示例#1
0
/* Subroutine */ int schktz_(logical *dotype, integer *nm, integer *mval, 
	integer *nn, integer *nval, real *thresh, logical *tsterr, real *a, 
	real *copya, real *s, real *copys, real *tau, real *work, integer *
	nout)
{
    /* Initialized data */

    static integer iseedy[4] = { 1988,1989,1990,1991 };

    /* Format strings */
    static char fmt_9999[] = "(\002 M =\002,i5,\002, N =\002,i5,\002, type"
	    " \002,i2,\002, test \002,i2,\002, ratio =\002,g12.5)";

    /* System generated locals */
    integer i__1, i__2, i__3, i__4;
    real r__1;

    /* Builtin functions */
    /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
    integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);

    /* Local variables */
    integer i__, k, m, n, im, in, lda;
    real eps;
    integer mode, info;
    char path[3];
    integer nrun;
    extern /* Subroutine */ int alahd_(integer *, char *);
    integer nfail, iseed[4], imode, mnmin, nerrs;
    extern doublereal sqrt12_(integer *, integer *, real *, integer *, real *, 
	     real *, integer *);
    integer lwork;
    extern doublereal srzt01_(integer *, integer *, real *, real *, integer *, 
	     real *, real *, integer *), srzt02_(integer *, integer *, real *, 
	     integer *, real *, real *, integer *), stzt01_(integer *, 
	    integer *, real *, real *, integer *, real *, real *, integer *), 
	    stzt02_(integer *, integer *, real *, integer *, real *, real *, 
	    integer *);
    extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer 
	    *, integer *), slaord_(char *, integer *, real *, integer 
	    *), slacpy_(char *, integer *, integer *, real *, integer 
	    *, real *, integer *), slaset_(char *, integer *, integer 
	    *, real *, real *, real *, integer *), slatms_(integer *, 
	    integer *, char *, integer *, char *, real *, integer *, real *, 
	    real *, integer *, integer *, char *, real *, integer *, real *, 
	    integer *);
    real result[6];
    extern /* Subroutine */ int serrtz_(char *, integer *), stzrqf_(
	    integer *, integer *, real *, integer *, real *, integer *), 
	    stzrzf_(integer *, integer *, real *, integer *, real *, real *, 
	    integer *, integer *);

    /* Fortran I/O blocks */
    static cilist io___21 = { 0, 0, 0, fmt_9999, 0 };



/*  -- LAPACK test routine (version 3.1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     January 2007 */

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

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

/*  SCHKTZ tests STZRQF and STZRZF. */

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

/*  DOTYPE  (input) LOGICAL array, dimension (NTYPES) */
/*          The matrix types to be used for testing.  Matrices of type j */
/*          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/*          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */

/*  NM      (input) INTEGER */
/*          The number of values of M contained in the vector MVAL. */

/*  MVAL    (input) INTEGER array, dimension (NM) */
/*          The values of the matrix row dimension M. */

/*  NN      (input) INTEGER */
/*          The number of values of N contained in the vector NVAL. */

/*  NVAL    (input) INTEGER array, dimension (NN) */
/*          The values of the matrix column dimension N. */

/*  THRESH  (input) REAL */
/*          The threshold value for the test ratios.  A result is */
/*          included in the output file if RESULT >= THRESH.  To have */
/*          every test ratio printed, use THRESH = 0. */

/*  TSTERR  (input) LOGICAL */
/*          Flag that indicates whether error exits are to be tested. */

/*  A       (workspace) REAL array, dimension (MMAX*NMAX) */
/*          where MMAX is the maximum value of M in MVAL and NMAX is the */
/*          maximum value of N in NVAL. */

/*  COPYA   (workspace) REAL array, dimension (MMAX*NMAX) */

/*  S       (workspace) REAL array, dimension */
/*                      (min(MMAX,NMAX)) */

/*  COPYS   (workspace) REAL array, dimension */
/*                      (min(MMAX,NMAX)) */

/*  TAU     (workspace) REAL array, dimension (MMAX) */

/*  WORK    (workspace) REAL array, dimension */
/*                      (MMAX*NMAX + 4*NMAX + MMAX) */

/*  NOUT    (input) INTEGER */
/*          The unit number for output. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Scalars in Common .. */
/*     .. */
/*     .. Common blocks .. */
/*     .. */
/*     .. Data statements .. */
    /* Parameter adjustments */
    --work;
    --tau;
    --copys;
    --s;
    --copya;
    --a;
    --nval;
    --mval;
    --dotype;

    /* Function Body */
/*     .. */
/*     .. Executable Statements .. */

/*     Initialize constants and the random number seed. */

    s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
    s_copy(path + 1, "TZ", (ftnlen)2, (ftnlen)2);
    nrun = 0;
    nfail = 0;
    nerrs = 0;
    for (i__ = 1; i__ <= 4; ++i__) {
	iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
    }
    eps = slamch_("Epsilon");

/*     Test the error exits */

    if (*tsterr) {
	serrtz_(path, nout);
    }
    infoc_1.infot = 0;

    i__1 = *nm;
    for (im = 1; im <= i__1; ++im) {

/*        Do for each value of M in MVAL. */

	m = mval[im];
	lda = max(1,m);

	i__2 = *nn;
	for (in = 1; in <= i__2; ++in) {

/*           Do for each value of N in NVAL for which M .LE. N. */

	    n = nval[in];
	    mnmin = min(m,n);
/* Computing MAX */
	    i__3 = 1, i__4 = n * n + (m << 2) + n, i__3 = max(i__3,i__4), 
		    i__4 = m * n + (mnmin << 1) + (n << 2);
	    lwork = max(i__3,i__4);

	    if (m <= n) {
		for (imode = 1; imode <= 3; ++imode) {
		    if (! dotype[imode]) {
			goto L50;
		    }

/*                 Do for each type of singular value distribution. */
/*                    0:  zero matrix */
/*                    1:  one small singular value */
/*                    2:  exponential distribution */

		    mode = imode - 1;

/*                 Test STZRQF */

/*                 Generate test matrix of size m by n using */
/*                 singular value distribution indicated by `mode'. */

		    if (mode == 0) {
			slaset_("Full", &m, &n, &c_b10, &c_b10, &a[1], &lda);
			i__3 = mnmin;
			for (i__ = 1; i__ <= i__3; ++i__) {
			    copys[i__] = 0.f;
/* L20: */
			}
		    } else {
			r__1 = 1.f / eps;
			slatms_(&m, &n, "Uniform", iseed, "Nonsymmetric", &
				copys[1], &imode, &r__1, &c_b15, &m, &n, 
				"No packing", &a[1], &lda, &work[1], &info);
			sgeqr2_(&m, &n, &a[1], &lda, &work[1], &work[mnmin + 
				1], &info);
			i__3 = m - 1;
			slaset_("Lower", &i__3, &n, &c_b10, &c_b10, &a[2], &
				lda);
			slaord_("Decreasing", &mnmin, &copys[1], &c__1);
		    }

/*                 Save A and its singular values */

		    slacpy_("All", &m, &n, &a[1], &lda, &copya[1], &lda);

/*                 Call STZRQF to reduce the upper trapezoidal matrix to */
/*                 upper triangular form. */

		    s_copy(srnamc_1.srnamt, "STZRQF", (ftnlen)32, (ftnlen)6);
		    stzrqf_(&m, &n, &a[1], &lda, &tau[1], &info);

/*                 Compute norm(svd(a) - svd(r)) */

		    result[0] = sqrt12_(&m, &m, &a[1], &lda, &copys[1], &work[
			    1], &lwork);

/*                 Compute norm( A - R*Q ) */

		    result[1] = stzt01_(&m, &n, &copya[1], &a[1], &lda, &tau[
			    1], &work[1], &lwork);

/*                 Compute norm(Q'*Q - I). */

		    result[2] = stzt02_(&m, &n, &a[1], &lda, &tau[1], &work[1]
, &lwork);

/*                 Test STZRZF */

/*                 Generate test matrix of size m by n using */
/*                 singular value distribution indicated by `mode'. */

		    if (mode == 0) {
			slaset_("Full", &m, &n, &c_b10, &c_b10, &a[1], &lda);
			i__3 = mnmin;
			for (i__ = 1; i__ <= i__3; ++i__) {
			    copys[i__] = 0.f;
/* L30: */
			}
		    } else {
			r__1 = 1.f / eps;
			slatms_(&m, &n, "Uniform", iseed, "Nonsymmetric", &
				copys[1], &imode, &r__1, &c_b15, &m, &n, 
				"No packing", &a[1], &lda, &work[1], &info);
			sgeqr2_(&m, &n, &a[1], &lda, &work[1], &work[mnmin + 
				1], &info);
			i__3 = m - 1;
			slaset_("Lower", &i__3, &n, &c_b10, &c_b10, &a[2], &
				lda);
			slaord_("Decreasing", &mnmin, &copys[1], &c__1);
		    }

/*                 Save A and its singular values */

		    slacpy_("All", &m, &n, &a[1], &lda, &copya[1], &lda);

/*                 Call STZRZF to reduce the upper trapezoidal matrix to */
/*                 upper triangular form. */

		    s_copy(srnamc_1.srnamt, "STZRZF", (ftnlen)32, (ftnlen)6);
		    stzrzf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lwork, &
			    info);

/*                 Compute norm(svd(a) - svd(r)) */

		    result[3] = sqrt12_(&m, &m, &a[1], &lda, &copys[1], &work[
			    1], &lwork);

/*                 Compute norm( A - R*Q ) */

		    result[4] = srzt01_(&m, &n, &copya[1], &a[1], &lda, &tau[
			    1], &work[1], &lwork);

/*                 Compute norm(Q'*Q - I). */

		    result[5] = srzt02_(&m, &n, &a[1], &lda, &tau[1], &work[1]
, &lwork);

/*                 Print information about the tests that did not pass */
/*                 the threshold. */

		    for (k = 1; k <= 6; ++k) {
			if (result[k - 1] >= *thresh) {
			    if (nfail == 0 && nerrs == 0) {
				alahd_(nout, path);
			    }
			    io___21.ciunit = *nout;
			    s_wsfe(&io___21);
			    do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
				    ;
			    do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
				    ;
			    do_fio(&c__1, (char *)&imode, (ftnlen)sizeof(
				    integer));
			    do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer))
				    ;
			    do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
				    sizeof(real));
			    e_wsfe();
			    ++nfail;
			}
/* L40: */
		    }
		    nrun += 6;
L50:
		    ;
		}
	    }
/* L60: */
	}
/* L70: */
    }

/*     Print a summary of the results. */

    alasum_(path, nout, &nfail, &nrun, &nerrs);


/*     End if SCHKTZ */

    return 0;
} /* schktz_ */
示例#2
0
/* Subroutine */ int 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 */
    static integer i__, j, k;
    static real c1, c2, s1, s2, t1, t2;
    static integer mn;
    static real anrm, bnrm, smin, smax;
    static integer iascl, ibscl, ismin, ismax;
    extern /* Subroutine */ int strsm_(char *, char *, char *, char *, 
	    integer *, integer *, real *, real *, integer *, real *, integer *
	    , ftnlen, ftnlen, ftnlen, ftnlen), slaic1_(integer *, integer *, 
	    real *, real *, real *, real *, real *, real *, real *), sorm2r_(
	    char *, char *, integer *, integer *, integer *, real *, integer *
	    , real *, real *, integer *, real *, integer *, ftnlen, ftnlen), 
	    slabad_(real *, real *);
    extern doublereal slamch_(char *, ftnlen), slange_(char *, integer *, 
	    integer *, real *, integer *, real *, ftnlen);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    static real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *, 
	    ftnlen), sgeqpf_(integer *, integer *, real *, integer *, integer 
	    *, real *, real *, integer *), slaset_(char *, integer *, integer 
	    *, real *, real *, real *, integer *, ftnlen);
    static real sminpr, smaxpr, smlnum;
    extern /* Subroutine */ int slatzm_(char *, integer *, integer *, real *, 
	    integer *, real *, real *, real *, integer *, real *, ftnlen), 
	    stzrqf_(integer *, integer *, real *, integer *, real *, integer *
	    );


/*  -- LAPACK driver routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     March 31, 1993 */

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

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

/*  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' [ inv(T11)*Q1'*B ] */
/*                [        0       ] */
/*  where Q1 consists of the first RANK columns of Q. */

/*  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 matrices B and X. NRHS >= 0. */

/*  A       (input/output) 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. */

/*  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, 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,M,N). */

/*  JPVT    (input/output) 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. */

/*  RCOND   (input) 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. */

/*  RANK    (output) 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. */

/*  WORK    (workspace) REAL array, dimension */
/*                      (max( min(M,N)+3*N, 2*min(M,N)+NRHS )), */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

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

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

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

    /* Function Body */
    mn = min(*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 < max(1,*m)) {
	*info = -5;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = max(1,*m);
	if (*ldb < max(i__1,*n)) {
	    *info = -7;
	}
    }

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

/*     Quick return if possible */

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

/*     Get machine parameters */

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

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

    anrm = slange_("M", m, n, &a[a_offset], lda, &work[1], (ftnlen)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, (ftnlen)1);
	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, (ftnlen)1);
	iascl = 2;
    } else if (anrm == 0.f) {

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

	i__1 = max(*m,*n);
	slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb, (ftnlen)
		1);
	*rank = 0;
	goto L100;
    }

    bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)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, (ftnlen)1);
	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, (ftnlen)1);
	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], dabs(r__1));
    smin = smax;
    if ((r__1 = a[a_dim1 + 1], dabs(r__1)) == 0.f) {
	*rank = 0;
	i__1 = max(*m,*n);
	slaset_("F", &i__1, nrhs, &c_b13, &c_b13, &b[b_offset], ldb, (ftnlen)
		1);
	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' * 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, (ftnlen)4, (ftnlen)
	    9);

/*     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, (ftnlen)4, (ftnlen)5, (
	    ftnlen)12, (ftnlen)8);

    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' * 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], (ftnlen)4);
/* 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, (ftnlen)1);
	slascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset], 
		lda, info, (ftnlen)1);
    } else if (iascl == 2) {
	slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
		 info, (ftnlen)1);
	slascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset], 
		lda, info, (ftnlen)1);
    }
    if (ibscl == 1) {
	slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info, (ftnlen)1);
    } else if (ibscl == 2) {
	slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
		 info, (ftnlen)1);
    }

L100:

    return 0;

/*     End of SGELSX */

} /* sgelsx_ */