Abdelrahman Said
469 lines
12 KiB
C
469 lines
12 KiB
C
/* -- 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 integer c__1 = 1;
|
|
static integer c__2 = 2;
|
|
|
|
/* > \brief \b DTREXC
|
|
|
|
=========== DOCUMENTATION ===========
|
|
|
|
Online html documentation available at
|
|
http://www.netlib.org/lapack/explore-html/
|
|
|
|
> \htmlonly
|
|
> Download DTREXC + dependencies
|
|
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrexc.
|
|
f">
|
|
> [TGZ]</a>
|
|
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrexc.
|
|
f">
|
|
> [ZIP]</a>
|
|
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrexc.
|
|
f">
|
|
> [TXT]</a>
|
|
> \endhtmlonly
|
|
|
|
Definition:
|
|
===========
|
|
|
|
SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
|
|
INFO )
|
|
|
|
CHARACTER COMPQ
|
|
INTEGER IFST, ILST, INFO, LDQ, LDT, N
|
|
DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )
|
|
|
|
|
|
> \par Purpose:
|
|
=============
|
|
>
|
|
> \verbatim
|
|
>
|
|
> DTREXC reorders the real Schur factorization of a real matrix
|
|
> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
|
|
> moved to row ILST.
|
|
>
|
|
> The real Schur form T is reordered by an orthogonal similarity
|
|
> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
|
|
> is updated by postmultiplying it with Z.
|
|
>
|
|
> T must be in Schur canonical form (as returned by DHSEQR), that is,
|
|
> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
|
|
> 2-by-2 diagonal block has its diagonal elements equal and its
|
|
> off-diagonal elements of opposite sign.
|
|
> \endverbatim
|
|
|
|
Arguments:
|
|
==========
|
|
|
|
> \param[in] COMPQ
|
|
> \verbatim
|
|
> COMPQ is CHARACTER*1
|
|
> = 'V': update the matrix Q of Schur vectors;
|
|
> = 'N': do not update Q.
|
|
> \endverbatim
|
|
>
|
|
> \param[in] N
|
|
> \verbatim
|
|
> N is INTEGER
|
|
> The order of the matrix T. N >= 0.
|
|
> \endverbatim
|
|
>
|
|
> \param[in,out] T
|
|
> \verbatim
|
|
> T is DOUBLE PRECISION array, dimension (LDT,N)
|
|
> On entry, the upper quasi-triangular matrix T, in Schur
|
|
> Schur canonical form.
|
|
> On exit, the reordered upper quasi-triangular matrix, again
|
|
> 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] Q
|
|
> \verbatim
|
|
> Q is DOUBLE PRECISION array, dimension (LDQ,N)
|
|
> On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
|
|
> On exit, if COMPQ = 'V', Q has been postmultiplied by the
|
|
> orthogonal transformation matrix Z which reorders T.
|
|
> If COMPQ = 'N', Q is not referenced.
|
|
> \endverbatim
|
|
>
|
|
> \param[in] LDQ
|
|
> \verbatim
|
|
> LDQ is INTEGER
|
|
> The leading dimension of the array Q. LDQ >= max(1,N).
|
|
> \endverbatim
|
|
>
|
|
> \param[in,out] IFST
|
|
> \verbatim
|
|
> IFST is INTEGER
|
|
> \endverbatim
|
|
>
|
|
> \param[in,out] ILST
|
|
> \verbatim
|
|
> ILST is INTEGER
|
|
>
|
|
> Specify the reordering of the diagonal blocks of T.
|
|
> The block with row index IFST is moved to row ILST, by a
|
|
> sequence of transpositions between adjacent blocks.
|
|
> On exit, if IFST pointed on entry to the second row of a
|
|
> 2-by-2 block, it is changed to point to the first row; ILST
|
|
> always points to the first row of the block in its final
|
|
> position (which may differ from its input value by +1 or -1).
|
|
> 1 <= IFST <= N; 1 <= ILST <= N.
|
|
> \endverbatim
|
|
>
|
|
> \param[out] WORK
|
|
> \verbatim
|
|
> WORK is DOUBLE PRECISION array, dimension (N)
|
|
> \endverbatim
|
|
>
|
|
> \param[out] INFO
|
|
> \verbatim
|
|
> INFO is INTEGER
|
|
> = 0: successful exit
|
|
> < 0: if INFO = -i, the i-th argument had an illegal value
|
|
> = 1: two adjacent blocks were too close to swap (the problem
|
|
> is very ill-conditioned); T may have been partially
|
|
> reordered, and ILST points to the first row of the
|
|
> current position of the block being moved.
|
|
> \endverbatim
|
|
|
|
Authors:
|
|
========
|
|
|
|
> \author Univ. of Tennessee
|
|
> \author Univ. of California Berkeley
|
|
> \author Univ. of Colorado Denver
|
|
> \author NAG Ltd.
|
|
|
|
> \date November 2011
|
|
|
|
> \ingroup doubleOTHERcomputational
|
|
|
|
=====================================================================
|
|
Subroutine */ int igraphdtrexc_(char *compq, integer *n, doublereal *t, integer *
|
|
ldt, doublereal *q, integer *ldq, integer *ifst, integer *ilst,
|
|
doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer q_dim1, q_offset, t_dim1, t_offset, i__1;
|
|
|
|
/* Local variables */
|
|
integer nbf, nbl, here;
|
|
extern logical igraphlsame_(char *, char *);
|
|
logical wantq;
|
|
extern /* Subroutine */ int igraphdlaexc_(logical *, integer *, doublereal *,
|
|
integer *, doublereal *, integer *, integer *, integer *, integer
|
|
*, doublereal *, integer *), igraphxerbla_(char *, integer *, ftnlen);
|
|
integer nbnext;
|
|
|
|
|
|
/* -- 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 arguments.
|
|
|
|
Parameter adjustments */
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1;
|
|
t -= t_offset;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1;
|
|
q -= q_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
wantq = igraphlsame_(compq, "V");
|
|
if (! wantq && ! igraphlsame_(compq, "N")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*ldt < max(1,*n)) {
|
|
*info = -4;
|
|
} else if (*ldq < 1 || wantq && *ldq < max(1,*n)) {
|
|
*info = -6;
|
|
} else if (*ifst < 1 || *ifst > *n) {
|
|
*info = -7;
|
|
} else if (*ilst < 1 || *ilst > *n) {
|
|
*info = -8;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
igraphxerbla_("DTREXC", &i__1, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n <= 1) {
|
|
return 0;
|
|
}
|
|
|
|
/* Determine the first row of specified block
|
|
and find out it is 1 by 1 or 2 by 2. */
|
|
|
|
if (*ifst > 1) {
|
|
if (t[*ifst + (*ifst - 1) * t_dim1] != 0.) {
|
|
--(*ifst);
|
|
}
|
|
}
|
|
nbf = 1;
|
|
if (*ifst < *n) {
|
|
if (t[*ifst + 1 + *ifst * t_dim1] != 0.) {
|
|
nbf = 2;
|
|
}
|
|
}
|
|
|
|
/* Determine the first row of the final block
|
|
and find out it is 1 by 1 or 2 by 2. */
|
|
|
|
if (*ilst > 1) {
|
|
if (t[*ilst + (*ilst - 1) * t_dim1] != 0.) {
|
|
--(*ilst);
|
|
}
|
|
}
|
|
nbl = 1;
|
|
if (*ilst < *n) {
|
|
if (t[*ilst + 1 + *ilst * t_dim1] != 0.) {
|
|
nbl = 2;
|
|
}
|
|
}
|
|
|
|
if (*ifst == *ilst) {
|
|
return 0;
|
|
}
|
|
|
|
if (*ifst < *ilst) {
|
|
|
|
/* Update ILST */
|
|
|
|
if (nbf == 2 && nbl == 1) {
|
|
--(*ilst);
|
|
}
|
|
if (nbf == 1 && nbl == 2) {
|
|
++(*ilst);
|
|
}
|
|
|
|
here = *ifst;
|
|
|
|
L10:
|
|
|
|
/* Swap block with next one below */
|
|
|
|
if (nbf == 1 || nbf == 2) {
|
|
|
|
/* Current block either 1 by 1 or 2 by 2 */
|
|
|
|
nbnext = 1;
|
|
if (here + nbf + 1 <= *n) {
|
|
if (t[here + nbf + 1 + (here + nbf) * t_dim1] != 0.) {
|
|
nbnext = 2;
|
|
}
|
|
}
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &here, &
|
|
nbf, &nbnext, &work[1], info);
|
|
if (*info != 0) {
|
|
*ilst = here;
|
|
return 0;
|
|
}
|
|
here += nbnext;
|
|
|
|
/* Test if 2 by 2 block breaks into two 1 by 1 blocks */
|
|
|
|
if (nbf == 2) {
|
|
if (t[here + 1 + here * t_dim1] == 0.) {
|
|
nbf = 3;
|
|
}
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Current block consists of two 1 by 1 blocks each of which
|
|
must be swapped individually */
|
|
|
|
nbnext = 1;
|
|
if (here + 3 <= *n) {
|
|
if (t[here + 3 + (here + 2) * t_dim1] != 0.) {
|
|
nbnext = 2;
|
|
}
|
|
}
|
|
i__1 = here + 1;
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
|
|
c__1, &nbnext, &work[1], info);
|
|
if (*info != 0) {
|
|
*ilst = here;
|
|
return 0;
|
|
}
|
|
if (nbnext == 1) {
|
|
|
|
/* Swap two 1 by 1 blocks, no problems possible */
|
|
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
here, &c__1, &nbnext, &work[1], info);
|
|
++here;
|
|
} else {
|
|
|
|
/* Recompute NBNEXT in case 2 by 2 split */
|
|
|
|
if (t[here + 2 + (here + 1) * t_dim1] == 0.) {
|
|
nbnext = 1;
|
|
}
|
|
if (nbnext == 2) {
|
|
|
|
/* 2 by 2 Block did not split */
|
|
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
here, &c__1, &nbnext, &work[1], info);
|
|
if (*info != 0) {
|
|
*ilst = here;
|
|
return 0;
|
|
}
|
|
here += 2;
|
|
} else {
|
|
|
|
/* 2 by 2 Block did split */
|
|
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
here, &c__1, &c__1, &work[1], info);
|
|
i__1 = here + 1;
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
i__1, &c__1, &c__1, &work[1], info);
|
|
here += 2;
|
|
}
|
|
}
|
|
}
|
|
if (here < *ilst) {
|
|
goto L10;
|
|
}
|
|
|
|
} else {
|
|
|
|
here = *ifst;
|
|
L20:
|
|
|
|
/* Swap block with next one above */
|
|
|
|
if (nbf == 1 || nbf == 2) {
|
|
|
|
/* Current block either 1 by 1 or 2 by 2 */
|
|
|
|
nbnext = 1;
|
|
if (here >= 3) {
|
|
if (t[here - 1 + (here - 2) * t_dim1] != 0.) {
|
|
nbnext = 2;
|
|
}
|
|
}
|
|
i__1 = here - nbnext;
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
|
|
nbnext, &nbf, &work[1], info);
|
|
if (*info != 0) {
|
|
*ilst = here;
|
|
return 0;
|
|
}
|
|
here -= nbnext;
|
|
|
|
/* Test if 2 by 2 block breaks into two 1 by 1 blocks */
|
|
|
|
if (nbf == 2) {
|
|
if (t[here + 1 + here * t_dim1] == 0.) {
|
|
nbf = 3;
|
|
}
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Current block consists of two 1 by 1 blocks each of which
|
|
must be swapped individually */
|
|
|
|
nbnext = 1;
|
|
if (here >= 3) {
|
|
if (t[here - 1 + (here - 2) * t_dim1] != 0.) {
|
|
nbnext = 2;
|
|
}
|
|
}
|
|
i__1 = here - nbnext;
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
|
|
nbnext, &c__1, &work[1], info);
|
|
if (*info != 0) {
|
|
*ilst = here;
|
|
return 0;
|
|
}
|
|
if (nbnext == 1) {
|
|
|
|
/* Swap two 1 by 1 blocks, no problems possible */
|
|
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
here, &nbnext, &c__1, &work[1], info);
|
|
--here;
|
|
} else {
|
|
|
|
/* Recompute NBNEXT in case 2 by 2 split */
|
|
|
|
if (t[here + (here - 1) * t_dim1] == 0.) {
|
|
nbnext = 1;
|
|
}
|
|
if (nbnext == 2) {
|
|
|
|
/* 2 by 2 Block did not split */
|
|
|
|
i__1 = here - 1;
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
i__1, &c__2, &c__1, &work[1], info);
|
|
if (*info != 0) {
|
|
*ilst = here;
|
|
return 0;
|
|
}
|
|
here += -2;
|
|
} else {
|
|
|
|
/* 2 by 2 Block did split */
|
|
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
here, &c__1, &c__1, &work[1], info);
|
|
i__1 = here - 1;
|
|
igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
|
|
i__1, &c__1, &c__1, &work[1], info);
|
|
here += -2;
|
|
}
|
|
}
|
|
}
|
|
if (here > *ilst) {
|
|
goto L20;
|
|
}
|
|
}
|
|
*ilst = here;
|
|
|
|
return 0;
|
|
|
|
/* End of DTREXC */
|
|
|
|
} /* igraphdtrexc_ */
|
|
|