/* -- 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 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 */
static integer i, j;
static doublecomplex 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 *);
static integer ii, jj;
static doublecomplex wa, wb;
static doublereal wn;
extern /* Subroutine */ int xerbla_(char *, integer *), zlacgv_(
integer *, doublecomplex *, integer *), zlarnv_(integer *,
integer *, integer *, doublecomplex *);
static doublecomplex 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
September 30, 1994
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
=====================================================================
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_("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 rig
ht
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_ */