zqrt15.c

Go to the documentation of this file.

/* zqrt15.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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__16 = 16;
static integer c__2 = 2;
static integer c__1 = 1;
static doublecomplex c_b22 = {2.,0.};
static integer c__0 = 0;

/* Subroutine */ int zqrt15_(integer *scale, integer *rksel, integer *m, 
        integer *n, integer *nrhs, doublecomplex *a, integer *lda, 
        doublecomplex *b, integer *ldb, doublereal *s, integer *rank, 
        doublereal *norma, doublereal *normb, integer *iseed, doublecomplex *
        work, integer *lwork)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
    doublereal d__1;

    /* Local variables */
    integer j, mn;
    doublereal eps;
    integer info;
    doublereal temp;
    extern doublereal dasum_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int zlarf_(char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
            integer *, doublecomplex *), zgemm_(char *, char *, 
            integer *, integer *, integer *, doublecomplex *, doublecomplex *, 
             integer *, doublecomplex *, integer *, doublecomplex *, 
            doublecomplex *, integer *);
    doublereal dummy[1];
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    extern doublereal dznrm2_(integer *, doublecomplex *, integer *), dlamch_(
            char *);
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, integer *, doublereal *, 
            integer *, integer *);
    extern doublereal dlarnd_(integer *, integer *);
    extern /* Subroutine */ int dlaord_(char *, integer *, doublereal *, 
            integer *), xerbla_(char *, integer *);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
            integer *, doublereal *);
    doublereal bignum;
    extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
            doublecomplex *, integer *), zlascl_(char *, integer *, integer *, 
             doublereal *, doublereal *, integer *, integer *, doublecomplex *
, integer *, integer *), zlaset_(char *, integer *, 
            integer *, doublecomplex *, doublecomplex *, doublecomplex *, 
            integer *), zlaror_(char *, char *, integer *, integer *, 
            doublecomplex *, integer *, integer *, doublecomplex *, integer *);
    doublereal smlnum;
    extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *, 
            doublecomplex *);


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  ZQRT15 generates a matrix with full or deficient rank and of various */
/*  norms. */

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

/*  SCALE   (input) INTEGER */
/*          SCALE = 1: normally scaled matrix */
/*          SCALE = 2: matrix scaled up */
/*          SCALE = 3: matrix scaled down */

/*  RKSEL   (input) INTEGER */
/*          RKSEL = 1: full rank matrix */
/*          RKSEL = 2: rank-deficient matrix */

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

/*  N       (input) INTEGER */
/*          The number of columns of A. */

/*  NRHS    (input) INTEGER */
/*          The number of columns of B. */

/*  A       (output) COMPLEX*16 array, dimension (LDA,N) */
/*          The M-by-N matrix A. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A. */

/*  B       (output) COMPLEX*16 array, dimension (LDB, NRHS) */
/*          A matrix that is in the range space of matrix A. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B. */

/*  S       (output) DOUBLE PRECISION array, dimension MIN(M,N) */
/*          Singular values of A. */

/*  RANK    (output) INTEGER */
/*          number of nonzero singular values of A. */

/*  NORMA   (output) DOUBLE PRECISION */
/*          one-norm norm of A. */

/*  NORMB   (output) DOUBLE PRECISION */
/*          one-norm norm of B. */

/*  ISEED   (input/output) integer array, dimension (4) */
/*          seed for random number generator. */

/*  WORK    (workspace) COMPLEX*16 array, dimension (LWORK) */

/*  LWORK   (input) INTEGER */
/*          length of work space required. */
/*          LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M) */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. 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;
    --s;
    --iseed;
    --work;

    /* Function Body */
    mn = min(*m,*n);
/* Computing MAX */
    i__1 = *m + mn, i__2 = mn * *nrhs, i__1 = max(i__1,i__2), i__2 = (*n << 1)
             + *m;
    if (*lwork < max(i__1,i__2)) {
        xerbla_("ZQRT15", &c__16);
        return 0;
    }

    smlnum = dlamch_("Safe minimum");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    eps = dlamch_("Epsilon");
    smlnum = smlnum / eps / eps;
    bignum = 1. / smlnum;

/*     Determine rank and (unscaled) singular values */

    if (*rksel == 1) {
        *rank = mn;
    } else if (*rksel == 2) {
        *rank = mn * 3 / 4;
        i__1 = mn;
        for (j = *rank + 1; j <= i__1; ++j) {
            s[j] = 0.;
/* L10: */
        }
    } else {
        xerbla_("ZQRT15", &c__2);
    }

    if (*rank > 0) {

/*        Nontrivial case */

        s[1] = 1.;
        i__1 = *rank;
        for (j = 2; j <= i__1; ++j) {
L20:
            temp = dlarnd_(&c__1, &iseed[1]);
            if (temp > .1) {
                s[j] = abs(temp);
            } else {
                goto L20;
            }
/* L30: */
        }
        dlaord_("Decreasing", rank, &s[1], &c__1);

/*        Generate 'rank' columns of a random orthogonal matrix in A */

        zlarnv_(&c__2, &iseed[1], m, &work[1]);
        d__1 = 1. / dznrm2_(m, &work[1], &c__1);
        zdscal_(m, &d__1, &work[1], &c__1);
        zlaset_("Full", m, rank, &c_b1, &c_b2, &a[a_offset], lda);
        zlarf_("Left", m, rank, &work[1], &c__1, &c_b22, &a[a_offset], lda, &
                work[*m + 1]);

/*        workspace used: m+mn */

/*        Generate consistent rhs in the range space of A */

        i__1 = *rank * *nrhs;
        zlarnv_(&c__2, &iseed[1], &i__1, &work[1]);
        zgemm_("No transpose", "No transpose", m, nrhs, rank, &c_b2, &a[
                a_offset], lda, &work[1], rank, &c_b1, &b[b_offset], ldb);

/*        work space used: <= mn *nrhs */

/*        generate (unscaled) matrix A */

        i__1 = *rank;
        for (j = 1; j <= i__1; ++j) {
            zdscal_(m, &s[j], &a[j * a_dim1 + 1], &c__1);
/* L40: */
        }
        if (*rank < *n) {
            i__1 = *n - *rank;
            zlaset_("Full", m, &i__1, &c_b1, &c_b1, &a[(*rank + 1) * a_dim1 + 
                    1], lda);
        }
        zlaror_("Right", "No initialization", m, n, &a[a_offset], lda, &iseed[
                1], &work[1], &info);

    } else {

/*        work space used 2*n+m */

/*        Generate null matrix and rhs */

        i__1 = mn;
        for (j = 1; j <= i__1; ++j) {
            s[j] = 0.;
/* L50: */
        }
        zlaset_("Full", m, n, &c_b1, &c_b1, &a[a_offset], lda);
        zlaset_("Full", m, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);

    }

/*     Scale the matrix */

    if (*scale != 1) {
        *norma = zlange_("Max", m, n, &a[a_offset], lda, dummy);
        if (*norma != 0.) {
            if (*scale == 2) {

/*              matrix scaled up */

                zlascl_("General", &c__0, &c__0, norma, &bignum, m, n, &a[
                        a_offset], lda, &info);
                dlascl_("General", &c__0, &c__0, norma, &bignum, &mn, &c__1, &
                        s[1], &mn, &info);
                zlascl_("General", &c__0, &c__0, norma, &bignum, m, nrhs, &b[
                        b_offset], ldb, &info);
            } else if (*scale == 3) {

/*              matrix scaled down */

                zlascl_("General", &c__0, &c__0, norma, &smlnum, m, n, &a[
                        a_offset], lda, &info);
                dlascl_("General", &c__0, &c__0, norma, &smlnum, &mn, &c__1, &
                        s[1], &mn, &info);
                zlascl_("General", &c__0, &c__0, norma, &smlnum, m, nrhs, &b[
                        b_offset], ldb, &info);
            } else {
                xerbla_("ZQRT15", &c__1);
                return 0;
            }
        }
    }

    *norma = dasum_(&mn, &s[1], &c__1);
    *normb = zlange_("One-norm", m, nrhs, &b[b_offset], ldb, dummy)
            ;

    return 0;

/*     End of ZQRT15 */

} /* zqrt15_ */