OpenBLAS/lapack-netlib/SRC/DEPRECATED/sgelsx.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 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 pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(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)}

/* procedure parameter types for -A and -C++ */


/*  -- 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__0 = 0;
static real c_b13 = 0.f;
static integer c__2 = 2;
static integer c__1 = 1;
static real c_b36 = 1.f;

/* > \brief <b> SGELSX solves overdetermined or underdetermined systems for GE matrices</b> */

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

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

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

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

/*       SUBROUTINE SGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */
/*                          WORK, INFO ) */

/*       INTEGER            INFO, LDA, LDB, M, N, NRHS, RANK */
/*       REAL               RCOND */
/*       INTEGER            JPVT( * ) */
/*       REAL               A( LDA, * ), B( LDB, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine SGELSY. */
/* > */
/* > SGELSX computes the minimum-norm solution to a real linear least */
/* > squares problem: */
/* >     minimize || A * X - B || */
/* > using a complete orthogonal factorization of A.  A is an M-by-N */
/* > matrix which may be rank-deficient. */
/* > */
/* > Several right hand side vectors b and solution vectors x can be */
/* > handled in a single call; they are stored as the columns of the */
/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
/* > matrix X. */
/* > */
/* > The routine first computes a QR factorization with column pivoting: */
/* >     A * P = Q * [ R11 R12 ] */
/* >                 [  0  R22 ] */
/* > with R11 defined as the largest leading submatrix whose estimated */
/* > condition number is less than 1/RCOND.  The order of R11, RANK, */
/* > is the effective rank of A. */
/* > */
/* > Then, R22 is considered to be negligible, and R12 is annihilated */
/* > by orthogonal transformations from the right, arriving at the */
/* > complete orthogonal factorization: */
/* >    A * P = Q * [ T11 0 ] * Z */
/* >                [  0  0 ] */
/* > The minimum-norm solution is then */
/* >    X = P * Z**T [ inv(T11)*Q1**T*B ] */
/* >                 [        0         ] */
/* > where Q1 consists of the first RANK columns of Q. */
/* > \endverbatim */

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

/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of rows of the matrix A.  M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* >          NRHS is INTEGER */
/* >          The number of right hand sides, i.e., the number of */
/* >          columns of matrices B and X. NRHS >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the M-by-N matrix A. */
/* >          On exit, A has been overwritten by details of its */
/* >          complete orthogonal factorization. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is REAL array, dimension (LDB,NRHS) */
/* >          On entry, the M-by-NRHS right hand side matrix B. */
/* >          On exit, the N-by-NRHS solution matrix X. */
/* >          If m >= n and RANK = n, the residual sum-of-squares for */
/* >          the solution in the i-th column is given by the sum of */
/* >          squares of elements N+1:M in that column. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of the array B. LDB >= f2cmax(1,M,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] JPVT */
/* > \verbatim */
/* >          JPVT is INTEGER array, dimension (N) */
/* >          On entry, if JPVT(i) .ne. 0, the i-th column of A is an */
/* >          initial column, otherwise it is a free column.  Before */
/* >          the QR factorization of A, all initial columns are */
/* >          permuted to the leading positions; only the remaining */
/* >          free columns are moved as a result of column pivoting */
/* >          during the factorization. */
/* >          On exit, if JPVT(i) = k, then the i-th column of A*P */
/* >          was the k-th column of A. */
/* > \endverbatim */
/* > */
/* > \param[in] RCOND */
/* > \verbatim */
/* >          RCOND is REAL */
/* >          RCOND is used to determine the effective rank of A, which */
/* >          is defined as the order of the largest leading triangular */
/* >          submatrix R11 in the QR factorization with pivoting of A, */
/* >          whose estimated condition number < 1/RCOND. */
/* > \endverbatim */
/* > */
/* > \param[out] RANK */
/* > \verbatim */
/* >          RANK is INTEGER */
/* >          The effective rank of A, i.e., the order of the submatrix */
/* >          R11.  This is the same as the order of the submatrix T11 */
/* >          in the complete orthogonal factorization of A. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension */
/* >                      (f2cmax( f2cmin(M,N)+3*N, 2*f2cmin(M,N)+NRHS )), */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INFO = -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 realGEsolve */

/*  ===================================================================== */
/* Subroutine */ void sgelsx_(integer *m, integer *n, integer *nrhs, real *a, 
	integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond, 
	integer *rank, real *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
    real r__1;

    /* Local variables */
    real anrm, bnrm, smin, smax;
    integer i__, j, k, iascl, ibscl, ismin, ismax;
    real c1, c2, s1, s2, t1, t2;
    extern /* Subroutine */ void strsm_(char *, char *, char *, char *, 
	    integer *, integer *, real *, real *, integer *, real *, integer *
	    ), slaic1_(integer *, integer *, 
	    real *, real *, real *, real *, real *, real *, real *), sorm2r_(
	    char *, char *, integer *, integer *, integer *, real *, integer *
	    , real *, real *, integer *, real *, integer *), 
	    slabad_(real *, real *);
    integer mn;
    extern real slamch_(char *), slange_(char *, integer *, integer *,
	     real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    real bignum;
    extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), sgeqpf_(integer *, integer *, real *, integer *, integer 
	    *, real *, real *, integer *), slaset_(char *, integer *, integer 
	    *, real *, real *, real *, integer *);
    real sminpr, smaxpr, smlnum;
    extern /* Subroutine */ void slatzm_(char *, integer *, integer *, real *, 
	    integer *, real *, real *, real *, integer *, real *), 
	    stzrqf_(integer *, integer *, real *, integer *, real *, integer *
	    );


/*  -- LAPACK driver 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 */


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


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

    /* Function Body */
    mn = f2cmin(*m,*n);
    ismin = mn + 1;
    ismax = (mn << 1) + 1;

/*     Test the input arguments. */

    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -5;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = f2cmax(1,*m);
	if (*ldb < f2cmax(i__1,*n)) {
	    *info = -7;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGELSX", &i__1, 6);
	return;
    }

/*     Quick return if possible */

/* Computing MIN */
    i__1 = f2cmin(*m,*n);
    if (f2cmin(i__1,*nrhs) == 0) {
	*rank = 0;
	return;
    }

/*     Get machine parameters */

    smlnum = slamch_("S") / slamch_("P");
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);

/*     Scale A, B if f2cmax elements outside range [SMLNUM,BIGNUM] */

    anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]);
    iascl = 0;
    if (anrm > 0.f && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
		info);
	iascl = 1;
    } else if (anrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
		info);
	iascl = 2;
    } else if (anrm == 0.f) {

/*        Matrix all zero. Return zero solution. */

	i__1 = f2cmax(*m,*n);
	slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb);
	*rank = 0;
	goto L100;
    }

    bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
    ibscl = 0;
    if (bnrm > 0.f && bnrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */

	slascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 1;
    } else if (bnrm > bignum) {

/*        Scale matrix norm down to BIGNUM */

	slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
		 info);
	ibscl = 2;
    }

/*     Compute QR factorization with column pivoting of A: */
/*        A * P = Q * R */

    sgeqpf_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], info);

/*     workspace 3*N. Details of Householder rotations stored */
/*     in WORK(1:MN). */

/*     Determine RANK using incremental condition estimation */

    work[ismin] = 1.f;
    work[ismax] = 1.f;
    smax = (r__1 = a[a_dim1 + 1], abs(r__1));
    smin = smax;
    if ((r__1 = a[a_dim1 + 1], abs(r__1)) == 0.f) {
	*rank = 0;
	i__1 = f2cmax(*m,*n);
	slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb);
	goto L100;
    } else {
	*rank = 1;
    }

L10:
    if (*rank < mn) {
	i__ = *rank + 1;
	slaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
		i__ + i__ * a_dim1], &sminpr, &s1, &c1);
	slaic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
		i__ + i__ * a_dim1], &smaxpr, &s2, &c2);

	if (smaxpr * *rcond <= sminpr) {
	    i__1 = *rank;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		work[ismin + i__ - 1] = s1 * work[ismin + i__ - 1];
		work[ismax + i__ - 1] = s2 * work[ismax + i__ - 1];
/* L20: */
	    }
	    work[ismin + *rank] = c1;
	    work[ismax + *rank] = c2;
	    smin = sminpr;
	    smax = smaxpr;
	    ++(*rank);
	    goto L10;
	}
    }

/*     Logically partition R = [ R11 R12 ] */
/*                             [  0  R22 ] */
/*     where R11 = R(1:RANK,1:RANK) */

/*     [R11,R12] = [ T11, 0 ] * Y */

    if (*rank < *n) {
	stzrqf_(rank, n, &a[a_offset], lda, &work[mn + 1], info);
    }

/*     Details of Householder rotations stored in WORK(MN+1:2*MN) */

/*     B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS) */

    sorm2r_("Left", "Transpose", m, nrhs, &mn, &a[a_offset], lda, &work[1], &
	    b[b_offset], ldb, &work[(mn << 1) + 1], info);

/*     workspace NRHS */

/*     B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */

    strsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b36, &
	    a[a_offset], lda, &b[b_offset], ldb);

    i__1 = *n;
    for (i__ = *rank + 1; i__ <= i__1; ++i__) {
	i__2 = *nrhs;
	for (j = 1; j <= i__2; ++j) {
	    b[i__ + j * b_dim1] = 0.f;
/* L30: */
	}
/* L40: */
    }

/*     B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS) */

    if (*rank < *n) {
	i__1 = *rank;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    i__2 = *n - *rank + 1;
	    slatzm_("Left", &i__2, nrhs, &a[i__ + (*rank + 1) * a_dim1], lda, 
		    &work[mn + i__], &b[i__ + b_dim1], &b[*rank + 1 + b_dim1],
		     ldb, &work[(mn << 1) + 1]);
/* L50: */
	}
    }

/*     workspace NRHS */

/*     B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */

    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
	i__2 = *n;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    work[(mn << 1) + i__] = 1.f;
/* L60: */
	}
	i__2 = *n;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    if (work[(mn << 1) + i__] == 1.f) {
		if (jpvt[i__] != i__) {
		    k = i__;
		    t1 = b[k + j * b_dim1];
		    t2 = b[jpvt[k] + j * b_dim1];
L70:
		    b[jpvt[k] + j * b_dim1] = t1;
		    work[(mn << 1) + k] = 0.f;
		    t1 = t2;
		    k = jpvt[k];
		    t2 = b[jpvt[k] + j * b_dim1];
		    if (jpvt[k] != i__) {
			goto L70;
		    }
		    b[i__ + j * b_dim1] = t1;
		    work[(mn << 1) + k] = 0.f;
		}
	    }
/* L80: */
	}
/* L90: */
    }

/*     Undo scaling */

    if (iascl == 1) {
	slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
		 info);
	slascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset], 
		lda, info);
    } else if (iascl == 2) {
	slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
		 info);
	slascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset], 
		lda, info);
    }
    if (ibscl == 1) {
	slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info);
    } else if (ibscl == 2) {
	slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info);
    }

L100:

    return;

/*     End of SGELSX */

} /* sgelsx_ */