#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int claein_(logical *rightv, logical *noinit, integer *n,
complex *h__, integer *ldh, complex *w, complex *v, complex *b,
integer *ldb, real *rwork, real *eps3, real *smlnum, integer *info)
{
/* -- LAPACK auxiliary routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
CLAEIN uses inverse iteration to find a right or left eigenvector
corresponding to the eigenvalue W of a complex upper Hessenberg
matrix H.
Arguments
=========
RIGHTV (input) LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.
NOINIT (input) LOGICAL
= .TRUE. : no initial vector supplied in V
= .FALSE.: initial vector supplied in V.
N (input) INTEGER
The order of the matrix H. N >= 0.
H (input) COMPLEX array, dimension (LDH,N)
The upper Hessenberg matrix H.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
W (input) COMPLEX
The eigenvalue of H whose corresponding right or left
eigenvector is to be computed.
V (input/output) COMPLEX array, dimension (N)
On entry, if NOINIT = .FALSE., V must contain a starting
vector for inverse iteration; otherwise V need not be set.
On exit, V contains the computed eigenvector, normalized so
that the component of largest magnitude has magnitude 1; here
the magnitude of a complex number (x,y) is taken to be
|x| + |y|.
B (workspace) COMPLEX array, dimension (LDB,N)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RWORK (workspace) REAL array, dimension (N)
EPS3 (input) REAL
A small machine-dependent value which is used to perturb
close eigenvalues, and to replace zero pivots.
SMLNUM (input) REAL
A machine-dependent value close to the underflow threshold.
INFO (output) INTEGER
= 0: successful exit
= 1: inverse iteration did not converge; V is set to the
last iterate.
=====================================================================
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer b_dim1, b_offset, h_dim1, h_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1, q__2;
/* Builtin functions */
double sqrt(doublereal), r_imag(complex *);
/* Local variables */
static integer i__, j;
static complex x, ei, ej;
static integer its, ierr;
static complex temp;
static real scale;
static char trans[1];
static real rtemp, rootn, vnorm;
extern doublereal scnrm2_(integer *, complex *, integer *);
extern integer icamax_(integer *, complex *, integer *);
extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*), clatrs_(char *, char *, char *, char *, integer *, complex *,
integer *, complex *, real *, real *, integer *);
extern doublereal scasum_(integer *, complex *, integer *);
static char normin[1];
static real nrmsml, growto;
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
--v;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--rwork;
/* Function Body */
*info = 0;
/* GROWTO is the threshold used in the acceptance test for an
eigenvector. */
rootn = sqrt((real) (*n));
growto = .1f / rootn;
/* Computing MAX */
r__1 = 1.f, r__2 = *eps3 * rootn;
nrmsml = dmax(r__1,r__2) * *smlnum;
/* Form B = H - W*I (except that the subdiagonal elements are not
stored). */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * h_dim1;
b[i__3].r = h__[i__4].r, b[i__3].i = h__[i__4].i;
/* L10: */
}
i__2 = j + j * b_dim1;
i__3 = j + j * h_dim1;
q__1.r = h__[i__3].r - w->r, q__1.i = h__[i__3].i - w->i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L20: */
}
if (*noinit) {
/* Initialize V. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
v[i__2].r = *eps3, v[i__2].i = 0.f;
/* L30: */
}
} else {
/* Scale supplied initial vector. */
vnorm = scnrm2_(n, &v[1], &c__1);
r__1 = *eps3 * rootn / dmax(vnorm,nrmsml);
csscal_(n, &r__1, &v[1], &c__1);
}
if (*rightv) {
/* LU decomposition with partial pivoting of B, replacing zero
pivots by EPS3. */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + 1 + i__ * h_dim1;
ei.r = h__[i__2].r, ei.i = h__[i__2].i;
i__2 = i__ + i__ * b_dim1;
if ((r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b[i__ + i__ *
b_dim1]), dabs(r__2)) < (r__3 = ei.r, dabs(r__3)) + (
r__4 = r_imag(&ei), dabs(r__4))) {
/* Interchange rows and eliminate. */
cladiv_(&q__1, &b[i__ + i__ * b_dim1], &ei);
x.r = q__1.r, x.i = q__1.i;
i__2 = i__ + i__ * b_dim1;
b[i__2].r = ei.r, b[i__2].i = ei.i;
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = i__ + 1 + j * b_dim1;
temp.r = b[i__3].r, temp.i = b[i__3].i;
i__3 = i__ + 1 + j * b_dim1;
i__4 = i__ + j * b_dim1;
q__2.r = x.r * temp.r - x.i * temp.i, q__2.i = x.r *
temp.i + x.i * temp.r;
q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4].i - q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
i__3 = i__ + j * b_dim1;
b[i__3].r = temp.r, b[i__3].i = temp.i;
/* L40: */
}
} else {
/* Eliminate without interchange. */
i__2 = i__ + i__ * b_dim1;
if (b[i__2].r == 0.f && b[i__2].i == 0.f) {
i__3 = i__ + i__ * b_dim1;
b[i__3].r = *eps3, b[i__3].i = 0.f;
}
cladiv_(&q__1, &ei, &b[i__ + i__ * b_dim1]);
x.r = q__1.r, x.i = q__1.i;
if (x.r != 0.f || x.i != 0.f) {
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = i__ + 1 + j * b_dim1;
i__4 = i__ + 1 + j * b_dim1;
i__5 = i__ + j * b_dim1;
q__2.r = x.r * b[i__5].r - x.i * b[i__5].i, q__2.i =
x.r * b[i__5].i + x.i * b[i__5].r;
q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4].i -
q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L50: */
}
}
}
/* L60: */
}
i__1 = *n + *n * b_dim1;
if (b[i__1].r == 0.f && b[i__1].i == 0.f) {
i__2 = *n + *n * b_dim1;
b[i__2].r = *eps3, b[i__2].i = 0.f;
}
*(unsigned char *)trans = 'N';
} else {
/* UL decomposition with partial pivoting of B, replacing zero
pivots by EPS3. */
for (j = *n; j >= 2; --j) {
i__1 = j + (j - 1) * h_dim1;
ej.r = h__[i__1].r, ej.i = h__[i__1].i;
i__1 = j + j * b_dim1;
if ((r__1 = b[i__1].r, dabs(r__1)) + (r__2 = r_imag(&b[j + j *
b_dim1]), dabs(r__2)) < (r__3 = ej.r, dabs(r__3)) + (r__4
= r_imag(&ej), dabs(r__4))) {
/* Interchange columns and eliminate. */
cladiv_(&q__1, &b[j + j * b_dim1], &ej);
x.r = q__1.r, x.i = q__1.i;
i__1 = j + j * b_dim1;
b[i__1].r = ej.r, b[i__1].i = ej.i;
i__1 = j - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + (j - 1) * b_dim1;
temp.r = b[i__2].r, temp.i = b[i__2].i;
i__2 = i__ + (j - 1) * b_dim1;
i__3 = i__ + j * b_dim1;
q__2.r = x.r * temp.r - x.i * temp.i, q__2.i = x.r *
temp.i + x.i * temp.r;
q__1.r = b[i__3].r - q__2.r, q__1.i = b[i__3].i - q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
i__2 = i__ + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
/* L70: */
}
} else {
/* Eliminate without interchange. */
i__1 = j + j * b_dim1;
if (b[i__1].r == 0.f && b[i__1].i == 0.f) {
i__2 = j + j * b_dim1;
b[i__2].r = *eps3, b[i__2].i = 0.f;
}
cladiv_(&q__1, &ej, &b[j + j * b_dim1]);
x.r = q__1.r, x.i = q__1.i;
if (x.r != 0.f || x.i != 0.f) {
i__1 = j - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + (j - 1) * b_dim1;
i__3 = i__ + (j - 1) * b_dim1;
i__4 = i__ + j * b_dim1;
q__2.r = x.r * b[i__4].r - x.i * b[i__4].i, q__2.i =
x.r * b[i__4].i + x.i * b[i__4].r;
q__1.r = b[i__3].r - q__2.r, q__1.i = b[i__3].i -
q__2.i;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L80: */
}
}
}
/* L90: */
}
i__1 = b_dim1 + 1;
if (b[i__1].r == 0.f && b[i__1].i == 0.f) {
i__2 = b_dim1 + 1;
b[i__2].r = *eps3, b[i__2].i = 0.f;
}
*(unsigned char *)trans = 'C';
}
*(unsigned char *)normin = 'N';
i__1 = *n;
for (its = 1; its <= i__1; ++its) {
/* Solve U*x = scale*v for a right eigenvector
or U'*x = scale*v for a left eigenvector,
overwriting x on v. */
clatrs_("Upper", trans, "Nonunit", normin, n, &b[b_offset], ldb, &v[1]
, &scale, &rwork[1], &ierr);
*(unsigned char *)normin = 'Y';
/* Test for sufficient growth in the norm of v. */
vnorm = scasum_(n, &v[1], &c__1);
if (vnorm >= growto * scale) {
goto L120;
}
/* Choose new orthogonal starting vector and try again. */
rtemp = *eps3 / (rootn + 1.f);
v[1].r = *eps3, v[1].i = 0.f;
i__2 = *n;
for (i__ = 2; i__ <= i__2; ++i__) {
i__3 = i__;
v[i__3].r = rtemp, v[i__3].i = 0.f;
/* L100: */
}
i__2 = *n - its + 1;
i__3 = *n - its + 1;
r__1 = *eps3 * rootn;
q__1.r = v[i__3].r - r__1, q__1.i = v[i__3].i;
v[i__2].r = q__1.r, v[i__2].i = q__1.i;
/* L110: */
}
/* Failure to find eigenvector in N iterations. */
*info = 1;
L120:
/* Normalize eigenvector. */
i__ = icamax_(n, &v[1], &c__1);
i__1 = i__;
r__3 = 1.f / ((r__1 = v[i__1].r, dabs(r__1)) + (r__2 = r_imag(&v[i__]),
dabs(r__2)));
csscal_(n, &r__3, &v[1], &c__1);
return 0;
/* End of CLAEIN */
} /* claein_ */