/* -- 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 clagge_(integer *m, integer *n, integer *kl, integer *ku,
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;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer i, j;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cscal_(integer *, complex *, complex *, integer *), cgemv_(char *
, integer *, integer *, complex *, complex *, integer *, complex *
, integer *, complex *, complex *, integer *);
extern real scnrm2_(integer *, complex *, integer *);
static complex wa, wb;
extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
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
=======
CLAGGE generates a complex general m by n matrix A, by pre- and post-
multiplying a real diagonal matrix D with random unitary matrices:
A = U*D*V. The lower and upper bandwidths may then be reduced to
kl and ku by additional unitary transformations.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
KL (input) INTEGER
The number of nonzero subdiagonals within the band of A.
0 <= KL <= M-1.
KU (input) INTEGER
The number of nonzero superdiagonals within the band of A.
0 <= KU <= N-1.
D (input) REAL array, dimension (min(M,N))
The diagonal elements of the diagonal matrix D.
A (output) COMPLEX array, dimension (LDA,N)
The generated m by n matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= M.
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 (M+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 (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0 || *kl > *m - 1) {
*info = -3;
} else if (*ku < 0 || *ku > *n - 1) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -7;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAGGE", &i__1);
return 0;
}
/* initialize A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i = 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 = min(*m,*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: */
}
/* pre- and post-multiply A by random unitary matrices */
for (i = min(*m,*n); i >= 1; --i) {
if (i < *m) {
/* generate random reflection */
i__1 = *m - i + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *m - 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 = *m - 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;
}
/* multiply A(i:m,i:n) by random reflection from the lef
t */
i__1 = *m - i + 1;
i__2 = *n - i + 1;
cgemv_("Conjugate transpose", &i__1, &i__2, &c_b2, &a[i + i *
a_dim1], lda, &work[1], &c__1, &c_b1, &work[*m + 1], &
c__1);
i__1 = *m - i + 1;
i__2 = *n - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__1, &i__2, &q__1, &work[1], &c__1, &work[*m + 1], &c__1,
&a[i + i * a_dim1], lda);
}
if (i < *n) {
/* 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;
}
/* multiply A(i:m,i:n) by random reflection from the rig
ht */
i__1 = *m - i + 1;
i__2 = *n - i + 1;
cgemv_("No transpose", &i__1, &i__2, &c_b2, &a[i + i * a_dim1],
lda, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *m - i + 1;
i__2 = *n - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__1, &i__2, &q__1, &work[*n + 1], &c__1, &work[1], &c__1,
&a[i + i * a_dim1], lda);
}
/* L40: */
}
/* Reduce number of subdiagonals to KL and number of superdiagonals
to KU
Computing MAX */
i__2 = *m - 1 - *kl, i__3 = *n - 1 - *ku;
i__1 = max(i__2,i__3);
for (i = 1; i <= i__1; ++i) {
if (*kl <= *ku) {
/* annihilate subdiagonal elements first (necessary if K
L = 0)
Computing MIN */
i__2 = *m - 1 - *kl;
if (i <= min(i__2,*n)) {
/* generate reflection to annihilate A(kl+i+1:m,i
) */
i__2 = *m - *kl - i + 1;
wn = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
i__2 = *kl + 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 = *kl + 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 = *m - *kl - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
i__2 = *kl + 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(kl+i:m,i+1:n) from the l
eft */
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i
+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
c__1, &c_b1, &work[1], &c__1);
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
i__2 = *kl + 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;
}
/* Computing MIN */
i__2 = *n - 1 - *ku;
if (i <= min(i__2,*m)) {
/* generate reflection to annihilate A(i,ku+i+1:n
) */
i__2 = *n - *ku - i + 1;
wn = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
i__2 = i + (*ku + 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 = i + (*ku + 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 - *ku - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
i__2 = i + (*ku + 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(i+1:m,ku+i:n) from the r
ight */
i__2 = *n - *ku - i + 1;
clacgv_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku +
i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
c_b1, &work[1], &c__1);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i)
* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
i__2 = i + (*ku + 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;
}
} else {
/* annihilate superdiagonal elements first (necessary if
KU = 0)
Computing MIN */
i__2 = *n - 1 - *ku;
if (i <= min(i__2,*m)) {
/* generate reflection to annihilate A(i,ku+i+1:n
) */
i__2 = *n - *ku - i + 1;
wn = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
i__2 = i + (*ku + 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 = i + (*ku + 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 - *ku - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
i__2 = i + (*ku + 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(i+1:m,ku+i:n) from the r
ight */
i__2 = *n - *ku - i + 1;
clacgv_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku +
i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
c_b1, &work[1], &c__1);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i)
* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
i__2 = i + (*ku + 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;
}
/* Computing MIN */
i__2 = *m - 1 - *kl;
if (i <= min(i__2,*n)) {
/* generate reflection to annihilate A(kl+i+1:m,i
) */
i__2 = *m - *kl - i + 1;
wn = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
i__2 = *kl + 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 = *kl + 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 = *m - *kl - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
i__2 = *kl + 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(kl+i:m,i+1:n) from the l
eft */
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i
+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
c__1, &c_b1, &work[1], &c__1);
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
i__2 = *kl + 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 = *m;
for (j = *kl + 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: */
}
i__2 = *n;
for (j = *ku + i + 1; j <= i__2; ++j) {
i__3 = i + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L60: */
}
/* L70: */
}
return 0;
/* End of CLAGGE */
} /* clagge_ */