BR, ldA);
+            if (*lWork > n2 * n1)
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(saxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(ssymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR / B_BR
+            BLAS(strsm)("R", "U", "N", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+    else
+        if (*uplo == 'L') {
+            // A_BL = A_BL * B_TL
+            BLAS(strmm)("R", "L", "N", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork > n2 * n1) {
+                // T = 1/2 * A_BR * B_BL
+                BLAS(ssymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(saxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            } else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(ssymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_TL = A_TL + A_BL' * B_BL + B_BL' * A_BL
+            BLAS(ssyr2k)("L", "T", &n1, &n2, ONE, A_BL, ldA, B_BL, ldB, ONE, A_TL, ldA);
+            if (*lWork > n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(saxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
+            else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(ssymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR * A_BL
+            BLAS(strmm)("L", "L", "T", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL * A_TR
+            BLAS(strmm)("L", "U", "N", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork > n2 * n1) {
+                // T = 1/2 * B_TR * A_BR
+                BLAS(ssymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(saxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            } else
+                // A_TR = A_TR + 1/2 B_TR A_BR
+                BLAS(ssymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TL = A_TL + A_TR * B_TR' + B_TR * A_TR'
+            BLAS(ssyr2k)("U", "N", &n1, &n2, ONE, A_TR, ldA, B_TR, ldB, ONE, A_TL, ldA);
+            if (*lWork > n2 * n1)
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(saxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
+            else
+                // A_TR = A_TR + 1/2 B_TR * A_BR
+                BLAS(ssymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR * B_BR
+            BLAS(strmm)("R", "U", "T", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+
+    // recursion(A_BR, B_BR)
+    RELAPACK_ssygst_rec(itype, uplo, &n2, A_BR, ldA, B_BR, ldB, Work, lWork, info);
+}

relapack/src/ssytrf.c

@@ -0,0 +1,238 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_ssytrf_rec(const char *, const int *, const int *, int *,
+    float *, const int *, int *, float *, const int *, int *);
+
+
+/** SSYTRF computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's ssytrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/da/de9/ssytrf_8f.html
+ * */
+void RELAPACK_ssytrf(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    float *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * sizeof(float));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy arguments
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_ssytrf_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** ssytrf's recursive compute kernel */
+static void RELAPACK_ssytrf_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_SSYTRF, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(ssytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_ssytrf_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+    const int   iONE[] = { 1 };
+
+    // Loop iterator
+    int i;
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = SREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        float *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_ssytrf_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        float *const A_BL   = A             + n1;
+        float *const A_BR   = A + *ldA * n1 + n1;
+        float *const A_BL_B = A             + *n;
+        float *const A_BR_B = A + *ldA * n1 + *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        float *const Work_BL =              Work                + n1;
+        float *const Work_BR = top ? Work : Work + *ldWork * n1 + n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_sgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(sgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_ssytrf_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            float *const A_BR_r = A_BR + *ldA * n2_out + n2_out;
+
+            // last row of A_BL
+            float *const A_BL_b = A_BL + n2_out;
+
+            // last row of Work_BL
+            float *const Work_BL_b = Work_BL + n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(sgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = SREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        float *const Work_R = top ? Work : Work + *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_ssytrf_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1  = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        float *const A_TL_T = A + *ldA * n_rest;
+        float *const A_TR_T = A + *ldA * (n_rest + n1);
+        float *const A_TL   = A + *ldA * n_rest        + n_rest;
+        float *const A_TR   = A + *ldA * (n_rest + n1) + n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        float *const Work_L  = Work;
+        float *const Work_TR = Work + *ldWork * (top ? n2_diff : n1) + n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_sgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(sgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_ssytrf_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(sgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/ssytrf_rec2.c

@@ -0,0 +1,351 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static int c__1 = 1;
+static float c_b8 = -1.f;
+static float c_b9 = 1.f;
+
+/** SSYTRF_REC2 computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagon al pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's slasyf.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_ssytrf_rec2(char *uplo, int *n, int *
+	nb, int *kb, float *a, int *lda, int *ipiv, float *w,
+	int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2;
+    float r__1, r__2, r__3;
+
+    /* Builtin functions */
+    double sqrt(double);
+
+    /* Local variables */
+    static int j, k;
+    static float t, r1, d11, d21, d22;
+    static int jj, kk, jp, kp, kw, kkw, imax, jmax;
+    static float alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int sscal_(int *, float *, float *, int *),
+	    sgemv_(char *, int *, int *, float *, float *, int *,
+	    float *, int *, float *, float *, int *, ftnlen);
+    static int kstep;
+    extern /* Subroutine */ int scopy_(int *, float *, int *, float *,
+	    int *), sswap_(int *, float *, int *, float *, int *
+	    );
+    static float absakk;
+    extern int isamax_(int *, float *, int *);
+    static float colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.f) + 1.f) / 8.f;
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	scopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    sgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b9, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	kstep = 1;
+	absakk = (r__1 = w[k + kw * w_dim1], dabs(r__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = isamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    colmax = (r__1 = w[imax + kw * w_dim1], dabs(r__1));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		scopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		scopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    sgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b9, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		i__1 = k - imax;
+		jmax = imax + isamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
+			 &c__1);
+		rowmax = (r__1 = w[jmax + (kw - 1) * w_dim1], dabs(r__1));
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    jmax = isamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+/* Computing MAX */
+		    r__2 = rowmax, r__3 = (r__1 = w[jmax + (kw - 1) * w_dim1],
+			     dabs(r__1));
+		    rowmax = dmax(r__2,r__3);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else if ((r__1 = w[imax + (kw - 1) * w_dim1], dabs(r__1)) >=
+			 alpha * rowmax) {
+		    kp = imax;
+		    scopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		} else {
+		    kp = imax;
+		    kstep = 2;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kp != kk) {
+		a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
+		i__1 = kk - 1 - kp;
+		scopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    scopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    sswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		sswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		scopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		r1 = 1.f / a[k + k * a_dim1];
+		i__1 = k - 1;
+		sscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+	    } else {
+		if (k > 2) {
+		    d21 = w[k - 1 + kw * w_dim1];
+		    d11 = w[k + kw * w_dim1] / d21;
+		    d22 = w[k - 1 + (kw - 1) * w_dim1] / d21;
+		    t = 1.f / (d11 * d22 - 1.f);
+		    d21 = t / d21;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			a[j + (k - 1) * a_dim1] = d21 * (d11 * w[j + (kw - 1)
+				* w_dim1] - w[j + kw * w_dim1]);
+			a[j + k * a_dim1] = d21 * (d22 * w[j + kw * w_dim1] -
+				w[j + (kw - 1) * w_dim1]);
+/* L20: */
+		    }
+		}
+		a[k - 1 + (k - 1) * a_dim1] = w[k - 1 + (kw - 1) * w_dim1];
+		a[k - 1 + k * a_dim1] = w[k - 1 + kw * w_dim1];
+		a[k + k * a_dim1] = w[k + kw * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    ++j;
+	}
+	++j;
+	if (jp != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    sswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
+	}
+	if (j < *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	i__1 = *n - k + 1;
+	scopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	i__1 = *n - k + 1;
+	i__2 = k - 1;
+	sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1], lda, &w[k
+		+ w_dim1], ldw, &c_b9, &w[k + k * w_dim1], &c__1, (ftnlen)12);
+	kstep = 1;
+	absakk = (r__1 = w[k + k * w_dim1], dabs(r__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + isamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    colmax = (r__1 = w[imax + k * w_dim1], dabs(r__1));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - k;
+		scopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		scopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		i__1 = *n - k + 1;
+		i__2 = k - 1;
+		sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1],
+			lda, &w[imax + w_dim1], ldw, &c_b9, &w[k + (k + 1) *
+			w_dim1], &c__1, (ftnlen)12);
+		i__1 = imax - k;
+		jmax = k - 1 + isamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
+			;
+		rowmax = (r__1 = w[jmax + (k + 1) * w_dim1], dabs(r__1));
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    jmax = imax + isamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+/* Computing MAX */
+		    r__2 = rowmax, r__3 = (r__1 = w[jmax + (k + 1) * w_dim1],
+			    dabs(r__1));
+		    rowmax = dmax(r__2,r__3);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else if ((r__1 = w[imax + (k + 1) * w_dim1], dabs(r__1)) >=
+			alpha * rowmax) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    scopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		} else {
+		    kp = imax;
+		    kstep = 2;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kp != kk) {
+		a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
+		i__1 = kp - kk - 1;
+		scopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    scopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    sswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		sswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		scopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    r1 = 1.f / a[k + k * a_dim1];
+		    i__1 = *n - k;
+		    sscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    d21 = w[k + 1 + k * w_dim1];
+		    d11 = w[k + 1 + (k + 1) * w_dim1] / d21;
+		    d22 = w[k + k * w_dim1] / d21;
+		    t = 1.f / (d11 * d22 - 1.f);
+		    d21 = t / d21;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			a[j + k * a_dim1] = d21 * (d11 * w[j + k * w_dim1] -
+				w[j + (k + 1) * w_dim1]);
+			a[j + (k + 1) * a_dim1] = d21 * (d22 * w[j + (k + 1) *
+				 w_dim1] - w[j + k * w_dim1]);
+/* L80: */
+		    }
+		}
+		a[k + k * a_dim1] = w[k + k * w_dim1];
+		a[k + 1 + k * a_dim1] = w[k + 1 + k * w_dim1];
+		a[k + 1 + (k + 1) * a_dim1] = w[k + 1 + (k + 1) * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    --j;
+	}
+	--j;
+	if (jp != jj && j >= 1) {
+	    sswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j > 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/ssytrf_rook.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_ssytrf_rook_rec(const char *, const int *, const int *, int *,
+    float *, const int *, int *, float *, const int *, int *);
+
+
+/** SSYTRF_ROOK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's ssytrf_rook.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/de/da4/ssytrf__rook_8f.html
+ * */
+void RELAPACK_ssytrf_rook(
+    const char *uplo, const int *n,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    float *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * sizeof(float));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("SSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_ssytrf_rook_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** ssytrf_rook's recursive compute kernel */
+static void RELAPACK_ssytrf_rook_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    float *A, const int *ldA, int *ipiv,
+    float *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_SSYTRF_ROOK, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(ssytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_ssytrf_rook_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+    const int   iONE[]  = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = SREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        float *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_ssytrf_rook_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2   = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        float *const A_BL   = A             + n1;
+        float *const A_BR   = A + *ldA * n1 + n1;
+        float *const A_BL_B = A             + *n;
+        float *const A_BR_B = A + *ldA * n1 + *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        float *const Work_BL =              Work                + n1;
+        float *const Work_BR = top ? Work : Work + *ldWork * n1 + n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_sgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(sgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_ssytrf_rook_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            float *const A_BR_r = A_BR + *ldA * n2_out + n2_out;
+
+            // last row of A_BL
+            float *const A_BL_b = A_BL + n2_out;
+
+            // last row of Work_BL
+            float *const Work_BL_b = Work_BL + n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(sgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = SREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        float *const Work_R = top ? Work : Work + *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_ssytrf_rook_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        float *const A_TL_T = A + *ldA * n_rest;
+        float *const A_TR_T = A + *ldA * (n_rest + n1);
+        float *const A_TL   = A + *ldA * n_rest        + n_rest;
+        float *const A_TR   = A + *ldA * (n_rest + n1) + n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        float *const Work_L  = Work;
+        float *const Work_TR = Work + *ldWork * (top ? n2_diff : n1) + n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_sgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(sgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_ssytrf_rook_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(sgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/ssytrf_rook_rec2.c

@@ -0,0 +1,451 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static int c__1 = 1;
+static float c_b9 = -1.f;
+static float c_b10 = 1.f;
+
+/** SSYTRF_ROOK_REC2 computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufma n ("rook") diagonal pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's slasyf_rook.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_ssytrf_rook_rec2(char *uplo, int *n,
+	int *nb, int *kb, float *a, int *lda, int *ipiv, float *
+	w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2;
+    float r__1;
+
+    /* Builtin functions */
+    double sqrt(double);
+
+    /* Local variables */
+    static int j, k, p;
+    static float t, r1, d11, d12, d21, d22;
+    static int ii, jj, kk, kp, kw, jp1, jp2, kkw;
+    static logical done;
+    static int imax, jmax;
+    static float alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int sscal_(int *, float *, float *, int *);
+    static float sfmin;
+    static int itemp;
+    extern /* Subroutine */ int sgemv_(char *, int *, int *, float *,
+	    float *, int *, float *, int *, float *, float *, int *,
+	    ftnlen);
+    static int kstep;
+    static float stemp;
+    extern /* Subroutine */ int scopy_(int *, float *, int *, float *,
+	    int *), sswap_(int *, float *, int *, float *, int *
+	    );
+    static float absakk;
+    extern double slamch_(char *, ftnlen);
+    extern int isamax_(int *, float *, int *);
+    static float colmax, rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.f) + 1.f) / 8.f;
+    sfmin = slamch_("S", (ftnlen)1);
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	p = k;
+	scopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    sgemv_("No transpose", &k, &i__1, &c_b9, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b10, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	absakk = (r__1 = w[k + kw * w_dim1], dabs(r__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = isamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    colmax = (r__1 = w[imax + kw * w_dim1], dabs(r__1));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    scopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L12:
+		scopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		scopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    sgemv_("No transpose", &k, &i__1, &c_b9, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b10, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = k - imax;
+		    jmax = imax + isamax_(&i__1, &w[imax + 1 + (kw - 1) *
+			    w_dim1], &c__1);
+		    rowmax = (r__1 = w[jmax + (kw - 1) * w_dim1], dabs(r__1));
+		} else {
+		    rowmax = 0.f;
+		}
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    itemp = isamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+		    stemp = (r__1 = w[itemp + (kw - 1) * w_dim1], dabs(r__1));
+		    if (stemp > rowmax) {
+			rowmax = stemp;
+			jmax = itemp;
+		    }
+		}
+		if (! ((r__1 = w[imax + (kw - 1) * w_dim1], dabs(r__1)) <
+			alpha * rowmax)) {
+		    kp = imax;
+		    scopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    scopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		}
+		if (! done) {
+		    goto L12;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kstep == 2 && p != k) {
+		i__1 = k - p;
+		scopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
+			a_dim1], lda);
+		scopy_(&p, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - k + 1;
+		sswap_(&i__1, &a[k + k * a_dim1], lda, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - kk + 1;
+		sswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
+			 ldw);
+	    }
+	    if (kp != kk) {
+		a[kp + k * a_dim1] = a[kk + k * a_dim1];
+		i__1 = k - 1 - kp;
+		scopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		scopy_(&kp, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - kk + 1;
+		sswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1],
+			 lda);
+		i__1 = *n - kk + 1;
+		sswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		scopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    if ((r__1 = a[k + k * a_dim1], dabs(r__1)) >= sfmin) {
+			r1 = 1.f / a[k + k * a_dim1];
+			i__1 = k - 1;
+			sscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    } else if (a[k + k * a_dim1] != 0.f) {
+			i__1 = k - 1;
+			for (ii = 1; ii <= i__1; ++ii) {
+			    a[ii + k * a_dim1] /= a[k + k * a_dim1];
+/* L14: */
+			}
+		    }
+		}
+	    } else {
+		if (k > 2) {
+		    d12 = w[k - 1 + kw * w_dim1];
+		    d11 = w[k + kw * w_dim1] / d12;
+		    d22 = w[k - 1 + (kw - 1) * w_dim1] / d12;
+		    t = 1.f / (d11 * d22 - 1.f);
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			a[j + (k - 1) * a_dim1] = t * ((d11 * w[j + (kw - 1) *
+				 w_dim1] - w[j + kw * w_dim1]) / d12);
+			a[j + k * a_dim1] = t * ((d22 * w[j + kw * w_dim1] -
+				w[j + (kw - 1) * w_dim1]) / d12);
+/* L20: */
+		    }
+		}
+		a[k - 1 + (k - 1) * a_dim1] = w[k - 1 + (kw - 1) * w_dim1];
+		a[k - 1 + k * a_dim1] = w[k - 1 + kw * w_dim1];
+		a[k + k * a_dim1] = w[k + kw * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    ++j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	++j;
+	if (jp2 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    sswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	jj = j - 1;
+	if (jp1 != jj && kstep == 2) {
+	    i__1 = *n - j + 1;
+	    sswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	if (j <= *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	p = k;
+	i__1 = *n - k + 1;
+	scopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	if (k > 1) {
+	    i__1 = *n - k + 1;
+	    i__2 = k - 1;
+	    sgemv_("No transpose", &i__1, &i__2, &c_b9, &a[k + a_dim1], lda, &
+		    w[k + w_dim1], ldw, &c_b10, &w[k + k * w_dim1], &c__1, (
+		    ftnlen)12);
+	}
+	absakk = (r__1 = w[k + k * w_dim1], dabs(r__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + isamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    colmax = (r__1 = w[imax + k * w_dim1], dabs(r__1));
+	} else {
+	    colmax = 0.f;
+	}
+	if (dmax(absakk,colmax) == 0.f) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = *n - k + 1;
+	    scopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+		    c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L72:
+		i__1 = imax - k;
+		scopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		scopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		if (k > 1) {
+		    i__1 = *n - k + 1;
+		    i__2 = k - 1;
+		    sgemv_("No transpose", &i__1, &i__2, &c_b9, &a[k + a_dim1]
+			    , lda, &w[imax + w_dim1], ldw, &c_b10, &w[k + (k
+			    + 1) * w_dim1], &c__1, (ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = imax - k;
+		    jmax = k - 1 + isamax_(&i__1, &w[k + (k + 1) * w_dim1], &
+			    c__1);
+		    rowmax = (r__1 = w[jmax + (k + 1) * w_dim1], dabs(r__1));
+		} else {
+		    rowmax = 0.f;
+		}
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    itemp = imax + isamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+		    stemp = (r__1 = w[itemp + (k + 1) * w_dim1], dabs(r__1));
+		    if (stemp > rowmax) {
+			rowmax = stemp;
+			jmax = itemp;
+		    }
+		}
+		if (! ((r__1 = w[imax + (k + 1) * w_dim1], dabs(r__1)) <
+			alpha * rowmax)) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    scopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    i__1 = *n - k + 1;
+		    scopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		}
+		if (! done) {
+		    goto L72;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kstep == 2 && p != k) {
+		i__1 = p - k;
+		scopy_(&i__1, &a[k + k * a_dim1], &c__1, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - p + 1;
+		scopy_(&i__1, &a[p + k * a_dim1], &c__1, &a[p + p * a_dim1], &
+			c__1);
+		sswap_(&k, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
+		sswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
+	    }
+	    if (kp != kk) {
+		a[kp + k * a_dim1] = a[kk + k * a_dim1];
+		i__1 = kp - k - 1;
+		scopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1)
+			* a_dim1], lda);
+		i__1 = *n - kp + 1;
+		scopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp *
+			a_dim1], &c__1);
+		sswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		sswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		scopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    if ((r__1 = a[k + k * a_dim1], dabs(r__1)) >= sfmin) {
+			r1 = 1.f / a[k + k * a_dim1];
+			i__1 = *n - k;
+			sscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    } else if (a[k + k * a_dim1] != 0.f) {
+			i__1 = *n;
+			for (ii = k + 1; ii <= i__1; ++ii) {
+			    a[ii + k * a_dim1] /= a[k + k * a_dim1];
+/* L74: */
+			}
+		    }
+		}
+	    } else {
+		if (k < *n - 1) {
+		    d21 = w[k + 1 + k * w_dim1];
+		    d11 = w[k + 1 + (k + 1) * w_dim1] / d21;
+		    d22 = w[k + k * w_dim1] / d21;
+		    t = 1.f / (d11 * d22 - 1.f);
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			a[j + k * a_dim1] = t * ((d11 * w[j + k * w_dim1] - w[
+				j + (k + 1) * w_dim1]) / d21);
+			a[j + (k + 1) * a_dim1] = t * ((d22 * w[j + (k + 1) *
+				w_dim1] - w[j + k * w_dim1]) / d21);
+/* L80: */
+		    }
+		}
+		a[k + k * a_dim1] = w[k + k * w_dim1];
+		a[k + 1 + k * a_dim1] = w[k + 1 + k * w_dim1];
+		a[k + 1 + (k + 1) * a_dim1] = w[k + 1 + (k + 1) * w_dim1];
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    --j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	--j;
+	if (jp2 != jj && j >= 1) {
+	    sswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	jj = j + 1;
+	if (jp1 != jj && kstep == 2) {
+	    sswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j >= 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/stgsyl.c

@@ -0,0 +1,274 @@
+#include "relapack.h"
+#include <math.h>
+
+static void RELAPACK_stgsyl_rec(const char *, const int *, const int *,
+    const int *, const float *, const int *, const float *, const int *,
+    float *, const int *, const float *, const int *, const float *,
+    const int *, float *, const int *, float *, float *, float *, int *, int *,
+    int *);
+
+
+/** STGSYL solves the generalized Sylvester equation.
+ *
+ * This routine is functionally equivalent to LAPACK's stgsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dc/d67/stgsyl_8f.html
+ * */
+void RELAPACK_stgsyl(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dif,
+    float *Work, const int *lWork, int *iWork, int *info
+) {
+
+    // Parse arguments
+    const int notran = LAPACK(lsame)(trans, "N");
+    const int tran = LAPACK(lsame)(trans, "T");
+
+    // Compute work buffer size
+    int lwmin = 1;
+    if (notran && (*ijob == 1 || *ijob == 2))
+        lwmin = MAX(1, 2 * *m * *n);
+    *info = 0;
+
+    // Check arguments
+    if (!tran && !notran)
+        *info = -1;
+    else if (notran && (*ijob < 0 || *ijob > 4))
+        *info = -2;
+    else if (*m <= 0)
+        *info = -3;
+    else if (*n <= 0)
+        *info = -4;
+    else if (*ldA < MAX(1, *m))
+        *info = -6;
+    else if (*ldB < MAX(1, *n))
+        *info = -8;
+    else if (*ldC < MAX(1, *m))
+        *info = -10;
+    else if (*ldD < MAX(1, *m))
+        *info = -12;
+    else if (*ldE < MAX(1, *n))
+        *info = -14;
+    else if (*ldF < MAX(1, *m))
+        *info = -16;
+    else if (*lWork < lwmin && *lWork != -1)
+        *info = -20;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("STGSYL", &minfo);
+        return;
+    }
+
+    if (*lWork == -1) {
+        // Work size query
+        *Work = lwmin;
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantrans = notran ? 'N' : 'T';
+
+    // Constant
+    const float ZERO[] = { 0. };
+
+    int isolve = 1;
+    int ifunc  = 0;
+    if (notran) {
+        if (*ijob >= 3) {
+            ifunc = *ijob - 2;
+            LAPACK(slaset)("F", m, n, ZERO, ZERO, C, ldC);
+            LAPACK(slaset)("F", m, n, ZERO, ZERO, F, ldF);
+        } else if (*ijob >= 1)
+            isolve = 2;
+    }
+
+    float scale2;
+    int iround;
+    for (iround = 1; iround <= isolve; iround++) {
+        *scale = 1;
+        float dscale = 0;
+        float dsum   = 1;
+        int pq;
+        RELAPACK_stgsyl_rec(&cleantrans, &ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, &dsum, &dscale, iWork, &pq, info);
+        if (dscale != 0) {
+            if (*ijob == 1 || *ijob == 3)
+                *dif = sqrt(2 * *m * *n) / (dscale * sqrt(dsum));
+            else
+                *dif = sqrt(pq) / (dscale * sqrt(dsum));
+        }
+        if (isolve == 2) {
+            if (iround == 1) {
+                if (notran)
+                    ifunc = *ijob;
+                scale2 = *scale;
+                LAPACK(slacpy)("F", m, n, C, ldC, Work, m);
+                LAPACK(slacpy)("F", m, n, F, ldF, Work + *m * *n, m);
+                LAPACK(slaset)("F", m, n, ZERO, ZERO, C, ldC);
+                LAPACK(slaset)("F", m, n, ZERO, ZERO, F, ldF);
+            } else {
+                LAPACK(slacpy)("F", m, n, Work, m, C, ldC);
+                LAPACK(slacpy)("F", m, n, Work + *m * *n, m, F, ldF);
+                *scale = scale2;
+            }
+        }
+    }
+}
+
+
+/** stgsyl's recursive vompute kernel */
+static void RELAPACK_stgsyl_rec(
+    const char *trans, const int *ifunc, const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC,
+    const float *D, const int *ldD, const float *E, const int *ldE,
+    float *F, const int *ldF,
+    float *scale, float *dsum, float *dscale,
+    int *iWork, int *pq, int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_STGSYL, 1) && *n <= MAX(CROSSOVER_STGSYL, 1)) {
+        // Unblocked
+        LAPACK(stgsy2)(trans, ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dsum, dscale, iWork, pq, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+    const int   iONE[] = { 1 };
+
+    // Outputs
+    float scale1[] = { 1. };
+    float scale2[] = { 1. };
+    int   info1[]  = { 0 };
+    int   info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        int m1 = SREC_SPLIT(*m);
+        if (A[m1 + *ldA * (m1 - 1)])
+            m1++;
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const float *const A_TL = A;
+        const float *const A_TR = A + *ldA * m1;
+        const float *const A_BR = A + *ldA * m1 + m1;
+
+        // C_T
+        // C_B
+        float *const C_T = C;
+        float *const C_B = C + m1;
+
+        // D_TL D_TR
+        // 0    D_BR
+        const float *const D_TL = D;
+        const float *const D_TR = D + *ldD * m1;
+        const float *const D_BR = D + *ldD * m1 + m1;
+
+        // F_T
+        // F_B
+        float *const F_T = F;
+        float *const F_B = F + m1;
+
+        if (*trans == 'N') {
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_stgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(sgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // F_T = F_T - D_TR * C_B
+            BLAS(sgemm)("N", "N", &m1, n, &m2, MONE, D_TR, ldD, C_B, ldC, scale1, F_T, ldF);
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_stgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m2, n, F_B, ldF, info);
+            }
+        } else {
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_stgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale1, &m2, n, F_B, ldF, info);
+            // C_B = C_B - A_TR^H * C_T
+            BLAS(sgemm)("T", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // C_B = C_B - D_TR^H * F_T
+            BLAS(sgemm)("T", "N", &m2, n, &m1, MONE, D_TR, ldD, F_T, ldC, ONE, C_B, ldC);
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_stgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_T, ldC, info);
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m1, n, F_T, ldF, info);
+            }
+        }
+    } else {
+        // Splitting
+        int n1 = SREC_SPLIT(*n);
+        if (B[n1 + *ldB * (n1 - 1)])
+            n1++;
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const float *const B_TL = B;
+        const float *const B_TR = B + *ldB * n1;
+        const float *const B_BR = B + *ldB * n1 + n1;
+
+        // C_L C_R
+        float *const C_L = C;
+        float *const C_R = C + *ldC * n1;
+
+        // E_TL E_TR
+        // 0    E_BR
+        const float *const E_TL = E;
+        const float *const E_TR = E + *ldE * n1;
+        const float *const E_BR = E + *ldE * n1 + n1;
+
+        // F_L F_R
+        float *const F_L = F;
+        float *const F_R = F + *ldF * n1;
+
+        if (*trans == 'N') {
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_stgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // C_R = C_R + F_L * B_TR
+            BLAS(sgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, B_TR, ldB, scale1, C_R, ldC);
+            // F_R = F_R + F_L * E_TR
+            BLAS(sgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, E_TR, ldE, scale1, F_R, ldF);
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_stgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n1, F_L, ldF, info);
+            }
+        } else {
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_stgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale1, dsum, dscale, iWork, pq, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale1, m, &n1, C_L, ldC, info);
+            // F_L = F_L + C_R * B_TR
+            BLAS(sgemm)("N", "T", m, &n1, &n2, ONE, C_R, ldC, B_TR, ldB, scale1, F_L, ldF);
+            // F_L = F_L + F_R * E_TR
+            BLAS(sgemm)("N", "T", m, &n1, &n2, ONE, F_R, ldF, E_TR, ldB, ONE, F_L, ldF);
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_stgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale2, dsum, dscale, iWork, pq, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n2, F_R, ldF, info);
+            }
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/strsyl.c

@@ -0,0 +1,169 @@
+#include "relapack.h"
+
+static void RELAPACK_strsyl_rec(const char *, const char *, const int *,
+    const int *, const int *, const float *, const int *, const float *,
+    const int *, float *, const int *, float *, int *);
+
+
+/** STRSYL solves the real Sylvester matrix equation.
+ *
+ * This routine is functionally equivalent to LAPACK's strsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d4/d7d/strsyl_8f.html
+ * */
+void RELAPACK_strsyl(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+
+    // Check arguments
+    const int notransA = LAPACK(lsame)(tranA, "N");
+    const int transA = LAPACK(lsame)(tranA, "T");
+    const int ctransA = LAPACK(lsame)(tranA, "C");
+    const int notransB = LAPACK(lsame)(tranB, "N");
+    const int transB = LAPACK(lsame)(tranB, "T");
+    const int ctransB = LAPACK(lsame)(tranB, "C");
+    *info = 0;
+    if (!transA && !ctransA && !notransA)
+        *info = -1;
+    else if (!transB && !ctransB && !notransB)
+        *info = -2;
+    else if (*isgn != 1 && *isgn != -1)
+        *info = -3;
+    else if (*m < 0)
+        *info = -4;
+    else if (*n < 0)
+        *info = -5;
+    else if (*ldA < MAX(1, *m))
+        *info = -7;
+    else if (*ldB < MAX(1, *n))
+        *info = -9;
+    else if (*ldC < MAX(1, *m))
+        *info = -11;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("STRSYL", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantranA = notransA ? 'N' : (transA ? 'T' : 'C');
+    const char cleantranB = notransB ? 'N' : (transB ? 'T' : 'C');
+
+    // Recursive kernel
+    RELAPACK_strsyl_rec(&cleantranA, &cleantranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+
+
+/** strsyl's recursive compute kernel */
+static void RELAPACK_strsyl_rec(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const float *A, const int *ldA, const float *B, const int *ldB,
+    float *C, const int *ldC, float *scale,
+    int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_STRSYL, 1) && *n <= MAX(CROSSOVER_STRSYL, 1)) {
+        // Unblocked
+        RELAPACK_strsyl_rec2(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+    const float MSGN[] = { -*isgn };
+    const int   iONE[] = { 1 };
+
+    // Outputs
+    float scale1[] = { 1. };
+    float scale2[] = { 1. };
+    int   info1[]  = { 0 };
+    int   info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        int m1 = SREC_SPLIT(*m);
+        if (A[m1 + *ldA * (m1 - 1)])
+            m1++;
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const float *const A_TL = A;
+        const float *const A_TR = A + *ldA * m1;
+        const float *const A_BR = A + *ldA * m1 + m1;
+
+        // C_T
+        // C_B
+        float *const C_T = C;
+        float *const C_B = C + m1;
+
+        if (*tranA == 'N') {
+            // recusion(A_BR, B, C_B)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale1, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(sgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // recusion(A_TL, B, C_T)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+        } else {
+            // recusion(A_TL, B, C_T)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale1, info1);
+            // C_B = C_B - A_TR' * C_T
+            BLAS(sgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // recusion(A_BR, B, C_B)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_B, ldC, info);
+        }
+    } else {
+        // Splitting
+        int n1 = SREC_SPLIT(*n);
+        if (B[n1 + *ldB * (n1 - 1)])
+            n1++;
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const float *const B_TL = B;
+        const float *const B_TR = B + *ldB * n1;
+        const float *const B_BR = B + *ldB * n1 + n1;
+
+        // C_L C_R
+        float *const C_L = C;
+        float *const C_R = C + *ldC * n1;
+
+        if (*tranB == 'N') {
+            // recusion(A, B_TL, C_L)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale1, info1);
+            // C_R = C_R -/+ C_L * B_TR
+            BLAS(sgemm)("N", "N", m, &n2, &n1, MSGN, C_L, ldC, B_TR, ldB, scale1, C_R, ldC);
+            // recusion(A, B_BR, C_R)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+        } else {
+            // recusion(A, B_BR, C_R)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale1, info1);
+            // C_L = C_L -/+ C_R * B_TR'
+            BLAS(sgemm)("N", "C", m, &n1, &n2, MSGN, C_R, ldC, B_TR, ldB, scale1, C_L, ldC);
+            // recusion(A, B_TL, C_L)
+            RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/strtri.c

@@ -0,0 +1,107 @@
+#include "relapack.h"
+
+static void RELAPACK_strtri_rec(const char *, const char *, const int *,
+    float *, const int *, int *);
+
+
+/** CTRTRI computes the inverse of a real upper or lower triangular matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's strtri.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/de/d76/strtri_8f.html
+ * */
+void RELAPACK_strtri(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int nounit = LAPACK(lsame)(diag, "N");
+    const int unit = LAPACK(lsame)(diag, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (!nounit && !unit)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("STRTRI", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower  ? 'L' : 'U';
+    const char cleandiag = nounit ? 'N' : 'U';
+
+    // check for singularity
+    if (nounit) {
+        int i;
+        for (i = 0; i < *n; i++)
+            if (A[i + *ldA * i] == 0) {
+                *info = i;
+                return;
+            }
+    }
+
+    // Recursive kernel
+    RELAPACK_strtri_rec(&cleanuplo, &cleandiag, n, A, ldA, info);
+}
+
+
+/** strtri's recursive compute kernel */
+static void RELAPACK_strtri_rec(
+    const char *uplo, const char *diag, const int *n,
+    float *A, const int *ldA,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_STRTRI, 1)) {
+        // Unblocked
+        LAPACK(strti2)(uplo, diag, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const float ONE[]  = { 1. };
+    const float MONE[] = { -1. };
+
+    // Splitting
+    const int n1 = SREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    float *const A_TL = A;
+    float *const A_TR = A + *ldA * n1;
+    float *const A_BL = A             + n1;
+    float *const A_BR = A + *ldA * n1 + n1;
+
+    // recursion(A_TL)
+    RELAPACK_strtri_rec(uplo, diag, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = - A_BL * A_TL
+        BLAS(strmm)("R", "L", "N", diag, &n2, &n1, MONE, A_TL, ldA, A_BL, ldA);
+        // A_BL = A_BR \ A_BL
+        BLAS(strsm)("L", "L", "N", diag, &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TR = - A_TL * A_TR
+        BLAS(strmm)("L", "U", "N", diag, &n1, &n2, MONE, A_TL, ldA, A_TR, ldA);
+        // A_TR = A_TR / A_BR
+        BLAS(strsm)("R", "U", "N", diag, &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_strtri_rec(uplo, diag, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/zgbtrf.c

@@ -0,0 +1,230 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_zgbtrf_rec(const int *, const int *, const int *,
+    const int *, double *, const int *, int *, double *, const int *, double *,
+    const int *, int *);
+
+
+/** ZGBTRF computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's zgbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dc/dcb/zgbtrf_8f.html
+ * */
+void RELAPACK_zgbtrf(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kl < 0)
+        *info = -3;
+    else if (*ku < 0)
+        *info = -4;
+    else if (*ldAb < 2 * *kl + *ku + 1)
+        *info = -6;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZGBTRF", &minfo);
+        return;
+    }
+
+    // Constant
+    const double ZERO[] = { 0., 0. };
+
+    // Result upper band width
+    const int kv = *ku + *kl;
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    double *const A = Ab + 2 * kv;
+
+    // Zero upper diagonal fill-in elements
+    int i, j;
+    for (j = 0; j < *n; j++) {
+        double *const A_j = A + 2 * *ldA * j;
+        for (i = MAX(0, j - kv); i < j - *ku; i++)
+            A_j[2 * i] = A_j[2 * i + 1] = 0.;
+    }
+
+    // Allocate work space
+    const int n1 = ZREC_SPLIT(*n);
+    const int mWorkl = (kv > n1) ? MAX(1, *m - *kl) : kv;
+    const int nWorkl = (kv > n1) ? n1 : kv;
+    const int mWorku = (*kl > n1) ? n1 : *kl;
+    const int nWorku = (*kl > n1) ? MAX(0, *n - *kl) : *kl;
+    double *Workl = malloc(mWorkl * nWorkl * 2 * sizeof(double));
+    double *Worku = malloc(mWorku * nWorku * 2 * sizeof(double));
+    LAPACK(zlaset)("L", &mWorkl, &nWorkl, ZERO, ZERO, Workl, &mWorkl);
+    LAPACK(zlaset)("U", &mWorku, &nWorku, ZERO, ZERO, Worku, &mWorku);
+
+    // Recursive kernel
+    RELAPACK_zgbtrf_rec(m, n, kl, ku, Ab, ldAb, ipiv, Workl, &mWorkl, Worku, &mWorku, info);
+
+    // Free work space
+    free(Workl);
+    free(Worku);
+}
+
+
+/** zgbtrf's recursive compute kernel */
+static void RELAPACK_zgbtrf_rec(
+    const int *m, const int *n, const int *kl, const int *ku,
+    double *Ab, const int *ldAb, int *ipiv,
+    double *Workl, const int *ldWorkl, double *Worku, const int *ldWorku,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_ZGBTRF, 1)) {
+        // Unblocked
+        LAPACK(zgbtf2)(m, n, kl, ku, Ab, ldAb, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const int    iONE[] = { 1 };
+
+    // Loop iterators
+    int i, j;
+
+    // Output upper band width
+    const int kv = *ku + *kl;
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    double *const A = Ab + 2 * kv;
+
+    // Splitting
+    const int n1  = MIN(ZREC_SPLIT(*n), *kl);
+    const int n2  = *n - n1;
+    const int m1  = MIN(n1, *m);
+    const int m2  = *m - m1;
+    const int mn1 = MIN(m1, n1);
+    const int mn2 = MIN(m2, n2);
+
+    // Ab_L *
+    //      Ab_BR
+    double *const Ab_L  = Ab;
+    double *const Ab_BR = Ab + 2 * *ldAb * n1;
+
+    // A_L A_R
+    double *const A_L = A;
+    double *const A_R = A + 2 * *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + 2 * *ldA * n1;
+    double *const A_BL = A                 + 2 * m1;
+    double *const A_BR = A + 2 * *ldA * n1 + 2 * m1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // Banded splitting
+    const int n21 = MIN(n2, kv - n1);
+    const int n22 = MIN(n2 - n21, n1);
+    const int m21 = MIN(m2, *kl - m1);
+    const int m22 = MIN(m2 - m21, m1);
+
+    //   n1 n21  n22
+    // m *  A_Rl ARr
+    double *const A_Rl = A_R;
+    double *const A_Rr = A_R + 2 * *ldA * n21;
+
+    //     n1    n21    n22
+    // m1  *     A_TRl  A_TRr
+    // m21 A_BLt A_BRtl A_BRtr
+    // m22 A_BLb A_BRbl A_BRbr
+    double *const A_TRl  = A_TR;
+    double *const A_TRr  = A_TR + 2 * *ldA * n21;
+    double *const A_BLt  = A_BL;
+    double *const A_BLb  = A_BL                  + 2 * m21;
+    double *const A_BRtl = A_BR;
+    double *const A_BRtr = A_BR + 2 * *ldA * n21;
+    double *const A_BRbl = A_BR                  + 2 * m21;
+    double *const A_BRbr = A_BR + 2 * *ldA * n21 + 2 * m21;
+
+    // recursion(Ab_L, ipiv_T)
+    RELAPACK_zgbtrf_rec(m, &n1, kl, ku, Ab_L, ldAb, ipiv_T, Workl, ldWorkl, Worku, ldWorku, info);
+
+    // Workl = A_BLb
+    LAPACK(zlacpy)("U", &m22, &n1, A_BLb, ldA, Workl, ldWorkl);
+
+    // partially redo swaps in A_L
+    for (i = 0; i < mn1; i++) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(zswap)(&i, A_L + 2 * i, ldA, A_L + 2 * ip, ldA);
+            else
+                BLAS(zswap)(&i, A_L + 2 * i, ldA, Workl + 2 * (ip - *kl), ldWorkl);
+        }
+    }
+
+    // apply pivots to A_Rl
+    LAPACK(zlaswp)(&n21, A_Rl, ldA, iONE, &mn1, ipiv_T, iONE);
+
+    // apply pivots to A_Rr columnwise
+    for (j = 0; j < n22; j++) {
+        double *const A_Rrj = A_Rr + 2 * *ldA * j;
+        for (i = j; i < mn1; i++) {
+            const int ip = ipiv_T[i] - 1;
+            if (ip != i) {
+                const double tmpr = A_Rrj[2 * i];
+                const double tmpc = A_Rrj[2 * i + 1];
+                A_Rrj[2 * i]     = A_Rrj[2 * ip];
+                A_Rrj[2 * i + 1] = A_Rrj[2 * ip + 1];
+                A_Rrj[2 * ip]     = tmpr;
+                A_Rrj[2 * ip + 1] = tmpc;
+            }
+        }
+    }
+
+    // A_TRl = A_TL \ A_TRl
+    BLAS(ztrsm)("L", "L", "N", "U", &m1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+    // Worku = A_TRr
+    LAPACK(zlacpy)("L", &m1, &n22, A_TRr, ldA, Worku, ldWorku);
+    // Worku = A_TL \ Worku
+    BLAS(ztrsm)("L", "L", "N", "U", &m1, &n22, ONE, A_TL, ldA, Worku, ldWorku);
+    // A_TRr = Worku
+    LAPACK(zlacpy)("L", &m1, &n22, Worku, ldWorku, A_TRr, ldA);
+    // A_BRtl = A_BRtl - A_BLt * A_TRl
+    BLAS(zgemm)("N", "N", &m21, &n21, &n1, MONE, A_BLt, ldA, A_TRl, ldA, ONE, A_BRtl, ldA);
+    // A_BRbl = A_BRbl - Workl * A_TRl
+    BLAS(zgemm)("N", "N", &m22, &n21, &n1, MONE, Workl, ldWorkl, A_TRl, ldA, ONE, A_BRbl, ldA);
+    // A_BRtr = A_BRtr - A_BLt * Worku
+    BLAS(zgemm)("N", "N", &m21, &n22, &n1, MONE, A_BLt, ldA, Worku, ldWorku, ONE, A_BRtr, ldA);
+    // A_BRbr = A_BRbr - Workl * Worku
+    BLAS(zgemm)("N", "N", &m22, &n22, &n1, MONE, Workl, ldWorkl, Worku, ldWorku, ONE, A_BRbr, ldA);
+
+    // partially undo swaps in A_L
+    for (i = mn1 - 1; i >= 0; i--) {
+        const int ip = ipiv_T[i] - 1;
+        if (ip != i) {
+            if (ip < *kl)
+                BLAS(zswap)(&i, A_L + 2 * i, ldA, A_L + 2 * ip, ldA);
+            else
+                BLAS(zswap)(&i, A_L + 2 * i, ldA, Workl + 2 * (ip - *kl), ldWorkl);
+        }
+    }
+
+    // recursion(Ab_BR, ipiv_B)
+    RELAPACK_zgbtrf_rec(&m2, &n2, kl, ku, Ab_BR, ldAb, ipiv_B, Workl, ldWorkl, Worku, ldWorku, info);
+    if (*info)
+        *info += n1;
+    // shift pivots
+    for (i = 0; i < mn2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/zgemmt.c

@@ -0,0 +1,167 @@
+#include "relapack.h"
+
+static void RELAPACK_zgemmt_rec(const char *, const char *, const char *,
+    const int *, const int *, const double *, const double *, const int *,
+    const double *, const int *, const double *, double *, const int *);
+
+static void RELAPACK_zgemmt_rec2(const char *, const char *, const char *,
+    const int *, const int *, const double *, const double *, const int *,
+    const double *, const int *, const double *, double *, const int *);
+
+
+/** ZGEMMT computes a matrix-matrix product with general matrices but updates
+ * only the upper or lower triangular part of the result matrix.
+ *
+ * This routine performs the same operation as the BLAS routine
+ * zgemm(transA, transB, n, n, k, alpha, A, ldA, B, ldB, beta, C, ldC)
+ * but only updates the triangular part of C specified by uplo:
+ * If (*uplo == 'L'), only the lower triangular part of C is updated,
+ * otherwise the upper triangular part is updated.
+ * */
+void RELAPACK_zgemmt(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+
+#if HAVE_XGEMMT
+    BLAS(zgemmt)(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+    return;
+#else
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int notransA = LAPACK(lsame)(transA, "N");
+    const int tranA = LAPACK(lsame)(transA, "T");
+    const int ctransA = LAPACK(lsame)(transA, "C");
+    const int notransB = LAPACK(lsame)(transB, "N");
+    const int tranB = LAPACK(lsame)(transB, "T");
+    const int ctransB = LAPACK(lsame)(transB, "C");
+    int info = 0;
+    if (!lower && !upper)
+        info = 1;
+    else if (!tranA && !ctransA && !notransA)
+        info = 2;
+    else if (!tranB && !ctransB && !notransB)
+        info = 3;
+    else if (*n < 0)
+        info = 4;
+    else if (*k < 0)
+        info = 5;
+    else if (*ldA < MAX(1, notransA ? *n : *k))
+        info = 8;
+    else if (*ldB < MAX(1, notransB ? *k : *n))
+        info = 10;
+    else if (*ldC < MAX(1, *n))
+        info = 13;
+    if (info) {
+        LAPACK(xerbla)("ZGEMMT", &info);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+    const char cleantransA = notransA ? 'N' : (tranA ? 'T' : 'C');
+    const char cleantransB = notransB ? 'N' : (tranB ? 'T' : 'C');
+
+    // Recursive kernel
+    RELAPACK_zgemmt_rec(&cleanuplo, &cleantransA, &cleantransB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+#endif
+}
+
+
+/** zgemmt's recursive compute kernel */
+static void RELAPACK_zgemmt_rec(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+
+    if (*n <= MAX(CROSSOVER_ZGEMMT, 1)) {
+        // Unblocked
+        RELAPACK_zgemmt_rec2(uplo, transA, transB, n, k, alpha, A, ldA, B, ldB, beta, C, ldC);
+        return;
+    }
+
+    // Splitting
+    const int n1 = ZREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_T
+    // A_B
+    const double *const A_T = A;
+    const double *const A_B = A + 2 * ((*transA == 'N') ? n1 : *ldA * n1);
+
+    // B_L B_R
+    const double *const B_L = B;
+    const double *const B_R = B + 2 * ((*transB == 'N') ? *ldB * n1 : n1);
+
+    // C_TL C_TR
+    // C_BL C_BR
+    double *const C_TL = C;
+    double *const C_TR = C + 2 * *ldC * n1;
+    double *const C_BL = C                 + 2 * n1;
+    double *const C_BR = C + 2 * *ldC * n1 + 2 * n1;
+
+    // recursion(C_TL)
+    RELAPACK_zgemmt_rec(uplo, transA, transB, &n1, k, alpha, A_T, ldA, B_L, ldB, beta, C_TL, ldC);
+
+    if (*uplo == 'L')
+        // C_BL = alpha A_B B_L + beta C_BL
+        BLAS(zgemm)(transA, transB, &n2, &n1, k, alpha, A_B, ldA, B_L, ldB, beta, C_BL, ldC);
+    else
+        // C_TR = alpha A_T B_R + beta C_TR
+        BLAS(zgemm)(transA, transB, &n1, &n2, k, alpha, A_T, ldA, B_R, ldB, beta, C_TR, ldC);
+
+    // recursion(C_BR)
+    RELAPACK_zgemmt_rec(uplo, transA, transB, &n2, k, alpha, A_B, ldA, B_R, ldB, beta, C_BR, ldC);
+}
+
+
+/** zgemmt's unblocked compute kernel */
+static void RELAPACK_zgemmt_rec2(
+    const char *uplo, const char *transA, const char *transB,
+    const int *n, const int *k,
+    const double *alpha, const double *A, const int *ldA,
+    const double *B, const int *ldB,
+    const double *beta, double *C, const int *ldC
+) {
+
+    const int incB = (*transB == 'N') ? 1 : *ldB;
+    const int incC = 1;
+
+    int i;
+    for (i = 0; i < *n; i++) {
+        // A_0
+        // A_i
+        const double *const A_0 = A;
+        const double *const A_i = A + 2 * ((*transA == 'N') ? i : *ldA * i);
+
+        // * B_i *
+        const double *const B_i = B + 2 * ((*transB == 'N') ? *ldB * i : i);
+
+        // * C_0i *
+        // * C_ii *
+        double *const C_0i = C + 2 * *ldC * i;
+        double *const C_ii = C + 2 * *ldC * i + 2 * i;
+
+        if (*uplo == 'L') {
+            const int nmi = *n - i;
+            if (*transA == 'N')
+                BLAS(zgemv)(transA, &nmi, k, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+            else
+                BLAS(zgemv)(transA, k, &nmi, alpha, A_i, ldA, B_i, &incB, beta, C_ii, &incC);
+        } else {
+            const int ip1 = i + 1;
+            if (*transA == 'N')
+                BLAS(zgemv)(transA, &ip1, k, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+            else
+                BLAS(zgemv)(transA, k, &ip1, alpha, A_0, ldA, B_i, &incB, beta, C_0i, &incC);
+        }
+    }
+}

relapack/src/zgetrf.c

@@ -0,0 +1,117 @@
+#include "relapack.h"
+
+static void RELAPACK_zgetrf_rec(const int *, const int *, double *,
+    const int *, int *, int *);
+
+
+/** ZGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
+ *
+ * This routine is functionally equivalent to LAPACK's zgetrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dd/dd1/zgetrf_8f.html
+ * */
+void RELAPACK_zgetrf(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    // Check arguments
+    *info = 0;
+    if (*m < 0)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZGETRF", &minfo);
+        return;
+    }
+
+    const int sn = MIN(*m, *n);
+
+    RELAPACK_zgetrf_rec(m, &sn, A, ldA, ipiv, info);
+
+    // Right remainder
+    if (*m < *n) {
+        // Constants
+        const double ONE[]  = { 1., 0. };
+        const int    iONE[] = { 1 };
+
+        // Splitting
+        const int rn = *n - *m;
+
+        // A_L A_R
+        const double *const A_L = A;
+        double *const       A_R = A + 2 * *ldA * *m;
+
+        // A_R = apply(ipiv, A_R)
+        LAPACK(zlaswp)(&rn, A_R, ldA, iONE, m, ipiv, iONE);
+        // A_R = A_L \ A_R
+        BLAS(ztrsm)("L", "L", "N", "U", m, &rn, ONE, A_L, ldA, A_R, ldA);
+    }
+}
+
+
+/** zgetrf's recursive compute kernel */
+static void RELAPACK_zgetrf_rec(
+    const int *m, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_ZGETRF, 1)) {
+        // Unblocked
+        LAPACK(zgetf2)(m, n, A, ldA, ipiv, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const int    iONE[] = { 1. };
+
+    // Splitting
+    const int n1 = ZREC_SPLIT(*n);
+    const int n2 = *n - n1;
+    const int m2 = *m - n1;
+
+    // A_L A_R
+    double *const A_L = A;
+    double *const A_R = A + 2 * *ldA * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + 2 * *ldA * n1;
+    double *const A_BL = A                 + 2 * n1;
+    double *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // ipiv_T
+    // ipiv_B
+    int *const ipiv_T = ipiv;
+    int *const ipiv_B = ipiv + n1;
+
+    // recursion(A_L, ipiv_T)
+    RELAPACK_zgetrf_rec(m, &n1, A_L, ldA, ipiv_T, info);
+    // apply pivots to A_R
+    LAPACK(zlaswp)(&n2, A_R, ldA, iONE, &n1, ipiv_T, iONE);
+
+    // A_TR = A_TL \ A_TR
+    BLAS(ztrsm)("L", "L", "N", "U", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+    // A_BR = A_BR - A_BL * A_TR
+    BLAS(zgemm)("N", "N", &m2, &n2, &n1, MONE, A_BL, ldA, A_TR, ldA, ONE, A_BR, ldA);
+
+    // recursion(A_BR, ipiv_B)
+    RELAPACK_zgetrf_rec(&m2, &n2, A_BR, ldA, ipiv_B, info);
+    if (*info)
+        *info += n1;
+    // apply pivots to A_BL
+    LAPACK(zlaswp)(&n1, A_BL, ldA, iONE, &n2, ipiv_B, iONE);
+    // shift pivots
+    int i;
+    for (i = 0; i < n2; i++)
+        ipiv_B[i] += n1;
+}

relapack/src/zhegst.c

@@ -0,0 +1,212 @@
+#include "relapack.h"
+#if XSYGST_ALLOW_MALLOC
+#include "stdlib.h"
+#endif
+
+static void RELAPACK_zhegst_rec(const int *, const char *, const int *,
+    double *, const int *, const double *, const int *,
+    double *, const int *, int *);
+
+
+/** ZHEGST reduces a complex Hermitian-definite generalized eigenproblem to standard form.
+ *
+ * This routine is functionally equivalent to LAPACK's zhegst.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/dc/d68/zhegst_8f.html
+ * */
+void RELAPACK_zhegst(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (*itype < 1 || *itype > 3)
+        *info = -1;
+    else if (!lower && !upper)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    else if (*ldB < MAX(1, *n))
+        *info = -7;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZHEGST", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Allocate work space
+    double *Work = NULL;
+    int    lWork = 0;
+#if XSYGST_ALLOW_MALLOC
+    const int n1 = ZREC_SPLIT(*n);
+    lWork = n1 * (*n - n1);
+    Work  = malloc(lWork * 2 * sizeof(double));
+    if (!Work)
+        lWork = 0;
+#endif
+
+    // recursive kernel
+    RELAPACK_zhegst_rec(itype, &cleanuplo, n, A, ldA, B, ldB, Work, &lWork, info);
+
+    // Free work space
+#if XSYGST_ALLOW_MALLOC
+    if (Work)
+        free(Work);
+#endif
+}
+
+
+/** zhegst's recursive compute kernel */
+static void RELAPACK_zhegst_rec(
+    const int *itype, const char *uplo, const int *n,
+    double *A, const int *ldA, const double *B, const int *ldB,
+    double *Work, const int *lWork, int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_ZHEGST, 1)) {
+        // Unblocked
+        LAPACK(zhegs2)(itype, uplo, n, A, ldA, B, ldB, info);
+        return;
+    }
+
+    // Constants
+    const double ZERO[]  = { 0., 0. };
+    const double ONE[]   = { 1., 0. };
+    const double MONE[]  = { -1., 0. };
+    const double HALF[]  = { .5, 0. };
+    const double MHALF[] = { -.5, 0. };
+    const int    iONE[]  = { 1 };
+
+    // Loop iterator
+    int i;
+
+    // Splitting
+    const int n1 = ZREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + 2 * *ldA * n1;
+    double *const A_BL = A                 + 2 * n1;
+    double *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // B_TL B_TR
+    // B_BL B_BR
+    const double *const B_TL = B;
+    const double *const B_TR = B + 2 * *ldB * n1;
+    const double *const B_BL = B                 + 2 * n1;
+    const double *const B_BR = B + 2 * *ldB * n1 + 2 * n1;
+
+    // recursion(A_TL, B_TL)
+    RELAPACK_zhegst_rec(itype, uplo, &n1, A_TL, ldA, B_TL, ldB, Work, lWork, info);
+
+    if (*itype == 1)
+        if (*uplo == 'L') {
+            // A_BL = A_BL / B_TL'
+            BLAS(ztrsm)("R", "L", "C", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork >= n2 * n1) {
+                // T = -1/2 * B_BL * A_TL
+                BLAS(zhemm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(zaxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            } else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(zhemm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BR = A_BR - A_BL * B_BL' - B_BL * A_BL'
+            BLAS(zher2k)("L", "N", &n2, &n1, MONE, A_BL, ldA, B_BL, ldB, ONE, A_BR, ldA);
+            if (*lWork >= n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(zaxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            else
+                // A_BL = A_BL - 1/2 B_BL * A_TL
+                BLAS(zhemm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR \ A_BL
+            BLAS(ztrsm)("L", "L", "N", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL' \ A_TR
+            BLAS(ztrsm)("L", "U", "C", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork >= n2 * n1) {
+                // T = -1/2 * A_TL * B_TR
+                BLAS(zhemm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(zaxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            } else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(zhemm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_BR = A_BR - A_TR' * B_TR - B_TR' * A_TR
+            BLAS(zher2k)("U", "C", &n2, &n1, MONE, A_TR, ldA, B_TR, ldB, ONE, A_BR, ldA);
+            if (*lWork >= n2 * n1)
+                // A_TR = A_BL + T
+                for (i = 0; i < n2; i++)
+                    BLAS(zaxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            else
+                // A_TR = A_TR - 1/2 A_TL * B_TR
+                BLAS(zhemm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR / B_BR
+            BLAS(ztrsm)("R", "U", "N", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+    else
+        if (*uplo == 'L') {
+            // A_BL = A_BL * B_TL
+            BLAS(ztrmm)("R", "L", "N", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
+            if (*lWork >= n2 * n1) {
+                // T = 1/2 * A_BR * B_BL
+                BLAS(zhemm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ZERO, Work, &n2);
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(zaxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            } else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(zhemm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_TL = A_TL + A_BL' * B_BL + B_BL' * A_BL
+            BLAS(zher2k)("L", "C", &n1, &n2, ONE, A_BL, ldA, B_BL, ldB, ONE, A_TL, ldA);
+            if (*lWork >= n2 * n1)
+                // A_BL = A_BL + T
+                for (i = 0; i < n1; i++)
+                    BLAS(zaxpy)(&n2, ONE, Work + 2 * n2 * i, iONE, A_BL + 2 * *ldA * i, iONE);
+            else
+                // A_BL = A_BL + 1/2 A_BR * B_BL
+                BLAS(zhemm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
+            // A_BL = B_BR * A_BL
+            BLAS(ztrmm)("L", "L", "C", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
+        } else {
+            // A_TR = B_TL * A_TR
+            BLAS(ztrmm)("L", "U", "N", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
+            if (*lWork >= n2 * n1) {
+                // T = 1/2 * B_TR * A_BR
+                BLAS(zhemm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ZERO, Work, &n1);
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(zaxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            } else
+                // A_TR = A_TR + 1/2 B_TR A_BR
+                BLAS(zhemm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TL = A_TL + A_TR * B_TR' + B_TR * A_TR'
+            BLAS(zher2k)("U", "N", &n1, &n2, ONE, A_TR, ldA, B_TR, ldB, ONE, A_TL, ldA);
+            if (*lWork >= n2 * n1)
+                // A_TR = A_TR + T
+                for (i = 0; i < n2; i++)
+                    BLAS(zaxpy)(&n1, ONE, Work + 2 * n1 * i, iONE, A_TR + 2 * *ldA * i, iONE);
+            else
+                // A_TR = A_TR + 1/2 B_TR * A_BR
+                BLAS(zhemm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
+            // A_TR = A_TR * B_BR
+            BLAS(ztrmm)("R", "U", "C", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
+        }
+
+    // recursion(A_BR, B_BR)
+    RELAPACK_zhegst_rec(itype, uplo, &n2, A_BR, ldA, B_BR, ldB, Work, lWork, info);
+}

relapack/src/zhetrf.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_zhetrf_rec(const char *, const int *, const int *, int *,
+    double *, const int *, int *, double *, const int *, int *);
+
+
+/** ZHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's zhetrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d6/dd3/zhetrf_8f.html
+ * */
+void RELAPACK_zhetrf(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    double *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(double));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZHETRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_zhetrf_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** zhetrf's recursive compute kernel */
+static void RELAPACK_zhetrf_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_ZHETRF, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(zhetf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_zhetrf_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const int    iONE[] = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = ZREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        double *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_zhetrf_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        double *const A_BL   = A                 + 2 * n1;
+        double *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        double *const A_BL_B = A                 + 2 * *n;
+        double *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        double *const Work_BL =              Work                    + 2 * n1;
+        double *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_zgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_zhetrf_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            double *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            double *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            double *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(zgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = ZREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        double *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_zhetrf_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        double *const A_TL_T = A + 2 * *ldA * n_rest;
+        double *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        double *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        double *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        double *const Work_L  = Work;
+        double *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_zgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_zhetrf_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(zgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/zhetrf_rec2.c

@@ -0,0 +1,524 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b1 = {1.,0.};
+static int c__1 = 1;
+
+/** ZHETRF_REC2 computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kau fman diagonal pivoting method
+ *
+ * This routine is a minor modification of LAPACK's zlahef.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_zhetrf_rec2(char *uplo, int *n, int *
+	nb, int *kb, doublecomplex *a, int *lda, int *ipiv,
+	doublecomplex *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    double d__1, d__2, d__3, d__4;
+    doublecomplex z__1, z__2, z__3, z__4;
+
+    /* Builtin functions */
+    double sqrt(double), d_imag(doublecomplex *);
+    void d_cnjg(doublecomplex *, doublecomplex *), z_div(doublecomplex *,
+	    doublecomplex *, doublecomplex *);
+
+    /* Local variables */
+    static int j, k;
+    static double t, r1;
+    static doublecomplex d11, d21, d22;
+    static int jj, kk, jp, kp, kw, kkw, imax, jmax;
+    static double alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    static int kstep;
+    extern /* Subroutine */ int zgemv_(char *, int *, int *,
+	    doublecomplex *, doublecomplex *, int *, doublecomplex *,
+	    int *, doublecomplex *, doublecomplex *, int *, ftnlen),
+	    zcopy_(int *, doublecomplex *, int *, doublecomplex *,
+	    int *), zswap_(int *, doublecomplex *, int *,
+	    doublecomplex *, int *);
+    static double absakk;
+    extern /* Subroutine */ int zdscal_(int *, double *,
+	    doublecomplex *, int *);
+    static double colmax;
+    extern /* Subroutine */ int zlacgv_(int *, doublecomplex *, int *)
+	    ;
+    extern int izamax_(int *, doublecomplex *, int *);
+    static double rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.) + 1.) / 8.;
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	i__1 = k - 1;
+	zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	i__1 = k + kw * w_dim1;
+	i__2 = k + k * a_dim1;
+	d__1 = a[i__2].r;
+	w[i__1].r = d__1, w[i__1].i = 0.;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    z__1.r = -1., z__1.i = -0.;
+	    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	    i__1 = k + kw * w_dim1;
+	    i__2 = k + kw * w_dim1;
+	    d__1 = w[i__2].r;
+	    w[i__1].r = d__1, w[i__1].i = 0.;
+	}
+	i__1 = k + kw * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    kw * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + k * a_dim1;
+	    d__1 = a[i__2].r;
+	    a[i__1].r = d__1, a[i__1].i = 0.;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - 1;
+		zcopy_(&i__1, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = imax + (kw - 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		d__1 = a[i__2].r;
+		w[i__1].r = d__1, w[i__1].i = 0.;
+		i__1 = k - imax;
+		zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		i__1 = k - imax;
+		zlacgv_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    z__1.r = -1., z__1.i = -0.;
+		    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    i__2 = imax + (kw - 1) * w_dim1;
+		    d__1 = w[i__2].r;
+		    w[i__1].r = d__1, w[i__1].i = 0.;
+		}
+		i__1 = k - imax;
+		jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
+			 &c__1);
+		i__1 = jmax + (kw - 1) * w_dim1;
+		rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			jmax + (kw - 1) * w_dim1]), abs(d__2));
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    jmax = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (
+			    d__2 = d_imag(&w[jmax + (kw - 1) * w_dim1]), abs(
+			    d__2));
+		    rowmax = max(d__3,d__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    if ((d__1 = w[i__1].r, abs(d__1)) >= alpha * rowmax) {
+			kp = imax;
+			zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+				w_dim1 + 1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		d__1 = a[i__2].r;
+		a[i__1].r = d__1, a[i__1].i = 0.;
+		i__1 = kk - 1 - kp;
+		zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		i__1 = kk - 1 - kp;
+		zlacgv_(&i__1, &a[kp + (kp + 1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    zcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    zswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		zswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    i__1 = k + k * a_dim1;
+		    r1 = 1. / a[i__1].r;
+		    i__1 = k - 1;
+		    zdscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    i__1 = k - 1;
+		    zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		}
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    d_cnjg(&z__2, &d21);
+		    z_div(&z__1, &w[k + kw * w_dim1], &z__2);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    z_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1. / (z__1.r - 1.);
+		    z__2.r = t, z__2.i = 0.;
+		    z_div(&z__1, &z__2, &d21);
+		    d21.r = z__1.r, d21.i = z__1.i;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			z__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
+				.i;
+			z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
+				d21.r * z__2.i + d21.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + k * a_dim1;
+			d_cnjg(&z__2, &d21);
+			i__3 = j + kw * w_dim1;
+			z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i =
+				z__2.r * z__3.i + z__2.i * z__3.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1;
+		zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		i__1 = k - 2;
+		zlacgv_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    ++j;
+	}
+	++j;
+	if (jp != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    zswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
+	}
+	if (j < *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	i__1 = k + k * w_dim1;
+	i__2 = k + k * a_dim1;
+	d__1 = a[i__2].r;
+	w[i__1].r = d__1, w[i__1].i = 0.;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &w[k + 1 + k *
+		    w_dim1], &c__1);
+	}
+	i__1 = *n - k + 1;
+	i__2 = k - 1;
+	z__1.r = -1., z__1.i = -0.;
+	zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &w[k
+		+ w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (ftnlen)12);
+	i__1 = k + k * w_dim1;
+	i__2 = k + k * w_dim1;
+	d__1 = w[i__2].r;
+	w[i__1].r = d__1, w[i__1].i = 0.;
+	i__1 = k + k * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    k * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + k * a_dim1;
+	    d__1 = a[i__2].r;
+	    a[i__1].r = d__1, a[i__1].i = 0.;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - k;
+		zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = imax - k;
+		zlacgv_(&i__1, &w[k + (k + 1) * w_dim1], &c__1);
+		i__1 = imax + (k + 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		d__1 = a[i__2].r;
+		w[i__1].r = d__1, w[i__1].i = 0.;
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    zcopy_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1, &w[
+			    imax + 1 + (k + 1) * w_dim1], &c__1);
+		}
+		i__1 = *n - k + 1;
+		i__2 = k - 1;
+		z__1.r = -1., z__1.i = -0.;
+		zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1],
+			lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) *
+			w_dim1], &c__1, (ftnlen)12);
+		i__1 = imax + (k + 1) * w_dim1;
+		i__2 = imax + (k + 1) * w_dim1;
+		d__1 = w[i__2].r;
+		w[i__1].r = d__1, w[i__1].i = 0.;
+		i__1 = imax - k;
+		jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
+			;
+		i__1 = jmax + (k + 1) * w_dim1;
+		rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			jmax + (k + 1) * w_dim1]), abs(d__2));
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    jmax = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (
+			    d__2 = d_imag(&w[jmax + (k + 1) * w_dim1]), abs(
+			    d__2));
+		    rowmax = max(d__3,d__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (k + 1) * w_dim1;
+		    if ((d__1 = w[i__1].r, abs(d__1)) >= alpha * rowmax) {
+			kp = imax;
+			i__1 = *n - k + 1;
+			zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k +
+				k * w_dim1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		d__1 = a[i__2].r;
+		a[i__1].r = d__1, a[i__1].i = 0.;
+		i__1 = kp - kk - 1;
+		zcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		i__1 = kp - kk - 1;
+		zlacgv_(&i__1, &a[kp + (kk + 1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    zswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		zswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    i__1 = k + k * a_dim1;
+		    r1 = 1. / a[i__1].r;
+		    i__1 = *n - k;
+		    zdscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    i__1 = *n - k;
+		    zlacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    d_cnjg(&z__2, &d21);
+		    z_div(&z__1, &w[k + k * w_dim1], &z__2);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1. / (z__1.r - 1.);
+		    z__2.r = t, z__2.i = 0.;
+		    z_div(&z__1, &z__2, &d21);
+		    d21.r = z__1.r, d21.i = z__1.i;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			d_cnjg(&z__2, &d21);
+			i__3 = j + k * w_dim1;
+			z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i =
+				z__2.r * z__3.i + z__2.i * z__3.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			z__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
+				.i;
+			z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
+				d21.r * z__2.i + d21.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = *n - k;
+		zlacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		i__1 = *n - k - 1;
+		zlacgv_(&i__1, &w[k + 2 + (k + 1) * w_dim1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    --j;
+	}
+	--j;
+	if (jp != jj && j >= 1) {
+	    zswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j > 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/zhetrf_rook.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_zhetrf_rook_rec(const char *, const int *, const int *, int *,
+    double *, const int *, int *, double *, const int *, int *);
+
+
+/** ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's zhetrf_rook.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d6/d6f/zhetrf__rook_8f.html
+ * */
+void RELAPACK_zhetrf_rook(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    double *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(double));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZHETRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_zhetrf_rook_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** zhetrf_rook's recursive compute kernel */
+static void RELAPACK_zhetrf_rook_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_ZHETRF_ROOK, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(zhetf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_zhetrf_rook_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const int    iONE[] = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = ZREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        double *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_zhetrf_rook_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        double *const A_BL   = A                 + 2 * n1;
+        double *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        double *const A_BL_B = A                 + 2 * *n;
+        double *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        double *const Work_BL =              Work                    + 2 * n1;
+        double *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_zgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_zhetrf_rook_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            double *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            double *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            double *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(zgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = ZREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        double *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_zhetrf_rook_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        double *const A_TL_T = A + 2 * *ldA * n_rest;
+        double *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        double *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        double *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        double *const Work_L  = Work;
+        double *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_zgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_zhetrf_rook_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(zgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/zhetrf_rook_rec2.c

@@ -0,0 +1,662 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b1 = {1.,0.};
+static int c__1 = 1;
+
+/** ZHETRF_ROOK_REC2 computes a partial factorization of a complex Hermitian indefinite matrix using the boun ded Bunch-Kaufman ("rook") diagonal pivoting method
+ *
+ * This routine is a minor modification of LAPACK's zlahef_rook.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_zhetrf_rook_rec2(char *uplo, int *n,
+	int *nb, int *kb, doublecomplex *a, int *lda, int *
+	ipiv, doublecomplex *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    double d__1, d__2;
+    doublecomplex z__1, z__2, z__3, z__4, z__5;
+
+    /* Builtin functions */
+    double sqrt(double), d_imag(doublecomplex *);
+    void d_cnjg(doublecomplex *, doublecomplex *), z_div(doublecomplex *,
+	    doublecomplex *, doublecomplex *);
+
+    /* Local variables */
+    static int j, k, p;
+    static double t, r1;
+    static doublecomplex d11, d21, d22;
+    static int ii, jj, kk, kp, kw, jp1, jp2, kkw;
+    static logical done;
+    static int imax, jmax;
+    static double alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    static double dtemp, sfmin;
+    static int itemp, kstep;
+    extern /* Subroutine */ int zgemv_(char *, int *, int *,
+	    doublecomplex *, doublecomplex *, int *, doublecomplex *,
+	    int *, doublecomplex *, doublecomplex *, int *, ftnlen),
+	    zcopy_(int *, doublecomplex *, int *, doublecomplex *,
+	    int *), zswap_(int *, doublecomplex *, int *,
+	    doublecomplex *, int *);
+    extern double dlamch_(char *, ftnlen);
+    static double absakk;
+    extern /* Subroutine */ int zdscal_(int *, double *,
+	    doublecomplex *, int *);
+    static double colmax;
+    extern /* Subroutine */ int zlacgv_(int *, doublecomplex *, int *)
+	    ;
+    extern int izamax_(int *, doublecomplex *, int *);
+    static double rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.) + 1.) / 8.;
+    sfmin = dlamch_("S", (ftnlen)1);
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	p = k;
+	if (k > 1) {
+	    i__1 = k - 1;
+	    zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &
+		    c__1);
+	}
+	i__1 = k + kw * w_dim1;
+	i__2 = k + k * a_dim1;
+	d__1 = a[i__2].r;
+	w[i__1].r = d__1, w[i__1].i = 0.;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    z__1.r = -1., z__1.i = -0.;
+	    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	    i__1 = k + kw * w_dim1;
+	    i__2 = k + kw * w_dim1;
+	    d__1 = w[i__2].r;
+	    w[i__1].r = d__1, w[i__1].i = 0.;
+	}
+	i__1 = k + kw * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    kw * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + kw * w_dim1;
+	    d__1 = w[i__2].r;
+	    a[i__1].r = d__1, a[i__1].i = 0.;
+	    if (k > 1) {
+		i__1 = k - 1;
+		zcopy_(&i__1, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1],
+			&c__1);
+	    }
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L12:
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    zcopy_(&i__1, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			    w_dim1 + 1], &c__1);
+		}
+		i__1 = imax + (kw - 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		d__1 = a[i__2].r;
+		w[i__1].r = d__1, w[i__1].i = 0.;
+		i__1 = k - imax;
+		zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		i__1 = k - imax;
+		zlacgv_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    z__1.r = -1., z__1.i = -0.;
+		    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    i__2 = imax + (kw - 1) * w_dim1;
+		    d__1 = w[i__2].r;
+		    w[i__1].r = d__1, w[i__1].i = 0.;
+		}
+		if (imax != k) {
+		    i__1 = k - imax;
+		    jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) *
+			    w_dim1], &c__1);
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
+			    w[jmax + (kw - 1) * w_dim1]), abs(d__2));
+		} else {
+		    rowmax = 0.;
+		}
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    itemp = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+		    i__1 = itemp + (kw - 1) * w_dim1;
+		    dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			    itemp + (kw - 1) * w_dim1]), abs(d__2));
+		    if (dtemp > rowmax) {
+			rowmax = dtemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (kw - 1) * w_dim1;
+		if (! ((d__1 = w[i__1].r, abs(d__1)) < alpha * rowmax)) {
+		    kp = imax;
+		    zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		}
+		if (! done) {
+		    goto L12;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kstep == 2 && p != k) {
+		i__1 = p + p * a_dim1;
+		i__2 = k + k * a_dim1;
+		d__1 = a[i__2].r;
+		a[i__1].r = d__1, a[i__1].i = 0.;
+		i__1 = k - 1 - p;
+		zcopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
+			a_dim1], lda);
+		i__1 = k - 1 - p;
+		zlacgv_(&i__1, &a[p + (p + 1) * a_dim1], lda);
+		if (p > 1) {
+		    i__1 = p - 1;
+		    zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 +
+			    1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    zswap_(&i__1, &a[k + (k + 1) * a_dim1], lda, &a[p + (k +
+			    1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		zswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
+			 ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		d__1 = a[i__2].r;
+		a[i__1].r = d__1, a[i__1].i = 0.;
+		i__1 = kk - 1 - kp;
+		zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		i__1 = kk - 1 - kp;
+		zlacgv_(&i__1, &a[kp + (kp + 1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    zcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    zswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		zswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    i__1 = k + k * a_dim1;
+		    t = a[i__1].r;
+		    if (abs(t) >= sfmin) {
+			r1 = 1. / t;
+			i__1 = k - 1;
+			zdscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    } else {
+			i__1 = k - 1;
+			for (ii = 1; ii <= i__1; ++ii) {
+			    i__2 = ii + k * a_dim1;
+			    i__3 = ii + k * a_dim1;
+			    z__1.r = a[i__3].r / t, z__1.i = a[i__3].i / t;
+			    a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L14: */
+			}
+		    }
+		    i__1 = k - 1;
+		    zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		}
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    d_cnjg(&z__2, &d21);
+		    z_div(&z__1, &w[k + kw * w_dim1], &z__2);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    z_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1. / (z__1.r - 1.);
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z_div(&z__2, &z__3, &d21);
+			z__1.r = t * z__2.r, z__1.i = t * z__2.i;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + k * a_dim1;
+			i__3 = j + kw * w_dim1;
+			z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			d_cnjg(&z__5, &d21);
+			z_div(&z__2, &z__3, &z__5);
+			z__1.r = t * z__2.r, z__1.i = t * z__2.i;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1;
+		zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+		i__1 = k - 2;
+		zlacgv_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    ++j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	++j;
+	if (jp2 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    zswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	++jj;
+	if (kstep == 2 && jp1 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    zswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	if (j < *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	p = k;
+	i__1 = k + k * w_dim1;
+	i__2 = k + k * a_dim1;
+	d__1 = a[i__2].r;
+	w[i__1].r = d__1, w[i__1].i = 0.;
+	if (k < *n) {
+	    i__1 = *n - k;
+	    zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &w[k + 1 + k *
+		    w_dim1], &c__1);
+	}
+	if (k > 1) {
+	    i__1 = *n - k + 1;
+	    i__2 = k - 1;
+	    z__1.r = -1., z__1.i = -0.;
+	    zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &
+		    w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (
+		    ftnlen)12);
+	    i__1 = k + k * w_dim1;
+	    i__2 = k + k * w_dim1;
+	    d__1 = w[i__2].r;
+	    w[i__1].r = d__1, w[i__1].i = 0.;
+	}
+	i__1 = k + k * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    k * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = k + k * a_dim1;
+	    i__2 = k + k * w_dim1;
+	    d__1 = w[i__2].r;
+	    a[i__1].r = d__1, a[i__1].i = 0.;
+	    if (k < *n) {
+		i__1 = *n - k;
+		zcopy_(&i__1, &w[k + 1 + k * w_dim1], &c__1, &a[k + 1 + k *
+			a_dim1], &c__1);
+	    }
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L72:
+		i__1 = imax - k;
+		zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = imax - k;
+		zlacgv_(&i__1, &w[k + (k + 1) * w_dim1], &c__1);
+		i__1 = imax + (k + 1) * w_dim1;
+		i__2 = imax + imax * a_dim1;
+		d__1 = a[i__2].r;
+		w[i__1].r = d__1, w[i__1].i = 0.;
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    zcopy_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1, &w[
+			    imax + 1 + (k + 1) * w_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = *n - k + 1;
+		    i__2 = k - 1;
+		    z__1.r = -1., z__1.i = -0.;
+		    zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1]
+			    , lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k +
+			    1) * w_dim1], &c__1, (ftnlen)12);
+		    i__1 = imax + (k + 1) * w_dim1;
+		    i__2 = imax + (k + 1) * w_dim1;
+		    d__1 = w[i__2].r;
+		    w[i__1].r = d__1, w[i__1].i = 0.;
+		}
+		if (imax != k) {
+		    i__1 = imax - k;
+		    jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &
+			    c__1);
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
+			    w[jmax + (k + 1) * w_dim1]), abs(d__2));
+		} else {
+		    rowmax = 0.;
+		}
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    itemp = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+		    i__1 = itemp + (k + 1) * w_dim1;
+		    dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			    itemp + (k + 1) * w_dim1]), abs(d__2));
+		    if (dtemp > rowmax) {
+			rowmax = dtemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (k + 1) * w_dim1;
+		if (! ((d__1 = w[i__1].r, abs(d__1)) < alpha * rowmax)) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    i__1 = *n - k + 1;
+		    zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		}
+		if (! done) {
+		    goto L72;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kstep == 2 && p != k) {
+		i__1 = p + p * a_dim1;
+		i__2 = k + k * a_dim1;
+		d__1 = a[i__2].r;
+		a[i__1].r = d__1, a[i__1].i = 0.;
+		i__1 = p - k - 1;
+		zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[p + (k + 1) *
+			a_dim1], lda);
+		i__1 = p - k - 1;
+		zlacgv_(&i__1, &a[p + (k + 1) * a_dim1], lda);
+		if (p < *n) {
+		    i__1 = *n - p;
+		    zcopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + 1 + p
+			    * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    zswap_(&i__1, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
+		}
+		zswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		d__1 = a[i__2].r;
+		a[i__1].r = d__1, a[i__1].i = 0.;
+		i__1 = kp - kk - 1;
+		zcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		i__1 = kp - kk - 1;
+		zlacgv_(&i__1, &a[kp + (kk + 1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    zswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		zswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    i__1 = k + k * a_dim1;
+		    t = a[i__1].r;
+		    if (abs(t) >= sfmin) {
+			r1 = 1. / t;
+			i__1 = *n - k;
+			zdscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    } else {
+			i__1 = *n;
+			for (ii = k + 1; ii <= i__1; ++ii) {
+			    i__2 = ii + k * a_dim1;
+			    i__3 = ii + k * a_dim1;
+			    z__1.r = a[i__3].r / t, z__1.i = a[i__3].i / t;
+			    a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L74: */
+			}
+		    }
+		    i__1 = *n - k;
+		    zlacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    d_cnjg(&z__2, &d21);
+		    z_div(&z__1, &w[k + k * w_dim1], &z__2);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    t = 1. / (z__1.r - 1.);
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			i__3 = j + k * w_dim1;
+			z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			d_cnjg(&z__5, &d21);
+			z_div(&z__2, &z__3, &z__5);
+			z__1.r = t * z__2.r, z__1.i = t * z__2.i;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z_div(&z__2, &z__3, &d21);
+			z__1.r = t * z__2.r, z__1.i = t * z__2.i;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = *n - k;
+		zlacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+		i__1 = *n - k - 1;
+		zlacgv_(&i__1, &w[k + 2 + (k + 1) * w_dim1], &c__1);
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    --j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	--j;
+	if (jp2 != jj && j >= 1) {
+	    zswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	--jj;
+	if (kstep == 2 && jp1 != jj && j >= 1) {
+	    zswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j > 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/zlauum.c

@@ -0,0 +1,87 @@
+#include "relapack.h"
+
+static void RELAPACK_zlauum_rec(const char *, const int *, double *,
+    const int *, int *);
+
+
+/** ZLAUUM computes the product U * U**H or L**H * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A.
+ *
+ * This routine is functionally equivalent to LAPACK's zlauum.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d8/d45/zlauum_8f.html
+ * */
+void RELAPACK_zlauum(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZLAUUM", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_zlauum_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** zlauum's recursive compute kernel */
+static void RELAPACK_zlauum_rec(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_ZLAUUM, 1)) {
+        // Unblocked
+        LAPACK(zlauu2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[] = { 1., 0. };
+
+    // Splitting
+    const int n1 = ZREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + 2 * *ldA * n1;
+    double *const A_BL = A                 + 2 * n1;
+    double *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_zlauum_rec(uplo, &n1, A_TL, ldA, info);
+
+    if (*uplo == 'L') {
+        // A_TL = A_TL + A_BL' * A_BL
+        BLAS(zherk)("L", "C", &n1, &n2, ONE, A_BL, ldA, ONE, A_TL, ldA);
+        // A_BL = A_BR' * A_BL
+        BLAS(ztrmm)("L", "L", "C", "N", &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TL = A_TL + A_TR * A_TR'
+        BLAS(zherk)("U", "N", &n1, &n2, ONE, A_TR, ldA, ONE, A_TL, ldA);
+        // A_TR = A_TR * A_BR'
+        BLAS(ztrmm)("R", "U", "C", "N", &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_zlauum_rec(uplo, &n2, A_BR, ldA, info);
+}

relapack/src/zpbtrf.c

@@ -0,0 +1,157 @@
+#include "relapack.h"
+#include "stdlib.h"
+
+static void RELAPACK_zpbtrf_rec(const char *, const int *, const int *,
+    double *, const int *, double *, const int *, int *);
+
+
+/** ZPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's zpbtrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/db/da9/zpbtrf_8f.html
+ * */
+void RELAPACK_zpbtrf(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*kd < 0)
+        *info = -3;
+    else if (*ldAb < *kd + 1)
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZPBTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Constant
+    const double ZERO[] = { 0., 0. };
+
+    // Allocate work space
+    const int n1 = ZREC_SPLIT(*n);
+    const int mWork = (*kd > n1) ? (lower ? *n - *kd : n1) : *kd;
+    const int nWork = (*kd > n1) ? (lower ? n1 : *n - *kd) : *kd;
+    double *Work = malloc(mWork * nWork * 2 * sizeof(double));
+    LAPACK(zlaset)(uplo, &mWork, &nWork, ZERO, ZERO, Work, &mWork);
+
+    // Recursive kernel
+    RELAPACK_zpbtrf_rec(&cleanuplo, n, kd, Ab, ldAb, Work, &mWork, info);
+
+    // Free work space
+    free(Work);
+}
+
+
+/** zpbtrf's recursive compute kernel */
+static void RELAPACK_zpbtrf_rec(
+    const char *uplo, const int *n, const int *kd,
+    double *Ab, const int *ldAb,
+    double *Work, const int *ldWork,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_ZPBTRF, 1)) {
+        // Unblocked
+        LAPACK(zpbtf2)(uplo, n, kd, Ab, ldAb, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+
+    // Unskew A
+    const int ldA[] = { *ldAb - 1 };
+    double *const A = Ab + 2 * ((*uplo == 'L') ? 0 : *kd);
+
+    // Splitting
+    const int n1 = MIN(ZREC_SPLIT(*n), *kd);
+    const int n2 = *n - n1;
+
+    // * *
+    // * Ab_BR
+    double *const Ab_BR = Ab + 2 * *ldAb * n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + 2 * *ldA * n1;
+    double *const A_BL = A                 + 2 * n1;
+    double *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_zpotrf(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    // Banded splitting
+    const int n21 = MIN(n2, *kd - n1);
+    const int n22 = MIN(n2 - n21, *kd);
+
+    //     n1    n21    n22
+    // n1  *     A_TRl  A_TRr
+    // n21 A_BLt A_BRtl A_BRtr
+    // n22 A_BLb A_BRbl A_BRbr
+    double *const A_TRl  = A_TR;
+    double *const A_TRr  = A_TR + 2 * *ldA * n21;
+    double *const A_BLt  = A_BL;
+    double *const A_BLb  = A_BL                   + 2 * n21;
+    double *const A_BRtl = A_BR;
+    double *const A_BRtr = A_BR + 2 * *ldA * n21;
+    double *const A_BRbl = A_BR                   + 2 * n21;
+    double *const A_BRbr = A_BR + 2 * *ldA * n21  + 2 * n21;
+
+    if (*uplo == 'L') {
+        // A_BLt = ABLt / A_TL'
+        BLAS(ztrsm)("R", "L", "C", "N", &n21, &n1, ONE, A_TL, ldA, A_BLt, ldA);
+        // A_BRtl = A_BRtl - A_BLt * A_BLt'
+        BLAS(zherk)("L", "N", &n21, &n1, MONE, A_BLt, ldA, ONE, A_BRtl, ldA);
+        // Work = A_BLb
+        LAPACK(zlacpy)("U", &n22, &n1, A_BLb, ldA, Work, ldWork);
+        // Work = Work / A_TL'
+        BLAS(ztrsm)("R", "L", "C", "N", &n22, &n1, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRbl = A_BRbl - Work * A_BLt'
+        BLAS(zgemm)("N", "C", &n22, &n21, &n1, MONE, Work, ldWork, A_BLt, ldA, ONE, A_BRbl, ldA);
+        // A_BRbr = A_BRbr - Work * Work'
+        BLAS(zherk)("L", "N", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_BLb = Work
+        LAPACK(zlacpy)("U", &n22, &n1, Work, ldWork, A_BLb, ldA);
+    } else {
+        // A_TRl = A_TL' \ A_TRl
+        BLAS(ztrsm)("L", "U", "C", "N", &n1, &n21, ONE, A_TL, ldA, A_TRl, ldA);
+        // A_BRtl = A_BRtl - A_TRl' * A_TRl
+        BLAS(zherk)("U", "C", &n21, &n1, MONE, A_TRl, ldA, ONE, A_BRtl, ldA);
+        // Work = A_TRr
+        LAPACK(zlacpy)("L", &n1, &n22, A_TRr, ldA, Work, ldWork);
+        // Work = A_TL' \ Work
+        BLAS(ztrsm)("L", "U", "C", "N", &n1, &n22, ONE, A_TL, ldA, Work, ldWork);
+        // A_BRtr = A_BRtr - A_TRl' * Work
+        BLAS(zgemm)("C", "N", &n21, &n22, &n1, MONE, A_TRl, ldA, Work, ldWork, ONE, A_BRtr, ldA);
+        // A_BRbr = A_BRbr - Work' * Work
+        BLAS(zherk)("U", "C", &n22, &n1, MONE, Work, ldWork, ONE, A_BRbr, ldA);
+        // A_TRr = Work
+        LAPACK(zlacpy)("L", &n1, &n22, Work, ldWork, A_TRr, ldA);
+    }
+
+    // recursion(A_BR)
+    if (*kd > n1)
+        RELAPACK_zpotrf(uplo, &n2, A_BR, ldA, info);
+    else
+        RELAPACK_zpbtrf_rec(uplo, &n2, kd, Ab_BR, ldAb, Work, ldWork, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/zpotrf.c

@@ -0,0 +1,92 @@
+#include "relapack.h"
+
+static void RELAPACK_zpotrf_rec(const char *, const int *, double *,
+        const int *, int *);
+
+
+/** ZPOTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's zpotrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d1/db9/zpotrf_8f.html
+ * */
+void RELAPACK_zpotrf(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZPOTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Recursive kernel
+    RELAPACK_zpotrf_rec(&cleanuplo, n, A, ldA, info);
+}
+
+
+/** zpotrf's recursive compute kernel */
+static void RELAPACK_zpotrf_rec(
+    const char *uplo, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    if (*n <= MAX(CROSSOVER_ZPOTRF, 1)) {
+        // Unblocked
+        LAPACK(zpotf2)(uplo, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+
+    // Splitting
+    const int n1 = ZREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + 2 * *ldA * n1;
+    double *const A_BL = A                 + 2 * n1;
+    double *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_zpotrf_rec(uplo, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = A_BL / A_TL'
+        BLAS(ztrsm)("R", "L", "C", "N", &n2, &n1, ONE, A_TL, ldA, A_BL, ldA);
+        // A_BR = A_BR - A_BL * A_BL'
+        BLAS(zherk)("L", "N", &n2, &n1, MONE, A_BL, ldA, ONE, A_BR, ldA);
+    } else {
+        // A_TR = A_TL' \ A_TR
+        BLAS(ztrsm)("L", "U", "C", "N", &n1, &n2, ONE, A_TL, ldA, A_TR, ldA);
+        // A_BR = A_BR - A_TR' * A_TR
+        BLAS(zherk)("U", "C", &n2, &n1, MONE, A_TR, ldA, ONE, A_BR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_zpotrf_rec(uplo, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}

relapack/src/zsytrf.c

@@ -0,0 +1,238 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_zsytrf_rec(const char *, const int *, const int *, int *,
+    double *, const int *, int *, double *, const int *, int *);
+
+
+/** ZSYTRF computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's zsytrf.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/da/d94/zsytrf_8f.html
+ * */
+void RELAPACK_zsytrf(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    double *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(double));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy arguments
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_zsytrf_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** zsytrf's recursive compute kernel */
+static void RELAPACK_zsytrf_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_ZSYTRF, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(zsytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_zsytrf_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const int    iONE[] = { 1 };
+
+    // Loop iterator
+    int i;
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = ZREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        double *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_zsytrf_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2 = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        double *const A_BL   = A                 + 2 * n1;
+        double *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        double *const A_BL_B = A                 + 2 * *n;
+        double *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        double *const Work_BL =              Work                    + 2 * n1;
+        double *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_zgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_zsytrf_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            double *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            double *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            double *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(zgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = ZREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        double *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_zsytrf_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1  = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        double *const A_TL_T = A + 2 * *ldA * n_rest;
+        double *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        double *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        double *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        double *const Work_L  = Work;
+        double *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_zgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_zsytrf_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(zgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/zsytrf_rec2.c

@@ -0,0 +1,452 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b1 = {1.,0.};
+static int c__1 = 1;
+
+/** ZSYTRF_REC2 computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagon al pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's zlasyf.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_zsytrf_rec2(char *uplo, int *n, int *
+	nb, int *kb, doublecomplex *a, int *lda, int *ipiv,
+	doublecomplex *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    double d__1, d__2, d__3, d__4;
+    doublecomplex z__1, z__2, z__3;
+
+    /* Builtin functions */
+    double sqrt(double), d_imag(doublecomplex *);
+    void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
+
+    /* Local variables */
+    static int j, k;
+    static doublecomplex t, r1, d11, d21, d22;
+    static int jj, kk, jp, kp, kw, kkw, imax, jmax;
+    static double alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    extern /* Subroutine */ int zscal_(int *, doublecomplex *,
+	    doublecomplex *, int *);
+    static int kstep;
+    extern /* Subroutine */ int zgemv_(char *, int *, int *,
+	    doublecomplex *, doublecomplex *, int *, doublecomplex *,
+	    int *, doublecomplex *, doublecomplex *, int *, ftnlen),
+	    zcopy_(int *, doublecomplex *, int *, doublecomplex *,
+	    int *), zswap_(int *, doublecomplex *, int *,
+	    doublecomplex *, int *);
+    static double absakk, colmax;
+    extern int izamax_(int *, doublecomplex *, int *);
+    static double rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.) + 1.) / 8.;
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	zcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    z__1.r = -1., z__1.i = -0.;
+	    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	kstep = 1;
+	i__1 = k + kw * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + kw *
+		w_dim1]), abs(d__2));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    kw * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		zcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    z__1.r = -1., z__1.i = -0.;
+		    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		i__1 = k - imax;
+		jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
+			 &c__1);
+		i__1 = jmax + (kw - 1) * w_dim1;
+		rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			jmax + (kw - 1) * w_dim1]), abs(d__2));
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    jmax = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (
+			    d__2 = d_imag(&w[jmax + (kw - 1) * w_dim1]), abs(
+			    d__2));
+		    rowmax = max(d__3,d__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (kw - 1) * w_dim1;
+		    if ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			    imax + (kw - 1) * w_dim1]), abs(d__2)) >= alpha *
+			    rowmax) {
+			kp = imax;
+			zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+				w_dim1 + 1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = kk - 1 - kp;
+		zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		if (kp > 1) {
+		    i__1 = kp - 1;
+		    zcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
+			    + 1], &c__1);
+		}
+		if (k < *n) {
+		    i__1 = *n - k;
+		    zswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
+			    + 1) * a_dim1], lda);
+		}
+		i__1 = *n - kk + 1;
+		zswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
+		r1.r = z__1.r, r1.i = z__1.i;
+		i__1 = k - 1;
+		zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    z_div(&z__1, &w[k + kw * w_dim1], &d21);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    z_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
+		    z_div(&z__1, &c_b1, &z__2);
+		    t.r = z__1.r, t.i = z__1.i;
+		    z_div(&z__1, &t, &d21);
+		    d21.r = z__1.r, d21.i = z__1.i;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			z__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
+				.i;
+			z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
+				d21.r * z__2.i + d21.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + k * a_dim1;
+			i__3 = j + kw * w_dim1;
+			z__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
+				.i;
+			z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
+				d21.r * z__2.i + d21.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    ++j;
+	}
+	++j;
+	if (jp != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    zswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
+	}
+	if (j < *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	i__1 = *n - k + 1;
+	zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	i__1 = *n - k + 1;
+	i__2 = k - 1;
+	z__1.r = -1., z__1.i = -0.;
+	zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &w[k
+		+ w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (ftnlen)12);
+	kstep = 1;
+	i__1 = k + k * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + k *
+		w_dim1]), abs(d__2));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    k * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	} else {
+	    if (absakk >= alpha * colmax) {
+		kp = k;
+	    } else {
+		i__1 = imax - k;
+		zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		zcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		i__1 = *n - k + 1;
+		i__2 = k - 1;
+		z__1.r = -1., z__1.i = -0.;
+		zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1],
+			lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) *
+			w_dim1], &c__1, (ftnlen)12);
+		i__1 = imax - k;
+		jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
+			;
+		i__1 = jmax + (k + 1) * w_dim1;
+		rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			jmax + (k + 1) * w_dim1]), abs(d__2));
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    jmax = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+/* Computing MAX */
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (
+			    d__2 = d_imag(&w[jmax + (k + 1) * w_dim1]), abs(
+			    d__2));
+		    rowmax = max(d__3,d__4);
+		}
+		if (absakk >= alpha * colmax * (colmax / rowmax)) {
+		    kp = k;
+		} else /* if(complicated condition) */ {
+		    i__1 = imax + (k + 1) * w_dim1;
+		    if ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			    imax + (k + 1) * w_dim1]), abs(d__2)) >= alpha *
+			    rowmax) {
+			kp = imax;
+			i__1 = *n - k + 1;
+			zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k +
+				k * w_dim1], &c__1);
+		    } else {
+			kp = imax;
+			kstep = 2;
+		    }
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kp != kk) {
+		i__1 = kp + kp * a_dim1;
+		i__2 = kk + kk * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = kp - kk - 1;
+		zcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
+			1) * a_dim1], lda);
+		if (kp < *n) {
+		    i__1 = *n - kp;
+		    zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+			    + kp * a_dim1], &c__1);
+		}
+		if (k > 1) {
+		    i__1 = k - 1;
+		    zswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		}
+		zswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
+		    r1.r = z__1.r, r1.i = z__1.i;
+		    i__1 = *n - k;
+		    zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    z_div(&z__1, &w[k + k * w_dim1], &d21);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
+		    z_div(&z__1, &c_b1, &z__2);
+		    t.r = z__1.r, t.i = z__1.i;
+		    z_div(&z__1, &t, &d21);
+		    d21.r = z__1.r, d21.i = z__1.i;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			i__3 = j + k * w_dim1;
+			z__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
+				.i;
+			z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
+				d21.r * z__2.i + d21.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			z__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
+				.i;
+			z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
+				d21.r * z__2.i + d21.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -kp;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	jj = j;
+	jp = ipiv[j];
+	if (jp < 0) {
+	    jp = -jp;
+	    --j;
+	}
+	--j;
+	if (jp != jj && j >= 1) {
+	    zswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j > 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/zsytrf_rook.c

@@ -0,0 +1,236 @@
+#include "relapack.h"
+#if XSYTRF_ALLOW_MALLOC
+#include <stdlib.h>
+#endif
+
+static void RELAPACK_zsytrf_rook_rec(const char *, const int *, const int *, int *,
+    double *, const int *, int *, double *, const int *, int *);
+
+
+/** ZSYTRF_ROOK computes the factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
+ *
+ * This routine is functionally equivalent to LAPACK's zsytrf_rook.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d6/d6e/zsytrf__rook_8f.html
+ * */
+void RELAPACK_zsytrf_rook(
+    const char *uplo, const int *n,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *lWork, int *info
+) {
+
+    // Required work size
+    const int cleanlWork = *n * (*n / 2);
+    int minlWork = cleanlWork;
+#if XSYTRF_ALLOW_MALLOC
+    minlWork = 1;
+#endif
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (*n < 0)
+        *info = -2;
+    else if (*ldA < MAX(1, *n))
+        *info = -4;
+    else if (*lWork < minlWork && *lWork != -1)
+        *info = -7;
+    else if (*lWork == -1) {
+        // Work size query
+        *Work = cleanlWork;
+        return;
+    }
+
+    // Ensure Work size
+    double *cleanWork = Work;
+#if XSYTRF_ALLOW_MALLOC
+    if (!*info && *lWork < cleanlWork) {
+        cleanWork = malloc(cleanlWork * 2 * sizeof(double));
+        if (!cleanWork)
+            *info = -7;
+    }
+#endif
+
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZSYTRF", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower ? 'L' : 'U';
+
+    // Dummy argument
+    int nout;
+
+    // Recursive kernel
+    RELAPACK_zsytrf_rook_rec(&cleanuplo, n, n, &nout, A, ldA, ipiv, cleanWork, n, info);
+
+#if XSYTRF_ALLOW_MALLOC
+    if (cleanWork != Work)
+        free(cleanWork);
+#endif
+}
+
+
+/** zsytrf_rook's recursive compute kernel */
+static void RELAPACK_zsytrf_rook_rec(
+    const char *uplo, const int *n_full, const int *n, int *n_out,
+    double *A, const int *ldA, int *ipiv,
+    double *Work, const int *ldWork, int *info
+) {
+
+    // top recursion level?
+    const int top = *n_full == *n;
+
+    if (*n <= MAX(CROSSOVER_ZSYTRF_ROOK, 3)) {
+        // Unblocked
+        if (top) {
+            LAPACK(zsytf2)(uplo, n, A, ldA, ipiv, info);
+            *n_out = *n;
+        } else
+            RELAPACK_zsytrf_rook_rec2(uplo, n_full, n, n_out, A, ldA, ipiv, Work, ldWork, info);
+        return;
+    }
+
+    int info1, info2;
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const int    iONE[] = { 1 };
+
+    const int n_rest = *n_full - *n;
+
+    if (*uplo == 'L') {
+        // Splitting (setup)
+        int n1 = ZREC_SPLIT(*n);
+        int n2 = *n - n1;
+
+        // Work_L *
+        double *const Work_L = Work;
+
+        // recursion(A_L)
+        int n1_out;
+        RELAPACK_zsytrf_rook_rec(uplo, n_full, &n1, &n1_out, A, ldA, ipiv, Work_L, ldWork, &info1);
+        n1 = n1_out;
+
+        // Splitting (continued)
+        n2 = *n - n1;
+        const int n_full2   = *n_full - n1;
+
+        // *      *
+        // A_BL   A_BR
+        // A_BL_B A_BR_B
+        double *const A_BL   = A                 + 2 * n1;
+        double *const A_BR   = A + 2 * *ldA * n1 + 2 * n1;
+        double *const A_BL_B = A                 + 2 * *n;
+        double *const A_BR_B = A + 2 * *ldA * n1 + 2 * *n;
+
+        // *        *
+        // Work_BL Work_BR
+        // *       *
+        // (top recursion level: use Work as Work_BR)
+        double *const Work_BL =              Work                    + 2 * n1;
+        double *const Work_BR = top ? Work : Work + 2 * *ldWork * n1 + 2 * n1;
+        const int ldWork_BR = top ? n2 : *ldWork;
+
+        // ipiv_T
+        // ipiv_B
+        int *const ipiv_B = ipiv + n1;
+
+        // A_BR = A_BR - A_BL Work_BL'
+        RELAPACK_zgemmt(uplo, "N", "T", &n2, &n1, MONE, A_BL, ldA, Work_BL, ldWork, ONE, A_BR, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n2, &n1, MONE, A_BL_B, ldA, Work_BL, ldWork, ONE, A_BR_B, ldA);
+
+        // recursion(A_BR)
+        int n2_out;
+        RELAPACK_zsytrf_rook_rec(uplo, &n_full2, &n2, &n2_out, A_BR, ldA, ipiv_B, Work_BR, &ldWork_BR, &info2);
+
+        if (n2_out != n2) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // last column of A_BR
+            double *const A_BR_r = A_BR + 2 * *ldA * n2_out + 2 * n2_out;
+
+            // last row of A_BL
+            double *const A_BL_b = A_BL + 2 * n2_out;
+
+            // last row of Work_BL
+            double *const Work_BL_b = Work_BL + 2 * n2_out;
+
+            // A_BR_r = A_BR_r + A_BL_b Work_BL_b'
+            BLAS(zgemv)("N", &n_restp1, &n1, ONE, A_BL_b, ldA, Work_BL_b, ldWork, ONE, A_BR_r, iONE);
+        }
+        n2 = n2_out;
+
+        // shift pivots
+        int i;
+        for (i = 0; i < n2; i++)
+            if (ipiv_B[i] > 0)
+                ipiv_B[i] += n1;
+            else
+                ipiv_B[i] -= n1;
+
+        *info  = info1 || info2;
+        *n_out = n1 + n2;
+    } else {
+        // Splitting (setup)
+        int n2 = ZREC_SPLIT(*n);
+        int n1 = *n - n2;
+
+        // * Work_R
+        // (top recursion level: use Work as Work_R)
+        double *const Work_R = top ? Work : Work + 2 * *ldWork * n1;
+
+        // recursion(A_R)
+        int n2_out;
+        RELAPACK_zsytrf_rook_rec(uplo, n_full, &n2, &n2_out, A, ldA, ipiv, Work_R, ldWork, &info2);
+        const int n2_diff = n2 - n2_out;
+        n2 = n2_out;
+
+        // Splitting (continued)
+        n1 = *n - n2;
+        const int n_full1 = *n_full - n2;
+
+        // * A_TL_T A_TR_T
+        // * A_TL   A_TR
+        // * *      *
+        double *const A_TL_T = A + 2 * *ldA * n_rest;
+        double *const A_TR_T = A + 2 * *ldA * (n_rest + n1);
+        double *const A_TL   = A + 2 * *ldA * n_rest        + 2 * n_rest;
+        double *const A_TR   = A + 2 * *ldA * (n_rest + n1) + 2 * n_rest;
+
+        // Work_L *
+        // *      Work_TR
+        // *      *
+        // (top recursion level: Work_R was Work)
+        double *const Work_L  = Work;
+        double *const Work_TR = Work + 2 * *ldWork * (top ? n2_diff : n1) + 2 * n_rest;
+        const int ldWork_L = top ? n1 : *ldWork;
+
+        // A_TL = A_TL - A_TR Work_TR'
+        RELAPACK_zgemmt(uplo, "N", "T", &n1, &n2, MONE, A_TR, ldA, Work_TR, ldWork, ONE, A_TL, ldA);
+        BLAS(zgemm)("N", "T", &n_rest, &n1, &n2, MONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, ldA);
+
+        // recursion(A_TL)
+        int n1_out;
+        RELAPACK_zsytrf_rook_rec(uplo, &n_full1, &n1, &n1_out, A, ldA, ipiv, Work_L, &ldWork_L, &info1);
+
+        if (n1_out != n1) {
+            // undo 1 column of updates
+            const int n_restp1 = n_rest + 1;
+
+            // A_TL_T_l = A_TL_T_l + A_TR_T Work_TR_t'
+            BLAS(zgemv)("N", &n_restp1, &n2, ONE, A_TR_T, ldA, Work_TR, ldWork, ONE, A_TL_T, iONE);
+        }
+        n1 = n1_out;
+
+        *info  = info2 || info1;
+        *n_out = n1 + n2;
+    }
+}

relapack/src/zsytrf_rook_rec2.c

@@ -0,0 +1,561 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b1 = {1.,0.};
+static int c__1 = 1;
+
+/** ZSYTRF_ROOK_REC2 computes a partial factorization of a complex symmetric matrix using the bounded Bunch-K aufman ("rook") diagonal pivoting method.
+ *
+ * This routine is a minor modification of LAPACK's zlasyf_rook.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * The blocked BLAS Level 3 updates were removed and moved to the
+ * recursive algorithm.
+ * */
+/* Subroutine */ void RELAPACK_zsytrf_rook_rec2(char *uplo, int *n,
+	int *nb, int *kb, doublecomplex *a, int *lda, int *
+	ipiv, doublecomplex *w, int *ldw, int *info, ftnlen uplo_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
+    double d__1, d__2;
+    doublecomplex z__1, z__2, z__3, z__4;
+
+    /* Builtin functions */
+    double sqrt(double), d_imag(doublecomplex *);
+    void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
+
+    /* Local variables */
+    static int j, k, p;
+    static doublecomplex t, r1, d11, d12, d21, d22;
+    static int ii, jj, kk, kp, kw, jp1, jp2, kkw;
+    static logical done;
+    static int imax, jmax;
+    static double alpha;
+    extern logical lsame_(char *, char *, ftnlen, ftnlen);
+    static double dtemp, sfmin;
+    extern /* Subroutine */ int zscal_(int *, doublecomplex *,
+	    doublecomplex *, int *);
+    static int itemp, kstep;
+    extern /* Subroutine */ int zgemv_(char *, int *, int *,
+	    doublecomplex *, doublecomplex *, int *, doublecomplex *,
+	    int *, doublecomplex *, doublecomplex *, int *, ftnlen),
+	    zcopy_(int *, doublecomplex *, int *, doublecomplex *,
+	    int *), zswap_(int *, doublecomplex *, int *,
+	    doublecomplex *, int *);
+    extern double dlamch_(char *, ftnlen);
+    static double absakk, colmax;
+    extern int izamax_(int *, doublecomplex *, int *);
+    static double rowmax;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    w_dim1 = *ldw;
+    w_offset = 1 + w_dim1;
+    w -= w_offset;
+
+    /* Function Body */
+    *info = 0;
+    alpha = (sqrt(17.) + 1.) / 8.;
+    sfmin = dlamch_("S", (ftnlen)1);
+    if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+	k = *n;
+L10:
+	kw = *nb + k - *n;
+	if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
+	    goto L30;
+	}
+	kstep = 1;
+	p = k;
+	zcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
+	if (k < *n) {
+	    i__1 = *n - k;
+	    z__1.r = -1., z__1.i = -0.;
+	    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1],
+		     lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
+		    w_dim1 + 1], &c__1, (ftnlen)12);
+	}
+	i__1 = k + kw * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + kw *
+		w_dim1]), abs(d__2));
+	if (k > 1) {
+	    i__1 = k - 1;
+	    imax = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
+	    i__1 = imax + kw * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    kw * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L12:
+		zcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
+			w_dim1 + 1], &c__1);
+		i__1 = k - imax;
+		zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
+			1 + (kw - 1) * w_dim1], &c__1);
+		if (k < *n) {
+		    i__1 = *n - k;
+		    z__1.r = -1., z__1.i = -0.;
+		    zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) *
+			    a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
+			    ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
+			    ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = k - imax;
+		    jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) *
+			    w_dim1], &c__1);
+		    i__1 = jmax + (kw - 1) * w_dim1;
+		    rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
+			    w[jmax + (kw - 1) * w_dim1]), abs(d__2));
+		} else {
+		    rowmax = 0.;
+		}
+		if (imax > 1) {
+		    i__1 = imax - 1;
+		    itemp = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
+		    i__1 = itemp + (kw - 1) * w_dim1;
+		    dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			    itemp + (kw - 1) * w_dim1]), abs(d__2));
+		    if (dtemp > rowmax) {
+			rowmax = dtemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (kw - 1) * w_dim1;
+		if (! ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax
+			+ (kw - 1) * w_dim1]), abs(d__2)) < alpha * rowmax)) {
+		    kp = imax;
+		    zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
+			    w_dim1 + 1], &c__1);
+		}
+		if (! done) {
+		    goto L12;
+		}
+	    }
+	    kk = k - kstep + 1;
+	    kkw = *nb + kk - *n;
+	    if (kstep == 2 && p != k) {
+		i__1 = k - p;
+		zcopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
+			a_dim1], lda);
+		zcopy_(&p, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - k + 1;
+		zswap_(&i__1, &a[k + k * a_dim1], lda, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - kk + 1;
+		zswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
+			 ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + k * a_dim1;
+		i__2 = kk + k * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = k - 1 - kp;
+		zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
+			1) * a_dim1], lda);
+		zcopy_(&kp, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
+			c__1);
+		i__1 = *n - kk + 1;
+		zswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1],
+			 lda);
+		i__1 = *n - kk + 1;
+		zswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
+			w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
+			c__1);
+		if (k > 1) {
+		    i__1 = k + k * a_dim1;
+		    if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k +
+			    k * a_dim1]), abs(d__2)) >= sfmin) {
+			z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
+			r1.r = z__1.r, r1.i = z__1.i;
+			i__1 = k - 1;
+			zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
+		    } else /* if(complicated condition) */ {
+			i__1 = k + k * a_dim1;
+			if (a[i__1].r != 0. || a[i__1].i != 0.) {
+			    i__1 = k - 1;
+			    for (ii = 1; ii <= i__1; ++ii) {
+				i__2 = ii + k * a_dim1;
+				z_div(&z__1, &a[ii + k * a_dim1], &a[k + k *
+					a_dim1]);
+				a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L14: */
+			    }
+			}
+		    }
+		}
+	    } else {
+		if (k > 2) {
+		    i__1 = k - 1 + kw * w_dim1;
+		    d12.r = w[i__1].r, d12.i = w[i__1].i;
+		    z_div(&z__1, &w[k + kw * w_dim1], &d12);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    z_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d12);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
+		    z_div(&z__1, &c_b1, &z__2);
+		    t.r = z__1.r, t.i = z__1.i;
+		    i__1 = k - 2;
+		    for (j = 1; j <= i__1; ++j) {
+			i__2 = j + (k - 1) * a_dim1;
+			i__3 = j + (kw - 1) * w_dim1;
+			z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + kw * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z_div(&z__2, &z__3, &d12);
+			z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
+				z__2.i + t.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + k * a_dim1;
+			i__3 = j + kw * w_dim1;
+			z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + (kw - 1) * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z_div(&z__2, &z__3, &d12);
+			z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
+				z__2.i + t.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L20: */
+		    }
+		}
+		i__1 = k - 1 + (k - 1) * a_dim1;
+		i__2 = k - 1 + (kw - 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k - 1 + k * a_dim1;
+		i__2 = k - 1 + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + k * a_dim1;
+		i__2 = k + kw * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k - 1] = -kp;
+	}
+	k -= kstep;
+	goto L10;
+L30:
+	j = k + 1;
+L60:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    ++j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	++j;
+	if (jp2 != jj && j <= *n) {
+	    i__1 = *n - j + 1;
+	    zswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	jj = j - 1;
+	if (jp1 != jj && kstep == 2) {
+	    i__1 = *n - j + 1;
+	    zswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
+		    ;
+	}
+	if (j <= *n) {
+	    goto L60;
+	}
+	*kb = *n - k;
+    } else {
+	k = 1;
+L70:
+	if ((k >= *nb && *nb < *n) || k > *n) {
+	    goto L90;
+	}
+	kstep = 1;
+	p = k;
+	i__1 = *n - k + 1;
+	zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
+	if (k > 1) {
+	    i__1 = *n - k + 1;
+	    i__2 = k - 1;
+	    z__1.r = -1., z__1.i = -0.;
+	    zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &
+		    w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (
+		    ftnlen)12);
+	}
+	i__1 = k + k * w_dim1;
+	absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + k *
+		w_dim1]), abs(d__2));
+	if (k < *n) {
+	    i__1 = *n - k;
+	    imax = k + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
+	    i__1 = imax + k * w_dim1;
+	    colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
+		    k * w_dim1]), abs(d__2));
+	} else {
+	    colmax = 0.;
+	}
+	if (max(absakk,colmax) == 0.) {
+	    if (*info == 0) {
+		*info = k;
+	    }
+	    kp = k;
+	    i__1 = *n - k + 1;
+	    zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+		    c__1);
+	} else {
+	    if (! (absakk < alpha * colmax)) {
+		kp = k;
+	    } else {
+		done = FALSE_;
+L72:
+		i__1 = imax - k;
+		zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
+			w_dim1], &c__1);
+		i__1 = *n - imax + 1;
+		zcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
+			1) * w_dim1], &c__1);
+		if (k > 1) {
+		    i__1 = *n - k + 1;
+		    i__2 = k - 1;
+		    z__1.r = -1., z__1.i = -0.;
+		    zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1]
+			    , lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k +
+			    1) * w_dim1], &c__1, (ftnlen)12);
+		}
+		if (imax != k) {
+		    i__1 = imax - k;
+		    jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &
+			    c__1);
+		    i__1 = jmax + (k + 1) * w_dim1;
+		    rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
+			    w[jmax + (k + 1) * w_dim1]), abs(d__2));
+		} else {
+		    rowmax = 0.;
+		}
+		if (imax < *n) {
+		    i__1 = *n - imax;
+		    itemp = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) *
+			    w_dim1], &c__1);
+		    i__1 = itemp + (k + 1) * w_dim1;
+		    dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
+			    itemp + (k + 1) * w_dim1]), abs(d__2));
+		    if (dtemp > rowmax) {
+			rowmax = dtemp;
+			jmax = itemp;
+		    }
+		}
+		i__1 = imax + (k + 1) * w_dim1;
+		if (! ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax
+			+ (k + 1) * w_dim1]), abs(d__2)) < alpha * rowmax)) {
+		    kp = imax;
+		    i__1 = *n - k + 1;
+		    zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		    done = TRUE_;
+		} else if (p == jmax || rowmax <= colmax) {
+		    kp = imax;
+		    kstep = 2;
+		    done = TRUE_;
+		} else {
+		    p = imax;
+		    colmax = rowmax;
+		    imax = jmax;
+		    i__1 = *n - k + 1;
+		    zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
+			    w_dim1], &c__1);
+		}
+		if (! done) {
+		    goto L72;
+		}
+	    }
+	    kk = k + kstep - 1;
+	    if (kstep == 2 && p != k) {
+		i__1 = p - k;
+		zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &a[p + k * a_dim1],
+			lda);
+		i__1 = *n - p + 1;
+		zcopy_(&i__1, &a[p + k * a_dim1], &c__1, &a[p + p * a_dim1], &
+			c__1);
+		zswap_(&k, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
+		zswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
+	    }
+	    if (kp != kk) {
+		i__1 = kp + k * a_dim1;
+		i__2 = kk + k * a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = kp - k - 1;
+		zcopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1)
+			* a_dim1], lda);
+		i__1 = *n - kp + 1;
+		zcopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp *
+			a_dim1], &c__1);
+		zswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
+		zswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
+	    }
+	    if (kstep == 1) {
+		i__1 = *n - k + 1;
+		zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
+			c__1);
+		if (k < *n) {
+		    i__1 = k + k * a_dim1;
+		    if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k +
+			    k * a_dim1]), abs(d__2)) >= sfmin) {
+			z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
+			r1.r = z__1.r, r1.i = z__1.i;
+			i__1 = *n - k;
+			zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
+		    } else /* if(complicated condition) */ {
+			i__1 = k + k * a_dim1;
+			if (a[i__1].r != 0. || a[i__1].i != 0.) {
+			    i__1 = *n;
+			    for (ii = k + 1; ii <= i__1; ++ii) {
+				i__2 = ii + k * a_dim1;
+				z_div(&z__1, &a[ii + k * a_dim1], &a[k + k *
+					a_dim1]);
+				a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L74: */
+			    }
+			}
+		    }
+		}
+	    } else {
+		if (k < *n - 1) {
+		    i__1 = k + 1 + k * w_dim1;
+		    d21.r = w[i__1].r, d21.i = w[i__1].i;
+		    z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
+		    d11.r = z__1.r, d11.i = z__1.i;
+		    z_div(&z__1, &w[k + k * w_dim1], &d21);
+		    d22.r = z__1.r, d22.i = z__1.i;
+		    z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
+			    d22.i + d11.i * d22.r;
+		    z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
+		    z_div(&z__1, &c_b1, &z__2);
+		    t.r = z__1.r, t.i = z__1.i;
+		    i__1 = *n;
+		    for (j = k + 2; j <= i__1; ++j) {
+			i__2 = j + k * a_dim1;
+			i__3 = j + k * w_dim1;
+			z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
+				z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
+				.r;
+			i__4 = j + (k + 1) * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z_div(&z__2, &z__3, &d21);
+			z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
+				z__2.i + t.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+			i__2 = j + (k + 1) * a_dim1;
+			i__3 = j + (k + 1) * w_dim1;
+			z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
+				z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
+				.r;
+			i__4 = j + k * w_dim1;
+			z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
+				.i;
+			z_div(&z__2, &z__3, &d21);
+			z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
+				z__2.i + t.i * z__2.r;
+			a[i__2].r = z__1.r, a[i__2].i = z__1.i;
+/* L80: */
+		    }
+		}
+		i__1 = k + k * a_dim1;
+		i__2 = k + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + k * a_dim1;
+		i__2 = k + 1 + k * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+		i__1 = k + 1 + (k + 1) * a_dim1;
+		i__2 = k + 1 + (k + 1) * w_dim1;
+		a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
+	    }
+	}
+	if (kstep == 1) {
+	    ipiv[k] = kp;
+	} else {
+	    ipiv[k] = -p;
+	    ipiv[k + 1] = -kp;
+	}
+	k += kstep;
+	goto L70;
+L90:
+	j = k - 1;
+L120:
+	kstep = 1;
+	jp1 = 1;
+	jj = j;
+	jp2 = ipiv[j];
+	if (jp2 < 0) {
+	    jp2 = -jp2;
+	    --j;
+	    jp1 = -ipiv[j];
+	    kstep = 2;
+	}
+	--j;
+	if (jp2 != jj && j >= 1) {
+	    zswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	jj = j + 1;
+	if (jp1 != jj && kstep == 2) {
+	    zswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda);
+	}
+	if (j >= 1) {
+	    goto L120;
+	}
+	*kb = k - 1;
+    }
+    return;
+}

relapack/src/ztgsyl.c

@@ -0,0 +1,268 @@
+#include "relapack.h"
+#include <math.h>
+
+static void RELAPACK_ztgsyl_rec(const char *, const int *, const int *,
+    const int *, const double *, const int *, const double *, const int *,
+    double *, const int *, const double *, const int *, const double *,
+    const int *, double *, const int *, double *, double *, double *, int *);
+
+
+/** ZTGSYL solves the generalized Sylvester equation.
+ *
+ * This routine is functionally equivalent to LAPACK's ztgsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/db/d68/ztgsyl_8f.html
+ * */
+void RELAPACK_ztgsyl(
+    const char *trans, const int *ijob, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dif,
+    double *Work, const int *lWork, int *iWork, int *info
+) {
+
+    // Parse arguments
+    const int notran = LAPACK(lsame)(trans, "N");
+    const int tran = LAPACK(lsame)(trans, "C");
+
+    // Compute work buffer size
+    int lwmin = 1;
+    if (notran && (*ijob == 1 || *ijob == 2))
+        lwmin = MAX(1, 2 * *m * *n);
+    *info = 0;
+
+    // Check arguments
+    if (!tran && !notran)
+        *info = -1;
+    else if (notran && (*ijob < 0 || *ijob > 4))
+        *info = -2;
+    else if (*m <= 0)
+        *info = -3;
+    else if (*n <= 0)
+        *info = -4;
+    else if (*ldA < MAX(1, *m))
+        *info = -6;
+    else if (*ldB < MAX(1, *n))
+        *info = -8;
+    else if (*ldC < MAX(1, *m))
+        *info = -10;
+    else if (*ldD < MAX(1, *m))
+        *info = -12;
+    else if (*ldE < MAX(1, *n))
+        *info = -14;
+    else if (*ldF < MAX(1, *m))
+        *info = -16;
+    else if (*lWork < lwmin && *lWork != -1)
+        *info = -20;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZTGSYL", &minfo);
+        return;
+    }
+
+    if (*lWork == -1) {
+        // Work size query
+        *Work = lwmin;
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantrans = notran ? 'N' : 'C';
+
+    // Constant
+    const double ZERO[] = { 0., 0. };
+
+    int isolve = 1;
+    int ifunc  = 0;
+    if (notran) {
+        if (*ijob >= 3) {
+            ifunc = *ijob - 2;
+            LAPACK(zlaset)("F", m, n, ZERO, ZERO, C, ldC);
+            LAPACK(zlaset)("F", m, n, ZERO, ZERO, F, ldF);
+        } else if (*ijob >= 1)
+            isolve = 2;
+    }
+
+    double scale2;
+    int iround;
+    for (iround = 1; iround <= isolve; iround++) {
+        *scale = 1;
+        double dscale = 0;
+        double dsum   = 1;
+        RELAPACK_ztgsyl_rec(&cleantrans, &ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, &dsum, &dscale, info);
+        if (dscale != 0) {
+            if (*ijob == 1 || *ijob == 3)
+                *dif = sqrt(2 * *m * *n) / (dscale * sqrt(dsum));
+            else
+                *dif = sqrt(*m * *n) / (dscale * sqrt(dsum));
+        }
+        if (isolve == 2) {
+            if (iround == 1) {
+                if (notran)
+                    ifunc = *ijob;
+                scale2 = *scale;
+                LAPACK(zlacpy)("F", m, n, C, ldC, Work, m);
+                LAPACK(zlacpy)("F", m, n, F, ldF, Work + 2 * *m * *n, m);
+                LAPACK(zlaset)("F", m, n, ZERO, ZERO, C, ldC);
+                LAPACK(zlaset)("F", m, n, ZERO, ZERO, F, ldF);
+            } else {
+                LAPACK(zlacpy)("F", m, n, Work, m, C, ldC);
+                LAPACK(zlacpy)("F", m, n, Work + 2 * *m * *n, m, F, ldF);
+                *scale = scale2;
+            }
+        }
+    }
+}
+
+
+/** ztgsyl's recursive vompute kernel */
+static void RELAPACK_ztgsyl_rec(
+    const char *trans, const int *ifunc, const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC,
+    const double *D, const int *ldD, const double *E, const int *ldE,
+    double *F, const int *ldF,
+    double *scale, double *dsum, double *dscale,
+    int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_ZTGSYL, 1) && *n <= MAX(CROSSOVER_ZTGSYL, 1)) {
+        // Unblocked
+        LAPACK(ztgsy2)(trans, ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dsum, dscale, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const int    iONE[] = { 1 };
+
+    // Outputs
+    double scale1[] = { 1., 0. };
+    double scale2[] = { 1., 0. };
+    int    info1[]  = { 0 };
+    int    info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        const int m1 = ZREC_SPLIT(*m);
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const double *const A_TL = A;
+        const double *const A_TR = A + 2 * *ldA * m1;
+        const double *const A_BR = A + 2 * *ldA * m1 + 2 * m1;
+
+        // C_T
+        // C_B
+        double *const C_T = C;
+        double *const C_B = C + 2 * m1;
+
+        // D_TL D_TR
+        // 0    D_BR
+        const double *const D_TL = D;
+        const double *const D_TR = D + 2 * *ldD * m1;
+        const double *const D_BR = D + 2 * *ldD * m1 + 2 * m1;
+
+        // F_T
+        // F_B
+        double *const F_T = F;
+        double *const F_B = F + 2 * m1;
+
+        if (*trans == 'N') {
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_ztgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale1, dsum, dscale, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(zgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // F_T = F_T - D_TR * C_B
+            BLAS(zgemm)("N", "N", &m1, n, &m2, MONE, D_TR, ldD, C_B, ldC, scale1, F_T, ldF);
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_ztgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, &m2, n, F_B, ldF, info);
+            }
+        } else {
+            // recursion(A_TL, B, C_T, D_TL, E, F_T)
+            RELAPACK_ztgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale1, dsum, dscale, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale1, &m2, n, F_B, ldF, info);
+            // C_B = C_B - A_TR^H * C_T
+            BLAS(zgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // C_B = C_B - D_TR^H * F_T
+            BLAS(zgemm)("C", "N", &m2, n, &m1, MONE, D_TR, ldD, F_T, ldC, ONE, C_B, ldC);
+            // recursion(A_BR, B, C_B, D_BR, E, F_B)
+            RELAPACK_ztgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_T, ldC, info);
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, &m1, n, F_T, ldF, info);
+            }
+        }
+    } else {
+        // Splitting
+        const int n1 = ZREC_SPLIT(*n);
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const double *const B_TL = B;
+        const double *const B_TR = B + 2 * *ldB * n1;
+        const double *const B_BR = B + 2 * *ldB * n1 + 2 * n1;
+
+        // C_L C_R
+        double *const C_L = C;
+        double *const C_R = C + 2 * *ldC * n1;
+
+        // E_TL E_TR
+        // 0    E_BR
+        const double *const E_TL = E;
+        const double *const E_TR = E + 2 * *ldE * n1;
+        const double *const E_BR = E + 2 * *ldE * n1 + 2 * n1;
+
+        // F_L F_R
+        double *const F_L = F;
+        double *const F_R = F + 2 * *ldF * n1;
+
+        if (*trans == 'N') {
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_ztgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale1, dsum, dscale, info1);
+            // C_R = C_R + F_L * B_TR
+            BLAS(zgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, B_TR, ldB, scale1, C_R, ldC);
+            // F_R = F_R + F_L * E_TR
+            BLAS(zgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, E_TR, ldE, scale1, F_R, ldF);
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_ztgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, m, &n1, F_L, ldF, info);
+            }
+        } else {
+            // recursion(A, B_BR, C_R, D, E_BR, F_R)
+            RELAPACK_ztgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale1, dsum, dscale, info1);
+            // apply scale
+            if (scale1[0] != 1)
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale1, m, &n1, C_L, ldC, info);
+            // F_L = F_L + C_R * B_TR
+            BLAS(zgemm)("N", "C", m, &n1, &n2, ONE, C_R, ldC, B_TR, ldB, scale1, F_L, ldF);
+            // F_L = F_L + F_R * E_TR
+            BLAS(zgemm)("N", "C", m, &n1, &n2, ONE, F_R, ldF, E_TR, ldB, ONE, F_L, ldF);
+            // recursion(A, B_TL, C_L, D, E_TL, F_L)
+            RELAPACK_ztgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale2, dsum, dscale, info2);
+            // apply scale
+            if (scale2[0] != 1) {
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, m, &n2, F_R, ldF, info);
+            }
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/ztrsyl.c

@@ -0,0 +1,163 @@
+#include "relapack.h"
+
+static void RELAPACK_ztrsyl_rec(const char *, const char *, const int *,
+    const int *, const int *, const double *, const int *, const double *,
+    const int *, double *, const int *, double *, int *);
+
+
+/** ZTRSYL solves the complex Sylvester matrix equation.
+ *
+ * This routine is functionally equivalent to LAPACK's ztrsyl.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d1/d36/ztrsyl_8f.html
+ * */
+void RELAPACK_ztrsyl(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+
+    // Check arguments
+    const int notransA = LAPACK(lsame)(tranA, "N");
+    const int ctransA = LAPACK(lsame)(tranA, "C");
+    const int notransB = LAPACK(lsame)(tranB, "N");
+    const int ctransB = LAPACK(lsame)(tranB, "C");
+    *info = 0;
+    if (!ctransA && !notransA)
+        *info = -1;
+    else if (!ctransB && !notransB)
+        *info = -2;
+    else if (*isgn != 1 && *isgn != -1)
+        *info = -3;
+    else if (*m < 0)
+        *info = -4;
+    else if (*n < 0)
+        *info = -5;
+    else if (*ldA < MAX(1, *m))
+        *info = -7;
+    else if (*ldB < MAX(1, *n))
+        *info = -9;
+    else if (*ldC < MAX(1, *m))
+        *info = -11;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZTRSYL", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleantranA = notransA ? 'N' : 'C';
+    const char cleantranB = notransB ? 'N' : 'C';
+
+    // Recursive kernel
+    RELAPACK_ztrsyl_rec(&cleantranA, &cleantranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+}
+
+
+/** ztrsyl's recursive compute kernel */
+static void RELAPACK_ztrsyl_rec(
+    const char *tranA, const char *tranB, const int *isgn,
+    const int *m, const int *n,
+    const double *A, const int *ldA, const double *B, const int *ldB,
+    double *C, const int *ldC, double *scale,
+    int *info
+) {
+
+    if (*m <= MAX(CROSSOVER_ZTRSYL, 1) && *n <= MAX(CROSSOVER_ZTRSYL, 1)) {
+        // Unblocked
+        RELAPACK_ztrsyl_rec2(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1., 0. };
+    const double MONE[] = { -1., 0. };
+    const double MSGN[] = { -*isgn, 0. };
+    const int    iONE[] = { 1 };
+
+    // Outputs
+    double scale1[] = { 1., 0. };
+    double scale2[] = { 1., 0. };
+    int    info1[]  = { 0 };
+    int    info2[]  = { 0 };
+
+    if (*m > *n) {
+        // Splitting
+        const int m1 = ZREC_SPLIT(*m);
+        const int m2 = *m - m1;
+
+        // A_TL A_TR
+        // 0    A_BR
+        const double *const A_TL = A;
+        const double *const A_TR = A + 2 * *ldA * m1;
+        const double *const A_BR = A + 2 * *ldA * m1 + 2 * m1;
+
+        // C_T
+        // C_B
+        double *const C_T = C;
+        double *const C_B = C + 2 * m1;
+
+        if (*tranA == 'N') {
+            // recusion(A_BR, B, C_B)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale1, info1);
+            // C_T = C_T - A_TR * C_B
+            BLAS(zgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
+            // recusion(A_TL, B, C_T)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
+        } else {
+            // recusion(A_TL, B, C_T)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale1, info1);
+            // C_B = C_B - A_TR' * C_T
+            BLAS(zgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
+            // recusion(A_BR, B, C_B)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_B, ldC, info);
+        }
+    } else {
+        // Splitting
+        const int n1 = ZREC_SPLIT(*n);
+        const int n2 = *n - n1;
+
+        // B_TL B_TR
+        // 0    B_BR
+        const double *const B_TL = B;
+        const double *const B_TR = B + 2 * *ldB * n1;
+        const double *const B_BR = B + 2 * *ldB * n1 + 2 * n1;
+
+        // C_L C_R
+        double *const C_L = C;
+        double *const C_R = C + 2 * *ldC * n1;
+
+        if (*tranB == 'N') {
+            // recusion(A, B_TL, C_L)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale1, info1);
+            // C_R = C_R -/+ C_L * B_TR
+            BLAS(zgemm)("N", "N", m, &n2, &n1, MSGN, C_L, ldC, B_TR, ldB, scale1, C_R, ldC);
+            // recusion(A, B_BR, C_R)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
+        } else {
+            // recusion(A, B_BR, C_R)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale1, info1);
+            // C_L = C_L -/+ C_R * B_TR'
+            BLAS(zgemm)("N", "C", m, &n1, &n2, MSGN, C_R, ldC, B_TR, ldB, scale1, C_L, ldC);
+            // recusion(A, B_TL, C_L)
+            RELAPACK_ztrsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale2, info2);
+            // apply scale
+            if (scale2[0] != 1)
+                LAPACK(zlascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
+        }
+    }
+
+    *scale = scale1[0] * scale2[0];
+    *info  = info1[0] || info2[0];
+}

relapack/src/ztrsyl_rec2.c

@@ -0,0 +1,394 @@
+/*  -- translated by f2c (version 20100827).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "../config.h"
+#include "f2c.h"
+
+#if BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES
+doublecomplex zdotu_fun(int *n, doublecomplex *x, int *incx, doublecomplex *y, int *incy) {
+    extern void zdotu_(doublecomplex *, int *, doublecomplex *, int *, doublecomplex *, int *);
+    doublecomplex result;
+    zdotu_(&result, n, x, incx, y, incy);
+    return result;
+}
+#define zdotu_ zdotu_fun
+
+doublecomplex zdotc_fun(int *n, doublecomplex *x, int *incx, doublecomplex *y, int *incy) {
+    extern void zdotc_(doublecomplex *, int *, doublecomplex *, int *, doublecomplex *, int *);
+    doublecomplex result;
+    zdotc_(&result, n, x, incx, y, incy);
+    return result;
+}
+#define zdotc_ zdotc_fun
+#endif
+
+#if LAPACK_BLAS_COMPLEX_FUNCTIONS_AS_ROUTINES
+doublecomplex zladiv_fun(doublecomplex *a, doublecomplex *b) {
+    extern void zladiv_(doublecomplex *, doublecomplex *, doublecomplex *);
+    doublecomplex result;
+    zladiv_(&result, a, b);
+    return result;
+}
+#define zladiv_ zladiv_fun
+#endif
+
+/* Table of constant values */
+
+static int c__1 = 1;
+
+/** RELAPACK_ZTRSYL_REC2 solves the complex Sylvester matrix equation (unblocked algorithm)
+ *
+ * This routine is an exact copy of LAPACK's ztrsyl.
+ * It serves as an unblocked kernel in the recursive algorithms.
+ * */
+/* Subroutine */ void RELAPACK_ztrsyl_rec2(char *trana, char *tranb, int
+	*isgn, int *m, int *n, doublecomplex *a, int *lda,
+	doublecomplex *b, int *ldb, doublecomplex *c__, int *ldc,
+	double *scale, int *info, ftnlen trana_len, ftnlen tranb_len)
+{
+    /* System generated locals */
+    int a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
+	    i__3, i__4;
+    double d__1, d__2;
+    doublecomplex z__1, z__2, z__3, z__4;
+
+    /* Builtin functions */
+    double d_imag(doublecomplex *);
+    void d_cnjg(doublecomplex *, doublecomplex *);
+
+    /* Local variables */
+    static int j, k, l;
+    static doublecomplex a11;
+    static double db;
+    static doublecomplex x11;
+    static double da11;
+    static doublecomplex vec;
+    static double dum[1], eps, sgn, smin;
+    static doublecomplex suml, sumr;
+    extern int lsame_(char *, char *, ftnlen, ftnlen);
+    /* Double Complex */ doublecomplex zdotc_(int *,
+	    doublecomplex *, int *, doublecomplex *, int *), zdotu_(
+	    int *, doublecomplex *, int *,
+	    doublecomplex *, int *);
+    extern /* Subroutine */ int dlabad_(double *, double *);
+    extern double dlamch_(char *, ftnlen);
+    static double scaloc;
+    extern /* Subroutine */ int xerbla_(char *, int *, ftnlen);
+    extern double zlange_(char *, int *, int *, doublecomplex *,
+	    int *, double *, ftnlen);
+    static double bignum;
+    extern /* Subroutine */ int zdscal_(int *, double *,
+	    doublecomplex *, int *);
+    /* Double Complex */ doublecomplex zladiv_(doublecomplex *,
+	     doublecomplex *);
+    static int notrna, notrnb;
+    static double smlnum;
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1;
+    b -= b_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1;
+    c__ -= c_offset;
+
+    /* Function Body */
+    notrna = lsame_(trana, "N", (ftnlen)1, (ftnlen)1);
+    notrnb = lsame_(tranb, "N", (ftnlen)1, (ftnlen)1);
+    *info = 0;
+    if (! notrna && ! lsame_(trana, "C", (ftnlen)1, (ftnlen)1)) {
+	*info = -1;
+    } else if (! notrnb && ! lsame_(tranb, "C", (ftnlen)1, (ftnlen)1)) {
+	*info = -2;
+    } else if (*isgn != 1 && *isgn != -1) {
+	*info = -3;
+    } else if (*m < 0) {
+	*info = -4;
+    } else if (*n < 0) {
+	*info = -5;
+    } else if (*lda < max(1,*m)) {
+	*info = -7;
+    } else if (*ldb < max(1,*n)) {
+	*info = -9;
+    } else if (*ldc < max(1,*m)) {
+	*info = -11;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("ZTRSY2", &i__1, (ftnlen)6);
+	return;
+    }
+    *scale = 1.;
+    if (*m == 0 || *n == 0) {
+	return;
+    }
+    eps = dlamch_("P", (ftnlen)1);
+    smlnum = dlamch_("S", (ftnlen)1);
+    bignum = 1. / smlnum;
+    dlabad_(&smlnum, &bignum);
+    smlnum = smlnum * (double) (*m * *n) / eps;
+    bignum = 1. / smlnum;
+/* Computing MAX */
+    d__1 = smlnum, d__2 = eps * zlange_("M", m, m, &a[a_offset], lda, dum, (
+	    ftnlen)1), d__1 = max(d__1,d__2), d__2 = eps * zlange_("M", n, n,
+	    &b[b_offset], ldb, dum, (ftnlen)1);
+    smin = max(d__1,d__2);
+    sgn = (double) (*isgn);
+    if (notrna && notrnb) {
+	i__1 = *n;
+	for (l = 1; l <= i__1; ++l) {
+	    for (k = *m; k >= 1; --k) {
+		i__2 = *m - k;
+/* Computing MIN */
+		i__3 = k + 1;
+/* Computing MIN */
+		i__4 = k + 1;
+		z__1 = zdotu_(&i__2, &a[k + min(i__3,*m) * a_dim1], lda, &c__[
+			min(i__4,*m) + l * c_dim1], &c__1);
+		suml.r = z__1.r, suml.i = z__1.i;
+		i__2 = l - 1;
+		z__1 = zdotu_(&i__2, &c__[k + c_dim1], ldc, &b[l * b_dim1 + 1]
+			, &c__1);
+		sumr.r = z__1.r, sumr.i = z__1.i;
+		i__2 = k + l * c_dim1;
+		z__3.r = sgn * sumr.r, z__3.i = sgn * sumr.i;
+		z__2.r = suml.r + z__3.r, z__2.i = suml.i + z__3.i;
+		z__1.r = c__[i__2].r - z__2.r, z__1.i = c__[i__2].i - z__2.i;
+		vec.r = z__1.r, vec.i = z__1.i;
+		scaloc = 1.;
+		i__2 = k + k * a_dim1;
+		i__3 = l + l * b_dim1;
+		z__2.r = sgn * b[i__3].r, z__2.i = sgn * b[i__3].i;
+		z__1.r = a[i__2].r + z__2.r, z__1.i = a[i__2].i + z__2.i;
+		a11.r = z__1.r, a11.i = z__1.i;
+		da11 = (d__1 = a11.r, abs(d__1)) + (d__2 = d_imag(&a11), abs(
+			d__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (d__1 = vec.r, abs(d__1)) + (d__2 = d_imag(&vec), abs(
+			d__2));
+		if (da11 < 1. && db > 1.) {
+		    if (db > bignum * da11) {
+			scaloc = 1. / db;
+		    }
+		}
+		z__3.r = scaloc, z__3.i = 0.;
+		z__2.r = vec.r * z__3.r - vec.i * z__3.i, z__2.i = vec.r *
+			z__3.i + vec.i * z__3.r;
+		z__1 = zladiv_(&z__2, &a11);
+		x11.r = z__1.r, x11.i = z__1.i;
+		if (scaloc != 1.) {
+		    i__2 = *n;
+		    for (j = 1; j <= i__2; ++j) {
+			zdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L10: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__2 = k + l * c_dim1;
+		c__[i__2].r = x11.r, c__[i__2].i = x11.i;
+/* L20: */
+	    }
+/* L30: */
+	}
+    } else if (! notrna && notrnb) {
+	i__1 = *n;
+	for (l = 1; l <= i__1; ++l) {
+	    i__2 = *m;
+	    for (k = 1; k <= i__2; ++k) {
+		i__3 = k - 1;
+		z__1 = zdotc_(&i__3, &a[k * a_dim1 + 1], &c__1, &c__[l *
+			c_dim1 + 1], &c__1);
+		suml.r = z__1.r, suml.i = z__1.i;
+		i__3 = l - 1;
+		z__1 = zdotu_(&i__3, &c__[k + c_dim1], ldc, &b[l * b_dim1 + 1]
+			, &c__1);
+		sumr.r = z__1.r, sumr.i = z__1.i;
+		i__3 = k + l * c_dim1;
+		z__3.r = sgn * sumr.r, z__3.i = sgn * sumr.i;
+		z__2.r = suml.r + z__3.r, z__2.i = suml.i + z__3.i;
+		z__1.r = c__[i__3].r - z__2.r, z__1.i = c__[i__3].i - z__2.i;
+		vec.r = z__1.r, vec.i = z__1.i;
+		scaloc = 1.;
+		d_cnjg(&z__2, &a[k + k * a_dim1]);
+		i__3 = l + l * b_dim1;
+		z__3.r = sgn * b[i__3].r, z__3.i = sgn * b[i__3].i;
+		z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+		a11.r = z__1.r, a11.i = z__1.i;
+		da11 = (d__1 = a11.r, abs(d__1)) + (d__2 = d_imag(&a11), abs(
+			d__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (d__1 = vec.r, abs(d__1)) + (d__2 = d_imag(&vec), abs(
+			d__2));
+		if (da11 < 1. && db > 1.) {
+		    if (db > bignum * da11) {
+			scaloc = 1. / db;
+		    }
+		}
+		z__3.r = scaloc, z__3.i = 0.;
+		z__2.r = vec.r * z__3.r - vec.i * z__3.i, z__2.i = vec.r *
+			z__3.i + vec.i * z__3.r;
+		z__1 = zladiv_(&z__2, &a11);
+		x11.r = z__1.r, x11.i = z__1.i;
+		if (scaloc != 1.) {
+		    i__3 = *n;
+		    for (j = 1; j <= i__3; ++j) {
+			zdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L40: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__3 = k + l * c_dim1;
+		c__[i__3].r = x11.r, c__[i__3].i = x11.i;
+/* L50: */
+	    }
+/* L60: */
+	}
+    } else if (! notrna && ! notrnb) {
+	for (l = *n; l >= 1; --l) {
+	    i__1 = *m;
+	    for (k = 1; k <= i__1; ++k) {
+		i__2 = k - 1;
+		z__1 = zdotc_(&i__2, &a[k * a_dim1 + 1], &c__1, &c__[l *
+			c_dim1 + 1], &c__1);
+		suml.r = z__1.r, suml.i = z__1.i;
+		i__2 = *n - l;
+/* Computing MIN */
+		i__3 = l + 1;
+/* Computing MIN */
+		i__4 = l + 1;
+		z__1 = zdotc_(&i__2, &c__[k + min(i__3,*n) * c_dim1], ldc, &b[
+			l + min(i__4,*n) * b_dim1], ldb);
+		sumr.r = z__1.r, sumr.i = z__1.i;
+		i__2 = k + l * c_dim1;
+		d_cnjg(&z__4, &sumr);
+		z__3.r = sgn * z__4.r, z__3.i = sgn * z__4.i;
+		z__2.r = suml.r + z__3.r, z__2.i = suml.i + z__3.i;
+		z__1.r = c__[i__2].r - z__2.r, z__1.i = c__[i__2].i - z__2.i;
+		vec.r = z__1.r, vec.i = z__1.i;
+		scaloc = 1.;
+		i__2 = k + k * a_dim1;
+		i__3 = l + l * b_dim1;
+		z__3.r = sgn * b[i__3].r, z__3.i = sgn * b[i__3].i;
+		z__2.r = a[i__2].r + z__3.r, z__2.i = a[i__2].i + z__3.i;
+		d_cnjg(&z__1, &z__2);
+		a11.r = z__1.r, a11.i = z__1.i;
+		da11 = (d__1 = a11.r, abs(d__1)) + (d__2 = d_imag(&a11), abs(
+			d__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (d__1 = vec.r, abs(d__1)) + (d__2 = d_imag(&vec), abs(
+			d__2));
+		if (da11 < 1. && db > 1.) {
+		    if (db > bignum * da11) {
+			scaloc = 1. / db;
+		    }
+		}
+		z__3.r = scaloc, z__3.i = 0.;
+		z__2.r = vec.r * z__3.r - vec.i * z__3.i, z__2.i = vec.r *
+			z__3.i + vec.i * z__3.r;
+		z__1 = zladiv_(&z__2, &a11);
+		x11.r = z__1.r, x11.i = z__1.i;
+		if (scaloc != 1.) {
+		    i__2 = *n;
+		    for (j = 1; j <= i__2; ++j) {
+			zdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L70: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__2 = k + l * c_dim1;
+		c__[i__2].r = x11.r, c__[i__2].i = x11.i;
+/* L80: */
+	    }
+/* L90: */
+	}
+    } else if (notrna && ! notrnb) {
+	for (l = *n; l >= 1; --l) {
+	    for (k = *m; k >= 1; --k) {
+		i__1 = *m - k;
+/* Computing MIN */
+		i__2 = k + 1;
+/* Computing MIN */
+		i__3 = k + 1;
+		z__1 = zdotu_(&i__1, &a[k + min(i__2,*m) * a_dim1], lda, &c__[
+			min(i__3,*m) + l * c_dim1], &c__1);
+		suml.r = z__1.r, suml.i = z__1.i;
+		i__1 = *n - l;
+/* Computing MIN */
+		i__2 = l + 1;
+/* Computing MIN */
+		i__3 = l + 1;
+		z__1 = zdotc_(&i__1, &c__[k + min(i__2,*n) * c_dim1], ldc, &b[
+			l + min(i__3,*n) * b_dim1], ldb);
+		sumr.r = z__1.r, sumr.i = z__1.i;
+		i__1 = k + l * c_dim1;
+		d_cnjg(&z__4, &sumr);
+		z__3.r = sgn * z__4.r, z__3.i = sgn * z__4.i;
+		z__2.r = suml.r + z__3.r, z__2.i = suml.i + z__3.i;
+		z__1.r = c__[i__1].r - z__2.r, z__1.i = c__[i__1].i - z__2.i;
+		vec.r = z__1.r, vec.i = z__1.i;
+		scaloc = 1.;
+		i__1 = k + k * a_dim1;
+		d_cnjg(&z__3, &b[l + l * b_dim1]);
+		z__2.r = sgn * z__3.r, z__2.i = sgn * z__3.i;
+		z__1.r = a[i__1].r + z__2.r, z__1.i = a[i__1].i + z__2.i;
+		a11.r = z__1.r, a11.i = z__1.i;
+		da11 = (d__1 = a11.r, abs(d__1)) + (d__2 = d_imag(&a11), abs(
+			d__2));
+		if (da11 <= smin) {
+		    a11.r = smin, a11.i = 0.;
+		    da11 = smin;
+		    *info = 1;
+		}
+		db = (d__1 = vec.r, abs(d__1)) + (d__2 = d_imag(&vec), abs(
+			d__2));
+		if (da11 < 1. && db > 1.) {
+		    if (db > bignum * da11) {
+			scaloc = 1. / db;
+		    }
+		}
+		z__3.r = scaloc, z__3.i = 0.;
+		z__2.r = vec.r * z__3.r - vec.i * z__3.i, z__2.i = vec.r *
+			z__3.i + vec.i * z__3.r;
+		z__1 = zladiv_(&z__2, &a11);
+		x11.r = z__1.r, x11.i = z__1.i;
+		if (scaloc != 1.) {
+		    i__1 = *n;
+		    for (j = 1; j <= i__1; ++j) {
+			zdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
+/* L100: */
+		    }
+		    *scale *= scaloc;
+		}
+		i__1 = k + l * c_dim1;
+		c__[i__1].r = x11.r, c__[i__1].i = x11.i;
+/* L110: */
+	    }
+/* L120: */
+	}
+    }
+    return;
+}

relapack/src/ztrtri.c

@@ -0,0 +1,107 @@
+#include "relapack.h"
+
+static void RELAPACK_ztrtri_rec(const char *, const char *, const int *,
+    double *, const int *, int *);
+
+
+/** CTRTRI computes the inverse of a complex upper or lower triangular matrix A.
+ *
+ * This routine is functionally equivalent to LAPACK's ztrtri.
+ * For details on its interface, see
+ * http://www.netlib.org/lapack/explore-html/d1/d0e/ztrtri_8f.html
+ * */
+void RELAPACK_ztrtri(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+) {
+
+    // Check arguments
+    const int lower = LAPACK(lsame)(uplo, "L");
+    const int upper = LAPACK(lsame)(uplo, "U");
+    const int nounit = LAPACK(lsame)(diag, "N");
+    const int unit = LAPACK(lsame)(diag, "U");
+    *info = 0;
+    if (!lower && !upper)
+        *info = -1;
+    else if (!nounit && !unit)
+        *info = -2;
+    else if (*n < 0)
+        *info = -3;
+    else if (*ldA < MAX(1, *n))
+        *info = -5;
+    if (*info) {
+        const int minfo = -*info;
+        LAPACK(xerbla)("ZTRTRI", &minfo);
+        return;
+    }
+
+    // Clean char * arguments
+    const char cleanuplo = lower  ? 'L' : 'U';
+    const char cleandiag = nounit ? 'N' : 'U';
+
+    // check for singularity
+    if (nounit) {
+        int i;
+        for (i = 0; i < *n; i++)
+            if (A[2 * (i + *ldA * i)] == 0 && A[2 * (i + *ldA * i) + 1] == 0) {
+                *info = i;
+                return;
+            }
+    }
+
+    // Recursive kernel
+    RELAPACK_ztrtri_rec(&cleanuplo, &cleandiag, n, A, ldA, info);
+}
+
+
+/** ztrtri's recursive compute kernel */
+static void RELAPACK_ztrtri_rec(
+    const char *uplo, const char *diag, const int *n,
+    double *A, const int *ldA,
+    int *info
+){
+
+    if (*n <= MAX(CROSSOVER_ZTRTRI, 1)) {
+        // Unblocked
+        LAPACK(ztrti2)(uplo, diag, n, A, ldA, info);
+        return;
+    }
+
+    // Constants
+    const double ONE[]  = { 1. };
+    const double MONE[] = { -1. };
+
+    // Splitting
+    const int n1 = ZREC_SPLIT(*n);
+    const int n2 = *n - n1;
+
+    // A_TL A_TR
+    // A_BL A_BR
+    double *const A_TL = A;
+    double *const A_TR = A + 2 * *ldA * n1;
+    double *const A_BL = A                 + 2 * n1;
+    double *const A_BR = A + 2 * *ldA * n1 + 2 * n1;
+
+    // recursion(A_TL)
+    RELAPACK_ztrtri_rec(uplo, diag, &n1, A_TL, ldA, info);
+    if (*info)
+        return;
+
+    if (*uplo == 'L') {
+        // A_BL = - A_BL * A_TL
+        BLAS(ztrmm)("R", "L", "N", diag, &n2, &n1, MONE, A_TL, ldA, A_BL, ldA);
+        // A_BL = A_BR \ A_BL
+        BLAS(ztrsm)("L", "L", "N", diag, &n2, &n1, ONE, A_BR, ldA, A_BL, ldA);
+    } else {
+        // A_TR = - A_TL * A_TR
+        BLAS(ztrmm)("L", "U", "N", diag, &n1, &n2, MONE, A_TL, ldA, A_TR, ldA);
+        // A_TR = A_TR / A_BR
+        BLAS(ztrsm)("R", "U", "N", diag, &n1, &n2, ONE, A_BR, ldA, A_TR, ldA);
+    }
+
+    // recursion(A_BR)
+    RELAPACK_ztrtri_rec(uplo, diag, &n2, A_BR, ldA, info);
+    if (*info)
+        *info += n1;
+}