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/* -- 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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__3 = 3;
static integer c__1 = 1;
/* Subroutine */ int claghe_(integer *n, integer *k, real *d, complex *a,
integer *lda, integer *iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *), r_cnjg(complex *, complex *);
/* Local variables */
extern /* Subroutine */ int cher2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, integer *);
static integer i, j;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *);
static complex alpha;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *), chemv_(char *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, complex *,
integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
extern real scnrm2_(integer *, complex *, integer *);
static complex wa, wb;
static real wn;
extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
integer *, integer *, integer *, complex *);
static complex 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
=======
CLAGHE generates a complex hermitian matrix A, by pre- and post-
multiplying a real diagonal matrix D with a random unitary matrix:
A = U*D*U'. 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) REAL array, dimension (N)
The diagonal elements of the diagonal matrix D.
A (output) COMPLEX array, dimension (LDA,N)
The generated n by n hermitian 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 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_("CLAGHE", &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.f, a[i__3].i = 0.f;
/* 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.f;
/* L30: */
}
/* Generate lower triangle of hermitian matrix */
for (i = *n - 1; i >= 1; --i) {
/* generate random reflection */
i__1 = *n - i + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
d__1 = wn / c_abs(&work[1]);
q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* 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;
chemv_("Lower", &i__1, &tau, &a[i + i * a_dim1], lda, &work[1], &c__1,
&c_b1, &work[*n + 1], &c__1);
/* compute v := y - 1/2 * tau * ( y, u ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__1 = *n - i + 1;
cdotc_(&q__4, &i__1, &work[*n + 1], &c__1, &work[1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *n - i + 1;
caxpy_(&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;
q__1.r = -1.f, q__1.i = 0.f;
cher2_("Lower", &i__1, &q__1, &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 = scnrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1);
d__1 = wn / c_abs(&a[*k + i + i * a_dim1]);
i__2 = *k + i + i * a_dim1;
q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *k + i + i * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *k - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*k + i + 1 + i * a_dim1], &c__1);
i__2 = *k + i + i * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* 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;
cgemv_("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;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__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;
chemv_("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);
/* compute v := y - 1/2 * tau * ( y, u ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__2 = *n - *k - i + 1;
cdotc_(&q__4, &i__2, &work[1], &c__1, &a[*k + i + i * a_dim1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = *n - *k - i + 1;
caxpy_(&i__2, &alpha, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1)
;
/* apply hermitian rank-2 update to A(k+i:n,k+i:n) */
i__2 = *n - *k - i + 1;
q__1.r = -1.f, q__1.i = 0.f;
cher2_("Lower", &i__2, &q__1, &a[*k + i + i * a_dim1], &c__1, &work[1]
, &c__1, &a[*k + i + (*k + i) * a_dim1], lda);
i__2 = *k + i + i * a_dim1;
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__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.f, a[i__3].i = 0.f;
/* L50: */
}
/* L60: */
}
/* Store full hermitian 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;
r_cnjg(&q__1, &a[i + j * a_dim1]);
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L70: */
}
/* L80: */
}
return 0;
/* End of CLAGHE */
} /* claghe_ */
|
