/* ztrevc.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_b2 = {1.,0.};
static integer c__1 = 1;
/* Subroutine */ int ztrevc_(char *side, char *howmny, logical *select,
integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl,
integer *ldvl, doublecomplex *vr, integer *ldvr, integer *mm, integer
*m, doublecomplex *work, doublereal *rwork, integer *info)
{
/* System generated locals */
integer t_dim1, t_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;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, k, ii, ki, is;
doublereal ulp;
logical allv;
doublereal unfl, ovfl, smin;
logical over;
doublereal scale;
extern logical lsame_(char *, char *);
doublereal remax;
logical leftv, bothv;
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
logical somev;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
integer *, doublereal *, doublecomplex *, integer *);
extern integer izamax_(integer *, doublecomplex *, integer *);
logical rightv;
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
doublereal smlnum;
extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, doublereal *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTREVC computes some or all of the right and/or left eigenvectors of */
/* a complex upper triangular matrix T. */
/* Matrices of this type are produced by the Schur factorization of */
/* a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. */
/* The right eigenvector x and the left eigenvector y of T corresponding */
/* to an eigenvalue w are defined by: */
/* T*x = w*x, (y**H)*T = w*(y**H) */
/* where y**H denotes the conjugate transpose of the vector y. */
/* The eigenvalues are not input to this routine, but are read directly */
/* from the diagonal of T. */
/* This routine returns the matrices X and/or Y of right and left */
/* eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */
/* input matrix. If Q is the unitary factor that reduces a matrix A to */
/* Schur form T, then Q*X and Q*Y are the matrices of right and left */
/* eigenvectors of A. */
/* 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 using the matrices supplied in */
/* VR and/or VL; */
/* = 'S': compute selected right and/or left eigenvectors, */
/* as indicated 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 matrix T. N >= 0. */
/* T (input/output) COMPLEX*16 array, dimension (LDT,N) */
/* The upper triangular matrix T. T is modified, but restored */
/* on exit. */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= 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 */
/* Schur vectors returned by ZHSEQR). */
/* On exit, if SIDE = 'L' or 'B', VL contains: */
/* if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */
/* if HOWMNY = 'B', the matrix Q*Y; */
/* if HOWMNY = 'S', the left eigenvectors of T 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 the array VL. LDVL >= 1, and if */
/* SIDE = 'L' 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 Q of */
/* Schur vectors returned by ZHSEQR). */
/* On exit, if SIDE = 'R' or 'B', VR contains: */
/* if HOWMNY = 'A', the matrix X of right eigenvectors of T; */
/* if HOWMNY = 'B', the matrix Q*X; */
/* if HOWMNY = 'S', the right eigenvectors of T 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 (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* The algorithm used in this program is basically backward (forward) */
/* substitution, with scaling to make the the code robust against */
/* possible overflow. */
/* Each eigenvector is normalized so that the element of largest */
/* magnitude has magnitude 1; here the magnitude of a complex number */
/* (x,y) is taken to be |x| + |y|. */
/* ===================================================================== */
/* .. 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;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_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 */
bothv = lsame_(side, "B");
rightv = lsame_(side, "R") || bothv;
leftv = lsame_(side, "L") || bothv;
allv = lsame_(howmny, "A");
over = lsame_(howmny, "B");
somev = lsame_(howmny, "S");
/* Set M to the number of columns required to store the selected */
/* eigenvectors. */
if (somev) {
*m = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (select[j]) {
++(*m);
}
/* L10: */
}
} else {
*m = *n;
}
*info = 0;
if (! rightv && ! leftv) {
*info = -1;
} else if (! allv && ! over && ! somev) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*ldt < max(1,*n)) {
*info = -6;
} else if (*ldvl < 1 || leftv && *ldvl < *n) {
*info = -8;
} else if (*ldvr < 1 || rightv && *ldvr < *n) {
*info = -10;
} else if (*mm < *m) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZTREVC", &i__1);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* Set the constants to control overflow. */
unfl = dlamch_("Safe minimum");
ovfl = 1. / unfl;
dlabad_(&unfl, &ovfl);
ulp = dlamch_("Precision");
smlnum = unfl * (*n / ulp);
/* Store the diagonal elements of T in working array WORK. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + *n;
i__3 = i__ + i__ * t_dim1;
work[i__2].r = t[i__3].r, work[i__2].i = t[i__3].i;
/* L20: */
}
/* Compute 1-norm of each column of strictly upper triangular */
/* part of T to control overflow in triangular solver. */
rwork[1] = 0.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
rwork[j] = dzasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
/* L30: */
}
if (rightv) {
/* Compute right eigenvectors. */
is = *m;
for (ki = *n; ki >= 1; --ki) {
if (somev) {
if (! select[ki]) {
goto L80;
}
}
/* Computing MAX */
i__1 = ki + ki * t_dim1;
d__3 = ulp * ((d__1 = t[i__1].r, abs(d__1)) + (d__2 = d_imag(&t[
ki + ki * t_dim1]), abs(d__2)));
smin = max(d__3,smlnum);
work[1].r = 1., work[1].i = 0.;
/* Form right-hand side. */
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k;
i__3 = k + ki * t_dim1;
z__1.r = -t[i__3].r, z__1.i = -t[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L40: */
}
/* Solve the triangular system: */
/* (T(1:KI-1,1:KI-1) - T(KI,KI))*X = SCALE*WORK. */
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k + k * t_dim1;
i__3 = k + k * t_dim1;
i__4 = ki + ki * t_dim1;
z__1.r = t[i__3].r - t[i__4].r, z__1.i = t[i__3].i - t[i__4]
.i;
t[i__2].r = z__1.r, t[i__2].i = z__1.i;
i__2 = k + k * t_dim1;
if ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[k + k *
t_dim1]), abs(d__2)) < smin) {
i__3 = k + k * t_dim1;
t[i__3].r = smin, t[i__3].i = 0.;
}
/* L50: */
}
if (ki > 1) {
i__1 = ki - 1;
zlatrs_("Upper", "No transpose", "Non-unit", "Y", &i__1, &t[
t_offset], ldt, &work[1], &scale, &rwork[1], info);
i__1 = ki;
work[i__1].r = scale, work[i__1].i = 0.;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
zcopy_(&ki, &work[1], &c__1, &vr[is * vr_dim1 + 1], &c__1);
ii = izamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
i__1 = ii + is * vr_dim1;
remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
&vr[ii + is * vr_dim1]), abs(d__2)));
zdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__1 = *n;
for (k = ki + 1; k <= i__1; ++k) {
i__2 = k + is * vr_dim1;
vr[i__2].r = 0., vr[i__2].i = 0.;
/* L60: */
}
} else {
if (ki > 1) {
i__1 = ki - 1;
z__1.r = scale, z__1.i = 0.;
zgemv_("N", n, &i__1, &c_b2, &vr[vr_offset], ldvr, &work[
1], &c__1, &z__1, &vr[ki * vr_dim1 + 1], &c__1);
}
ii = izamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
i__1 = ii + ki * vr_dim1;
remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
&vr[ii + ki * vr_dim1]), abs(d__2)));
zdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
}
/* Set back the original diagonal elements of T. */
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k + k * t_dim1;
i__3 = k + *n;
t[i__2].r = work[i__3].r, t[i__2].i = work[i__3].i;
/* L70: */
}
--is;
L80:
;
}
}
if (leftv) {
/* Compute left eigenvectors. */
is = 1;
i__1 = *n;
for (ki = 1; ki <= i__1; ++ki) {
if (somev) {
if (! select[ki]) {
goto L130;
}
}
/* Computing MAX */
i__2 = ki + ki * t_dim1;
d__3 = ulp * ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[
ki + ki * t_dim1]), abs(d__2)));
smin = max(d__3,smlnum);
i__2 = *n;
work[i__2].r = 1., work[i__2].i = 0.;
/* Form right-hand side. */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
i__3 = k;
d_cnjg(&z__2, &t[ki + k * t_dim1]);
z__1.r = -z__2.r, z__1.i = -z__2.i;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* L90: */
}
/* Solve the triangular system: */
/* (T(KI+1:N,KI+1:N) - T(KI,KI))'*X = SCALE*WORK. */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
i__3 = k + k * t_dim1;
i__4 = k + k * t_dim1;
i__5 = ki + ki * t_dim1;
z__1.r = t[i__4].r - t[i__5].r, z__1.i = t[i__4].i - t[i__5]
.i;
t[i__3].r = z__1.r, t[i__3].i = z__1.i;
i__3 = k + k * t_dim1;
if ((d__1 = t[i__3].r, abs(d__1)) + (d__2 = d_imag(&t[k + k *
t_dim1]), abs(d__2)) < smin) {
i__4 = k + k * t_dim1;
t[i__4].r = smin, t[i__4].i = 0.;
}
/* L100: */
}
if (ki < *n) {
i__2 = *n - ki;
zlatrs_("Upper", "Conjugate transpose", "Non-unit", "Y", &
i__2, &t[ki + 1 + (ki + 1) * t_dim1], ldt, &work[ki +
1], &scale, &rwork[1], info);
i__2 = ki;
work[i__2].r = scale, work[i__2].i = 0.;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
i__2 = *n - ki + 1;
zcopy_(&i__2, &work[ki], &c__1, &vl[ki + is * vl_dim1], &c__1)
;
i__2 = *n - ki + 1;
ii = izamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki - 1;
i__2 = ii + is * vl_dim1;
remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
&vl[ii + is * vl_dim1]), abs(d__2)));
i__2 = *n - ki + 1;
zdscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
i__2 = ki - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = k + is * vl_dim1;
vl[i__3].r = 0., vl[i__3].i = 0.;
/* L110: */
}
} else {
if (ki < *n) {
i__2 = *n - ki;
z__1.r = scale, z__1.i = 0.;
zgemv_("N", n, &i__2, &c_b2, &vl[(ki + 1) * vl_dim1 + 1],
ldvl, &work[ki + 1], &c__1, &z__1, &vl[ki *
vl_dim1 + 1], &c__1);
}
ii = izamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
i__2 = ii + ki * vl_dim1;
remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
&vl[ii + ki * vl_dim1]), abs(d__2)));
zdscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
}
/* Set back the original diagonal elements of T. */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
i__3 = k + k * t_dim1;
i__4 = k + *n;
t[i__3].r = work[i__4].r, t[i__3].i = work[i__4].i;
/* L120: */
}
++is;
L130:
;
}
}
return 0;
/* End of ZTREVC */
} /* ztrevc_ */
