sqrt14.c

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/* sqrt14.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__10 = 10;
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b15 = 1.f;

doublereal sqrt14_(char *trans, integer *m, integer *n, integer *nrhs, real *
        a, integer *lda, real *x, integer *ldx, real *work, integer *lwork)
{
    /* System generated locals */
    integer a_dim1, a_offset, x_dim1, x_offset, i__1, i__2, i__3;
    real ret_val, r__1, r__2, r__3;

    /* Local variables */
    integer i__, j;
    real err;
    integer info;
    real anrm;
    logical tpsd;
    real xnrm;
    extern logical lsame_(char *, char *);
    real rwork[1];
    extern /* Subroutine */ int sgelq2_(integer *, integer *, real *, integer 
            *, real *, real *, integer *), sgeqr2_(integer *, integer *, real 
            *, integer *, real *, real *, integer *);
    extern doublereal slamch_(char *), slange_(char *, integer *, 
            integer *, real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *), slascl_(
            char *, integer *, integer *, real *, real *, integer *, integer *
, real *, integer *, integer *), slacpy_(char *, integer *
, integer *, real *, integer *, real *, integer *);
    integer ldwork;


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

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

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

/*  SQRT14 checks whether X is in the row space of A or A'.  It does so */
/*  by scaling both X and A such that their norms are in the range */
/*  [sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X] */
/*  (if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'), */
/*  and returning the norm of the trailing triangle, scaled by */
/*  MAX(M,N,NRHS)*eps. */

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

/*  TRANS   (input) CHARACTER*1 */
/*          = 'N':  No transpose, check for X in the row space of A */
/*          = 'T':  Transpose, check for X in the row space of A'. */

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

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

/*  NRHS    (input) INTEGER */
/*          The number of right hand sides, i.e., the number of columns */
/*          of X. */

/*  A       (input) REAL array, dimension (LDA,N) */
/*          The M-by-N matrix A. */

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

/*  X       (input) REAL array, dimension (LDX,NRHS) */
/*          If TRANS = 'N', the N-by-NRHS matrix X. */
/*          IF TRANS = 'T', the M-by-NRHS matrix X. */

/*  LDX     (input) INTEGER */
/*          The leading dimension of the array X. */

/*  WORK    (workspace) REAL array dimension (LWORK) */

/*  LWORK   (input) INTEGER */
/*          length of workspace array required */
/*          If TRANS = 'N', LWORK >= (M+NRHS)*(N+2); */
/*          if TRANS = 'T', LWORK >= (N+NRHS)*(M+2). */

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

/*     .. 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;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    --work;

    /* Function Body */
    ret_val = 0.f;
    if (lsame_(trans, "N")) {
        ldwork = *m + *nrhs;
        tpsd = FALSE_;
        if (*lwork < (*m + *nrhs) * (*n + 2)) {
            xerbla_("SQRT14", &c__10);
            return ret_val;
        } else if (*n <= 0 || *nrhs <= 0) {
            return ret_val;
        }
    } else if (lsame_(trans, "T")) {
        ldwork = *m;
        tpsd = TRUE_;
        if (*lwork < (*n + *nrhs) * (*m + 2)) {
            xerbla_("SQRT14", &c__10);
            return ret_val;
        } else if (*m <= 0 || *nrhs <= 0) {
            return ret_val;
        }
    } else {
        xerbla_("SQRT14", &c__1);
        return ret_val;
    }

/*     Copy and scale A */

    slacpy_("All", m, n, &a[a_offset], lda, &work[1], &ldwork);
    anrm = slange_("M", m, n, &work[1], &ldwork, rwork);
    if (anrm != 0.f) {
        slascl_("G", &c__0, &c__0, &anrm, &c_b15, m, n, &work[1], &ldwork, &
                info);
    }

/*     Copy X or X' into the right place and scale it */

    if (tpsd) {

/*        Copy X into columns n+1:n+nrhs of work */

        slacpy_("All", m, nrhs, &x[x_offset], ldx, &work[*n * ldwork + 1], &
                ldwork);
        xnrm = slange_("M", m, nrhs, &work[*n * ldwork + 1], &ldwork, rwork);
        if (xnrm != 0.f) {
            slascl_("G", &c__0, &c__0, &xnrm, &c_b15, m, nrhs, &work[*n * 
                    ldwork + 1], &ldwork, &info);
        }
        i__1 = *n + *nrhs;
        anrm = slange_("One-norm", m, &i__1, &work[1], &ldwork, rwork);

/*        Compute QR factorization of X */

        i__1 = *n + *nrhs;
/* Computing MIN */
        i__2 = *m, i__3 = *n + *nrhs;
        sgeqr2_(m, &i__1, &work[1], &ldwork, &work[ldwork * (*n + *nrhs) + 1], 
                 &work[ldwork * (*n + *nrhs) + min(i__2, i__3)+ 1], &info);

/*        Compute largest entry in upper triangle of */
/*        work(n+1:m,n+1:n+nrhs) */

        err = 0.f;
        i__1 = *n + *nrhs;
        for (j = *n + 1; j <= i__1; ++j) {
            i__2 = min(*m,j);
            for (i__ = *n + 1; i__ <= i__2; ++i__) {
/* Computing MAX */
                r__2 = err, r__3 = (r__1 = work[i__ + (j - 1) * *m], dabs(
                        r__1));
                err = dmax(r__2,r__3);
/* L10: */
            }
/* L20: */
        }

    } else {

/*        Copy X' into rows m+1:m+nrhs of work */

        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            i__2 = *nrhs;
            for (j = 1; j <= i__2; ++j) {
                work[*m + j + (i__ - 1) * ldwork] = x[i__ + j * x_dim1];
/* L30: */
            }
/* L40: */
        }

        xnrm = slange_("M", nrhs, n, &work[*m + 1], &ldwork, rwork)
                ;
        if (xnrm != 0.f) {
            slascl_("G", &c__0, &c__0, &xnrm, &c_b15, nrhs, n, &work[*m + 1], 
                    &ldwork, &info);
        }

/*        Compute LQ factorization of work */

        sgelq2_(&ldwork, n, &work[1], &ldwork, &work[ldwork * *n + 1], &work[
                ldwork * (*n + 1) + 1], &info);

/*        Compute largest entry in lower triangle in */
/*        work(m+1:m+nrhs,m+1:n) */

        err = 0.f;
        i__1 = *n;
        for (j = *m + 1; j <= i__1; ++j) {
            i__2 = ldwork;
            for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
                r__2 = err, r__3 = (r__1 = work[i__ + (j - 1) * ldwork], dabs(
                        r__1));
                err = dmax(r__2,r__3);
/* L50: */
            }
/* L60: */
        }

    }

/* Computing MAX */
    i__1 = max(*m,*n);
    ret_val = err / ((real) max(i__1,*nrhs) * slamch_("Epsilon"));

    return ret_val;

/*     End of SQRT14 */

} /* sqrt14_ */