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agent_compositor_test/references/igraph-1.0.1/vendor/lapack/dtrevc.c
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Abdelrahman Said a11edf0c53 Add graph references
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/* -- translated by f2c (version 20240504).
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"
/* Table of constant values */
static logical c_false = FALSE_;
static integer c__1 = 1;
static doublereal c_b22 = 1.;
static doublereal c_b25 = 0.;
static integer c__2 = 2;
static logical c_true = TRUE_;
/* > \brief \b DTREVC
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DTREVC + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrevc.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrevc.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrevc.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, INFO )
CHARACTER HOWMNY, SIDE
INTEGER INFO, LDT, LDVL, LDVR, M, MM, N
LOGICAL SELECT( * )
DOUBLE PRECISION T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ),
$ WORK( * )
> \par Purpose:
=============
>
> \verbatim
>
> DTREVC computes some or all of the right and/or left eigenvectors of
> a real upper quasi-triangular matrix T.
> Matrices of this type are produced by the Schur factorization of
> a real general matrix: A = Q*T*Q**T, as computed by DHSEQR.
>
> The right eigenvector x and the left eigenvector y of T corresponding
> to an eigenvalue w are defined by:
>
> T*x = w*x, (y**T)*T = w*(y**T)
>
> where y**T denotes the transpose of y.
> The eigenvalues are not input to this routine, but are read directly
> from the diagonal blocks 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 orthogonal 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.
> \endverbatim
Arguments:
==========
> \param[in] SIDE
> \verbatim
> SIDE is CHARACTER*1
> = 'R': compute right eigenvectors only;
> = 'L': compute left eigenvectors only;
> = 'B': compute both right and left eigenvectors.
> \endverbatim
>
> \param[in] HOWMNY
> \verbatim
> HOWMNY is 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,
> as indicated by the logical array SELECT.
> \endverbatim
>
> \param[in,out] SELECT
> \verbatim
> SELECT is LOGICAL array, dimension (N)
> If HOWMNY = 'S', SELECT specifies the eigenvectors to be
> computed.
> If w(j) is a real eigenvalue, the corresponding real
> eigenvector is computed if SELECT(j) is .TRUE..
> If w(j) and w(j+1) are the real and imaginary parts of a
> complex eigenvalue, the corresponding complex eigenvector is
> computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
> on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
> .FALSE..
> Not referenced if HOWMNY = 'A' or 'B'.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix T. N >= 0.
> \endverbatim
>
> \param[in] T
> \verbatim
> T is DOUBLE PRECISION array, dimension (LDT,N)
> The upper quasi-triangular matrix T in Schur canonical form.
> \endverbatim
>
> \param[in] LDT
> \verbatim
> LDT is INTEGER
> The leading dimension of the array T. LDT >= max(1,N).
> \endverbatim
>
> \param[in,out] VL
> \verbatim
> VL is DOUBLE PRECISION 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 orthogonal matrix Q
> of Schur vectors returned by DHSEQR).
> 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.
> A complex eigenvector corresponding to a complex eigenvalue
> is stored in two consecutive columns, the first holding the
> real part, and the second the imaginary part.
> Not referenced if SIDE = 'R'.
> \endverbatim
>
> \param[in] LDVL
> \verbatim
> LDVL is INTEGER
> The leading dimension of the array VL. LDVL >= 1, and if
> SIDE = 'L' or 'B', LDVL >= N.
> \endverbatim
>
> \param[in,out] VR
> \verbatim
> VR is DOUBLE PRECISION 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 orthogonal matrix Q
> of Schur vectors returned by DHSEQR).
> 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.
> A complex eigenvector corresponding to a complex eigenvalue
> is stored in two consecutive columns, the first holding the
> real part and the second the imaginary part.
> Not referenced if SIDE = 'L'.
> \endverbatim
>
> \param[in] LDVR
> \verbatim
> LDVR is INTEGER
> The leading dimension of the array VR. LDVR >= 1, and if
> SIDE = 'R' or 'B', LDVR >= N.
> \endverbatim
>
> \param[in] MM
> \verbatim
> MM is INTEGER
> The number of columns in the arrays VL and/or VR. MM >= M.
> \endverbatim
>
> \param[out] M
> \verbatim
> M is 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 real eigenvector occupies one column and each
> selected complex eigenvector occupies two columns.
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (3*N)
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date November 2011
> \ingroup doubleOTHERcomputational
> \par Further Details:
=====================
>
> \verbatim
>
> 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|.
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdtrevc_(char *side, char *howmny, logical *select,
integer *n, doublereal *t, integer *ldt, doublereal *vl, integer *
ldvl, doublereal *vr, integer *ldvr, integer *mm, integer *m,
doublereal *work, integer *info)
{
/* System generated locals */
integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
doublereal d__1, d__2, d__3, d__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
doublereal x[4] /* was [2][2] */;
integer j1, j2, n2, ii, ki, ip, is;
doublereal wi, wr, rec, ulp, beta, emax;
logical pair;
extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
logical allv;
integer ierr;
doublereal unfl, ovfl, smin;
logical over;
doublereal vmax;
integer jnxt;
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal scale;
extern logical igraphlsame_(char *, char *);
extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
doublereal remax;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
logical leftv, bothv;
extern /* Subroutine */ int igraphdaxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
doublereal vcrit;
logical somev;
doublereal xnorm;
extern /* Subroutine */ int igraphdlaln2_(logical *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *
, doublereal *, integer *, doublereal *, doublereal *, integer *),
igraphdlabad_(doublereal *, doublereal *);
extern doublereal igraphdlamch_(char *);
extern integer igraphidamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
doublereal bignum;
logical rightv;
doublereal smlnum;
/* -- LAPACK computational routine (version 3.4.0) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
November 2011
=====================================================================
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;
/* Function Body */
bothv = igraphlsame_(side, "B");
rightv = igraphlsame_(side, "R") || bothv;
leftv = igraphlsame_(side, "L") || bothv;
allv = igraphlsame_(howmny, "A");
over = igraphlsame_(howmny, "B");
somev = igraphlsame_(howmny, "S");
*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 {
/* Set M to the number of columns required to store the selected
eigenvectors, standardize the array SELECT if necessary, and
test MM. */
if (somev) {
*m = 0;
pair = FALSE_;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (pair) {
pair = FALSE_;
select[j] = FALSE_;
} else {
if (j < *n) {
if (t[j + 1 + j * t_dim1] == 0.) {
if (select[j]) {
++(*m);
}
} else {
pair = TRUE_;
if (select[j] || select[j + 1]) {
select[j] = TRUE_;
*m += 2;
}
}
} else {
if (select[*n]) {
++(*m);
}
}
}
/* L10: */
}
} else {
*m = *n;
}
if (*mm < *m) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DTREVC", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* Set the constants to control overflow. */
unfl = igraphdlamch_("Safe minimum");
ovfl = 1. / unfl;
igraphdlabad_(&unfl, &ovfl);
ulp = igraphdlamch_("Precision");
smlnum = unfl * (*n / ulp);
bignum = (1. - ulp) / smlnum;
/* Compute 1-norm of each column of strictly upper triangular
part of T to control overflow in triangular solver. */
work[1] = 0.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
work[j] = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
work[j] += (d__1 = t[i__ + j * t_dim1], abs(d__1));
/* L20: */
}
/* L30: */
}
/* Index IP is used to specify the real or complex eigenvalue:
IP = 0, real eigenvalue,
1, first of conjugate complex pair: (wr,wi)
-1, second of conjugate complex pair: (wr,wi) */
n2 = *n << 1;
if (rightv) {
/* Compute right eigenvectors. */
ip = 0;
is = *m;
for (ki = *n; ki >= 1; --ki) {
if (ip == 1) {
goto L130;
}
if (ki == 1) {
goto L40;
}
if (t[ki + (ki - 1) * t_dim1] == 0.) {
goto L40;
}
ip = -1;
L40:
if (somev) {
if (ip == 0) {
if (! select[ki]) {
goto L130;
}
} else {
if (! select[ki - 1]) {
goto L130;
}
}
}
/* Compute the KI-th eigenvalue (WR,WI). */
wr = t[ki + ki * t_dim1];
wi = 0.;
if (ip != 0) {
wi = sqrt((d__1 = t[ki + (ki - 1) * t_dim1], abs(d__1))) *
sqrt((d__2 = t[ki - 1 + ki * t_dim1], abs(d__2)));
}
/* Computing MAX */
d__1 = ulp * (abs(wr) + abs(wi));
smin = max(d__1,smlnum);
if (ip == 0) {
/* Real right eigenvector */
work[ki + *n] = 1.;
/* Form right-hand side */
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
work[k + *n] = -t[k + ki * t_dim1];
/* L50: */
}
/* Solve the upper quasi-triangular system:
(T(1:KI-1,1:KI-1) - WR)*X = SCALE*WORK. */
jnxt = ki - 1;
for (j = ki - 1; j >= 1; --j) {
if (j > jnxt) {
goto L60;
}
j1 = j;
j2 = j;
jnxt = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.) {
j1 = j - 1;
jnxt = j - 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
igraphdlaln2_(&c_false, &c__1, &c__1, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm,
&ierr);
/* Scale X(1,1) to avoid overflow when updating
the right-hand side. */
if (xnorm > 1.) {
if (work[j] > bignum / xnorm) {
x[0] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.) {
igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);
}
work[j + *n] = x[0];
/* Update right-hand side */
i__1 = j - 1;
d__1 = -x[0];
igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
} else {
/* 2-by-2 diagonal block */
igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b22, &t[j -
1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &
work[j - 1 + *n], n, &wr, &c_b25, x, &c__2, &
scale, &xnorm, &ierr);
/* Scale X(1,1) and X(2,1) to avoid overflow when
updating the right-hand side. */
if (xnorm > 1.) {
/* Computing MAX */
d__1 = work[j - 1], d__2 = work[j];
beta = max(d__1,d__2);
if (beta > bignum / xnorm) {
x[0] /= xnorm;
x[1] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.) {
igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);
}
work[j - 1 + *n] = x[0];
work[j + *n] = x[1];
/* Update right-hand side */
i__1 = j - 2;
d__1 = -x[0];
igraphdaxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[*n + 1], &c__1);
i__1 = j - 2;
d__1 = -x[1];
igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
}
L60:
;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
igraphdcopy_(&ki, &work[*n + 1], &c__1, &vr[is * vr_dim1 + 1], &
c__1);
ii = igraphidamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
remax = 1. / (d__1 = vr[ii + is * vr_dim1], abs(d__1));
igraphdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__1 = *n;
for (k = ki + 1; k <= i__1; ++k) {
vr[k + is * vr_dim1] = 0.;
/* L70: */
}
} else {
if (ki > 1) {
i__1 = ki - 1;
igraphdgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
work[*n + 1], &c__1, &work[ki + *n], &vr[ki *
vr_dim1 + 1], &c__1);
}
ii = igraphidamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
remax = 1. / (d__1 = vr[ii + ki * vr_dim1], abs(d__1));
igraphdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
}
} else {
/* Complex right eigenvector.
Initial solve
[ (T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I* WI)]*X = 0.
[ (T(KI,KI-1) T(KI,KI) ) ] */
if ((d__1 = t[ki - 1 + ki * t_dim1], abs(d__1)) >= (d__2 = t[
ki + (ki - 1) * t_dim1], abs(d__2))) {
work[ki - 1 + *n] = 1.;
work[ki + n2] = wi / t[ki - 1 + ki * t_dim1];
} else {
work[ki - 1 + *n] = -wi / t[ki + (ki - 1) * t_dim1];
work[ki + n2] = 1.;
}
work[ki + *n] = 0.;
work[ki - 1 + n2] = 0.;
/* Form right-hand side */
i__1 = ki - 2;
for (k = 1; k <= i__1; ++k) {
work[k + *n] = -work[ki - 1 + *n] * t[k + (ki - 1) *
t_dim1];
work[k + n2] = -work[ki + n2] * t[k + ki * t_dim1];
/* L80: */
}
/* Solve upper quasi-triangular system:
(T(1:KI-2,1:KI-2) - (WR+i*WI))*X = SCALE*(WORK+i*WORK2) */
jnxt = ki - 2;
for (j = ki - 2; j >= 1; --j) {
if (j > jnxt) {
goto L90;
}
j1 = j;
j2 = j;
jnxt = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.) {
j1 = j - 1;
jnxt = j - 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
igraphdlaln2_(&c_false, &c__1, &c__2, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &wi, x, &c__2, &scale, &xnorm, &
ierr);
/* Scale X(1,1) and X(1,2) to avoid overflow when
updating the right-hand side. */
if (xnorm > 1.) {
if (work[j] > bignum / xnorm) {
x[0] /= xnorm;
x[2] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.) {
igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);
igraphdscal_(&ki, &scale, &work[n2 + 1], &c__1);
}
work[j + *n] = x[0];
work[j + n2] = x[2];
/* Update the right-hand side */
i__1 = j - 1;
d__1 = -x[0];
igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
i__1 = j - 1;
d__1 = -x[2];
igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
n2 + 1], &c__1);
} else {
/* 2-by-2 diagonal block */
igraphdlaln2_(&c_false, &c__2, &c__2, &smin, &c_b22, &t[j -
1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &
work[j - 1 + *n], n, &wr, &wi, x, &c__2, &
scale, &xnorm, &ierr);
/* Scale X to avoid overflow when updating
the right-hand side. */
if (xnorm > 1.) {
/* Computing MAX */
d__1 = work[j - 1], d__2 = work[j];
beta = max(d__1,d__2);
if (beta > bignum / xnorm) {
rec = 1. / xnorm;
x[0] *= rec;
x[2] *= rec;
x[1] *= rec;
x[3] *= rec;
scale *= rec;
}
}
/* Scale if necessary */
if (scale != 1.) {
igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);
igraphdscal_(&ki, &scale, &work[n2 + 1], &c__1);
}
work[j - 1 + *n] = x[0];
work[j + *n] = x[1];
work[j - 1 + n2] = x[2];
work[j + n2] = x[3];
/* Update the right-hand side */
i__1 = j - 2;
d__1 = -x[0];
igraphdaxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[*n + 1], &c__1);
i__1 = j - 2;
d__1 = -x[1];
igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
i__1 = j - 2;
d__1 = -x[2];
igraphdaxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[n2 + 1], &c__1);
i__1 = j - 2;
d__1 = -x[3];
igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[
n2 + 1], &c__1);
}
L90:
;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
igraphdcopy_(&ki, &work[*n + 1], &c__1, &vr[(is - 1) * vr_dim1
+ 1], &c__1);
igraphdcopy_(&ki, &work[n2 + 1], &c__1, &vr[is * vr_dim1 + 1], &
c__1);
emax = 0.;
i__1 = ki;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
d__3 = emax, d__4 = (d__1 = vr[k + (is - 1) * vr_dim1]
, abs(d__1)) + (d__2 = vr[k + is * vr_dim1],
abs(d__2));
emax = max(d__3,d__4);
/* L100: */
}
remax = 1. / emax;
igraphdscal_(&ki, &remax, &vr[(is - 1) * vr_dim1 + 1], &c__1);
igraphdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__1 = *n;
for (k = ki + 1; k <= i__1; ++k) {
vr[k + (is - 1) * vr_dim1] = 0.;
vr[k + is * vr_dim1] = 0.;
/* L110: */
}
} else {
if (ki > 2) {
i__1 = ki - 2;
igraphdgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
work[*n + 1], &c__1, &work[ki - 1 + *n], &vr[(
ki - 1) * vr_dim1 + 1], &c__1);
i__1 = ki - 2;
igraphdgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
work[n2 + 1], &c__1, &work[ki + n2], &vr[ki *
vr_dim1 + 1], &c__1);
} else {
igraphdscal_(n, &work[ki - 1 + *n], &vr[(ki - 1) * vr_dim1
+ 1], &c__1);
igraphdscal_(n, &work[ki + n2], &vr[ki * vr_dim1 + 1], &
c__1);
}
emax = 0.;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
d__3 = emax, d__4 = (d__1 = vr[k + (ki - 1) * vr_dim1]
, abs(d__1)) + (d__2 = vr[k + ki * vr_dim1],
abs(d__2));
emax = max(d__3,d__4);
/* L120: */
}
remax = 1. / emax;
igraphdscal_(n, &remax, &vr[(ki - 1) * vr_dim1 + 1], &c__1);
igraphdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
}
}
--is;
if (ip != 0) {
--is;
}
L130:
if (ip == 1) {
ip = 0;
}
if (ip == -1) {
ip = 1;
}
/* L140: */
}
}
if (leftv) {
/* Compute left eigenvectors. */
ip = 0;
is = 1;
i__1 = *n;
for (ki = 1; ki <= i__1; ++ki) {
if (ip == -1) {
goto L250;
}
if (ki == *n) {
goto L150;
}
if (t[ki + 1 + ki * t_dim1] == 0.) {
goto L150;
}
ip = 1;
L150:
if (somev) {
if (! select[ki]) {
goto L250;
}
}
/* Compute the KI-th eigenvalue (WR,WI). */
wr = t[ki + ki * t_dim1];
wi = 0.;
if (ip != 0) {
wi = sqrt((d__1 = t[ki + (ki + 1) * t_dim1], abs(d__1))) *
sqrt((d__2 = t[ki + 1 + ki * t_dim1], abs(d__2)));
}
/* Computing MAX */
d__1 = ulp * (abs(wr) + abs(wi));
smin = max(d__1,smlnum);
if (ip == 0) {
/* Real left eigenvector. */
work[ki + *n] = 1.;
/* Form right-hand side */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
work[k + *n] = -t[ki + k * t_dim1];
/* L160: */
}
/* Solve the quasi-triangular system:
(T(KI+1:N,KI+1:N) - WR)**T*X = SCALE*WORK */
vmax = 1.;
vcrit = bignum;
jnxt = ki + 1;
i__2 = *n;
for (j = ki + 1; j <= i__2; ++j) {
if (j < jnxt) {
goto L170;
}
j1 = j;
j2 = j;
jnxt = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.) {
j2 = j + 1;
jnxt = j + 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block
Scale if necessary to avoid overflow when forming
the right-hand side. */
if (work[j] > vcrit) {
rec = 1. / vmax;
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &rec, &work[ki + *n], &c__1);
vmax = 1.;
vcrit = bignum;
}
i__3 = j - ki - 1;
work[j + *n] -= igraphddot_(&i__3, &t[ki + 1 + j * t_dim1],
&c__1, &work[ki + 1 + *n], &c__1);
/* Solve (T(J,J)-WR)**T*X = WORK */
igraphdlaln2_(&c_false, &c__1, &c__1, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm,
&ierr);
/* Scale if necessary */
if (scale != 1.) {
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &scale, &work[ki + *n], &c__1);
}
work[j + *n] = x[0];
/* Computing MAX */
d__2 = (d__1 = work[j + *n], abs(d__1));
vmax = max(d__2,vmax);
vcrit = bignum / vmax;
} else {
/* 2-by-2 diagonal block
Scale if necessary to avoid overflow when forming
the right-hand side.
Computing MAX */
d__1 = work[j], d__2 = work[j + 1];
beta = max(d__1,d__2);
if (beta > vcrit) {
rec = 1. / vmax;
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &rec, &work[ki + *n], &c__1);
vmax = 1.;
vcrit = bignum;
}
i__3 = j - ki - 1;
work[j + *n] -= igraphddot_(&i__3, &t[ki + 1 + j * t_dim1],
&c__1, &work[ki + 1 + *n], &c__1);
i__3 = j - ki - 1;
work[j + 1 + *n] -= igraphddot_(&i__3, &t[ki + 1 + (j + 1) *
t_dim1], &c__1, &work[ki + 1 + *n], &c__1);
/* Solve
[T(J,J)-WR T(J,J+1) ]**T * X = SCALE*( WORK1 )
[T(J+1,J) T(J+1,J+1)-WR] ( WORK2 ) */
igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm,
&ierr);
/* Scale if necessary */
if (scale != 1.) {
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &scale, &work[ki + *n], &c__1);
}
work[j + *n] = x[0];
work[j + 1 + *n] = x[1];
/* Computing MAX */
d__3 = (d__1 = work[j + *n], abs(d__1)), d__4 = (d__2
= work[j + 1 + *n], abs(d__2)), d__3 = max(
d__3,d__4);
vmax = max(d__3,vmax);
vcrit = bignum / vmax;
}
L170:
;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
i__2 = *n - ki + 1;
igraphdcopy_(&i__2, &work[ki + *n], &c__1, &vl[ki + is *
vl_dim1], &c__1);
i__2 = *n - ki + 1;
ii = igraphidamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki -
1;
remax = 1. / (d__1 = vl[ii + is * vl_dim1], abs(d__1));
i__2 = *n - ki + 1;
igraphdscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
i__2 = ki - 1;
for (k = 1; k <= i__2; ++k) {
vl[k + is * vl_dim1] = 0.;
/* L180: */
}
} else {
if (ki < *n) {
i__2 = *n - ki;
igraphdgemv_("N", n, &i__2, &c_b22, &vl[(ki + 1) * vl_dim1
+ 1], ldvl, &work[ki + 1 + *n], &c__1, &work[
ki + *n], &vl[ki * vl_dim1 + 1], &c__1);
}
ii = igraphidamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
remax = 1. / (d__1 = vl[ii + ki * vl_dim1], abs(d__1));
igraphdscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
}
} else {
/* Complex left eigenvector.
Initial solve:
((T(KI,KI) T(KI,KI+1) )**T - (WR - I* WI))*X = 0.
((T(KI+1,KI) T(KI+1,KI+1)) ) */
if ((d__1 = t[ki + (ki + 1) * t_dim1], abs(d__1)) >= (d__2 =
t[ki + 1 + ki * t_dim1], abs(d__2))) {
work[ki + *n] = wi / t[ki + (ki + 1) * t_dim1];
work[ki + 1 + n2] = 1.;
} else {
work[ki + *n] = 1.;
work[ki + 1 + n2] = -wi / t[ki + 1 + ki * t_dim1];
}
work[ki + 1 + *n] = 0.;
work[ki + n2] = 0.;
/* Form right-hand side */
i__2 = *n;
for (k = ki + 2; k <= i__2; ++k) {
work[k + *n] = -work[ki + *n] * t[ki + k * t_dim1];
work[k + n2] = -work[ki + 1 + n2] * t[ki + 1 + k * t_dim1]
;
/* L190: */
}
/* Solve complex quasi-triangular system:
( T(KI+2,N:KI+2,N) - (WR-i*WI) )*X = WORK1+i*WORK2 */
vmax = 1.;
vcrit = bignum;
jnxt = ki + 2;
i__2 = *n;
for (j = ki + 2; j <= i__2; ++j) {
if (j < jnxt) {
goto L200;
}
j1 = j;
j2 = j;
jnxt = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.) {
j2 = j + 1;
jnxt = j + 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block
Scale if necessary to avoid overflow when
forming the right-hand side elements. */
if (work[j] > vcrit) {
rec = 1. / vmax;
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &rec, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &rec, &work[ki + n2], &c__1);
vmax = 1.;
vcrit = bignum;
}
i__3 = j - ki - 2;
work[j + *n] -= igraphddot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + *n], &c__1);
i__3 = j - ki - 2;
work[j + n2] -= igraphddot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + n2], &c__1);
/* Solve (T(J,J)-(WR-i*WI))*(X11+i*X12)= WK+I*WK2 */
d__1 = -wi;
igraphdlaln2_(&c_false, &c__1, &c__2, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &d__1, x, &c__2, &scale, &xnorm, &
ierr);
/* Scale if necessary */
if (scale != 1.) {
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &scale, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &scale, &work[ki + n2], &c__1);
}
work[j + *n] = x[0];
work[j + n2] = x[2];
/* Computing MAX */
d__3 = (d__1 = work[j + *n], abs(d__1)), d__4 = (d__2
= work[j + n2], abs(d__2)), d__3 = max(d__3,
d__4);
vmax = max(d__3,vmax);
vcrit = bignum / vmax;
} else {
/* 2-by-2 diagonal block
Scale if necessary to avoid overflow when forming
the right-hand side elements.
Computing MAX */
d__1 = work[j], d__2 = work[j + 1];
beta = max(d__1,d__2);
if (beta > vcrit) {
rec = 1. / vmax;
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &rec, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &rec, &work[ki + n2], &c__1);
vmax = 1.;
vcrit = bignum;
}
i__3 = j - ki - 2;
work[j + *n] -= igraphddot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + *n], &c__1);
i__3 = j - ki - 2;
work[j + n2] -= igraphddot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + n2], &c__1);
i__3 = j - ki - 2;
work[j + 1 + *n] -= igraphddot_(&i__3, &t[ki + 2 + (j + 1) *
t_dim1], &c__1, &work[ki + 2 + *n], &c__1);
i__3 = j - ki - 2;
work[j + 1 + n2] -= igraphddot_(&i__3, &t[ki + 2 + (j + 1) *
t_dim1], &c__1, &work[ki + 2 + n2], &c__1);
/* Solve 2-by-2 complex linear equation
([T(j,j) T(j,j+1) ]**T-(wr-i*wi)*I)*X = SCALE*B
([T(j+1,j) T(j+1,j+1)] ) */
d__1 = -wi;
igraphdlaln2_(&c_true, &c__2, &c__2, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &d__1, x, &c__2, &scale, &xnorm, &
ierr);
/* Scale if necessary */
if (scale != 1.) {
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &scale, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
igraphdscal_(&i__3, &scale, &work[ki + n2], &c__1);
}
work[j + *n] = x[0];
work[j + n2] = x[2];
work[j + 1 + *n] = x[1];
work[j + 1 + n2] = x[3];
/* Computing MAX */
d__1 = abs(x[0]), d__2 = abs(x[2]), d__1 = max(d__1,
d__2), d__2 = abs(x[1]), d__1 = max(d__1,d__2)
, d__2 = abs(x[3]), d__1 = max(d__1,d__2);
vmax = max(d__1,vmax);
vcrit = bignum / vmax;
}
L200:
;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
i__2 = *n - ki + 1;
igraphdcopy_(&i__2, &work[ki + *n], &c__1, &vl[ki + is *
vl_dim1], &c__1);
i__2 = *n - ki + 1;
igraphdcopy_(&i__2, &work[ki + n2], &c__1, &vl[ki + (is + 1) *
vl_dim1], &c__1);
emax = 0.;
i__2 = *n;
for (k = ki; k <= i__2; ++k) {
/* Computing MAX */
d__3 = emax, d__4 = (d__1 = vl[k + is * vl_dim1], abs(
d__1)) + (d__2 = vl[k + (is + 1) * vl_dim1],
abs(d__2));
emax = max(d__3,d__4);
/* L220: */
}
remax = 1. / emax;
i__2 = *n - ki + 1;
igraphdscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
i__2 = *n - ki + 1;
igraphdscal_(&i__2, &remax, &vl[ki + (is + 1) * vl_dim1], &c__1)
;
i__2 = ki - 1;
for (k = 1; k <= i__2; ++k) {
vl[k + is * vl_dim1] = 0.;
vl[k + (is + 1) * vl_dim1] = 0.;
/* L230: */
}
} else {
if (ki < *n - 1) {
i__2 = *n - ki - 1;
igraphdgemv_("N", n, &i__2, &c_b22, &vl[(ki + 2) * vl_dim1
+ 1], ldvl, &work[ki + 2 + *n], &c__1, &work[
ki + *n], &vl[ki * vl_dim1 + 1], &c__1);
i__2 = *n - ki - 1;
igraphdgemv_("N", n, &i__2, &c_b22, &vl[(ki + 2) * vl_dim1
+ 1], ldvl, &work[ki + 2 + n2], &c__1, &work[
ki + 1 + n2], &vl[(ki + 1) * vl_dim1 + 1], &
c__1);
} else {
igraphdscal_(n, &work[ki + *n], &vl[ki * vl_dim1 + 1], &
c__1);
igraphdscal_(n, &work[ki + 1 + n2], &vl[(ki + 1) * vl_dim1
+ 1], &c__1);
}
emax = 0.;
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing MAX */
d__3 = emax, d__4 = (d__1 = vl[k + ki * vl_dim1], abs(
d__1)) + (d__2 = vl[k + (ki + 1) * vl_dim1],
abs(d__2));
emax = max(d__3,d__4);
/* L240: */
}
remax = 1. / emax;
igraphdscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
igraphdscal_(n, &remax, &vl[(ki + 1) * vl_dim1 + 1], &c__1);
}
}
++is;
if (ip != 0) {
++is;
}
L250:
if (ip == -1) {
ip = 0;
}
if (ip == 1) {
ip = -1;
}
/* L260: */
}
}
return 0;
/* End of DTREVC */
} /* igraphdtrevc_ */
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