/* -- 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 real c_b12 = 0.f;
static real c_b19 = -1.f;
static real c_b26 = 1.f;
/* Subroutine */ int slagsy_(integer *n, integer *k, real *d, real *a,
integer *lda, integer *iseed, real *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1;
/* Builtin functions */
double r_sign(real *, real *);
/* Local variables */
extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *);
extern real sdot_(integer *, real *, integer *, real *, integer *),
snrm2_(integer *, real *, integer *);
static integer i, j;
extern /* Subroutine */ int ssyr2_(char *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *);
static real alpha;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
sgemv_(char *, integer *, integer *, real *, real *, integer *,
real *, integer *, real *, real *, integer *), saxpy_(
integer *, real *, real *, integer *, real *, integer *), ssymv_(
char *, integer *, real *, real *, integer *, real *, integer *,
real *, real *, integer *);
static real wa, wb, wn;
extern /* Subroutine */ int xerbla_(char *, integer *), slarnv_(
integer *, integer *, integer *, real *);
static real 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
=======
SLAGSY 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) REAL array, dimension (N)
The diagonal elements of the diagonal matrix D.
A (output) REAL 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) REAL 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_("SLAGSY", &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.f;
/* 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;
slarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i + 1;
wn = snrm2_(&i__1, &work[1], &c__1);
wa = r_sign(&wn, &work[1]);
if (wn == 0.f) {
tau = 0.f;
} else {
wb = work[1] + wa;
i__1 = *n - i;
r__1 = 1.f / wb;
sscal_(&i__1, &r__1, &work[2], &c__1);
work[1] = 1.f;
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;
ssymv_("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 * -.5f * sdot_(&i__1, &work[*n + 1], &c__1, &work[1], &
c__1);
i__1 = *n - i + 1;
saxpy_(&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;
ssyr2_("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 = snrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1);
wa = r_sign(&wn, &a[*k + i + i * a_dim1]);
if (wn == 0.f) {
tau = 0.f;
} else {
wb = a[*k + i + i * a_dim1] + wa;
i__2 = *n - *k - i;
r__1 = 1.f / wb;
sscal_(&i__2, &r__1, &a[*k + i + 1 + i * a_dim1], &c__1);
a[*k + i + i * a_dim1] = 1.f;
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;
sgemv_("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;
r__1 = -(doublereal)tau;
sger_(&i__2, &i__3, &r__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;
ssymv_("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 * -.5f * sdot_(&i__2, &work[1], &c__1, &a[*k + i + i *
a_dim1], &c__1);
i__2 = *n - *k - i + 1;
saxpy_(&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;
ssyr2_("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] = -(doublereal)wa;
i__2 = *n;
for (j = *k + i + 1; j <= i__2; ++j) {
a[j + i * a_dim1] = 0.f;
/* 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 SLAGSY */
} /* slagsy_ */