dget51.c

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/* dget51.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_b9 = 1.;
static doublereal c_b10 = 0.;
static doublereal c_b13 = -1.;

/* Subroutine */ int dget51_(integer *itype, integer *n, doublereal *a, 
        integer *lda, doublereal *b, integer *ldb, doublereal *u, integer *
        ldu, doublereal *v, integer *ldv, doublereal *work, doublereal *
        result)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, u_dim1, u_offset, v_dim1, 
            v_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Local variables */
    doublereal ulp;
    integer jcol;
    doublereal unfl;
    integer jrow, jdiag;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
            integer *, doublereal *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *);
    doublereal anorm, wnorm;
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
            integer *, doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
            doublereal *, 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 */
/*  ======= */

/*       DGET51  generally checks a decomposition of the form */

/*               A = U B V' */

/*       where ' means transpose and U and V are orthogonal. */

/*       Specifically, if ITYPE=1 */

/*               RESULT = | A - U B V' | / ( |A| n ulp ) */

/*       If ITYPE=2, then: */

/*               RESULT = | A - B | / ( |A| n ulp ) */

/*       If ITYPE=3, then: */

/*               RESULT = | I - UU' | / ( n ulp ) */

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

/*  ITYPE   (input) INTEGER */
/*          Specifies the type of tests to be performed. */
/*          =1: RESULT = | A - U B V' | / ( |A| n ulp ) */
/*          =2: RESULT = | A - B | / ( |A| n ulp ) */
/*          =3: RESULT = | I - UU' | / ( n ulp ) */

/*  N       (input) INTEGER */
/*          The size of the matrix.  If it is zero, DGET51 does nothing. */
/*          It must be at least zero. */

/*  A       (input) DOUBLE PRECISION array, dimension (LDA, N) */
/*          The original (unfactored) matrix. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of A.  It must be at least 1 */
/*          and at least N. */

/*  B       (input) DOUBLE PRECISION array, dimension (LDB, N) */
/*          The factored matrix. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of B.  It must be at least 1 */
/*          and at least N. */

/*  U       (input) DOUBLE PRECISION array, dimension (LDU, N) */
/*          The orthogonal matrix on the left-hand side in the */
/*          decomposition. */
/*          Not referenced if ITYPE=2 */

/*  LDU     (input) INTEGER */
/*          The leading dimension of U.  LDU must be at least N and */
/*          at least 1. */

/*  V       (input) DOUBLE PRECISION array, dimension (LDV, N) */
/*          The orthogonal matrix on the left-hand side in the */
/*          decomposition. */
/*          Not referenced if ITYPE=2 */

/*  LDV     (input) INTEGER */
/*          The leading dimension of V.  LDV must be at least N and */
/*          at least 1. */

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

/*  RESULT  (output) DOUBLE PRECISION */
/*          The values computed by the test specified by ITYPE.  The */
/*          value is currently limited to 1/ulp, to avoid overflow. */
/*          Errors are flagged by RESULT=10/ulp. */

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

/*     .. 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;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    --work;

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

/*     Constants */

    unfl = dlamch_("Safe minimum");
    ulp = dlamch_("Epsilon") * dlamch_("Base");

/*     Some Error Checks */

    if (*itype < 1 || *itype > 3) {
        *result = 10. / ulp;
        return 0;
    }

    if (*itype <= 2) {

/*        Tests scaled by the norm(A) */

/* Computing MAX */
        d__1 = dlange_("1", n, n, &a[a_offset], lda, &work[1]);
        anorm = max(d__1,unfl);

        if (*itype == 1) {

/*           ITYPE=1: Compute W = A - UBV' */

            dlacpy_(" ", n, n, &a[a_offset], lda, &work[1], n);
/* Computing 2nd power */
            i__1 = *n;
            dgemm_("N", "N", n, n, n, &c_b9, &u[u_offset], ldu, &b[b_offset], 
                    ldb, &c_b10, &work[i__1 * i__1 + 1], n);

/* Computing 2nd power */
            i__1 = *n;
            dgemm_("N", "C", n, n, n, &c_b13, &work[i__1 * i__1 + 1], n, &v[
                    v_offset], ldv, &c_b9, &work[1], n);

        } else {

/*           ITYPE=2: Compute W = A - B */

            dlacpy_(" ", n, n, &b[b_offset], ldb, &work[1], n);

            i__1 = *n;
            for (jcol = 1; jcol <= i__1; ++jcol) {
                i__2 = *n;
                for (jrow = 1; jrow <= i__2; ++jrow) {
                    work[jrow + *n * (jcol - 1)] -= a[jrow + jcol * a_dim1];
/* L10: */
                }
/* L20: */
            }
        }

/*        Compute norm(W)/ ( ulp*norm(A) ) */

/* Computing 2nd power */
        i__1 = *n;
        wnorm = dlange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]);

        if (anorm > wnorm) {
            *result = wnorm / anorm / (*n * ulp);
        } else {
            if (anorm < 1.) {
/* Computing MIN */
                d__1 = wnorm, d__2 = *n * anorm;
                *result = min(d__1,d__2) / anorm / (*n * ulp);
            } else {
/* Computing MIN */
                d__1 = wnorm / anorm, d__2 = (doublereal) (*n);
                *result = min(d__1,d__2) / (*n * ulp);
            }
        }

    } else {

/*        Tests not scaled by norm(A) */

/*        ITYPE=3: Compute  UU' - I */

        dgemm_("N", "C", n, n, n, &c_b9, &u[u_offset], ldu, &u[u_offset], ldu, 
                 &c_b10, &work[1], n);

        i__1 = *n;
        for (jdiag = 1; jdiag <= i__1; ++jdiag) {
            work[(*n + 1) * (jdiag - 1) + 1] += -1.;
/* L30: */
        }

/* Computing MIN */
/* Computing 2nd power */
        i__1 = *n;
        d__1 = dlange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]), d__2 = (doublereal) (*n);
        *result = min(d__1,d__2) / (*n * ulp);
    }

    return 0;

/*     End of DGET51 */

} /* dget51_ */