/* slaein.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 slaein_(logical *rightv, logical *noinit, integer *n,
real *h__, integer *ldh, real *wr, real *wi, real *vr, real *vi, real
*b, integer *ldb, real *work, real *eps3, real *smlnum, real *bignum,
integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, h_dim1, h_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j;
real w, x, y;
integer i1, i2, i3;
real w1, ei, ej, xi, xr, rec;
integer its, ierr;
real temp, norm, vmax;
extern doublereal snrm2_(integer *, real *, integer *);
real scale;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
char trans[1];
real vcrit;
extern doublereal sasum_(integer *, real *, integer *);
real rootn, vnorm;
extern doublereal slapy2_(real *, real *);
real absbii, absbjj;
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ int sladiv_(real *, real *, real *, real *, real *
, real *);
char normin[1];
real nrmsml;
extern /* Subroutine */ int slatrs_(char *, char *, char *, char *,
integer *, real *, integer *, real *, real *, real *, integer *);
real growto;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAEIN uses inverse iteration to find a right or left eigenvector */
/* corresponding to the eigenvalue (WR,WI) of a real 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 (VR,VI). */
/* = .FALSE.: initial vector supplied in (VR,VI). */
/* N (input) INTEGER */
/* The order of the matrix H. N >= 0. */
/* H (input) REAL array, dimension (LDH,N) */
/* The upper Hessenberg matrix H. */
/* LDH (input) INTEGER */
/* The leading dimension of the array H. LDH >= max(1,N). */
/* WR (input) REAL */
/* WI (input) REAL */
/* The real and imaginary parts of the eigenvalue of H whose */
/* corresponding right or left eigenvector is to be computed. */
/* VR (input/output) REAL array, dimension (N) */
/* VI (input/output) REAL array, dimension (N) */
/* On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain */
/* a real starting vector for inverse iteration using the real */
/* eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI */
/* must contain the real and imaginary parts of a complex */
/* starting vector for inverse iteration using the complex */
/* eigenvalue (WR,WI); otherwise VR and VI need not be set. */
/* On exit, if WI = 0.0 (real eigenvalue), VR contains the */
/* computed real eigenvector; if WI.ne.0.0 (complex eigenvalue), */
/* VR and VI contain the real and imaginary parts of the */
/* computed complex eigenvector. The eigenvector is 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|. */
/* VI is not referenced if WI = 0.0. */
/* B (workspace) REAL array, dimension (LDB,N) */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= N+1. */
/* WORK (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. */
/* BIGNUM (input) REAL */
/* A machine-dependent value close to the overflow threshold. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* = 1: inverse iteration did not converge; VR is set to the */
/* last iterate, and so is VI if WI.ne.0.0. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
--vr;
--vi;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* 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 - (WR,WI)*I (except that the subdiagonal elements and */
/* the imaginary parts of the diagonal 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__) {
b[i__ + j * b_dim1] = h__[i__ + j * h_dim1];
/* L10: */
}
b[j + j * b_dim1] = h__[j + j * h_dim1] - *wr;
/* L20: */
}
if (*wi == 0.f) {
/* Real eigenvalue. */
if (*noinit) {
/* Set initial vector. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
vr[i__] = *eps3;
/* L30: */
}
} else {
/* Scale supplied initial vector. */
vnorm = snrm2_(n, &vr[1], &c__1);
r__1 = *eps3 * rootn / dmax(vnorm,nrmsml);
sscal_(n, &r__1, &vr[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__) {
ei = h__[i__ + 1 + i__ * h_dim1];
if ((r__1 = b[i__ + i__ * b_dim1], dabs(r__1)) < dabs(ei)) {
/* Interchange rows and eliminate. */
x = b[i__ + i__ * b_dim1] / ei;
b[i__ + i__ * b_dim1] = ei;
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
temp = b[i__ + 1 + j * b_dim1];
b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - x *
temp;
b[i__ + j * b_dim1] = temp;
/* L40: */
}
} else {
/* Eliminate without interchange. */
if (b[i__ + i__ * b_dim1] == 0.f) {
b[i__ + i__ * b_dim1] = *eps3;
}
x = ei / b[i__ + i__ * b_dim1];
if (x != 0.f) {
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
b[i__ + 1 + j * b_dim1] -= x * b[i__ + j * b_dim1]
;
/* L50: */
}
}
}
/* L60: */
}
if (b[*n + *n * b_dim1] == 0.f) {
b[*n + *n * b_dim1] = *eps3;
}
*(unsigned char *)trans = 'N';
} else {
/* UL decomposition with partial pivoting of B, replacing zero */
/* pivots by EPS3. */
for (j = *n; j >= 2; --j) {
ej = h__[j + (j - 1) * h_dim1];
if ((r__1 = b[j + j * b_dim1], dabs(r__1)) < dabs(ej)) {
/* Interchange columns and eliminate. */
x = b[j + j * b_dim1] / ej;
b[j + j * b_dim1] = ej;
i__1 = j - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = b[i__ + (j - 1) * b_dim1];
b[i__ + (j - 1) * b_dim1] = b[i__ + j * b_dim1] - x *
temp;
b[i__ + j * b_dim1] = temp;
/* L70: */
}
} else {
/* Eliminate without interchange. */
if (b[j + j * b_dim1] == 0.f) {
b[j + j * b_dim1] = *eps3;
}
x = ej / b[j + j * b_dim1];
if (x != 0.f) {
i__1 = j - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + (j - 1) * b_dim1] -= x * b[i__ + j *
b_dim1];
/* L80: */
}
}
}
/* L90: */
}
if (b[b_dim1 + 1] == 0.f) {
b[b_dim1 + 1] = *eps3;
}
*(unsigned char *)trans = 'T';
}
*(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. */
slatrs_("Upper", trans, "Nonunit", normin, n, &b[b_offset], ldb, &
vr[1], &scale, &work[1], &ierr);
*(unsigned char *)normin = 'Y';
/* Test for sufficient growth in the norm of v. */
vnorm = sasum_(n, &vr[1], &c__1);
if (vnorm >= growto * scale) {
goto L120;
}
/* Choose new orthogonal starting vector and try again. */
temp = *eps3 / (rootn + 1.f);
vr[1] = *eps3;
i__2 = *n;
for (i__ = 2; i__ <= i__2; ++i__) {
vr[i__] = temp;
/* L100: */
}
vr[*n - its + 1] -= *eps3 * rootn;
/* L110: */
}
/* Failure to find eigenvector in N iterations. */
*info = 1;
L120:
/* Normalize eigenvector. */
i__ = isamax_(n, &vr[1], &c__1);
r__2 = 1.f / (r__1 = vr[i__], dabs(r__1));
sscal_(n, &r__2, &vr[1], &c__1);
} else {
/* Complex eigenvalue. */
if (*noinit) {
/* Set initial vector. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
vr[i__] = *eps3;
vi[i__] = 0.f;
/* L130: */
}
} else {
/* Scale supplied initial vector. */
r__1 = snrm2_(n, &vr[1], &c__1);
r__2 = snrm2_(n, &vi[1], &c__1);
norm = slapy2_(&r__1, &r__2);
rec = *eps3 * rootn / dmax(norm,nrmsml);
sscal_(n, &rec, &vr[1], &c__1);
sscal_(n, &rec, &vi[1], &c__1);
}
if (*rightv) {
/* LU decomposition with partial pivoting of B, replacing zero */
/* pivots by EPS3. */
/* The imaginary part of the (i,j)-th element of U is stored in */
/* B(j+1,i). */
b[b_dim1 + 2] = -(*wi);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
b[i__ + 1 + b_dim1] = 0.f;
/* L140: */
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
absbii = slapy2_(&b[i__ + i__ * b_dim1], &b[i__ + 1 + i__ *
b_dim1]);
ei = h__[i__ + 1 + i__ * h_dim1];
if (absbii < dabs(ei)) {
/* Interchange rows and eliminate. */
xr = b[i__ + i__ * b_dim1] / ei;
xi = b[i__ + 1 + i__ * b_dim1] / ei;
b[i__ + i__ * b_dim1] = ei;
b[i__ + 1 + i__ * b_dim1] = 0.f;
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
temp = b[i__ + 1 + j * b_dim1];
b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - xr *
temp;
b[j + 1 + (i__ + 1) * b_dim1] = b[j + 1 + i__ *
b_dim1] - xi * temp;
b[i__ + j * b_dim1] = temp;
b[j + 1 + i__ * b_dim1] = 0.f;
/* L150: */
}
b[i__ + 2 + i__ * b_dim1] = -(*wi);
b[i__ + 1 + (i__ + 1) * b_dim1] -= xi * *wi;
b[i__ + 2 + (i__ + 1) * b_dim1] += xr * *wi;
} else {
/* Eliminate without interchanging rows. */
if (absbii == 0.f) {
b[i__ + i__ * b_dim1] = *eps3;
b[i__ + 1 + i__ * b_dim1] = 0.f;
absbii = *eps3;
}
ei = ei / absbii / absbii;
xr = b[i__ + i__ * b_dim1] * ei;
xi = -b[i__ + 1 + i__ * b_dim1] * ei;
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
b[i__ + 1 + j * b_dim1] = b[i__ + 1 + j * b_dim1] -
xr * b[i__ + j * b_dim1] + xi * b[j + 1 + i__
* b_dim1];
b[j + 1 + (i__ + 1) * b_dim1] = -xr * b[j + 1 + i__ *
b_dim1] - xi * b[i__ + j * b_dim1];
/* L160: */
}
b[i__ + 2 + (i__ + 1) * b_dim1] -= *wi;
}
/* Compute 1-norm of offdiagonal elements of i-th row. */
i__2 = *n - i__;
i__3 = *n - i__;
work[i__] = sasum_(&i__2, &b[i__ + (i__ + 1) * b_dim1], ldb)
+ sasum_(&i__3, &b[i__ + 2 + i__ * b_dim1], &c__1);
/* L170: */
}
if (b[*n + *n * b_dim1] == 0.f && b[*n + 1 + *n * b_dim1] == 0.f)
{
b[*n + *n * b_dim1] = *eps3;
}
work[*n] = 0.f;
i1 = *n;
i2 = 1;
i3 = -1;
} else {
/* UL decomposition with partial pivoting of conjg(B), */
/* replacing zero pivots by EPS3. */
/* The imaginary part of the (i,j)-th element of U is stored in */
/* B(j+1,i). */
b[*n + 1 + *n * b_dim1] = *wi;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
b[*n + 1 + j * b_dim1] = 0.f;
/* L180: */
}
for (j = *n; j >= 2; --j) {
ej = h__[j + (j - 1) * h_dim1];
absbjj = slapy2_(&b[j + j * b_dim1], &b[j + 1 + j * b_dim1]);
if (absbjj < dabs(ej)) {
/* Interchange columns and eliminate */
xr = b[j + j * b_dim1] / ej;
xi = b[j + 1 + j * b_dim1] / ej;
b[j + j * b_dim1] = ej;
b[j + 1 + j * b_dim1] = 0.f;
i__1 = j - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = b[i__ + (j - 1) * b_dim1];
b[i__ + (j - 1) * b_dim1] = b[i__ + j * b_dim1] - xr *
temp;
b[j + i__ * b_dim1] = b[j + 1 + i__ * b_dim1] - xi *
temp;
b[i__ + j * b_dim1] = temp;
b[j + 1 + i__ * b_dim1] = 0.f;
/* L190: */
}
b[j + 1 + (j - 1) * b_dim1] = *wi;
b[j - 1 + (j - 1) * b_dim1] += xi * *wi;
b[j + (j - 1) * b_dim1] -= xr * *wi;
} else {
/* Eliminate without interchange. */
if (absbjj == 0.f) {
b[j + j * b_dim1] = *eps3;
b[j + 1 + j * b_dim1] = 0.f;
absbjj = *eps3;
}
ej = ej / absbjj / absbjj;
xr = b[j + j * b_dim1] * ej;
xi = -b[j + 1 + j * b_dim1] * ej;
i__1 = j - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + (j - 1) * b_dim1] = b[i__ + (j - 1) * b_dim1]
- xr * b[i__ + j * b_dim1] + xi * b[j + 1 +
i__ * b_dim1];
b[j + i__ * b_dim1] = -xr * b[j + 1 + i__ * b_dim1] -
xi * b[i__ + j * b_dim1];
/* L200: */
}
b[j + (j - 1) * b_dim1] += *wi;
}
/* Compute 1-norm of offdiagonal elements of j-th column. */
i__1 = j - 1;
i__2 = j - 1;
work[j] = sasum_(&i__1, &b[j * b_dim1 + 1], &c__1) + sasum_(&
i__2, &b[j + 1 + b_dim1], ldb);
/* L210: */
}
if (b[b_dim1 + 1] == 0.f && b[b_dim1 + 2] == 0.f) {
b[b_dim1 + 1] = *eps3;
}
work[1] = 0.f;
i1 = 1;
i2 = *n;
i3 = 1;
}
i__1 = *n;
for (its = 1; its <= i__1; ++its) {
scale = 1.f;
vmax = 1.f;
vcrit = *bignum;
/* Solve U*(xr,xi) = scale*(vr,vi) for a right eigenvector, */
/* or U'*(xr,xi) = scale*(vr,vi) for a left eigenvector, */
/* overwriting (xr,xi) on (vr,vi). */
i__2 = i2;
i__3 = i3;
for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3)
{
if (work[i__] > vcrit) {
rec = 1.f / vmax;
sscal_(n, &rec, &vr[1], &c__1);
sscal_(n, &rec, &vi[1], &c__1);
scale *= rec;
vmax = 1.f;
vcrit = *bignum;
}
xr = vr[i__];
xi = vi[i__];
if (*rightv) {
i__4 = *n;
for (j = i__ + 1; j <= i__4; ++j) {
xr = xr - b[i__ + j * b_dim1] * vr[j] + b[j + 1 + i__
* b_dim1] * vi[j];
xi = xi - b[i__ + j * b_dim1] * vi[j] - b[j + 1 + i__
* b_dim1] * vr[j];
/* L220: */
}
} else {
i__4 = i__ - 1;
for (j = 1; j <= i__4; ++j) {
xr = xr - b[j + i__ * b_dim1] * vr[j] + b[i__ + 1 + j
* b_dim1] * vi[j];
xi = xi - b[j + i__ * b_dim1] * vi[j] - b[i__ + 1 + j
* b_dim1] * vr[j];
/* L230: */
}
}
w = (r__1 = b[i__ + i__ * b_dim1], dabs(r__1)) + (r__2 = b[
i__ + 1 + i__ * b_dim1], dabs(r__2));
if (w > *smlnum) {
if (w < 1.f) {
w1 = dabs(xr) + dabs(xi);
if (w1 > w * *bignum) {
rec = 1.f / w1;
sscal_(n, &rec, &vr[1], &c__1);
sscal_(n, &rec, &vi[1], &c__1);
xr = vr[i__];
xi = vi[i__];
scale *= rec;
vmax *= rec;
}
}
/* Divide by diagonal element of B. */
sladiv_(&xr, &xi, &b[i__ + i__ * b_dim1], &b[i__ + 1 +
i__ * b_dim1], &vr[i__], &vi[i__]);
/* Computing MAX */
r__3 = (r__1 = vr[i__], dabs(r__1)) + (r__2 = vi[i__],
dabs(r__2));
vmax = dmax(r__3,vmax);
vcrit = *bignum / vmax;
} else {
i__4 = *n;
for (j = 1; j <= i__4; ++j) {
vr[j] = 0.f;
vi[j] = 0.f;
/* L240: */
}
vr[i__] = 1.f;
vi[i__] = 1.f;
scale = 0.f;
vmax = 1.f;
vcrit = *bignum;
}
/* L250: */
}
/* Test for sufficient growth in the norm of (VR,VI). */
vnorm = sasum_(n, &vr[1], &c__1) + sasum_(n, &vi[1], &c__1);
if (vnorm >= growto * scale) {
goto L280;
}
/* Choose a new orthogonal starting vector and try again. */
y = *eps3 / (rootn + 1.f);
vr[1] = *eps3;
vi[1] = 0.f;
i__3 = *n;
for (i__ = 2; i__ <= i__3; ++i__) {
vr[i__] = y;
vi[i__] = 0.f;
/* L260: */
}
vr[*n - its + 1] -= *eps3 * rootn;
/* L270: */
}
/* Failure to find eigenvector in N iterations */
*info = 1;
L280:
/* Normalize eigenvector. */
vnorm = 0.f;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
r__3 = vnorm, r__4 = (r__1 = vr[i__], dabs(r__1)) + (r__2 = vi[
i__], dabs(r__2));
vnorm = dmax(r__3,r__4);
/* L290: */
}
r__1 = 1.f / vnorm;
sscal_(n, &r__1, &vr[1], &c__1);
r__1 = 1.f / vnorm;
sscal_(n, &r__1, &vi[1], &c__1);
}
return 0;
/* End of SLAEIN */
} /* slaein_ */