OpenBLAS/lapack-netlib/SRC/sggrqf.c

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif

#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif

#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif

typedef blasint integer;

typedef unsigned 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;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;

typedef char logical1;
typedef char integer1;

#define TRUE_ (1)
#define FALSE_ (0)

/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif

/* I/O stuff */

typedef int flag;
typedef int ftnlen;
typedef int ftnint;

/*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;

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) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(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)))

#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/*  -- translated by f2c (version 20000121).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/




/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;

/* > \brief \b SGGRQF */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download SGGRQF + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggrqf.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggrqf.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggrqf.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE SGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK, */
/*                          LWORK, INFO ) */

/*       INTEGER            INFO, LDA, LDB, LWORK, M, N, P */
/*       REAL               A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB( * ), */
/*      $                   WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGGRQF computes a generalized RQ factorization of an M-by-N matrix A */
/* > and a P-by-N matrix B: */
/* > */
/* >             A = R*Q,        B = Z*T*Q, */
/* > */
/* > where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal */
/* > matrix, and R and T assume one of the forms: */
/* > */
/* > if M <= N,  R = ( 0  R12 ) M,   or if M > N,  R = ( R11 ) M-N, */
/* >                  N-M  M                           ( R21 ) N */
/* >                                                      N */
/* > */
/* > where R12 or R21 is upper triangular, and */
/* > */
/* > if P >= N,  T = ( T11 ) N  ,   or if P < N,  T = ( T11  T12 ) P, */
/* >                 (  0  ) P-N                         P   N-P */
/* >                    N */
/* > */
/* > where T11 is upper triangular. */
/* > */
/* > In particular, if B is square and nonsingular, the GRQ factorization */
/* > of A and B implicitly gives the RQ factorization of A*inv(B): */
/* > */
/* >              A*inv(B) = (R*inv(T))*Z**T */
/* > */
/* > where inv(B) denotes the inverse of the matrix B, and Z**T denotes the */
/* > transpose of the matrix Z. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of rows of the matrix A.  M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] P */
/* > \verbatim */
/* >          P is INTEGER */
/* >          The number of rows of the matrix B.  P >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns of the matrices A and B. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the M-by-N matrix A. */
/* >          On exit, if M <= N, the upper triangle of the subarray */
/* >          A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R; */
/* >          if M > N, the elements on and above the (M-N)-th subdiagonal */
/* >          contain the M-by-N upper trapezoidal matrix R; the remaining */
/* >          elements, with the array TAUA, represent the orthogonal */
/* >          matrix Q as a product of elementary reflectors (see Further */
/* >          Details). */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] TAUA */
/* > \verbatim */
/* >          TAUA is REAL array, dimension (f2cmin(M,N)) */
/* >          The scalar factors of the elementary reflectors which */
/* >          represent the orthogonal matrix Q (see Further Details). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is REAL array, dimension (LDB,N) */
/* >          On entry, the P-by-N matrix B. */
/* >          On exit, the elements on and above the diagonal of the array */
/* >          contain the f2cmin(P,N)-by-N upper trapezoidal matrix T (T is */
/* >          upper triangular if P >= N); the elements below the diagonal, */
/* >          with the array TAUB, represent the orthogonal matrix Z as a */
/* >          product of elementary reflectors (see Further Details). */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of the array B. LDB >= f2cmax(1,P). */
/* > \endverbatim */
/* > */
/* > \param[out] TAUB */
/* > \verbatim */
/* >          TAUB is REAL array, dimension (f2cmin(P,N)) */
/* >          The scalar factors of the elementary reflectors which */
/* >          represent the orthogonal matrix Z (see Further Details). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (MAX(1,LWORK)) */
/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The dimension of the array WORK. LWORK >= f2cmax(1,N,M,P). */
/* >          For optimum performance LWORK >= f2cmax(N,M,P)*f2cmax(NB1,NB2,NB3), */
/* >          where NB1 is the optimal blocksize for the RQ factorization */
/* >          of an M-by-N matrix, NB2 is the optimal blocksize for the */
/* >          QR factorization of a P-by-N matrix, and NB3 is the optimal */
/* >          blocksize for a call of SORMRQ. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the optimal size of the WORK array, returns */
/* >          this value as the first entry of the WORK array, and no error */
/* >          message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INF0= -i, the i-th argument had an illegal value. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup realOTHERcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  The matrix Q is represented as a product of elementary reflectors */
/* > */
/* >     Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H(i) = I - taua * v * v**T */
/* > */
/* >  where taua is a real scalar, and v is a real vector with */
/* >  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in */
/* >  A(m-k+i,1:n-k+i-1), and taua in TAUA(i). */
/* >  To form Q explicitly, use LAPACK subroutine SORGRQ. */
/* >  To use Q to update another matrix, use LAPACK subroutine SORMRQ. */
/* > */
/* >  The matrix Z is represented as a product of elementary reflectors */
/* > */
/* >     Z = H(1) H(2) . . . H(k), where k = f2cmin(p,n). */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H(i) = I - taub * v * v**T */
/* > */
/* >  where taub is a real scalar, and v is a real vector with */
/* >  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i), */
/* >  and taub in TAUB(i). */
/* >  To form Z explicitly, use LAPACK subroutine SORGQR. */
/* >  To use Z to update another matrix, use LAPACK subroutine SORMQR. */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void sggrqf_(integer *m, integer *p, integer *n, real *a, 
	integer *lda, real *taua, real *b, integer *ldb, real *taub, real *
	work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;

    /* Local variables */
    integer lopt, nb;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *), sgerqf_(integer *, 
	    integer *, real *, integer *, real *, real *, integer *, integer *
	    );
    integer nb1, nb2, nb3, lwkopt;
    logical lquery;
    extern /* Subroutine */ void sormrq_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);


/*  -- LAPACK computational routine (version 3.7.0) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     December 2016 */


/*  ===================================================================== */


/*     Test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --taua;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --taub;
    --work;

    /* Function Body */
    *info = 0;
    nb1 = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    nb2 = ilaenv_(&c__1, "SGEQRF", " ", p, n, &c_n1, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    nb3 = ilaenv_(&c__1, "SORMRQ", " ", m, n, p, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
    i__1 = f2cmax(nb1,nb2);
    nb = f2cmax(i__1,nb3);
/* Computing MAX */
    i__1 = f2cmax(*n,*m);
    lwkopt = f2cmax(i__1,*p) * nb;
    work[1] = (real) lwkopt;
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*p < 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -5;
    } else if (*ldb < f2cmax(1,*p)) {
	*info = -8;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = f2cmax(1,*m), i__1 = f2cmax(i__1,*p);
	if (*lwork < f2cmax(i__1,*n) && ! lquery) {
	    *info = -11;
	}
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGGRQF", &i__1, (ftnlen)6);
	return;
    } else if (lquery) {
	return;
    }

/*     RQ factorization of M-by-N matrix A: A = R*Q */

    sgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
    lopt = work[1];

/*     Update B := B*Q**T */

    i__1 = f2cmin(*m,*n);
/* Computing MAX */
    i__2 = 1, i__3 = *m - *n + 1;
    sormrq_("Right", "Transpose", p, n, &i__1, &a[f2cmax(i__2,i__3) + a_dim1], 
	    lda, &taua[1], &b[b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
    i__1 = lopt, i__2 = (integer) work[1];
    lopt = f2cmax(i__1,i__2);

/*     QR factorization of P-by-N matrix B: B = Z*T */

    sgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
    i__1 = lopt, i__2 = (integer) work[1];
    work[1] = (real) f2cmax(i__1,i__2);

    return;

/*     End of SGGRQF */

} /* sggrqf_ */