/*  -- translated by f2c (version 19940927).

   You must link the resulting object file with the libraries:

	-lf2c -lm   (in that order)

*/

#include "f2c.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 */

    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 *);

    static integer i, j;

    static 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 *);

    static doublereal wa, wb, wn;

    extern /* Subroutine */ int xerbla_(char *, integer *), dlarnv_(

	    integer *, integer *, integer *, doublereal *);

    static doublereal tau;

/*  -- LAPACK auxiliary test routine (version 2.0)   

       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   

       Courant Institute, Argonne National Lab, and Rice University   

       February 29, 1992   

    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   

    ===================================================================== 

       Test the input arguments   

       Parameter adjustments */

    --d;

    a_dim1 = *lda;

    a_offset = a_dim1 + 1;

    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 rig

ht   

          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_ */