zlagsy.c

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/* zlagsy.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__3 = 3;
static integer c__1 = 1;

/* Subroutine */ int zlagsy_(integer *n, integer *k, doublereal *d__, 
        doublecomplex *a, integer *lda, integer *iseed, doublecomplex *work, 
        integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, 
            i__9;
    doublereal d__1;
    doublecomplex z__1, z__2, z__3, z__4;

    /* Builtin functions */
    double z_abs(doublecomplex *);
    void z_div(doublecomplex *, doublecomplex *, doublecomplex *);

    /* Local variables */
    integer i__, j, ii, jj;
    doublecomplex wa, wb;
    doublereal wn;
    doublecomplex tau, alpha;
    extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zscal_(integer *, doublecomplex *, 
            doublecomplex *, integer *);
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *), 
            zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zsymv_(char *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *);
    extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *), zlacgv_(
            integer *, doublecomplex *, integer *), zlarnv_(integer *, 
            integer *, integer *, doublecomplex *);


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

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

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

/*  ZLAGSY generates a complex symmetric matrix A, by pre- and post- */
/*  multiplying a real diagonal matrix D with a random unitary matrix: */
/*  A = U*D*U**T. The semi-bandwidth may then be reduced to k by */
/*  additional unitary 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) COMPLEX*16 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) COMPLEX*16 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_("ZLAGSY", &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__) {
            i__3 = i__ + j * a_dim1;
            a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
        }
/* L20: */
    }
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        i__2 = i__ + i__ * a_dim1;
        i__3 = i__;
        a[i__2].r = d__[i__3], a[i__2].i = 0.;
/* L30: */
    }

/*     Generate lower triangle of symmetric matrix */

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

/*        generate random reflection */

        i__1 = *n - i__ + 1;
        zlarnv_(&c__3, &iseed[1], &i__1, &work[1]);
        i__1 = *n - i__ + 1;
        wn = dznrm2_(&i__1, &work[1], &c__1);
        d__1 = wn / z_abs(&work[1]);
        z__1.r = d__1 * work[1].r, z__1.i = d__1 * work[1].i;
        wa.r = z__1.r, wa.i = z__1.i;
        if (wn == 0.) {
            tau.r = 0., tau.i = 0.;
        } else {
            z__1.r = work[1].r + wa.r, z__1.i = work[1].i + wa.i;
            wb.r = z__1.r, wb.i = z__1.i;
            i__1 = *n - i__;
            z_div(&z__1, &c_b2, &wb);
            zscal_(&i__1, &z__1, &work[2], &c__1);
            work[1].r = 1., work[1].i = 0.;
            z_div(&z__1, &wb, &wa);
            d__1 = z__1.r;
            tau.r = d__1, tau.i = 0.;
        }

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

/*        compute  y := tau * A * conjg(u) */

        i__1 = *n - i__ + 1;
        zlacgv_(&i__1, &work[1], &c__1);
        i__1 = *n - i__ + 1;
        zsymv_("Lower", &i__1, &tau, &a[i__ + i__ * a_dim1], lda, &work[1], &
                c__1, &c_b1, &work[*n + 1], &c__1);
        i__1 = *n - i__ + 1;
        zlacgv_(&i__1, &work[1], &c__1);

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

        z__3.r = -.5, z__3.i = -0.;
        z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i + 
                z__3.i * tau.r;
        i__1 = *n - i__ + 1;
        zdotc_(&z__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
        z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i 
                + z__2.i * z__4.r;
        alpha.r = z__1.r, alpha.i = z__1.i;
        i__1 = *n - i__ + 1;
        zaxpy_(&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) */

/*        CALL ZSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, */
/*        $               A( I, I ), LDA ) */

        i__1 = *n;
        for (jj = i__; jj <= i__1; ++jj) {
            i__2 = *n;
            for (ii = jj; ii <= i__2; ++ii) {
                i__3 = ii + jj * a_dim1;
                i__4 = ii + jj * a_dim1;
                i__5 = ii - i__ + 1;
                i__6 = *n + jj - i__ + 1;
                z__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
                        i__6].i, z__3.i = work[i__5].r * work[i__6].i + work[
                        i__5].i * work[i__6].r;
                z__2.r = a[i__4].r - z__3.r, z__2.i = a[i__4].i - z__3.i;
                i__7 = *n + ii - i__ + 1;
                i__8 = jj - i__ + 1;
                z__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
                        i__8].i, z__4.i = work[i__7].r * work[i__8].i + work[
                        i__7].i * work[i__8].r;
                z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i;
                a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L40: */
            }
/* L50: */
        }
/* L60: */
    }

/*     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 = dznrm2_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
        d__1 = wn / z_abs(&a[*k + i__ + i__ * a_dim1]);
        i__2 = *k + i__ + i__ * a_dim1;
        z__1.r = d__1 * a[i__2].r, z__1.i = d__1 * a[i__2].i;
        wa.r = z__1.r, wa.i = z__1.i;
        if (wn == 0.) {
            tau.r = 0., tau.i = 0.;
        } else {
            i__2 = *k + i__ + i__ * a_dim1;
            z__1.r = a[i__2].r + wa.r, z__1.i = a[i__2].i + wa.i;
            wb.r = z__1.r, wb.i = z__1.i;
            i__2 = *n - *k - i__;
            z_div(&z__1, &c_b2, &wb);
            zscal_(&i__2, &z__1, &a[*k + i__ + 1 + i__ * a_dim1], &c__1);
            i__2 = *k + i__ + i__ * a_dim1;
            a[i__2].r = 1., a[i__2].i = 0.;
            z_div(&z__1, &wb, &wa);
            d__1 = z__1.r;
            tau.r = d__1, tau.i = 0.;
        }

/*        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;
        zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i__ + (i__ 
                + 1) * a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &
                c_b1, &work[1], &c__1);
        i__2 = *n - *k - i__ + 1;
        i__3 = *k - 1;
        z__1.r = -tau.r, z__1.i = -tau.i;
        zgerc_(&i__2, &i__3, &z__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 * conjg(u) */

        i__2 = *n - *k - i__ + 1;
        zlacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
        i__2 = *n - *k - i__ + 1;
        zsymv_("Lower", &i__2, &tau, &a[*k + i__ + (*k + i__) * a_dim1], lda, 
                &a[*k + i__ + i__ * a_dim1], &c__1, &c_b1, &work[1], &c__1);
        i__2 = *n - *k - i__ + 1;
        zlacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);

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

        z__3.r = -.5, z__3.i = -0.;
        z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i + 
                z__3.i * tau.r;
        i__2 = *n - *k - i__ + 1;
        zdotc_(&z__4, &i__2, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
                c__1);
        z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i 
                + z__2.i * z__4.r;
        alpha.r = z__1.r, alpha.i = z__1.i;
        i__2 = *n - *k - i__ + 1;
        zaxpy_(&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) */

/*        CALL ZSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1, */
/*        $               A( K+I, K+I ), LDA ) */

        i__2 = *n;
        for (jj = *k + i__; jj <= i__2; ++jj) {
            i__3 = *n;
            for (ii = jj; ii <= i__3; ++ii) {
                i__4 = ii + jj * a_dim1;
                i__5 = ii + jj * a_dim1;
                i__6 = ii + i__ * a_dim1;
                i__7 = jj - *k - i__ + 1;
                z__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i, 
                        z__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[
                        i__7].r;
                z__2.r = a[i__5].r - z__3.r, z__2.i = a[i__5].i - z__3.i;
                i__8 = ii - *k - i__ + 1;
                i__9 = jj + i__ * a_dim1;
                z__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i, 
                        z__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[
                        i__9].r;
                z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i;
                a[i__4].r = z__1.r, a[i__4].i = z__1.i;
/* L70: */
            }
/* L80: */
        }

        i__2 = *k + i__ + i__ * a_dim1;
        z__1.r = -wa.r, z__1.i = -wa.i;
        a[i__2].r = z__1.r, a[i__2].i = z__1.i;
        i__2 = *n;
        for (j = *k + i__ + 1; j <= i__2; ++j) {
            i__3 = j + i__ * a_dim1;
            a[i__3].r = 0., a[i__3].i = 0.;
/* L90: */
        }
/* L100: */
    }

/*     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__) {
            i__3 = j + i__ * a_dim1;
            i__4 = i__ + j * a_dim1;
            a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
/* L110: */
        }
/* L120: */
    }
    return 0;

/*     End of ZLAGSY */

} /* zlagsy_ */