dbdt03.c

Go to the documentation of this file.

/* dbdt03.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 doublereal c_b6 = -1.;
static integer c__1 = 1;
static doublereal c_b8 = 0.;

/* Subroutine */ int dbdt03_(char *uplo, integer *n, integer *kd, doublereal *
        d__, doublereal *e, doublereal *u, integer *ldu, doublereal *s, 
        doublereal *vt, integer *ldvt, doublereal *work, doublereal *resid)
{
    /* System generated locals */
    integer u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2;
    doublereal d__1, d__2, d__3, d__4;

    /* Local variables */
    integer i__, j;
    doublereal eps;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *);
    extern doublereal dasum_(integer *, doublereal *, integer *);
    doublereal bnorm;
    extern doublereal dlamch_(char *);
    extern integer idamax_(integer *, doublereal *, integer *);


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

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

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

/*  DBDT03 reconstructs a bidiagonal matrix B from its SVD: */
/*     S = U' * B * V */
/*  where U and V are orthogonal matrices and S is diagonal. */

/*  The test ratio to test the singular value decomposition is */
/*     RESID = norm( B - U * S * VT ) / ( n * norm(B) * EPS ) */
/*  where VT = V' and EPS is the machine precision. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the matrix B is upper or lower bidiagonal. */
/*          = 'U':  Upper bidiagonal */
/*          = 'L':  Lower bidiagonal */

/*  N       (input) INTEGER */
/*          The order of the matrix B. */

/*  KD      (input) INTEGER */
/*          The bandwidth of the bidiagonal matrix B.  If KD = 1, the */
/*          matrix B is bidiagonal, and if KD = 0, B is diagonal and E is */
/*          not referenced.  If KD is greater than 1, it is assumed to be */
/*          1, and if KD is less than 0, it is assumed to be 0. */

/*  D       (input) DOUBLE PRECISION array, dimension (N) */
/*          The n diagonal elements of the bidiagonal matrix B. */

/*  E       (input) DOUBLE PRECISION array, dimension (N-1) */
/*          The (n-1) superdiagonal elements of the bidiagonal matrix B */
/*          if UPLO = 'U', or the (n-1) subdiagonal elements of B if */
/*          UPLO = 'L'. */

/*  U       (input) DOUBLE PRECISION array, dimension (LDU,N) */
/*          The n by n orthogonal matrix U in the reduction B = U'*A*P. */

/*  LDU     (input) INTEGER */
/*          The leading dimension of the array U.  LDU >= max(1,N) */

/*  S       (input) DOUBLE PRECISION array, dimension (N) */
/*          The singular values from the SVD of B, sorted in decreasing */
/*          order. */

/*  VT      (input) DOUBLE PRECISION array, dimension (LDVT,N) */
/*          The n by n orthogonal matrix V' in the reduction */
/*          B = U * S * V'. */

/*  LDVT    (input) INTEGER */
/*          The leading dimension of the array VT. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N) */

/*  RESID   (output) DOUBLE PRECISION */
/*          The test ratio:  norm(B - U * S * V') / ( n * norm(A) * EPS ) */

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

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

/*     Quick return if possible */

    /* Parameter adjustments */
    --d__;
    --e;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    --s;
    vt_dim1 = *ldvt;
    vt_offset = 1 + vt_dim1;
    vt -= vt_offset;
    --work;

    /* Function Body */
    *resid = 0.;
    if (*n <= 0) {
        return 0;
    }

/*     Compute B - U * S * V' one column at a time. */

    bnorm = 0.;
    if (*kd >= 1) {

/*        B is bidiagonal. */

        if (lsame_(uplo, "U")) {

/*           B is upper bidiagonal. */

            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = *n;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    work[*n + i__] = s[i__] * vt[i__ + j * vt_dim1];
/* L10: */
                }
                dgemv_("No transpose", n, n, &c_b6, &u[u_offset], ldu, &work[*
                        n + 1], &c__1, &c_b8, &work[1], &c__1);
                work[j] += d__[j];
                if (j > 1) {
                    work[j - 1] += e[j - 1];
/* Computing MAX */
                    d__3 = bnorm, d__4 = (d__1 = d__[j], abs(d__1)) + (d__2 = 
                            e[j - 1], abs(d__2));
                    bnorm = max(d__3,d__4);
                } else {
/* Computing MAX */
                    d__2 = bnorm, d__3 = (d__1 = d__[j], abs(d__1));
                    bnorm = max(d__2,d__3);
                }
/* Computing MAX */
                d__1 = *resid, d__2 = dasum_(n, &work[1], &c__1);
                *resid = max(d__1,d__2);
/* L20: */
            }
        } else {

/*           B is lower bidiagonal. */

            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = *n;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    work[*n + i__] = s[i__] * vt[i__ + j * vt_dim1];
/* L30: */
                }
                dgemv_("No transpose", n, n, &c_b6, &u[u_offset], ldu, &work[*
                        n + 1], &c__1, &c_b8, &work[1], &c__1);
                work[j] += d__[j];
                if (j < *n) {
                    work[j + 1] += e[j];
/* Computing MAX */
                    d__3 = bnorm, d__4 = (d__1 = d__[j], abs(d__1)) + (d__2 = 
                            e[j], abs(d__2));
                    bnorm = max(d__3,d__4);
                } else {
/* Computing MAX */
                    d__2 = bnorm, d__3 = (d__1 = d__[j], abs(d__1));
                    bnorm = max(d__2,d__3);
                }
/* Computing MAX */
                d__1 = *resid, d__2 = dasum_(n, &work[1], &c__1);
                *resid = max(d__1,d__2);
/* L40: */
            }
        }
    } else {

/*        B is diagonal. */

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            i__2 = *n;
            for (i__ = 1; i__ <= i__2; ++i__) {
                work[*n + i__] = s[i__] * vt[i__ + j * vt_dim1];
/* L50: */
            }
            dgemv_("No transpose", n, n, &c_b6, &u[u_offset], ldu, &work[*n + 
                    1], &c__1, &c_b8, &work[1], &c__1);
            work[j] += d__[j];
/* Computing MAX */
            d__1 = *resid, d__2 = dasum_(n, &work[1], &c__1);
            *resid = max(d__1,d__2);
/* L60: */
        }
        j = idamax_(n, &d__[1], &c__1);
        bnorm = (d__1 = d__[j], abs(d__1));
    }

/*     Compute norm(B - U * S * V') / ( n * norm(B) * EPS ) */

    eps = dlamch_("Precision");

    if (bnorm <= 0.) {
        if (*resid != 0.) {
            *resid = 1. / eps;
        }
    } else {
        if (bnorm >= *resid) {
            *resid = *resid / bnorm / ((doublereal) (*n) * eps);
        } else {
            if (bnorm < 1.) {
/* Computing MIN */
                d__1 = *resid, d__2 = (doublereal) (*n) * bnorm;
                *resid = min(d__1,d__2) / bnorm / ((doublereal) (*n) * eps);
            } else {
/* Computing MIN */
                d__1 = *resid / bnorm, d__2 = (doublereal) (*n);
                *resid = min(d__1,d__2) / ((doublereal) (*n) * eps);
            }
        }
    }

    return 0;

/*     End of DBDT03 */

} /* dbdt03_ */