/* -- 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 claror_(char *side, char *init, integer *m, integer *n,
complex *a, integer *lda, integer *iseed, complex *x, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
complex q__1, q__2;
/* Builtin functions */
double c_abs(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
static integer kbeg, jcol;
static real xabs;
static integer irow, j;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cscal_(integer *, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
static complex csign;
static integer ixfrm, itype, nxfrm;
static real xnorm;
extern real scnrm2_(integer *, complex *, integer *);
extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
extern /* Complex */ VOID clarnd_(complex *, integer *, integer *);
extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *), xerbla_(char *,
integer *);
static real factor;
static complex xnorms;
/* -- 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
=======
CLAROR pre- or post-multiplies an M by N matrix A by a random
unitary matrix U, overwriting A. A may optionally be
initialized to the identity matrix before multiplying by U.
U is generated using the method of G.W. Stewart
( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ).
(BLAS-2 version)
Arguments
=========
SIDE - CHARACTER*1
SIDE specifies whether A is multiplied on the left or right
by U.
SIDE = 'L' Multiply A on the left (premultiply) by U
SIDE = 'R' Multiply A on the right (postmultiply) by U*
SIDE = 'C' Multiply A on the left by U and the right by U*
SIDE = 'T' Multiply A on the left by U and the right by U'
Not modified.
INIT - CHARACTER*1
INIT specifies whether or not A should be initialized to
the identity matrix.
INIT = 'I' Initialize A to (a section of) the
identity matrix before applying U.
INIT = 'N' No initialization. Apply U to the
input matrix A.
INIT = 'I' may be used to generate square (i.e., unitary)
or rectangular orthogonal matrices (orthogonality being
in the sense of CDOTC):
For square matrices, M=N, and SIDE many be either 'L' or
'R'; the rows will be orthogonal to each other, as will the
columns.
For rectangular matrices where M < N, SIDE = 'R' will
produce a dense matrix whose rows will be orthogonal and
whose columns will not, while SIDE = 'L' will produce a
matrix whose rows will be orthogonal, and whose first M
columns will be orthogonal, the remaining columns being
zero.
For matrices where M > N, just use the previous
explaination, interchanging 'L' and 'R' and "rows" and
"columns".
Not modified.
M - INTEGER
Number of rows of A. Not modified.
N - INTEGER
Number of columns of A. Not modified.
A - COMPLEX array, dimension ( LDA, N )
Input and output array. Overwritten by U A ( if SIDE = 'L' )
or by A U ( if SIDE = 'R' )
or by U A U* ( if SIDE = 'C')
or by U A U' ( if SIDE = 'T') on exit.
LDA - INTEGER
Leading dimension of A. Must be at least MAX ( 1, M ).
Not modified.
ISEED - INTEGER array, dimension ( 4 )
On entry ISEED specifies the seed of the random number
generator. The array elements should be between 0 and 4095;
if not they will be reduced mod 4096. Also, ISEED(4) must
be odd. The random number generator uses a linear
congruential sequence limited to small integers, and so
should produce machine independent random numbers. The
values of ISEED are changed on exit, and can be used in the
next call to CLAROR to continue the same random number
sequence.
Modified.
X - COMPLEX array, dimension ( 3*MAX( M, N ) )
Workspace. Of length:
2*M + N if SIDE = 'L',
2*N + M if SIDE = 'R',
3*N if SIDE = 'C' or 'T'.
Modified.
INFO - INTEGER
An error flag. It is set to:
0 if no error.
1 if CLARND returned a bad random number (installation
problem)
-1 if SIDE is not L, R, C, or T.
-3 if M is negative.
-4 if N is negative or if SIDE is C or T and N is not equal
to M.
-6 if LDA is less than M.
=====================================================================
Parameter adjustments */
a_dim1 = *lda;
a_offset = a_dim1 + 1;
a -= a_offset;
--iseed;
--x;
/* Function Body */
if (*n == 0 || *m == 0) {
return 0;
}
itype = 0;
if (lsame_(side, "L")) {
itype = 1;
} else if (lsame_(side, "R")) {
itype = 2;
} else if (lsame_(side, "C")) {
itype = 3;
} else if (lsame_(side, "T")) {
itype = 4;
}
/* Check for argument errors. */
*info = 0;
if (itype == 0) {
*info = -1;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0 || itype == 3 && *n != *m) {
*info = -4;
} else if (*lda < *m) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLAROR", &i__1);
return 0;
}
if (itype == 1) {
nxfrm = *m;
} else {
nxfrm = *n;
}
/* Initialize A to the identity matrix if desired */
if (lsame_(init, "I")) {
claset_("Full", m, n, &c_b1, &c_b2, &a[a_offset], lda);
}
/* If no rotation possible, still multiply by
a random complex number from the circle |x| = 1
2) Compute Rotation by computing Householder
Transformations H(2), H(3), ..., H(n). Note that the
order in which they are computed is irrelevant. */
i__1 = nxfrm;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
x[i__2].r = 0.f, x[i__2].i = 0.f;
/* L40: */
}
i__1 = nxfrm;
for (ixfrm = 2; ixfrm <= i__1; ++ixfrm) {
kbeg = nxfrm - ixfrm + 1;
/* Generate independent normal( 0, 1 ) random numbers */
i__2 = nxfrm;
for (j = kbeg; j <= i__2; ++j) {
i__3 = j;
clarnd_(&q__1, &c__3, &iseed[1]);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L50: */
}
/* Generate a Householder transformation from the random vector
X */
xnorm = scnrm2_(&ixfrm, &x[kbeg], &c__1);
xabs = c_abs(&x[kbeg]);
if (xabs != 0.f) {
i__2 = kbeg;
q__1.r = x[i__2].r / xabs, q__1.i = x[i__2].i / xabs;
csign.r = q__1.r, csign.i = q__1.i;
} else {
csign.r = 1.f, csign.i = 0.f;
}
q__1.r = xnorm * csign.r, q__1.i = xnorm * csign.i;
xnorms.r = q__1.r, xnorms.i = q__1.i;
i__2 = nxfrm + kbeg;
q__1.r = -(doublereal)csign.r, q__1.i = -(doublereal)csign.i;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
factor = xnorm * (xnorm + xabs);
if (dabs(factor) < 1e-20f) {
*info = 1;
i__2 = -(*info);
xerbla_("CLAROR", &i__2);
return 0;
} else {
factor = 1.f / factor;
}
i__2 = kbeg;
i__3 = kbeg;
q__1.r = x[i__3].r + xnorms.r, q__1.i = x[i__3].i + xnorms.i;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
/* Apply Householder transformation to A */
if (itype == 1 || itype == 3 || itype == 4) {
/* Apply H(k) on the left of A */
cgemv_("C", &ixfrm, n, &c_b2, &a[kbeg + a_dim1], lda, &x[kbeg], &
c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1);
q__2.r = factor, q__2.i = 0.f;
q__1.r = -(doublereal)q__2.r, q__1.i = -(doublereal)q__2.i;
cgerc_(&ixfrm, n, &q__1, &x[kbeg], &c__1, &x[(nxfrm << 1) + 1], &
c__1, &a[kbeg + a_dim1], lda);
}
if (itype >= 2 && itype <= 4) {
/* Apply H(k)* (or H(k)') on the right of A */
if (itype == 4) {
clacgv_(&ixfrm, &x[kbeg], &c__1);
}
cgemv_("N", m, &ixfrm, &c_b2, &a[kbeg * a_dim1 + 1], lda, &x[kbeg]
, &c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1);
q__2.r = factor, q__2.i = 0.f;
q__1.r = -(doublereal)q__2.r, q__1.i = -(doublereal)q__2.i;
cgerc_(m, &ixfrm, &q__1, &x[(nxfrm << 1) + 1], &c__1, &x[kbeg], &
c__1, &a[kbeg * a_dim1 + 1], lda);
}
/* L60: */
}
clarnd_(&q__1, &c__3, &iseed[1]);
x[1].r = q__1.r, x[1].i = q__1.i;
xabs = c_abs(&x[1]);
if (xabs != 0.f) {
q__1.r = x[1].r / xabs, q__1.i = x[1].i / xabs;
csign.r = q__1.r, csign.i = q__1.i;
} else {
csign.r = 1.f, csign.i = 0.f;
}
i__1 = nxfrm << 1;
x[i__1].r = csign.r, x[i__1].i = csign.i;
/* Scale the matrix A by D. */
if (itype == 1 || itype == 3 || itype == 4) {
i__1 = *m;
for (irow = 1; irow <= i__1; ++irow) {
r_cnjg(&q__1, &x[nxfrm + irow]);
cscal_(n, &q__1, &a[irow + a_dim1], lda);
/* L70: */
}
}
if (itype == 2 || itype == 3) {
i__1 = *n;
for (jcol = 1; jcol <= i__1; ++jcol) {
cscal_(m, &x[nxfrm + jcol], &a[jcol * a_dim1 + 1], &c__1);
/* L80: */
}
}
if (itype == 4) {
i__1 = *n;
for (jcol = 1; jcol <= i__1; ++jcol) {
r_cnjg(&q__1, &x[nxfrm + jcol]);
cscal_(m, &q__1, &a[jcol * a_dim1 + 1], &c__1);
/* L90: */
}
}
return 0;
/* End of CLAROR */
} /* claror_ */