Add graph references
This commit is contained in:
Abdelrahman Said
+468
@@ -0,0 +1,468 @@
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/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c__2 = 2;
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/* > \brief \b DTREXC
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=========== DOCUMENTATION ===========
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Online html documentation available at
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http://www.netlib.org/lapack/explore-html/
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> \htmlonly
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> Download DTREXC + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrexc.
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f">
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> [TGZ]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrexc.
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f">
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> [ZIP]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrexc.
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f">
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> [TXT]</a>
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> \endhtmlonly
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Definition:
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===========
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SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
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INFO )
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CHARACTER COMPQ
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INTEGER IFST, ILST, INFO, LDQ, LDT, N
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DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )
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> \par Purpose:
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=============
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>
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> \verbatim
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>
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> DTREXC reorders the real Schur factorization of a real matrix
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> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
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> moved to row ILST.
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>
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> The real Schur form T is reordered by an orthogonal similarity
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> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
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> is updated by postmultiplying it with Z.
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>
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> T must be in Schur canonical form (as returned by DHSEQR), that is,
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> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
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> 2-by-2 diagonal block has its diagonal elements equal and its
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> off-diagonal elements of opposite sign.
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> \endverbatim
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Arguments:
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==========
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> \param[in] COMPQ
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> \verbatim
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> COMPQ is CHARACTER*1
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> = 'V': update the matrix Q of Schur vectors;
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> = 'N': do not update Q.
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> \endverbatim
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>
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> \param[in] N
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> \verbatim
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> N is INTEGER
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> The order of the matrix T. N >= 0.
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> \endverbatim
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>
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> \param[in,out] T
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> \verbatim
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> T is DOUBLE PRECISION array, dimension (LDT,N)
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> On entry, the upper quasi-triangular matrix T, in Schur
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> Schur canonical form.
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> On exit, the reordered upper quasi-triangular matrix, again
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> in Schur canonical form.
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> \endverbatim
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>
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> \param[in] LDT
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> \verbatim
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> LDT is INTEGER
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> The leading dimension of the array T. LDT >= max(1,N).
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> \endverbatim
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>
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> \param[in,out] Q
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> \verbatim
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> Q is DOUBLE PRECISION array, dimension (LDQ,N)
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> On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
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> On exit, if COMPQ = 'V', Q has been postmultiplied by the
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> orthogonal transformation matrix Z which reorders T.
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> If COMPQ = 'N', Q is not referenced.
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> \endverbatim
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>
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> \param[in] LDQ
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> \verbatim
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> LDQ is INTEGER
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> The leading dimension of the array Q. LDQ >= max(1,N).
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> \endverbatim
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>
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> \param[in,out] IFST
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> \verbatim
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> IFST is INTEGER
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> \endverbatim
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>
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> \param[in,out] ILST
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> \verbatim
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> ILST is INTEGER
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>
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> Specify the reordering of the diagonal blocks of T.
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> The block with row index IFST is moved to row ILST, by a
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> sequence of transpositions between adjacent blocks.
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> On exit, if IFST pointed on entry to the second row of a
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> 2-by-2 block, it is changed to point to the first row; ILST
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> always points to the first row of the block in its final
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> position (which may differ from its input value by +1 or -1).
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> 1 <= IFST <= N; 1 <= ILST <= N.
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> \endverbatim
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>
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> \param[out] WORK
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> \verbatim
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> WORK is DOUBLE PRECISION array, dimension (N)
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> \endverbatim
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>
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> \param[out] INFO
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> \verbatim
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> INFO is INTEGER
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> = 0: successful exit
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> < 0: if INFO = -i, the i-th argument had an illegal value
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> = 1: two adjacent blocks were too close to swap (the problem
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> is very ill-conditioned); T may have been partially
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> reordered, and ILST points to the first row of the
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> current position of the block being moved.
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> \endverbatim
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Authors:
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========
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> \author Univ. of Tennessee
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> \author Univ. of California Berkeley
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> \author Univ. of Colorado Denver
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> \author NAG Ltd.
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> \date November 2011
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> \ingroup doubleOTHERcomputational
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=====================================================================
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Subroutine */ int igraphdtrexc_(char *compq, integer *n, doublereal *t, integer *
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ldt, doublereal *q, integer *ldq, integer *ifst, integer *ilst,
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doublereal *work, integer *info)
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{
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/* System generated locals */
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integer q_dim1, q_offset, t_dim1, t_offset, i__1;
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/* Local variables */
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integer nbf, nbl, here;
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extern logical igraphlsame_(char *, char *);
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logical wantq;
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extern /* Subroutine */ int igraphdlaexc_(logical *, integer *, doublereal *,
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integer *, doublereal *, integer *, integer *, integer *, integer
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*, doublereal *, integer *), igraphxerbla_(char *, integer *, ftnlen);
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integer nbnext;
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/* -- LAPACK computational routine (version 3.4.0) --
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-- LAPACK is a software package provided by Univ. of Tennessee, --
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-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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November 2011
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=====================================================================
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Decode and test the input arguments.
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Parameter adjustments */
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t_dim1 = *ldt;
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t_offset = 1 + t_dim1;
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t -= t_offset;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1;
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q -= q_offset;
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--work;
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/* Function Body */
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*info = 0;
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wantq = igraphlsame_(compq, "V");
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if (! wantq && ! igraphlsame_(compq, "N")) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*ldt < max(1,*n)) {
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*info = -4;
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} else if (*ldq < 1 || wantq && *ldq < max(1,*n)) {
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*info = -6;
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} else if (*ifst < 1 || *ifst > *n) {
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*info = -7;
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} else if (*ilst < 1 || *ilst > *n) {
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*info = -8;
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}
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if (*info != 0) {
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i__1 = -(*info);
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igraphxerbla_("DTREXC", &i__1, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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if (*n <= 1) {
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return 0;
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}
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/* Determine the first row of specified block
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and find out it is 1 by 1 or 2 by 2. */
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if (*ifst > 1) {
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if (t[*ifst + (*ifst - 1) * t_dim1] != 0.) {
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--(*ifst);
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}
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}
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nbf = 1;
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if (*ifst < *n) {
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if (t[*ifst + 1 + *ifst * t_dim1] != 0.) {
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nbf = 2;
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}
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}
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/* Determine the first row of the final block
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and find out it is 1 by 1 or 2 by 2. */
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if (*ilst > 1) {
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if (t[*ilst + (*ilst - 1) * t_dim1] != 0.) {
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--(*ilst);
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}
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}
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nbl = 1;
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if (*ilst < *n) {
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if (t[*ilst + 1 + *ilst * t_dim1] != 0.) {
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nbl = 2;
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}
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}
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if (*ifst == *ilst) {
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return 0;
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}
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if (*ifst < *ilst) {
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/* Update ILST */
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if (nbf == 2 && nbl == 1) {
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--(*ilst);
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}
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if (nbf == 1 && nbl == 2) {
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++(*ilst);
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}
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here = *ifst;
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L10:
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/* Swap block with next one below */
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if (nbf == 1 || nbf == 2) {
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/* Current block either 1 by 1 or 2 by 2 */
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nbnext = 1;
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if (here + nbf + 1 <= *n) {
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if (t[here + nbf + 1 + (here + nbf) * t_dim1] != 0.) {
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nbnext = 2;
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}
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}
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &here, &
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nbf, &nbnext, &work[1], info);
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if (*info != 0) {
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*ilst = here;
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return 0;
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}
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here += nbnext;
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/* Test if 2 by 2 block breaks into two 1 by 1 blocks */
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if (nbf == 2) {
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if (t[here + 1 + here * t_dim1] == 0.) {
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nbf = 3;
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}
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}
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} else {
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/* Current block consists of two 1 by 1 blocks each of which
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must be swapped individually */
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nbnext = 1;
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if (here + 3 <= *n) {
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if (t[here + 3 + (here + 2) * t_dim1] != 0.) {
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nbnext = 2;
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}
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}
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i__1 = here + 1;
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
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c__1, &nbnext, &work[1], info);
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if (*info != 0) {
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*ilst = here;
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return 0;
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}
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if (nbnext == 1) {
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/* Swap two 1 by 1 blocks, no problems possible */
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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here, &c__1, &nbnext, &work[1], info);
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++here;
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} else {
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/* Recompute NBNEXT in case 2 by 2 split */
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if (t[here + 2 + (here + 1) * t_dim1] == 0.) {
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nbnext = 1;
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}
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if (nbnext == 2) {
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/* 2 by 2 Block did not split */
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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here, &c__1, &nbnext, &work[1], info);
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if (*info != 0) {
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*ilst = here;
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return 0;
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}
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here += 2;
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} else {
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/* 2 by 2 Block did split */
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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here, &c__1, &c__1, &work[1], info);
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i__1 = here + 1;
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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i__1, &c__1, &c__1, &work[1], info);
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here += 2;
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}
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}
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}
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if (here < *ilst) {
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goto L10;
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}
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} else {
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here = *ifst;
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L20:
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/* Swap block with next one above */
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if (nbf == 1 || nbf == 2) {
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/* Current block either 1 by 1 or 2 by 2 */
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nbnext = 1;
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if (here >= 3) {
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if (t[here - 1 + (here - 2) * t_dim1] != 0.) {
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nbnext = 2;
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}
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}
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i__1 = here - nbnext;
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
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nbnext, &nbf, &work[1], info);
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if (*info != 0) {
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*ilst = here;
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return 0;
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}
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here -= nbnext;
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/* Test if 2 by 2 block breaks into two 1 by 1 blocks */
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if (nbf == 2) {
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if (t[here + 1 + here * t_dim1] == 0.) {
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nbf = 3;
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}
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}
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} else {
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/* Current block consists of two 1 by 1 blocks each of which
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must be swapped individually */
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nbnext = 1;
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if (here >= 3) {
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if (t[here - 1 + (here - 2) * t_dim1] != 0.) {
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nbnext = 2;
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}
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}
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i__1 = here - nbnext;
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
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nbnext, &c__1, &work[1], info);
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if (*info != 0) {
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*ilst = here;
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return 0;
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}
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if (nbnext == 1) {
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/* Swap two 1 by 1 blocks, no problems possible */
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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here, &nbnext, &c__1, &work[1], info);
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--here;
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} else {
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/* Recompute NBNEXT in case 2 by 2 split */
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if (t[here + (here - 1) * t_dim1] == 0.) {
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nbnext = 1;
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}
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if (nbnext == 2) {
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/* 2 by 2 Block did not split */
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i__1 = here - 1;
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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i__1, &c__2, &c__1, &work[1], info);
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if (*info != 0) {
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*ilst = here;
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return 0;
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}
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here += -2;
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} else {
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/* 2 by 2 Block did split */
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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here, &c__1, &c__1, &work[1], info);
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i__1 = here - 1;
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igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
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i__1, &c__1, &c__1, &work[1], info);
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here += -2;
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}
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}
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}
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if (here > *ilst) {
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goto L20;
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}
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}
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*ilst = here;
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return 0;
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/* End of DTREXC */
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} /* igraphdtrexc_ */
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Reference in New Issue
Block a user