path: root/contrib/libs/clapack/sgelss.c

/* sgelss.f -- translated by f2c (version 20061008).
   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"
#include "blaswrap.h"

/* Table of constant values */

static integer c__6 = 6;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b74 = 0.f;
static real c_b108 = 1.f;

/* Subroutine */ int sgelss_(integer *m, integer *n, integer *nrhs, real *a, 
	integer *lda, real *b, integer *ldb, real *s, real *rcond, integer *
	rank, real *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
    real r__1;

    /* Local variables */
    integer i__, bl, ie, il, mm;
    real eps, thr, anrm, bnrm;
    integer itau;
    real vdum[1];
    integer iascl, ibscl, chunk;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    real sfmin;
    integer minmn, maxmn;
    extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, 
	    real *, integer *, real *, integer *, real *, real *, integer *);
    integer itaup, itauq;
    extern /* Subroutine */ int srscl_(integer *, real *, real *, integer *);
    integer mnthr, iwork;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *), slabad_(real *, real *);
    integer bdspac;
    extern /* Subroutine */ int sgebrd_(integer *, integer *, real *, integer 
	    *, real *, real *, real *, real *, real *, integer *, integer *);
    extern doublereal slamch_(char *), slange_(char *, integer *, 
	    integer *, real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    real bignum;
    extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *), slascl_(char *, integer 
	    *, integer *, real *, real *, integer *, integer *, real *, 
	    integer *, integer *), sgeqrf_(integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *), slacpy_(char 
	    *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
	    real *, integer *), sbdsqr_(char *, integer *, integer *, 
	    integer *, integer *, real *, real *, real *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *), sorgbr_(
	    char *, integer *, integer *, integer *, real *, integer *, real *
, real *, integer *, integer *);
    integer ldwork;
    extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *, 
	    integer *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *, integer *);
    integer minwrk, maxwrk;
    real smlnum;
    extern /* Subroutine */ int sormlq_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);
    logical lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);


/*  -- LAPACK driver routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SGELSS computes the minimum norm solution to a real linear least */
/*  squares problem: */

/*  Minimize 2-norm(| b - A*x |). */

/*  using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those */
/*  singular values which are less than RCOND times the largest singular */
/*  value. */

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

/*  M       (input) INTEGER */
/*          The number of rows of the matrix A. M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns of the matrix A. N >= 0. */

/*  NRHS    (input) INTEGER */
/*          The number of right hand sides, i.e., the number of columns */
/*          of the matrices B and X. NRHS >= 0. */

/*  A       (input/output) REAL array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix A. */
/*          On exit, the first min(m,n) rows of A are overwritten with */
/*          its right singular vectors, stored rowwise. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,M). */

/*  B       (input/output) REAL array, dimension (LDB,NRHS) */
/*          On entry, the M-by-NRHS right hand side matrix B. */
/*          On exit, B is overwritten by 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. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B. LDB >= max(1,max(M,N)). */

/*  S       (output) REAL array, dimension (min(M,N)) */
/*          The singular values of A in decreasing order. */
/*          The condition number of A in the 2-norm = S(1)/S(min(m,n)). */

/*  RCOND   (input) REAL */
/*          RCOND is used to determine the effective rank of A. */
/*          Singular values S(i) <= RCOND*S(1) are treated as zero. */
/*          If RCOND < 0, machine precision is used instead. */

/*  RANK    (output) INTEGER */
/*          The effective rank of A, i.e., the number of singular values */
/*          which are greater than RCOND*S(1). */

/*  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. LWORK >= 1, and also: */
/*          LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) */
/*          For good performance, LWORK should generally be larger. */

/*          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. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/*          > 0:  the algorithm for computing the SVD failed to converge; */
/*                if INFO = i, i off-diagonal elements of an intermediate */
/*                bidiagonal form did not converge to zero. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input arguments */

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

    /* Function Body */
    *info = 0;
    minmn = min(*m,*n);
    maxmn = max(*m,*n);
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < max(1,*m)) {
	*info = -5;
    } else if (*ldb < max(1,maxmn)) {
	*info = -7;
    }

/*     Compute workspace */
/*      (Note: Comments in the code beginning "Workspace:" describe the */
/*       minimal amount of workspace needed at that point in the code, */
/*       as well as the preferred amount for good performance. */
/*       NB refers to the optimal block size for the immediately */
/*       following subroutine, as returned by ILAENV.) */

    if (*info == 0) {
	minwrk = 1;
	maxwrk = 1;
	if (minmn > 0) {
	    mm = *m;
	    mnthr = ilaenv_(&c__6, "SGELSS", " ", m, n, nrhs, &c_n1);
	    if (*m >= *n && *m >= mnthr) {

/*              Path 1a - overdetermined, with many more rows than */
/*                        columns */

		mm = *n;
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "SGEQRF", 
			" ", m, n, &c_n1, &c_n1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "SORMQR", 
			"LT", m, nrhs, n, &c_n1);
		maxwrk = max(i__1,i__2);
	    }
	    if (*m >= *n) {

/*              Path 1 - overdetermined or exactly determined */

/*              Compute workspace needed for SBDSQR */

/* Computing MAX */
		i__1 = 1, i__2 = *n * 5;
		bdspac = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, 
			"SGEBRD", " ", &mm, n, &c_n1, &c_n1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "SORMBR"
, "QLT", &mm, nrhs, n, &c_n1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, 
			"SORGBR", "P", n, n, n, &c_n1);
		maxwrk = max(i__1,i__2);
		maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * *nrhs;
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,
			i__2);
		minwrk = max(i__1,bdspac);
		maxwrk = max(minwrk,maxwrk);
	    }
	    if (*n > *m) {

/*              Compute workspace needed for SBDSQR */

/* Computing MAX */
		i__1 = 1, i__2 = *m * 5;
		bdspac = max(i__1,i__2);
/* Computing MAX */
		i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1,
			i__2);
		minwrk = max(i__1,bdspac);
		if (*n >= mnthr) {

/*                 Path 2a - underdetermined, with many more columns */
/*                 than rows */

		    maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, &
			    c_n1, &c_n1);
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * 
			    ilaenv_(&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1);
		    maxwrk = max(i__1,i__2);
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * 
			    ilaenv_(&c__1, "SORMBR", "QLT", m, nrhs, m, &c_n1);
		    maxwrk = max(i__1,i__2);
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * 
			    ilaenv_(&c__1, "SORGBR", "P", m, m, m, &c_n1);
		    maxwrk = max(i__1,i__2);
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + *m + bdspac;
		    maxwrk = max(i__1,i__2);
		    if (*nrhs > 1) {
/* Computing MAX */
			i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
			maxwrk = max(i__1,i__2);
		    } else {
/* Computing MAX */
			i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
			maxwrk = max(i__1,i__2);
		    }
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "SORMLQ"
, "LT", n, nrhs, m, &c_n1);
		    maxwrk = max(i__1,i__2);
		} else {

/*                 Path 2 - underdetermined */

		    maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "SGEBRD", 
			    " ", m, n, &c_n1, &c_n1);
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, 
			    "SORMBR", "QLT", m, nrhs, m, &c_n1);
		    maxwrk = max(i__1,i__2);
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "SORG"
			    "BR", "P", m, n, m, &c_n1);
		    maxwrk = max(i__1,i__2);
		    maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *n * *nrhs;
		    maxwrk = max(i__1,i__2);
		}
	    }
	    maxwrk = max(minwrk,maxwrk);
	}
	work[1] = (real) maxwrk;

	if (*lwork < minwrk && ! lquery) {
	    *info = -12;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGELSS", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
	*rank = 0;
	return 0;
    }

/*     Get machine parameters */

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

/*     Scale A if max element 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 = max(*m,*n);
	slaset_("F", &i__1, nrhs, &c_b74, &c_b74, &b[b_offset], ldb);
	slaset_("F", &minmn, &c__1, &c_b74, &c_b74, &s[1], &c__1);
	*rank = 0;
	goto L70;
    }

/*     Scale B if max element outside range [SMLNUM,BIGNUM] */

    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;
    }

/*     Overdetermined case */

    if (*m >= *n) {

/*        Path 1 - overdetermined or exactly determined */

	mm = *m;
	if (*m >= mnthr) {

/*           Path 1a - overdetermined, with many more rows than columns */

	    mm = *n;
	    itau = 1;
	    iwork = itau + *n;

/*           Compute A=Q*R */
/*           (Workspace: need 2*N, prefer N+N*NB) */

	    i__1 = *lwork - iwork + 1;
	    sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, 
		     info);

/*           Multiply B by transpose(Q) */
/*           (Workspace: need N+NRHS, prefer N+NRHS*NB) */

	    i__1 = *lwork - iwork + 1;
	    sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[iwork], &i__1, info);

/*           Zero out below R */

	    if (*n > 1) {
		i__1 = *n - 1;
		i__2 = *n - 1;
		slaset_("L", &i__1, &i__2, &c_b74, &c_b74, &a[a_dim1 + 2], 
			lda);
	    }
	}

	ie = 1;
	itauq = ie + *n;
	itaup = itauq + *n;
	iwork = itaup + *n;

/*        Bidiagonalize R in A */
/*        (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */

	i__1 = *lwork - iwork + 1;
	sgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		work[itaup], &work[iwork], &i__1, info);

/*        Multiply B by transpose of left bidiagonalizing vectors of R */
/*        (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */

	i__1 = *lwork - iwork + 1;
	sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], 
		&b[b_offset], ldb, &work[iwork], &i__1, info);

/*        Generate right bidiagonalizing vectors of R in A */
/*        (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */

	i__1 = *lwork - iwork + 1;
	sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
		i__1, info);
	iwork = ie + *n;

/*        Perform bidiagonal QR iteration */
/*          multiply B by transpose of left singular vectors */
/*          compute right singular vectors in A */
/*        (Workspace: need BDSPAC) */

	sbdsqr_("U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, 
		vdum, &c__1, &b[b_offset], ldb, &work[iwork], info)
		;
	if (*info != 0) {
	    goto L70;
	}

/*        Multiply B by reciprocals of singular values */

/* Computing MAX */
	r__1 = *rcond * s[1];
	thr = dmax(r__1,sfmin);
	if (*rcond < 0.f) {
/* Computing MAX */
	    r__1 = eps * s[1];
	    thr = dmax(r__1,sfmin);
	}
	*rank = 0;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (s[i__] > thr) {
		srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
		++(*rank);
	    } else {
		slaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b[i__ + b_dim1], 
			ldb);
	    }
/* L10: */
	}

/*        Multiply B by right singular vectors */
/*        (Workspace: need N, prefer N*NRHS) */

	if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
	    sgemm_("T", "N", n, nrhs, n, &c_b108, &a[a_offset], lda, &b[
		    b_offset], ldb, &c_b74, &work[1], ldb);
	    slacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb)
		    ;
	} else if (*nrhs > 1) {
	    chunk = *lwork / *n;
	    i__1 = *nrhs;
	    i__2 = chunk;
	    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
		i__3 = *nrhs - i__ + 1;
		bl = min(i__3,chunk);
		sgemm_("T", "N", n, &bl, n, &c_b108, &a[a_offset], lda, &b[
			i__ * b_dim1 + 1], ldb, &c_b74, &work[1], n);
		slacpy_("G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb);
/* L20: */
	    }
	} else {
	    sgemv_("T", n, n, &c_b108, &a[a_offset], lda, &b[b_offset], &c__1, 
		     &c_b74, &work[1], &c__1);
	    scopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
	}

    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max(
		i__2,*nrhs), i__1 = *n - *m * 3;
	if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) {

/*        Path 2a - underdetermined, with many more columns than rows */
/*        and sufficient workspace for an efficient algorithm */

	    ldwork = *m;
/* Computing MAX */
/* Computing MAX */
	    i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = 
		    max(i__3,*nrhs), i__4 = *n - *m * 3;
	    i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda + 
		    *m + *m * *nrhs;
	    if (*lwork >= max(i__2,i__1)) {
		ldwork = *lda;
	    }
	    itau = 1;
	    iwork = *m + 1;

/*        Compute A=L*Q */
/*        (Workspace: need 2*M, prefer M+M*NB) */

	    i__2 = *lwork - iwork + 1;
	    sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, 
		     info);
	    il = iwork;

/*        Copy L to WORK(IL), zeroing out above it */

	    slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
	    i__2 = *m - 1;
	    i__1 = *m - 1;
	    slaset_("U", &i__2, &i__1, &c_b74, &c_b74, &work[il + ldwork], &
		    ldwork);
	    ie = il + ldwork * *m;
	    itauq = ie + *m;
	    itaup = itauq + *m;
	    iwork = itaup + *m;

/*        Bidiagonalize L in WORK(IL) */
/*        (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */

	    i__2 = *lwork - iwork + 1;
	    sgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], 
		    &work[itaup], &work[iwork], &i__2, info);

/*        Multiply B by transpose of left bidiagonalizing vectors of L */
/*        (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */

	    i__2 = *lwork - iwork + 1;
	    sormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
		    itauq], &b[b_offset], ldb, &work[iwork], &i__2, info);

/*        Generate right bidiagonalizing vectors of R in WORK(IL) */
/*        (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */

	    i__2 = *lwork - iwork + 1;
	    sorgbr_("P", m, m, m, &work[il], &ldwork, &work[itaup], &work[
		    iwork], &i__2, info);
	    iwork = ie + *m;

/*        Perform bidiagonal QR iteration, */
/*           computing right singular vectors of L in WORK(IL) and */
/*           multiplying B by transpose of left singular vectors */
/*        (Workspace: need M*M+M+BDSPAC) */

	    sbdsqr_("U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &
		    ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork]
, info);
	    if (*info != 0) {
		goto L70;
	    }

/*        Multiply B by reciprocals of singular values */

/* Computing MAX */
	    r__1 = *rcond * s[1];
	    thr = dmax(r__1,sfmin);
	    if (*rcond < 0.f) {
/* Computing MAX */
		r__1 = eps * s[1];
		thr = dmax(r__1,sfmin);
	    }
	    *rank = 0;
	    i__2 = *m;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		if (s[i__] > thr) {
		    srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
		    ++(*rank);
		} else {
		    slaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b[i__ + b_dim1]
, ldb);
		}
/* L30: */
	    }
	    iwork = ie;

/*        Multiply B by right singular vectors of L in WORK(IL) */
/*        (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */

	    if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) {
		sgemm_("T", "N", m, nrhs, m, &c_b108, &work[il], &ldwork, &b[
			b_offset], ldb, &c_b74, &work[iwork], ldb);
		slacpy_("G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb);
	    } else if (*nrhs > 1) {
		chunk = (*lwork - iwork + 1) / *m;
		i__2 = *nrhs;
		i__1 = chunk;
		for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += 
			i__1) {
/* Computing MIN */
		    i__3 = *nrhs - i__ + 1;
		    bl = min(i__3,chunk);
		    sgemm_("T", "N", m, &bl, m, &c_b108, &work[il], &ldwork, &
			    b[i__ * b_dim1 + 1], ldb, &c_b74, &work[iwork], m);
		    slacpy_("G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1]
, ldb);
/* L40: */
		}
	    } else {
		sgemv_("T", m, m, &c_b108, &work[il], &ldwork, &b[b_dim1 + 1], 
			 &c__1, &c_b74, &work[iwork], &c__1);
		scopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1);
	    }

/*        Zero out below first M rows of B */

	    i__1 = *n - *m;
	    slaset_("F", &i__1, nrhs, &c_b74, &c_b74, &b[*m + 1 + b_dim1], 
		    ldb);
	    iwork = itau + *m;

/*        Multiply transpose(Q) by B */
/*        (Workspace: need M+NRHS, prefer M+NRHS*NB) */

	    i__1 = *lwork - iwork + 1;
	    sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
		    b_offset], ldb, &work[iwork], &i__1, info);

	} else {

/*        Path 2 - remaining underdetermined cases */

	    ie = 1;
	    itauq = ie + *m;
	    itaup = itauq + *m;
	    iwork = itaup + *m;

/*        Bidiagonalize A */
/*        (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */

	    i__1 = *lwork - iwork + 1;
	    sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		    work[itaup], &work[iwork], &i__1, info);

/*        Multiply B by transpose of left bidiagonalizing vectors */
/*        (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */

	    i__1 = *lwork - iwork + 1;
	    sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
, &b[b_offset], ldb, &work[iwork], &i__1, info);

/*        Generate right bidiagonalizing vectors in A */
/*        (Workspace: need 4*M, prefer 3*M+M*NB) */

	    i__1 = *lwork - iwork + 1;
	    sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
		    iwork], &i__1, info);
	    iwork = ie + *m;

/*        Perform bidiagonal QR iteration, */
/*           computing right singular vectors of A in A and */
/*           multiplying B by transpose of left singular vectors */
/*        (Workspace: need BDSPAC) */

	    sbdsqr_("L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], 
		    lda, vdum, &c__1, &b[b_offset], ldb, &work[iwork], info);
	    if (*info != 0) {
		goto L70;
	    }

/*        Multiply B by reciprocals of singular values */

/* Computing MAX */
	    r__1 = *rcond * s[1];
	    thr = dmax(r__1,sfmin);
	    if (*rcond < 0.f) {
/* Computing MAX */
		r__1 = eps * s[1];
		thr = dmax(r__1,sfmin);
	    }
	    *rank = 0;
	    i__1 = *m;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		if (s[i__] > thr) {
		    srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
		    ++(*rank);
		} else {
		    slaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b[i__ + b_dim1]
, ldb);
		}
/* L50: */
	    }

/*        Multiply B by right singular vectors of A */
/*        (Workspace: need N, prefer N*NRHS) */

	    if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
		sgemm_("T", "N", n, nrhs, m, &c_b108, &a[a_offset], lda, &b[
			b_offset], ldb, &c_b74, &work[1], ldb);
		slacpy_("F", n, nrhs, &work[1], ldb, &b[b_offset], ldb);
	    } else if (*nrhs > 1) {
		chunk = *lwork / *n;
		i__1 = *nrhs;
		i__2 = chunk;
		for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
			i__2) {
/* Computing MIN */
		    i__3 = *nrhs - i__ + 1;
		    bl = min(i__3,chunk);
		    sgemm_("T", "N", n, &bl, m, &c_b108, &a[a_offset], lda, &
			    b[i__ * b_dim1 + 1], ldb, &c_b74, &work[1], n);
		    slacpy_("F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], 
			    ldb);
/* L60: */
		}
	    } else {
		sgemv_("T", m, n, &c_b108, &a[a_offset], lda, &b[b_offset], &
			c__1, &c_b74, &work[1], &c__1);
		scopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
	    }
	}
    }

/*     Undo scaling */

    if (iascl == 1) {
	slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, 
		 info);
	slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
		minmn, info);
    } else if (iascl == 2) {
	slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, 
		 info);
	slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
		minmn, 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);
    }

L70:
    work[1] = (real) maxwrk;
    return 0;

/*     End of SGELSS */

} /* sgelss_ */