/* ztgevc.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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
/* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select,
integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer
*ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *
ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork,
integer *info)
{
/* System generated locals */
integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
doublecomplex d__;
integer i__, j;
doublecomplex ca, cb;
integer je, im, jr;
doublereal big;
logical lsa, lsb;
doublereal ulp;
doublecomplex sum;
integer ibeg, ieig, iend;
doublereal dmin__;
integer isrc;
doublereal temp;
doublecomplex suma, sumb;
doublereal xmax, scale;
logical ilall;
integer iside;
doublereal sbeta;
extern logical lsame_(char *, char *);
doublereal small;
logical compl;
doublereal anorm, bnorm;
logical compr;
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *),
dlabad_(doublereal *, doublereal *);
logical ilbbad;
doublereal acoefa, bcoefa, acoeff;
doublecomplex bcoeff;
logical ilback;
doublereal ascale, bscale;
extern doublereal dlamch_(char *);
doublecomplex salpha;
doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal bignum;
logical ilcomp;
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
integer ihwmny;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTGEVC computes some or all of the right and/or left eigenvectors of */
/* a pair of complex matrices (S,P), where S and P are upper triangular. */
/* Matrix pairs of this type are produced by the generalized Schur */
/* factorization of a complex matrix pair (A,B): */
/* A = Q*S*Z**H, B = Q*P*Z**H */
/* as computed by ZGGHRD + ZHGEQZ. */
/* The right eigenvector x and the left eigenvector y of (S,P) */
/* corresponding to an eigenvalue w are defined by: */
/* S*x = w*P*x, (y**H)*S = w*(y**H)*P, */
/* where y**H denotes the conjugate tranpose of y. */
/* The eigenvalues are not input to this routine, but are computed */
/* directly from the diagonal elements of S and P. */
/* This routine returns the matrices X and/or Y of right and left */
/* eigenvectors of (S,P), or the products Z*X and/or Q*Y, */
/* where Z and Q are input matrices. */
/* If Q and Z are the unitary factors from the generalized Schur */
/* factorization of a matrix pair (A,B), then Z*X and Q*Y */
/* are the matrices of right and left eigenvectors of (A,B). */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'R': compute right eigenvectors only; */
/* = 'L': compute left eigenvectors only; */
/* = 'B': compute both right and left eigenvectors. */
/* HOWMNY (input) CHARACTER*1 */
/* = 'A': compute all right and/or left eigenvectors; */
/* = 'B': compute all right and/or left eigenvectors, */
/* backtransformed by the matrices in VR and/or VL; */
/* = 'S': compute selected right and/or left eigenvectors, */
/* specified by the logical array SELECT. */
/* SELECT (input) LOGICAL array, dimension (N) */
/* If HOWMNY='S', SELECT specifies the eigenvectors to be */
/* computed. The eigenvector corresponding to the j-th */
/* eigenvalue is computed if SELECT(j) = .TRUE.. */
/* Not referenced if HOWMNY = 'A' or 'B'. */
/* N (input) INTEGER */
/* The order of the matrices S and P. N >= 0. */
/* S (input) COMPLEX*16 array, dimension (LDS,N) */
/* The upper triangular matrix S from a generalized Schur */
/* factorization, as computed by ZHGEQZ. */
/* LDS (input) INTEGER */
/* The leading dimension of array S. LDS >= max(1,N). */
/* P (input) COMPLEX*16 array, dimension (LDP,N) */
/* The upper triangular matrix P from a generalized Schur */
/* factorization, as computed by ZHGEQZ. P must have real */
/* diagonal elements. */
/* LDP (input) INTEGER */
/* The leading dimension of array P. LDP >= max(1,N). */
/* VL (input/output) COMPLEX*16 array, dimension (LDVL,MM) */
/* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
/* contain an N-by-N matrix Q (usually the unitary matrix Q */
/* of left Schur vectors returned by ZHGEQZ). */
/* On exit, if SIDE = 'L' or 'B', VL contains: */
/* if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */
/* if HOWMNY = 'B', the matrix Q*Y; */
/* if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */
/* SELECT, stored consecutively in the columns of */
/* VL, in the same order as their eigenvalues. */
/* Not referenced if SIDE = 'R'. */
/* LDVL (input) INTEGER */
/* The leading dimension of array VL. LDVL >= 1, and if */
/* SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. */
/* VR (input/output) COMPLEX*16 array, dimension (LDVR,MM) */
/* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
/* contain an N-by-N matrix Q (usually the unitary matrix Z */
/* of right Schur vectors returned by ZHGEQZ). */
/* On exit, if SIDE = 'R' or 'B', VR contains: */
/* if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
/* if HOWMNY = 'B', the matrix Z*X; */
/* if HOWMNY = 'S', the right eigenvectors of (S,P) specified by */
/* SELECT, stored consecutively in the columns of */
/* VR, in the same order as their eigenvalues. */
/* Not referenced if SIDE = 'L'. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1, and if */
/* SIDE = 'R' or 'B', LDVR >= N. */
/* MM (input) INTEGER */
/* The number of columns in the arrays VL and/or VR. MM >= M. */
/* M (output) INTEGER */
/* The number of columns in the arrays VL and/or VR actually */
/* used to store the eigenvectors. If HOWMNY = 'A' or 'B', M */
/* is set to N. Each selected eigenvector occupies one column. */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and Test the input parameters */
/* Parameter adjustments */
--select;
s_dim1 = *lds;
s_offset = 1 + s_dim1;
s -= s_offset;
p_dim1 = *ldp;
p_offset = 1 + p_dim1;
p -= p_offset;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
--rwork;
/* Function Body */
if (lsame_(howmny, "A")) {
ihwmny = 1;
ilall = TRUE_;
ilback = FALSE_;
} else if (lsame_(howmny, "S")) {
ihwmny = 2;
ilall = FALSE_;
ilback = FALSE_;
} else if (lsame_(howmny, "B")) {
ihwmny = 3;
ilall = TRUE_;
ilback = TRUE_;
} else {
ihwmny = -1;
}
if (lsame_(side, "R")) {
iside = 1;
compl = FALSE_;
compr = TRUE_;
} else if (lsame_(side, "L")) {
iside = 2;
compl = TRUE_;
compr = FALSE_;
} else if (lsame_(side, "B")) {
iside = 3;
compl = TRUE_;
compr = TRUE_;
} else {
iside = -1;
}
*info = 0;
if (iside < 0) {
*info = -1;
} else if (ihwmny < 0) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*lds < max(1,*n)) {
*info = -6;
} else if (*ldp < max(1,*n)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZTGEVC", &i__1);
return 0;
}
/* Count the number of eigenvectors */
if (! ilall) {
im = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (select[j]) {
++im;
}
/* L10: */
}
} else {
im = *n;
}
/* Check diagonal of B */
ilbbad = FALSE_;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (d_imag(&p[j + j * p_dim1]) != 0.) {
ilbbad = TRUE_;
}
/* L20: */
}
if (ilbbad) {
*info = -7;
} else if (compl && *ldvl < *n || *ldvl < 1) {
*info = -10;
} else if (compr && *ldvr < *n || *ldvr < 1) {
*info = -12;
} else if (*mm < im) {
*info = -13;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZTGEVC", &i__1);
return 0;
}
/* Quick return if possible */
*m = im;
if (*n == 0) {
return 0;
}
/* Machine Constants */
safmin = dlamch_("Safe minimum");
big = 1. / safmin;
dlabad_(&safmin, &big);
ulp = dlamch_("Epsilon") * dlamch_("Base");
small = safmin * *n / ulp;
big = 1. / small;
bignum = 1. / (safmin * *n);
/* Compute the 1-norm of each column of the strictly upper triangular */
/* part of A and B to check for possible overflow in the triangular */
/* solver. */
i__1 = s_dim1 + 1;
anorm = (d__1 = s[i__1].r, abs(d__1)) + (d__2 = d_imag(&s[s_dim1 + 1]),
abs(d__2));
i__1 = p_dim1 + 1;
bnorm = (d__1 = p[i__1].r, abs(d__1)) + (d__2 = d_imag(&p[p_dim1 + 1]),
abs(d__2));
rwork[1] = 0.;
rwork[*n + 1] = 0.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
rwork[j] = 0.;
rwork[*n + j] = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * s_dim1;
rwork[j] += (d__1 = s[i__3].r, abs(d__1)) + (d__2 = d_imag(&s[i__
+ j * s_dim1]), abs(d__2));
i__3 = i__ + j * p_dim1;
rwork[*n + j] += (d__1 = p[i__3].r, abs(d__1)) + (d__2 = d_imag(&
p[i__ + j * p_dim1]), abs(d__2));
/* L30: */
}
/* Computing MAX */
i__2 = j + j * s_dim1;
d__3 = anorm, d__4 = rwork[j] + ((d__1 = s[i__2].r, abs(d__1)) + (
d__2 = d_imag(&s[j + j * s_dim1]), abs(d__2)));
anorm = max(d__3,d__4);
/* Computing MAX */
i__2 = j + j * p_dim1;
d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = p[i__2].r, abs(d__1)) +
(d__2 = d_imag(&p[j + j * p_dim1]), abs(d__2)));
bnorm = max(d__3,d__4);
/* L40: */
}
ascale = 1. / max(anorm,safmin);
bscale = 1. / max(bnorm,safmin);
/* Left eigenvectors */
if (compl) {
ieig = 0;
/* Main loop over eigenvalues */
i__1 = *n;
for (je = 1; je <= i__1; ++je) {
if (ilall) {
ilcomp = TRUE_;
} else {
ilcomp = select[je];
}
if (ilcomp) {
++ieig;
i__2 = je + je * s_dim1;
i__3 = je + je * p_dim1;
if ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
* s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__3].r,
abs(d__1)) <= safmin) {
/* Singular matrix pencil -- return unit eigenvector */
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
i__3 = jr + ieig * vl_dim1;
vl[i__3].r = 0., vl[i__3].i = 0.;
/* L50: */
}
i__2 = ieig + ieig * vl_dim1;
vl[i__2].r = 1., vl[i__2].i = 0.;
goto L140;
}
/* Non-singular eigenvalue: */
/* Compute coefficients a and b in */
/* H */
/* y ( a A - b B ) = 0 */
/* Computing MAX */
i__2 = je + je * s_dim1;
i__3 = je + je * p_dim1;
d__4 = ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je
+ je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
p[i__3].r, abs(d__1)) * bscale, d__4 = max(d__4,d__5);
temp = 1. / max(d__4,safmin);
i__2 = je + je * s_dim1;
z__2.r = temp * s[i__2].r, z__2.i = temp * s[i__2].i;
z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
salpha.r = z__1.r, salpha.i = z__1.i;
i__2 = je + je * p_dim1;
sbeta = temp * p[i__2].r * bscale;
acoeff = sbeta * ascale;
z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
bcoeff.r = z__1.r, bcoeff.i = z__1.i;
/* Scale to avoid underflow */
lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
+ (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
scale = 1.;
if (lsa) {
scale = small / abs(sbeta) * min(anorm,big);
}
if (lsb) {
/* Computing MAX */
d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
+ (d__2 = d_imag(&salpha), abs(d__2))) * min(
bnorm,big);
scale = max(d__3,d__4);
}
if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
d__5 = 1., d__6 = abs(acoeff), d__5 = max(d__5,d__6),
d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
d_imag(&bcoeff), abs(d__2));
d__3 = scale, d__4 = 1. / (safmin * max(d__5,d__6));
scale = min(d__3,d__4);
if (lsa) {
acoeff = ascale * (scale * sbeta);
} else {
acoeff = scale * acoeff;
}
if (lsb) {
z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
bcoeff.r = z__1.r, bcoeff.i = z__1.i;
} else {
z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
bcoeff.r = z__1.r, bcoeff.i = z__1.i;
}
}
acoefa = abs(acoeff);
bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
bcoeff), abs(d__2));
xmax = 1.;
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
i__3 = jr;
work[i__3].r = 0., work[i__3].i = 0.;
/* L60: */
}
i__2 = je;
work[i__2].r = 1., work[i__2].i = 0.;
/* Computing MAX */
d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
d__1 = max(d__1,d__2);
dmin__ = max(d__1,safmin);
/* H */
/* Triangular solve of (a A - b B) y = 0 */
/* H */
/* (rowwise in (a A - b B) , or columnwise in a A - b B) */
i__2 = *n;
for (j = je + 1; j <= i__2; ++j) {
/* Compute */
/* j-1 */
/* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
/* k=je */
/* (Scale if necessary) */
temp = 1. / xmax;
if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum *
temp) {
i__3 = j - 1;
for (jr = je; jr <= i__3; ++jr) {
i__4 = jr;
i__5 = jr;
z__1.r = temp * work[i__5].r, z__1.i = temp *
work[i__5].i;
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
/* L70: */
}
xmax = 1.;
}
suma.r = 0., suma.i = 0.;
sumb.r = 0., sumb.i = 0.;
i__3 = j - 1;
for (jr = je; jr <= i__3; ++jr) {
d_cnjg(&z__3, &s[jr + j * s_dim1]);
i__4 = jr;
z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
.i, z__2.i = z__3.r * work[i__4].i + z__3.i *
work[i__4].r;
z__1.r = suma.r + z__2.r, z__1.i = suma.i + z__2.i;
suma.r = z__1.r, suma.i = z__1.i;
d_cnjg(&z__3, &p[jr + j * p_dim1]);
i__4 = jr;
z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
.i, z__2.i = z__3.r * work[i__4].i + z__3.i *
work[i__4].r;
z__1.r = sumb.r + z__2.r, z__1.i = sumb.i + z__2.i;
sumb.r = z__1.r, sumb.i = z__1.i;
/* L80: */
}
z__2.r = acoeff * suma.r, z__2.i = acoeff * suma.i;
d_cnjg(&z__4, &bcoeff);
z__3.r = z__4.r * sumb.r - z__4.i * sumb.i, z__3.i =
z__4.r * sumb.i + z__4.i * sumb.r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
sum.r = z__1.r, sum.i = z__1.i;
/* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */
/* with scaling and perturbation of the denominator */
i__3 = j + j * s_dim1;
z__3.r = acoeff * s[i__3].r, z__3.i = acoeff * s[i__3].i;
i__4 = j + j * p_dim1;
z__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
z__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
.r;
z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
d_cnjg(&z__1, &z__2);
d__.r = z__1.r, d__.i = z__1.i;
if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
d__2)) <= dmin__) {
z__1.r = dmin__, z__1.i = 0.;
d__.r = z__1.r, d__.i = z__1.i;
}
if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
d__2)) < 1.) {
if ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum),
abs(d__2)) >= bignum * ((d__3 = d__.r, abs(
d__3)) + (d__4 = d_imag(&d__), abs(d__4)))) {
temp = 1. / ((d__1 = sum.r, abs(d__1)) + (d__2 =
d_imag(&sum), abs(d__2)));
i__3 = j - 1;
for (jr = je; jr <= i__3; ++jr) {
i__4 = jr;
i__5 = jr;
z__1.r = temp * work[i__5].r, z__1.i = temp *
work[i__5].i;
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
/* L90: */
}
xmax = temp * xmax;
z__1.r = temp * sum.r, z__1.i = temp * sum.i;
sum.r = z__1.r, sum.i = z__1.i;
}
}
i__3 = j;
z__2.r = -sum.r, z__2.i = -sum.i;
zladiv_(&z__1, &z__2, &d__);
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* Computing MAX */
i__3 = j;
d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
d__2 = d_imag(&work[j]), abs(d__2));
xmax = max(d__3,d__4);
/* L100: */
}
/* Back transform eigenvector if HOWMNY='B'. */
if (ilback) {
i__2 = *n + 1 - je;
zgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl,
&work[je], &c__1, &c_b1, &work[*n + 1], &c__1);
isrc = 2;
ibeg = 1;
} else {
isrc = 1;
ibeg = je;
}
/* Copy and scale eigenvector into column of VL */
xmax = 0.;
i__2 = *n;
for (jr = ibeg; jr <= i__2; ++jr) {
/* Computing MAX */
i__3 = (isrc - 1) * *n + jr;
d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
d__2));
xmax = max(d__3,d__4);
/* L110: */
}
if (xmax > safmin) {
temp = 1. / xmax;
i__2 = *n;
for (jr = ibeg; jr <= i__2; ++jr) {
i__3 = jr + ieig * vl_dim1;
i__4 = (isrc - 1) * *n + jr;
z__1.r = temp * work[i__4].r, z__1.i = temp * work[
i__4].i;
vl[i__3].r = z__1.r, vl[i__3].i = z__1.i;
/* L120: */
}
} else {
ibeg = *n + 1;
}
i__2 = ibeg - 1;
for (jr = 1; jr <= i__2; ++jr) {
i__3 = jr + ieig * vl_dim1;
vl[i__3].r = 0., vl[i__3].i = 0.;
/* L130: */
}
}
L140:
;
}
}
/* Right eigenvectors */
if (compr) {
ieig = im + 1;
/* Main loop over eigenvalues */
for (je = *n; je >= 1; --je) {
if (ilall) {
ilcomp = TRUE_;
} else {
ilcomp = select[je];
}
if (ilcomp) {
--ieig;
i__1 = je + je * s_dim1;
i__2 = je + je * p_dim1;
if ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
* s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__2].r,
abs(d__1)) <= safmin) {
/* Singular matrix pencil -- return unit eigenvector */
i__1 = *n;
for (jr = 1; jr <= i__1; ++jr) {
i__2 = jr + ieig * vr_dim1;
vr[i__2].r = 0., vr[i__2].i = 0.;
/* L150: */
}
i__1 = ieig + ieig * vr_dim1;
vr[i__1].r = 1., vr[i__1].i = 0.;
goto L250;
}
/* Non-singular eigenvalue: */
/* Compute coefficients a and b in */
/* ( a A - b B ) x = 0 */
/* Computing MAX */
i__1 = je + je * s_dim1;
i__2 = je + je * p_dim1;
d__4 = ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je
+ je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
p[i__2].r, abs(d__1)) * bscale, d__4 = max(d__4,d__5);
temp = 1. / max(d__4,safmin);
i__1 = je + je * s_dim1;
z__2.r = temp * s[i__1].r, z__2.i = temp * s[i__1].i;
z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
salpha.r = z__1.r, salpha.i = z__1.i;
i__1 = je + je * p_dim1;
sbeta = temp * p[i__1].r * bscale;
acoeff = sbeta * ascale;
z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
bcoeff.r = z__1.r, bcoeff.i = z__1.i;
/* Scale to avoid underflow */
lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
+ (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
scale = 1.;
if (lsa) {
scale = small / abs(sbeta) * min(anorm,big);
}
if (lsb) {
/* Computing MAX */
d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
+ (d__2 = d_imag(&salpha), abs(d__2))) * min(
bnorm,big);
scale = max(d__3,d__4);
}
if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
d__5 = 1., d__6 = abs(acoeff), d__5 = max(d__5,d__6),
d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
d_imag(&bcoeff), abs(d__2));
d__3 = scale, d__4 = 1. / (safmin * max(d__5,d__6));
scale = min(d__3,d__4);
if (lsa) {
acoeff = ascale * (scale * sbeta);
} else {
acoeff = scale * acoeff;
}
if (lsb) {
z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
bcoeff.r = z__1.r, bcoeff.i = z__1.i;
} else {
z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
bcoeff.r = z__1.r, bcoeff.i = z__1.i;
}
}
acoefa = abs(acoeff);
bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
bcoeff), abs(d__2));
xmax = 1.;
i__1 = *n;
for (jr = 1; jr <= i__1; ++jr) {
i__2 = jr;
work[i__2].r = 0., work[i__2].i = 0.;
/* L160: */
}
i__1 = je;
work[i__1].r = 1., work[i__1].i = 0.;
/* Computing MAX */
d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
d__1 = max(d__1,d__2);
dmin__ = max(d__1,safmin);
/* Triangular solve of (a A - b B) x = 0 (columnwise) */
/* WORK(1:j-1) contains sums w, */
/* WORK(j+1:JE) contains x */
i__1 = je - 1;
for (jr = 1; jr <= i__1; ++jr) {
i__2 = jr;
i__3 = jr + je * s_dim1;
z__2.r = acoeff * s[i__3].r, z__2.i = acoeff * s[i__3].i;
i__4 = jr + je * p_dim1;
z__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
z__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
.r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L170: */
}
i__1 = je;
work[i__1].r = 1., work[i__1].i = 0.;
for (j = je - 1; j >= 1; --j) {
/* Form x(j) := - w(j) / d */
/* with scaling and perturbation of the denominator */
i__1 = j + j * s_dim1;
z__2.r = acoeff * s[i__1].r, z__2.i = acoeff * s[i__1].i;
i__2 = j + j * p_dim1;
z__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i,
z__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2]
.r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
d__.r = z__1.r, d__.i = z__1.i;
if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
d__2)) <= dmin__) {
z__1.r = dmin__, z__1.i = 0.;
d__.r = z__1.r, d__.i = z__1.i;
}
if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
d__2)) < 1.) {
i__1 = j;
if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
&work[j]), abs(d__2)) >= bignum * ((d__3 =
d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs(
d__4)))) {
i__1 = j;
temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
d__2 = d_imag(&work[j]), abs(d__2)));
i__1 = je;
for (jr = 1; jr <= i__1; ++jr) {
i__2 = jr;
i__3 = jr;
z__1.r = temp * work[i__3].r, z__1.i = temp *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L180: */
}
}
}
i__1 = j;
i__2 = j;
z__2.r = -work[i__2].r, z__2.i = -work[i__2].i;
zladiv_(&z__1, &z__2, &d__);
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
if (j > 1) {
/* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
i__1 = j;
if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
&work[j]), abs(d__2)) > 1.) {
i__1 = j;
temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
d__2 = d_imag(&work[j]), abs(d__2)));
if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >=
bignum * temp) {
i__1 = je;
for (jr = 1; jr <= i__1; ++jr) {
i__2 = jr;
i__3 = jr;
z__1.r = temp * work[i__3].r, z__1.i =
temp * work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i =
z__1.i;
/* L190: */
}
}
}
i__1 = j;
z__1.r = acoeff * work[i__1].r, z__1.i = acoeff *
work[i__1].i;
ca.r = z__1.r, ca.i = z__1.i;
i__1 = j;
z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[
i__1].i, z__1.i = bcoeff.r * work[i__1].i +
bcoeff.i * work[i__1].r;
cb.r = z__1.r, cb.i = z__1.i;
i__1 = j - 1;
for (jr = 1; jr <= i__1; ++jr) {
i__2 = jr;
i__3 = jr;
i__4 = jr + j * s_dim1;
z__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i,
z__3.i = ca.r * s[i__4].i + ca.i * s[i__4]
.r;
z__2.r = work[i__3].r + z__3.r, z__2.i = work[
i__3].i + z__3.i;
i__5 = jr + j * p_dim1;
z__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i,
z__4.i = cb.r * p[i__5].i + cb.i * p[i__5]
.r;
z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
z__4.i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L200: */
}
}
/* L210: */
}
/* Back transform eigenvector if HOWMNY='B'. */
if (ilback) {
zgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1],
&c__1, &c_b1, &work[*n + 1], &c__1);
isrc = 2;
iend = *n;
} else {
isrc = 1;
iend = je;
}
/* Copy and scale eigenvector into column of VR */
xmax = 0.;
i__1 = iend;
for (jr = 1; jr <= i__1; ++jr) {
/* Computing MAX */
i__2 = (isrc - 1) * *n + jr;
d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + (
d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
d__2));
xmax = max(d__3,d__4);
/* L220: */
}
if (xmax > safmin) {
temp = 1. / xmax;
i__1 = iend;
for (jr = 1; jr <= i__1; ++jr) {
i__2 = jr + ieig * vr_dim1;
i__3 = (isrc - 1) * *n + jr;
z__1.r = temp * work[i__3].r, z__1.i = temp * work[
i__3].i;
vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
/* L230: */
}
} else {
iend = 0;
}
i__1 = *n;
for (jr = iend + 1; jr <= i__1; ++jr) {
i__2 = jr + ieig * vr_dim1;
vr[i__2].r = 0., vr[i__2].i = 0.;
/* L240: */
}
}
L250:
;
}
}
return 0;
/* End of ZTGEVC */
} /* ztgevc_ */