dlagsy.c

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/* dlagsy.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__3 = 3;
static integer c__1 = 1;
static doublereal c_b12 = 0.;
static doublereal c_b19 = -1.;
static doublereal c_b26 = 1.;

/* Subroutine */ int dlagsy_(integer *n, integer *k, doublereal *d__, 
        doublereal *a, integer *lda, integer *iseed, doublereal *work, 
        integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    doublereal d__1;

    /* Builtin functions */
    double d_sign(doublereal *, doublereal *);

    /* Local variables */
    integer i__, j;
    doublereal wa, wb, wn, tau;
    extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *);
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
            integer *), dnrm2_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *);
    doublereal alpha;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
            integer *), dgemv_(char *, integer *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            doublereal *, integer *), daxpy_(integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *), dsymv_(char *, 
            integer *, doublereal *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *), 
            xerbla_(char *, integer *), dlarnv_(integer *, integer *, 
            integer *, doublereal *);


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

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

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

/*  DLAGSY generates a real symmetric matrix A, by pre- and post- */
/*  multiplying a real diagonal matrix D with a random orthogonal matrix: */
/*  A = U*D*U'. The semi-bandwidth may then be reduced to k by additional */
/*  orthogonal transformations. */

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

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  K       (input) INTEGER */
/*          The number of nonzero subdiagonals within the band of A. */
/*          0 <= K <= N-1. */

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

/*  A       (output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          The generated n by n symmetric matrix A (the full matrix is */
/*          stored). */

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

/*  ISEED   (input/output) INTEGER array, dimension (4) */
/*          On entry, the seed of the random number generator; the array */
/*          elements must be between 0 and 4095, and ISEED(4) must be */
/*          odd. */
/*          On exit, the seed is updated. */

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

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

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

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

/*     Test the input arguments */

    /* Parameter adjustments */
    --d__;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --iseed;
    --work;

    /* Function Body */
    *info = 0;
    if (*n < 0) {
        *info = -1;
    } else if (*k < 0 || *k > *n - 1) {
        *info = -2;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    }
    if (*info < 0) {
        i__1 = -(*info);
        xerbla_("DLAGSY", &i__1);
        return 0;
    }

/*     initialize lower triangle of A to diagonal matrix */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        i__2 = *n;
        for (i__ = j + 1; i__ <= i__2; ++i__) {
            a[i__ + j * a_dim1] = 0.;
/* L10: */
        }
/* L20: */
    }
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        a[i__ + i__ * a_dim1] = d__[i__];
/* L30: */
    }

/*     Generate lower triangle of symmetric matrix */

    for (i__ = *n - 1; i__ >= 1; --i__) {

/*        generate random reflection */

        i__1 = *n - i__ + 1;
        dlarnv_(&c__3, &iseed[1], &i__1, &work[1]);
        i__1 = *n - i__ + 1;
        wn = dnrm2_(&i__1, &work[1], &c__1);
        wa = d_sign(&wn, &work[1]);
        if (wn == 0.) {
            tau = 0.;
        } else {
            wb = work[1] + wa;
            i__1 = *n - i__;
            d__1 = 1. / wb;
            dscal_(&i__1, &d__1, &work[2], &c__1);
            work[1] = 1.;
            tau = wb / wa;
        }

/*        apply random reflection to A(i:n,i:n) from the left */
/*        and the right */

/*        compute  y := tau * A * u */

        i__1 = *n - i__ + 1;
        dsymv_("Lower", &i__1, &tau, &a[i__ + i__ * a_dim1], lda, &work[1], &
                c__1, &c_b12, &work[*n + 1], &c__1);

/*        compute  v := y - 1/2 * tau * ( y, u ) * u */

        i__1 = *n - i__ + 1;
        alpha = tau * -.5 * ddot_(&i__1, &work[*n + 1], &c__1, &work[1], &
                c__1);
        i__1 = *n - i__ + 1;
        daxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);

/*        apply the transformation as a rank-2 update to A(i:n,i:n) */

        i__1 = *n - i__ + 1;
        dsyr2_("Lower", &i__1, &c_b19, &work[1], &c__1, &work[*n + 1], &c__1, 
                &a[i__ + i__ * a_dim1], lda);
/* L40: */
    }

/*     Reduce number of subdiagonals to K */

    i__1 = *n - 1 - *k;
    for (i__ = 1; i__ <= i__1; ++i__) {

/*        generate reflection to annihilate A(k+i+1:n,i) */

        i__2 = *n - *k - i__ + 1;
        wn = dnrm2_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
        wa = d_sign(&wn, &a[*k + i__ + i__ * a_dim1]);
        if (wn == 0.) {
            tau = 0.;
        } else {
            wb = a[*k + i__ + i__ * a_dim1] + wa;
            i__2 = *n - *k - i__;
            d__1 = 1. / wb;
            dscal_(&i__2, &d__1, &a[*k + i__ + 1 + i__ * a_dim1], &c__1);
            a[*k + i__ + i__ * a_dim1] = 1.;
            tau = wb / wa;
        }

/*        apply reflection to A(k+i:n,i+1:k+i-1) from the left */

        i__2 = *n - *k - i__ + 1;
        i__3 = *k - 1;
        dgemv_("Transpose", &i__2, &i__3, &c_b26, &a[*k + i__ + (i__ + 1) * 
                a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &c_b12, &
                work[1], &c__1);
        i__2 = *n - *k - i__ + 1;
        i__3 = *k - 1;
        d__1 = -tau;
        dger_(&i__2, &i__3, &d__1, &a[*k + i__ + i__ * a_dim1], &c__1, &work[
                1], &c__1, &a[*k + i__ + (i__ + 1) * a_dim1], lda);

/*        apply reflection to A(k+i:n,k+i:n) from the left and the right */

/*        compute  y := tau * A * u */

        i__2 = *n - *k - i__ + 1;
        dsymv_("Lower", &i__2, &tau, &a[*k + i__ + (*k + i__) * a_dim1], lda, 
                &a[*k + i__ + i__ * a_dim1], &c__1, &c_b12, &work[1], &c__1);

/*        compute  v := y - 1/2 * tau * ( y, u ) * u */

        i__2 = *n - *k - i__ + 1;
        alpha = tau * -.5 * ddot_(&i__2, &work[1], &c__1, &a[*k + i__ + i__ * 
                a_dim1], &c__1);
        i__2 = *n - *k - i__ + 1;
        daxpy_(&i__2, &alpha, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
                c__1);

/*        apply symmetric rank-2 update to A(k+i:n,k+i:n) */

        i__2 = *n - *k - i__ + 1;
        dsyr2_("Lower", &i__2, &c_b19, &a[*k + i__ + i__ * a_dim1], &c__1, &
                work[1], &c__1, &a[*k + i__ + (*k + i__) * a_dim1], lda);

        a[*k + i__ + i__ * a_dim1] = -wa;
        i__2 = *n;
        for (j = *k + i__ + 1; j <= i__2; ++j) {
            a[j + i__ * a_dim1] = 0.;
/* L50: */
        }
/* L60: */
    }

/*     Store full symmetric matrix */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        i__2 = *n;
        for (i__ = j + 1; i__ <= i__2; ++i__) {
            a[j + i__ * a_dim1] = a[i__ + j * a_dim1];
/* L70: */
        }
/* L80: */
    }
    return 0;

/*     End of DLAGSY */

} /* dlagsy_ */