Add graph references
This commit is contained in:
Abdelrahman Said
+524
@@ -0,0 +1,524 @@
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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__4 = 4;
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static logical c_false = FALSE_;
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static integer c_n1 = -1;
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static integer c__2 = 2;
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static integer c__3 = 3;
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/* > \brief \b DLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonica
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l form, by an orthogonal similarity transformation.
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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 DLAEXC + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaexc.
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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/dlaexc.
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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/dlaexc.
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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 DLAEXC( WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK,
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INFO )
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LOGICAL WANTQ
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INTEGER INFO, J1, LDQ, LDT, N, N1, N2
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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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> DLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in
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> an upper quasi-triangular matrix T by an orthogonal similarity
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> transformation.
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>
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> T must be in Schur canonical form, that is, block upper triangular
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> with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block
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> has its diagonal elemnts equal and its off-diagonal elements of
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> opposite sign.
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> \endverbatim
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Arguments:
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==========
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> \param[in] WANTQ
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> \verbatim
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> WANTQ is LOGICAL
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> = .TRUE. : accumulate the transformation in the matrix Q;
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> = .FALSE.: do not accumulate the transformation.
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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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> canonical form.
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> On exit, the updated matrix T, again 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 WANTQ is .TRUE., the orthogonal matrix Q.
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> On exit, if WANTQ is .TRUE., the updated matrix Q.
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> If WANTQ is .FALSE., 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.
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> LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N.
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> \endverbatim
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>
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> \param[in] J1
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> \verbatim
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> J1 is INTEGER
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> The index of the first row of the first block T11.
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> \endverbatim
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>
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> \param[in] N1
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> \verbatim
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> N1 is INTEGER
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> The order of the first block T11. N1 = 0, 1 or 2.
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> \endverbatim
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>
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> \param[in] N2
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> \verbatim
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> N2 is INTEGER
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> The order of the second block T22. N2 = 0, 1 or 2.
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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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> = 1: the transformed matrix T would be too far from Schur
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> form; the blocks are not swapped and T and Q are
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> unchanged.
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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 September 2012
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> \ingroup doubleOTHERauxiliary
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=====================================================================
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Subroutine */ int igraphdlaexc_(logical *wantq, integer *n, doublereal *t,
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integer *ldt, doublereal *q, integer *ldq, integer *j1, integer *n1,
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integer *n2, 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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doublereal d__1, d__2, d__3;
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/* Local variables */
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doublereal d__[16] /* was [4][4] */;
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integer k;
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doublereal u[3], x[4] /* was [2][2] */;
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integer j2, j3, j4;
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doublereal u1[3], u2[3];
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integer nd;
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doublereal cs, t11, t22, t33, sn, wi1, wi2, wr1, wr2, eps, tau, tau1,
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tau2;
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integer ierr;
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doublereal temp;
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extern /* Subroutine */ int igraphdrot_(integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, doublereal *);
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doublereal scale, dnorm, xnorm;
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extern /* Subroutine */ int igraphdlanv2_(doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *), igraphdlasy2_(
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logical *, logical *, integer *, integer *, integer *, doublereal
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*, integer *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *);
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extern doublereal igraphdlamch_(char *), igraphdlange_(char *, integer *,
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integer *, doublereal *, integer *, doublereal *);
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extern /* Subroutine */ int igraphdlarfg_(integer *, doublereal *, doublereal *,
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integer *, doublereal *), igraphdlacpy_(char *, integer *, integer *,
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doublereal *, integer *, doublereal *, integer *),
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igraphdlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *), igraphdlarfx_(char *, integer *, integer *, doublereal *,
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doublereal *, doublereal *, integer *, doublereal *);
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doublereal thresh, smlnum;
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/* -- LAPACK auxiliary routine (version 3.4.2) --
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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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September 2012
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=====================================================================
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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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/* Quick return if possible */
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if (*n == 0 || *n1 == 0 || *n2 == 0) {
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return 0;
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}
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if (*j1 + *n1 > *n) {
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return 0;
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}
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j2 = *j1 + 1;
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j3 = *j1 + 2;
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j4 = *j1 + 3;
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if (*n1 == 1 && *n2 == 1) {
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/* Swap two 1-by-1 blocks. */
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t11 = t[*j1 + *j1 * t_dim1];
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t22 = t[j2 + j2 * t_dim1];
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/* Determine the transformation to perform the interchange. */
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d__1 = t22 - t11;
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igraphdlartg_(&t[*j1 + j2 * t_dim1], &d__1, &cs, &sn, &temp);
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/* Apply transformation to the matrix T. */
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if (j3 <= *n) {
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i__1 = *n - *j1 - 1;
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igraphdrot_(&i__1, &t[*j1 + j3 * t_dim1], ldt, &t[j2 + j3 * t_dim1],
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ldt, &cs, &sn);
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}
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i__1 = *j1 - 1;
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igraphdrot_(&i__1, &t[*j1 * t_dim1 + 1], &c__1, &t[j2 * t_dim1 + 1], &c__1,
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&cs, &sn);
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t[*j1 + *j1 * t_dim1] = t22;
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t[j2 + j2 * t_dim1] = t11;
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if (*wantq) {
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/* Accumulate transformation in the matrix Q. */
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igraphdrot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[j2 * q_dim1 + 1], &c__1,
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&cs, &sn);
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}
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} else {
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/* Swapping involves at least one 2-by-2 block.
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Copy the diagonal block of order N1+N2 to the local array D
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and compute its norm. */
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nd = *n1 + *n2;
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igraphdlacpy_("Full", &nd, &nd, &t[*j1 + *j1 * t_dim1], ldt, d__, &c__4);
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dnorm = igraphdlange_("Max", &nd, &nd, d__, &c__4, &work[1]);
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/* Compute machine-dependent threshold for test for accepting
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swap. */
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eps = igraphdlamch_("P");
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smlnum = igraphdlamch_("S") / eps;
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/* Computing MAX */
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d__1 = eps * 10. * dnorm;
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thresh = max(d__1,smlnum);
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/* Solve T11*X - X*T22 = scale*T12 for X. */
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igraphdlasy2_(&c_false, &c_false, &c_n1, n1, n2, d__, &c__4, &d__[*n1 + 1 +
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(*n1 + 1 << 2) - 5], &c__4, &d__[(*n1 + 1 << 2) - 4], &c__4, &
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scale, x, &c__2, &xnorm, &ierr);
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/* Swap the adjacent diagonal blocks. */
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k = *n1 + *n1 + *n2 - 3;
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switch (k) {
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case 1: goto L10;
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case 2: goto L20;
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case 3: goto L30;
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}
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L10:
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/* N1 = 1, N2 = 2: generate elementary reflector H so that:
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( scale, X11, X12 ) H = ( 0, 0, * ) */
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u[0] = scale;
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u[1] = x[0];
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u[2] = x[2];
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igraphdlarfg_(&c__3, &u[2], u, &c__1, &tau);
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u[2] = 1.;
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t11 = t[*j1 + *j1 * t_dim1];
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/* Perform swap provisionally on diagonal block in D. */
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igraphdlarfx_("L", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
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igraphdlarfx_("R", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
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/* Test whether to reject swap.
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Computing MAX */
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d__2 = abs(d__[2]), d__3 = abs(d__[6]), d__2 = max(d__2,d__3), d__3 =
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(d__1 = d__[10] - t11, abs(d__1));
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if (max(d__2,d__3) > thresh) {
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goto L50;
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}
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/* Accept swap: apply transformation to the entire matrix T. */
|
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i__1 = *n - *j1 + 1;
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igraphdlarfx_("L", &c__3, &i__1, u, &tau, &t[*j1 + *j1 * t_dim1], ldt, &
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work[1]);
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igraphdlarfx_("R", &j2, &c__3, u, &tau, &t[*j1 * t_dim1 + 1], ldt, &work[1]);
|
||||
|
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t[j3 + *j1 * t_dim1] = 0.;
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t[j3 + j2 * t_dim1] = 0.;
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t[j3 + j3 * t_dim1] = t11;
|
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|
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if (*wantq) {
|
||||
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/* Accumulate transformation in the matrix Q. */
|
||||
|
||||
igraphdlarfx_("R", n, &c__3, u, &tau, &q[*j1 * q_dim1 + 1], ldq, &work[
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||||
1]);
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||||
}
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goto L40;
|
||||
|
||||
L20:
|
||||
|
||||
/* N1 = 2, N2 = 1: generate elementary reflector H so that:
|
||||
|
||||
H ( -X11 ) = ( * )
|
||||
( -X21 ) = ( 0 )
|
||||
( scale ) = ( 0 ) */
|
||||
|
||||
u[0] = -x[0];
|
||||
u[1] = -x[1];
|
||||
u[2] = scale;
|
||||
igraphdlarfg_(&c__3, u, &u[1], &c__1, &tau);
|
||||
u[0] = 1.;
|
||||
t33 = t[j3 + j3 * t_dim1];
|
||||
|
||||
/* Perform swap provisionally on diagonal block in D. */
|
||||
|
||||
igraphdlarfx_("L", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
|
||||
igraphdlarfx_("R", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
|
||||
|
||||
/* Test whether to reject swap.
|
||||
|
||||
Computing MAX */
|
||||
d__2 = abs(d__[1]), d__3 = abs(d__[2]), d__2 = max(d__2,d__3), d__3 =
|
||||
(d__1 = d__[0] - t33, abs(d__1));
|
||||
if (max(d__2,d__3) > thresh) {
|
||||
goto L50;
|
||||
}
|
||||
|
||||
/* Accept swap: apply transformation to the entire matrix T. */
|
||||
|
||||
igraphdlarfx_("R", &j3, &c__3, u, &tau, &t[*j1 * t_dim1 + 1], ldt, &work[1]);
|
||||
i__1 = *n - *j1;
|
||||
igraphdlarfx_("L", &c__3, &i__1, u, &tau, &t[*j1 + j2 * t_dim1], ldt, &work[
|
||||
1]);
|
||||
|
||||
t[*j1 + *j1 * t_dim1] = t33;
|
||||
t[j2 + *j1 * t_dim1] = 0.;
|
||||
t[j3 + *j1 * t_dim1] = 0.;
|
||||
|
||||
if (*wantq) {
|
||||
|
||||
/* Accumulate transformation in the matrix Q. */
|
||||
|
||||
igraphdlarfx_("R", n, &c__3, u, &tau, &q[*j1 * q_dim1 + 1], ldq, &work[
|
||||
1]);
|
||||
}
|
||||
goto L40;
|
||||
|
||||
L30:
|
||||
|
||||
/* N1 = 2, N2 = 2: generate elementary reflectors H(1) and H(2) so
|
||||
that:
|
||||
|
||||
H(2) H(1) ( -X11 -X12 ) = ( * * )
|
||||
( -X21 -X22 ) ( 0 * )
|
||||
( scale 0 ) ( 0 0 )
|
||||
( 0 scale ) ( 0 0 ) */
|
||||
|
||||
u1[0] = -x[0];
|
||||
u1[1] = -x[1];
|
||||
u1[2] = scale;
|
||||
igraphdlarfg_(&c__3, u1, &u1[1], &c__1, &tau1);
|
||||
u1[0] = 1.;
|
||||
|
||||
temp = -tau1 * (x[2] + u1[1] * x[3]);
|
||||
u2[0] = -temp * u1[1] - x[3];
|
||||
u2[1] = -temp * u1[2];
|
||||
u2[2] = scale;
|
||||
igraphdlarfg_(&c__3, u2, &u2[1], &c__1, &tau2);
|
||||
u2[0] = 1.;
|
||||
|
||||
/* Perform swap provisionally on diagonal block in D. */
|
||||
|
||||
igraphdlarfx_("L", &c__3, &c__4, u1, &tau1, d__, &c__4, &work[1])
|
||||
;
|
||||
igraphdlarfx_("R", &c__4, &c__3, u1, &tau1, d__, &c__4, &work[1])
|
||||
;
|
||||
igraphdlarfx_("L", &c__3, &c__4, u2, &tau2, &d__[1], &c__4, &work[1]);
|
||||
igraphdlarfx_("R", &c__4, &c__3, u2, &tau2, &d__[4], &c__4, &work[1]);
|
||||
|
||||
/* Test whether to reject swap.
|
||||
|
||||
Computing MAX */
|
||||
d__1 = abs(d__[2]), d__2 = abs(d__[6]), d__1 = max(d__1,d__2), d__2 =
|
||||
abs(d__[3]), d__1 = max(d__1,d__2), d__2 = abs(d__[7]);
|
||||
if (max(d__1,d__2) > thresh) {
|
||||
goto L50;
|
||||
}
|
||||
|
||||
/* Accept swap: apply transformation to the entire matrix T. */
|
||||
|
||||
i__1 = *n - *j1 + 1;
|
||||
igraphdlarfx_("L", &c__3, &i__1, u1, &tau1, &t[*j1 + *j1 * t_dim1], ldt, &
|
||||
work[1]);
|
||||
igraphdlarfx_("R", &j4, &c__3, u1, &tau1, &t[*j1 * t_dim1 + 1], ldt, &work[
|
||||
1]);
|
||||
i__1 = *n - *j1 + 1;
|
||||
igraphdlarfx_("L", &c__3, &i__1, u2, &tau2, &t[j2 + *j1 * t_dim1], ldt, &
|
||||
work[1]);
|
||||
igraphdlarfx_("R", &j4, &c__3, u2, &tau2, &t[j2 * t_dim1 + 1], ldt, &work[1]
|
||||
);
|
||||
|
||||
t[j3 + *j1 * t_dim1] = 0.;
|
||||
t[j3 + j2 * t_dim1] = 0.;
|
||||
t[j4 + *j1 * t_dim1] = 0.;
|
||||
t[j4 + j2 * t_dim1] = 0.;
|
||||
|
||||
if (*wantq) {
|
||||
|
||||
/* Accumulate transformation in the matrix Q. */
|
||||
|
||||
igraphdlarfx_("R", n, &c__3, u1, &tau1, &q[*j1 * q_dim1 + 1], ldq, &
|
||||
work[1]);
|
||||
igraphdlarfx_("R", n, &c__3, u2, &tau2, &q[j2 * q_dim1 + 1], ldq, &work[
|
||||
1]);
|
||||
}
|
||||
|
||||
L40:
|
||||
|
||||
if (*n2 == 2) {
|
||||
|
||||
/* Standardize new 2-by-2 block T11 */
|
||||
|
||||
igraphdlanv2_(&t[*j1 + *j1 * t_dim1], &t[*j1 + j2 * t_dim1], &t[j2 + *
|
||||
j1 * t_dim1], &t[j2 + j2 * t_dim1], &wr1, &wi1, &wr2, &
|
||||
wi2, &cs, &sn);
|
||||
i__1 = *n - *j1 - 1;
|
||||
igraphdrot_(&i__1, &t[*j1 + (*j1 + 2) * t_dim1], ldt, &t[j2 + (*j1 + 2)
|
||||
* t_dim1], ldt, &cs, &sn);
|
||||
i__1 = *j1 - 1;
|
||||
igraphdrot_(&i__1, &t[*j1 * t_dim1 + 1], &c__1, &t[j2 * t_dim1 + 1], &
|
||||
c__1, &cs, &sn);
|
||||
if (*wantq) {
|
||||
igraphdrot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[j2 * q_dim1 + 1], &
|
||||
c__1, &cs, &sn);
|
||||
}
|
||||
}
|
||||
|
||||
if (*n1 == 2) {
|
||||
|
||||
/* Standardize new 2-by-2 block T22 */
|
||||
|
||||
j3 = *j1 + *n2;
|
||||
j4 = j3 + 1;
|
||||
igraphdlanv2_(&t[j3 + j3 * t_dim1], &t[j3 + j4 * t_dim1], &t[j4 + j3 *
|
||||
t_dim1], &t[j4 + j4 * t_dim1], &wr1, &wi1, &wr2, &wi2, &
|
||||
cs, &sn);
|
||||
if (j3 + 2 <= *n) {
|
||||
i__1 = *n - j3 - 1;
|
||||
igraphdrot_(&i__1, &t[j3 + (j3 + 2) * t_dim1], ldt, &t[j4 + (j3 + 2)
|
||||
* t_dim1], ldt, &cs, &sn);
|
||||
}
|
||||
i__1 = j3 - 1;
|
||||
igraphdrot_(&i__1, &t[j3 * t_dim1 + 1], &c__1, &t[j4 * t_dim1 + 1], &
|
||||
c__1, &cs, &sn);
|
||||
if (*wantq) {
|
||||
igraphdrot_(n, &q[j3 * q_dim1 + 1], &c__1, &q[j4 * q_dim1 + 1], &
|
||||
c__1, &cs, &sn);
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
return 0;
|
||||
|
||||
/* Exit with INFO = 1 if swap was rejected. */
|
||||
|
||||
L50:
|
||||
*info = 1;
|
||||
return 0;
|
||||
|
||||
/* End of DLAEXC */
|
||||
|
||||
} /* igraphdlaexc_ */
|
||||
|
||||
Reference in New Issue
Block a user