#include "blaswrap.h"
/* zlatm6.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c__4 = 4;
static integer c__8 = 8;
static integer c__24 = 24;
/* Subroutine */ int zlatm6_(integer *type__, integer *n, doublecomplex *a,
integer *lda, doublecomplex *b, doublecomplex *x, integer *ldx,
doublecomplex *y, integer *ldy, doublecomplex *alpha, doublecomplex *
beta, doublecomplex *wx, doublecomplex *wy, doublereal *s, doublereal
*dif)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, y_dim1,
y_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
static integer i__, j;
static doublecomplex z__[64] /* was [8][8] */;
static integer info;
static doublecomplex work[26];
static doublereal rwork[50];
extern /* Subroutine */ int zlakf2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *), zgesvd_(char *, char *, integer *,
integer *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
/* -- LAPACK test routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
ZLATM6 generates test matrices for the generalized eigenvalue
problem, their corresponding right and left eigenvector matrices,
and also reciprocal condition numbers for all eigenvalues and
the reciprocal condition numbers of eigenvectors corresponding to
the 1th and 5th eigenvalues.
Test Matrices
=============
Two kinds of test matrix pairs
(A, B) = inverse(YH) * (Da, Db) * inverse(X)
are used in the tests:
Type 1:
Da = 1+a 0 0 0 0 Db = 1 0 0 0 0
0 2+a 0 0 0 0 1 0 0 0
0 0 3+a 0 0 0 0 1 0 0
0 0 0 4+a 0 0 0 0 1 0
0 0 0 0 5+a , 0 0 0 0 1
and Type 2:
Da = 1+i 0 0 0 0 Db = 1 0 0 0 0
0 1-i 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 1 0 0
0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0
0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 .
In both cases the same inverse(YH) and inverse(X) are used to compute
(A, B), giving the exact eigenvectors to (A,B) as (YH, X):
YH: = 1 0 -y y -y X = 1 0 -x -x x
0 1 -y y -y 0 1 x -x -x
0 0 1 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 1 0
0 0 0 0 1, 0 0 0 0 1 , where
a, b, x and y will have all values independently of each other.
Arguments
=========
TYPE (input) INTEGER
Specifies the problem type (see futher details).
N (input) INTEGER
Size of the matrices A and B.
A (output) COMPLEX*16 array, dimension (LDA, N).
On exit A N-by-N is initialized according to TYPE.
LDA (input) INTEGER
The leading dimension of A and of B.
B (output) COMPLEX*16 array, dimension (LDA, N).
On exit B N-by-N is initialized according to TYPE.
X (output) COMPLEX*16 array, dimension (LDX, N).
On exit X is the N-by-N matrix of right eigenvectors.
LDX (input) INTEGER
The leading dimension of X.
Y (output) COMPLEX*16 array, dimension (LDY, N).
On exit Y is the N-by-N matrix of left eigenvectors.
LDY (input) INTEGER
The leading dimension of Y.
ALPHA (input) COMPLEX*16
BETA (input) COMPLEX*16
Weighting constants for matrix A.
WX (input) COMPLEX*16
Constant for right eigenvector matrix.
WY (input) COMPLEX*16
Constant for left eigenvector matrix.
S (output) DOUBLE PRECISION array, dimension (N)
S(i) is the reciprocal condition number for eigenvalue i.
DIF (output) DOUBLE PRECISION array, dimension (N)
DIF(i) is the reciprocal condition number for eigenvector i.
=====================================================================
Generate test problem ...
(Da, Db) ...
Parameter adjustments */
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--s;
--dif;
/* Function Body */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (i__ == j) {
i__3 = i__ + i__ * a_dim1;
z__2.r = (doublereal) i__, z__2.i = 0.;
z__1.r = z__2.r + alpha->r, z__1.i = z__2.i + alpha->i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = i__ + i__ * b_dim1;
b[i__3].r = 1., b[i__3].i = 0.;
} else {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
}
/* L10: */
}
/* L20: */
}
if (*type__ == 2) {
i__1 = a_dim1 + 1;
a[i__1].r = 1., a[i__1].i = 1.;
i__1 = (a_dim1 << 1) + 2;
d_cnjg(&z__1, &a[a_dim1 + 1]);
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 3 + 3;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = (a_dim1 << 2) + 4;
z__2.r = alpha->r + 1., z__2.i = alpha->i + 0.;
d__1 = z__2.r;
z__3.r = beta->r + 1., z__3.i = beta->i + 0.;
d__2 = z__3.r;
z__1.r = d__1, z__1.i = d__2;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 5 + 5;
d_cnjg(&z__1, &a[(a_dim1 << 2) + 4]);
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
}
/* Form X and Y */
zlacpy_("F", n, n, &b[b_offset], lda, &y[y_offset], ldy);
i__1 = y_dim1 + 3;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = y_dim1 + 4;
d_cnjg(&z__1, wy);
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = y_dim1 + 5;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = (y_dim1 << 1) + 3;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = (y_dim1 << 1) + 4;
d_cnjg(&z__1, wy);
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = (y_dim1 << 1) + 5;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
zlacpy_("F", n, n, &b[b_offset], lda, &x[x_offset], ldx);
i__1 = x_dim1 * 3 + 1;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = (x_dim1 << 2) + 1;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = x_dim1 * 5 + 1;
x[i__1].r = wx->r, x[i__1].i = wx->i;
i__1 = x_dim1 * 3 + 2;
x[i__1].r = wx->r, x[i__1].i = wx->i;
i__1 = (x_dim1 << 2) + 2;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = x_dim1 * 5 + 2;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
/* Form (A, B) */
i__1 = b_dim1 * 3 + 1;
z__1.r = wx->r + wy->r, z__1.i = wx->i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = b_dim1 * 3 + 2;
z__2.r = -wx->r, z__2.i = -wx->i;
z__1.r = z__2.r + wy->r, z__1.i = z__2.i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = (b_dim1 << 2) + 1;
z__1.r = wx->r - wy->r, z__1.i = wx->i - wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = (b_dim1 << 2) + 2;
z__1.r = wx->r - wy->r, z__1.i = wx->i - wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = b_dim1 * 5 + 1;
z__2.r = -wx->r, z__2.i = -wx->i;
z__1.r = z__2.r + wy->r, z__1.i = z__2.i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = b_dim1 * 5 + 2;
z__1.r = wx->r + wy->r, z__1.i = wx->i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = a_dim1 * 3 + 1;
i__2 = a_dim1 + 1;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = a_dim1 * 3 + 3;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 3 + 2;
z__3.r = -wx->r, z__3.i = -wx->i;
i__2 = (a_dim1 << 1) + 2;
z__2.r = z__3.r * a[i__2].r - z__3.i * a[i__2].i, z__2.i = z__3.r * a[
i__2].i + z__3.i * a[i__2].r;
i__3 = a_dim1 * 3 + 3;
z__4.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__4.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = (a_dim1 << 2) + 1;
i__2 = a_dim1 + 1;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = (a_dim1 << 2) + 4;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = (a_dim1 << 2) + 2;
i__2 = (a_dim1 << 1) + 2;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = (a_dim1 << 2) + 4;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 5 + 1;
z__3.r = -wx->r, z__3.i = -wx->i;
i__2 = a_dim1 + 1;
z__2.r = z__3.r * a[i__2].r - z__3.i * a[i__2].i, z__2.i = z__3.r * a[
i__2].i + z__3.i * a[i__2].r;
i__3 = a_dim1 * 5 + 5;
z__4.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__4.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 5 + 2;
i__2 = (a_dim1 << 1) + 2;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = a_dim1 * 5 + 5;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
/* Compute condition numbers */
s[1] = 1. / sqrt((z_abs(wy) * 3. * z_abs(wy) + 1.) / (z_abs(&a[a_dim1 + 1] ) * z_abs(&a[a_dim1 + 1]) + 1.));
s[2] = 1. / sqrt((z_abs(wy) * 3. * z_abs(wy) + 1.) / (z_abs(&a[(a_dim1 <<
1) + 2]) * z_abs(&a[(a_dim1 << 1) + 2]) + 1.));
s[3] = 1. / sqrt((z_abs(wx) * 2. * z_abs(wx) + 1.) / (z_abs(&a[a_dim1 * 3
+ 3]) * z_abs(&a[a_dim1 * 3 + 3]) + 1.));
s[4] = 1. / sqrt((z_abs(wx) * 2. * z_abs(wx) + 1.) / (z_abs(&a[(a_dim1 <<
2) + 4]) * z_abs(&a[(a_dim1 << 2) + 4]) + 1.));
s[5] = 1. / sqrt((z_abs(wx) * 2. * z_abs(wx) + 1.) / (z_abs(&a[a_dim1 * 5
+ 5]) * z_abs(&a[a_dim1 * 5 + 5]) + 1.));
zlakf2_(&c__1, &c__4, &a[a_offset], lda, &a[(a_dim1 << 1) + 2], &b[
b_offset], &b[(b_dim1 << 1) + 2], z__, &c__8);
zgesvd_("N", "N", &c__8, &c__8, z__, &c__8, rwork, work, &c__1, &work[1],
&c__1, &work[2], &c__24, &rwork[8], &info);
dif[1] = rwork[7];
zlakf2_(&c__4, &c__1, &a[a_offset], lda, &a[a_dim1 * 5 + 5], &b[b_offset],
&b[b_dim1 * 5 + 5], z__, &c__8);
zgesvd_("N", "N", &c__8, &c__8, z__, &c__8, rwork, work, &c__1, &work[1],
&c__1, &work[2], &c__24, &rwork[8], &info);
dif[5] = rwork[7];
return 0;
/* End of ZLATM6 */
} /* zlatm6_ */