/* -- 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_b11 = 1.;
static doublereal c_b13 = 0.;
/* Subroutine */ int dlagge_(integer *m, integer *n, integer *kl, integer *ku,
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 dnrm2_(integer *, doublereal *, integer *);
static integer i, j;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dgemv_(char *, integer *, 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
=======
DLAGGE generates a real general m by n matrix A, by pre- and post-
multiplying a real diagonal matrix D with random orthogonal matrices:
A = U*D*V. The lower and upper bandwidths may then be reduced to
kl and ku by additional orthogonal 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) DOUBLE PRECISION array, dimension (min(M,N))
The diagonal elements of the diagonal matrix D.
A (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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_("DLAGGE", &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) {
a[i + j * a_dim1] = 0.;
/* L10: */
}
/* L20: */
}
i__1 = min(*m,*n);
for (i = 1; i <= i__1; ++i) {
a[i + i * a_dim1] = d[i];
/* L30: */
}
/* pre- and post-multiply A by random orthogonal matrices */
for (i = min(*m,*n); i >= 1; --i) {
if (i < *m) {
/* generate random reflection */
i__1 = *m - i + 1;
dlarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *m - 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 = *m - i;
d__1 = 1. / wb;
dscal_(&i__1, &d__1, &work[2], &c__1);
work[1] = 1.;
tau = wb / wa;
}
/* multiply A(i:m,i:n) by random reflection from the lef
t */
i__1 = *m - i + 1;
i__2 = *n - i + 1;
dgemv_("Transpose", &i__1, &i__2, &c_b11, &a[i + i * a_dim1], lda,
&work[1], &c__1, &c_b13, &work[*m + 1], &c__1);
i__1 = *m - i + 1;
i__2 = *n - i + 1;
d__1 = -tau;
dger_(&i__1, &i__2, &d__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;
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;
}
/* multiply A(i:m,i:n) by random reflection from the rig
ht */
i__1 = *m - i + 1;
i__2 = *n - i + 1;
dgemv_("No transpose", &i__1, &i__2, &c_b11, &a[i + i * a_dim1],
lda, &work[1], &c__1, &c_b13, &work[*n + 1], &c__1);
i__1 = *m - i + 1;
i__2 = *n - i + 1;
d__1 = -tau;
dger_(&i__1, &i__2, &d__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 = dnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
wa = d_sign(&wn, &a[*kl + i + i * a_dim1]);
if (wn == 0.) {
tau = 0.;
} else {
wb = a[*kl + i + i * a_dim1] + wa;
i__2 = *m - *kl - i;
d__1 = 1. / wb;
dscal_(&i__2, &d__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
a[*kl + i + i * a_dim1] = 1.;
tau = wb / wa;
}
/* apply reflection to A(kl+i:m,i+1:n) from the l
eft */
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
dgemv_("Transpose", &i__2, &i__3, &c_b11, &a[*kl + i + (i + 1)
* a_dim1], lda, &a[*kl + i + i * a_dim1], &c__1, &
c_b13, &work[1], &c__1);
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
d__1 = -tau;
dger_(&i__2, &i__3, &d__1, &a[*kl + i + i * a_dim1], &c__1, &
work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
a[*kl + i + i * a_dim1] = -wa;
}
/* 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 = dnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
wa = d_sign(&wn, &a[i + (*ku + i) * a_dim1]);
if (wn == 0.) {
tau = 0.;
} else {
wb = a[i + (*ku + i) * a_dim1] + wa;
i__2 = *n - *ku - i;
d__1 = 1. / wb;
dscal_(&i__2, &d__1, &a[i + (*ku + i + 1) * a_dim1], lda);
a[i + (*ku + i) * a_dim1] = 1.;
tau = wb / wa;
}
/* apply reflection to A(i+1:m,ku+i:n) from the r
ight */
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
dgemv_("No transpose", &i__2, &i__3, &c_b11, &a[i + 1 + (*ku
+ i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda,
&c_b13, &work[1], &c__1);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
d__1 = -tau;
dger_(&i__2, &i__3, &d__1, &work[1], &c__1, &a[i + (*ku + i) *
a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
a[i + (*ku + i) * a_dim1] = -wa;
}
} 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 = dnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
wa = d_sign(&wn, &a[i + (*ku + i) * a_dim1]);
if (wn == 0.) {
tau = 0.;
} else {
wb = a[i + (*ku + i) * a_dim1] + wa;
i__2 = *n - *ku - i;
d__1 = 1. / wb;
dscal_(&i__2, &d__1, &a[i + (*ku + i + 1) * a_dim1], lda);
a[i + (*ku + i) * a_dim1] = 1.;
tau = wb / wa;
}
/* apply reflection to A(i+1:m,ku+i:n) from the r
ight */
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
dgemv_("No transpose", &i__2, &i__3, &c_b11, &a[i + 1 + (*ku
+ i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda,
&c_b13, &work[1], &c__1);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
d__1 = -tau;
dger_(&i__2, &i__3, &d__1, &work[1], &c__1, &a[i + (*ku + i) *
a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
a[i + (*ku + i) * a_dim1] = -wa;
}
/* 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 = dnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
wa = d_sign(&wn, &a[*kl + i + i * a_dim1]);
if (wn == 0.) {
tau = 0.;
} else {
wb = a[*kl + i + i * a_dim1] + wa;
i__2 = *m - *kl - i;
d__1 = 1. / wb;
dscal_(&i__2, &d__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
a[*kl + i + i * a_dim1] = 1.;
tau = wb / wa;
}
/* apply reflection to A(kl+i:m,i+1:n) from the l
eft */
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
dgemv_("Transpose", &i__2, &i__3, &c_b11, &a[*kl + i + (i + 1)
* a_dim1], lda, &a[*kl + i + i * a_dim1], &c__1, &
c_b13, &work[1], &c__1);
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
d__1 = -tau;
dger_(&i__2, &i__3, &d__1, &a[*kl + i + i * a_dim1], &c__1, &
work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
a[*kl + i + i * a_dim1] = -wa;
}
}
i__2 = *m;
for (j = *kl + i + 1; j <= i__2; ++j) {
a[j + i * a_dim1] = 0.;
/* L50: */
}
i__2 = *n;
for (j = *ku + i + 1; j <= i__2; ++j) {
a[i + j * a_dim1] = 0.;
/* L60: */
}
/* L70: */
}
return 0;
/* End of DLAGGE */
} /* dlagge_ */