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/* zlaein.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"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int zlaein_(logical *rightv, logical *noinit, integer *n,
doublecomplex *h__, integer *ldh, doublecomplex *w, doublecomplex *v,
doublecomplex *b, integer *ldb, doublereal *rwork, doublereal *eps3,
doublereal *smlnum, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, h_dim1, h_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2;
/* Builtin functions */
double sqrt(doublereal), d_imag(doublecomplex *);
/* Local variables */
integer i__, j;
doublecomplex x, ei, ej;
integer its, ierr;
doublecomplex temp;
doublereal scale;
char trans[1];
doublereal rtemp, rootn, vnorm;
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
extern integer izamax_(integer *, doublecomplex *, integer *);
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
char normin[1];
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
doublereal nrmsml;
extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, doublereal *, integer *);
doublereal growto;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLAEIN 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*16 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*16 */
/* The eigenvalue of H whose corresponding right or left */
/* eigenvector is to be computed. */
/* V (input/output) COMPLEX*16 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*16 array, dimension (LDB,N) */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* EPS3 (input) DOUBLE PRECISION */
/* A small machine-dependent value which is used to perturb */
/* close eigenvalues, and to replace zero pivots. */
/* SMLNUM (input) DOUBLE PRECISION */
/* 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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
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((doublereal) (*n));
growto = .1 / rootn;
/* Computing MAX */
d__1 = 1., d__2 = *eps3 * rootn;
nrmsml = max(d__1,d__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;
z__1.r = h__[i__3].r - w->r, z__1.i = h__[i__3].i - w->i;
b[i__2].r = z__1.r, b[i__2].i = z__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.;
/* L30: */
}
} else {
/* Scale supplied initial vector. */
vnorm = dznrm2_(n, &v[1], &c__1);
d__1 = *eps3 * rootn / max(vnorm,nrmsml);
zdscal_(n, &d__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 ((d__1 = b[i__2].r, abs(d__1)) + (d__2 = d_imag(&b[i__ + i__ *
b_dim1]), abs(d__2)) < (d__3 = ei.r, abs(d__3)) + (d__4 =
d_imag(&ei), abs(d__4))) {
/* Interchange rows and eliminate. */
zladiv_(&z__1, &b[i__ + i__ * b_dim1], &ei);
x.r = z__1.r, x.i = z__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;
z__2.r = x.r * temp.r - x.i * temp.i, z__2.i = x.r *
temp.i + x.i * temp.r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4].i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__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. && b[i__2].i == 0.) {
i__3 = i__ + i__ * b_dim1;
b[i__3].r = *eps3, b[i__3].i = 0.;
}
zladiv_(&z__1, &ei, &b[i__ + i__ * b_dim1]);
x.r = z__1.r, x.i = z__1.i;
if (x.r != 0. || x.i != 0.) {
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;
z__2.r = x.r * b[i__5].r - x.i * b[i__5].i, z__2.i =
x.r * b[i__5].i + x.i * b[i__5].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4].i -
z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L50: */
}
}
}
/* L60: */
}
i__1 = *n + *n * b_dim1;
if (b[i__1].r == 0. && b[i__1].i == 0.) {
i__2 = *n + *n * b_dim1;
b[i__2].r = *eps3, b[i__2].i = 0.;
}
*(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 ((d__1 = b[i__1].r, abs(d__1)) + (d__2 = d_imag(&b[j + j *
b_dim1]), abs(d__2)) < (d__3 = ej.r, abs(d__3)) + (d__4 =
d_imag(&ej), abs(d__4))) {
/* Interchange columns and eliminate. */
zladiv_(&z__1, &b[j + j * b_dim1], &ej);
x.r = z__1.r, x.i = z__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;
z__2.r = x.r * temp.r - x.i * temp.i, z__2.i = x.r *
temp.i + x.i * temp.r;
z__1.r = b[i__3].r - z__2.r, z__1.i = b[i__3].i - z__2.i;
b[i__2].r = z__1.r, b[i__2].i = z__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. && b[i__1].i == 0.) {
i__2 = j + j * b_dim1;
b[i__2].r = *eps3, b[i__2].i = 0.;
}
zladiv_(&z__1, &ej, &b[j + j * b_dim1]);
x.r = z__1.r, x.i = z__1.i;
if (x.r != 0. || x.i != 0.) {
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;
z__2.r = x.r * b[i__4].r - x.i * b[i__4].i, z__2.i =
x.r * b[i__4].i + x.i * b[i__4].r;
z__1.r = b[i__3].r - z__2.r, z__1.i = b[i__3].i -
z__2.i;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L80: */
}
}
}
/* L90: */
}
i__1 = b_dim1 + 1;
if (b[i__1].r == 0. && b[i__1].i == 0.) {
i__2 = b_dim1 + 1;
b[i__2].r = *eps3, b[i__2].i = 0.;
}
*(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. */
zlatrs_("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 = dzasum_(n, &v[1], &c__1);
if (vnorm >= growto * scale) {
goto L120;
}
/* Choose new orthogonal starting vector and try again. */
rtemp = *eps3 / (rootn + 1.);
v[1].r = *eps3, v[1].i = 0.;
i__2 = *n;
for (i__ = 2; i__ <= i__2; ++i__) {
i__3 = i__;
v[i__3].r = rtemp, v[i__3].i = 0.;
/* L100: */
}
i__2 = *n - its + 1;
i__3 = *n - its + 1;
d__1 = *eps3 * rootn;
z__1.r = v[i__3].r - d__1, z__1.i = v[i__3].i;
v[i__2].r = z__1.r, v[i__2].i = z__1.i;
/* L110: */
}
/* Failure to find eigenvector in N iterations. */
*info = 1;
L120:
/* Normalize eigenvector. */
i__ = izamax_(n, &v[1], &c__1);
i__1 = i__;
d__3 = 1. / ((d__1 = v[i__1].r, abs(d__1)) + (d__2 = d_imag(&v[i__]), abs(
d__2)));
zdscal_(n, &d__3, &v[1], &c__1);
return 0;
/* End of ZLAEIN */
} /* zlaein_ */
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