Add graph references
This commit is contained in:
Abdelrahman Said
+677
@@ -0,0 +1,677 @@
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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 doublereal c_b9 = 0.;
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static doublereal c_b10 = 1.;
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static integer c__0 = 0;
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static integer c__1 = 1;
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static integer c__2 = 2;
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/* > \brief \b DSTEQR
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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 DSTEQR + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsteqr.
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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/dsteqr.
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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/dsteqr.
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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 DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
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CHARACTER COMPZ
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INTEGER INFO, LDZ, N
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DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
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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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> DSTEQR computes all eigenvalues and, optionally, eigenvectors of a
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> symmetric tridiagonal matrix using the implicit QL or QR method.
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> The eigenvectors of a full or band symmetric matrix can also be found
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> if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to
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> tridiagonal form.
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> \endverbatim
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Arguments:
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==========
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> \param[in] COMPZ
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> \verbatim
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> COMPZ is CHARACTER*1
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> = 'N': Compute eigenvalues only.
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> = 'V': Compute eigenvalues and eigenvectors of the original
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> symmetric matrix. On entry, Z must contain the
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> orthogonal matrix used to reduce the original matrix
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> to tridiagonal form.
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> = 'I': Compute eigenvalues and eigenvectors of the
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> tridiagonal matrix. Z is initialized to the identity
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> matrix.
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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. N >= 0.
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> \endverbatim
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>
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> \param[in,out] D
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> \verbatim
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> D is DOUBLE PRECISION array, dimension (N)
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> On entry, the diagonal elements of the tridiagonal matrix.
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> On exit, if INFO = 0, the eigenvalues in ascending order.
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> \endverbatim
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>
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> \param[in,out] E
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> \verbatim
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> E is DOUBLE PRECISION array, dimension (N-1)
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> On entry, the (n-1) subdiagonal elements of the tridiagonal
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> matrix.
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> On exit, E has been destroyed.
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> \endverbatim
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>
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> \param[in,out] Z
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> \verbatim
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> Z is DOUBLE PRECISION array, dimension (LDZ, N)
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> On entry, if COMPZ = 'V', then Z contains the orthogonal
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> matrix used in the reduction to tridiagonal form.
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> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
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> orthonormal eigenvectors of the original symmetric matrix,
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> and if COMPZ = 'I', Z contains the orthonormal eigenvectors
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> of the symmetric tridiagonal matrix.
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> If COMPZ = 'N', then Z is not referenced.
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> \endverbatim
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>
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> \param[in] LDZ
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> \verbatim
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> LDZ is INTEGER
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> The leading dimension of the array Z. LDZ >= 1, and if
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> eigenvectors are desired, then LDZ >= max(1,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 (max(1,2*N-2))
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> If COMPZ = 'N', then WORK is not referenced.
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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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> > 0: the algorithm has failed to find all the eigenvalues in
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> a total of 30*N iterations; if INFO = i, then i
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> elements of E have not converged to zero; on exit, D
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> and E contain the elements of a symmetric tridiagonal
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> matrix which is orthogonally similar to the original
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> matrix.
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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 auxOTHERcomputational
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=====================================================================
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Subroutine */ int igraphdsteqr_(char *compz, integer *n, doublereal *d__,
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doublereal *e, doublereal *z__, integer *ldz, doublereal *work,
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integer *info)
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{
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/* System generated locals */
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integer z_dim1, z_offset, i__1, i__2;
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doublereal d__1, d__2;
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/* Builtin functions */
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double sqrt(doublereal), d_sign(doublereal *, doublereal *);
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/* Local variables */
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doublereal b, c__, f, g;
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integer i__, j, k, l, m;
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doublereal p, r__, s;
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integer l1, ii, mm, lm1, mm1, nm1;
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doublereal rt1, rt2, eps;
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integer lsv;
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doublereal tst, eps2;
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integer lend, jtot;
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extern /* Subroutine */ int igraphdlae2_(doublereal *, doublereal *, doublereal
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*, doublereal *, doublereal *);
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extern logical igraphlsame_(char *, char *);
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extern /* Subroutine */ int igraphdlasr_(char *, char *, char *, integer *,
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integer *, doublereal *, doublereal *, doublereal *, integer *);
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doublereal anorm;
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extern /* Subroutine */ int igraphdswap_(integer *, doublereal *, integer *,
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doublereal *, integer *), igraphdlaev2_(doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *);
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integer lendm1, lendp1;
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extern doublereal igraphdlapy2_(doublereal *, doublereal *), igraphdlamch_(char *);
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integer iscale;
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extern /* Subroutine */ int igraphdlascl_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, integer *, doublereal *,
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integer *, integer *), igraphdlaset_(char *, integer *, integer
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*, doublereal *, doublereal *, doublereal *, integer *);
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doublereal safmin;
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extern /* Subroutine */ int igraphdlartg_(doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *);
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doublereal safmax;
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extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
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extern doublereal igraphdlanst_(char *, integer *, doublereal *, doublereal *);
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extern /* Subroutine */ int igraphdlasrt_(char *, integer *, doublereal *,
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integer *);
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integer lendsv;
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doublereal ssfmin;
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integer nmaxit, icompz;
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doublereal ssfmax;
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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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Test the input parameters.
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Parameter adjustments */
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--d__;
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--e;
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z_dim1 = *ldz;
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z_offset = 1 + z_dim1;
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z__ -= z_offset;
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--work;
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/* Function Body */
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*info = 0;
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if (igraphlsame_(compz, "N")) {
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icompz = 0;
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} else if (igraphlsame_(compz, "V")) {
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icompz = 1;
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} else if (igraphlsame_(compz, "I")) {
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icompz = 2;
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} else {
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icompz = -1;
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}
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if (icompz < 0) {
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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 (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
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*info = -6;
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}
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if (*info != 0) {
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i__1 = -(*info);
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igraphxerbla_("DSTEQR", &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 == 0) {
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return 0;
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}
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if (*n == 1) {
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if (icompz == 2) {
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z__[z_dim1 + 1] = 1.;
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}
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return 0;
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}
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/* Determine the unit roundoff and over/underflow thresholds. */
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eps = igraphdlamch_("E");
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/* Computing 2nd power */
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d__1 = eps;
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eps2 = d__1 * d__1;
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safmin = igraphdlamch_("S");
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safmax = 1. / safmin;
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ssfmax = sqrt(safmax) / 3.;
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ssfmin = sqrt(safmin) / eps2;
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/* Compute the eigenvalues and eigenvectors of the tridiagonal
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matrix. */
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if (icompz == 2) {
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igraphdlaset_("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz);
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}
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nmaxit = *n * 30;
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jtot = 0;
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/* Determine where the matrix splits and choose QL or QR iteration
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for each block, according to whether top or bottom diagonal
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element is smaller. */
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l1 = 1;
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nm1 = *n - 1;
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L10:
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if (l1 > *n) {
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goto L160;
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}
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if (l1 > 1) {
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e[l1 - 1] = 0.;
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}
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if (l1 <= nm1) {
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i__1 = nm1;
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for (m = l1; m <= i__1; ++m) {
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tst = (d__1 = e[m], abs(d__1));
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if (tst == 0.) {
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goto L30;
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}
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if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m
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+ 1], abs(d__2))) * eps) {
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e[m] = 0.;
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goto L30;
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}
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/* L20: */
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}
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}
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m = *n;
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L30:
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l = l1;
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lsv = l;
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lend = m;
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lendsv = lend;
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l1 = m + 1;
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if (lend == l) {
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goto L10;
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}
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/* Scale submatrix in rows and columns L to LEND */
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i__1 = lend - l + 1;
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anorm = igraphdlanst_("M", &i__1, &d__[l], &e[l]);
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iscale = 0;
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if (anorm == 0.) {
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goto L10;
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}
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if (anorm > ssfmax) {
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iscale = 1;
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i__1 = lend - l + 1;
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igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
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info);
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i__1 = lend - l;
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igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
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info);
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} else if (anorm < ssfmin) {
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iscale = 2;
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||||
i__1 = lend - l + 1;
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igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
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||||
info);
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i__1 = lend - l;
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||||
igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
|
||||
info);
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||||
}
|
||||
|
||||
/* Choose between QL and QR iteration */
|
||||
|
||||
if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
|
||||
lend = lsv;
|
||||
l = lendsv;
|
||||
}
|
||||
|
||||
if (lend > l) {
|
||||
|
||||
/* QL Iteration
|
||||
|
||||
Look for small subdiagonal element. */
|
||||
|
||||
L40:
|
||||
if (l != lend) {
|
||||
lendm1 = lend - 1;
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||||
i__1 = lendm1;
|
||||
for (m = l; m <= i__1; ++m) {
|
||||
/* Computing 2nd power */
|
||||
d__2 = (d__1 = e[m], abs(d__1));
|
||||
tst = d__2 * d__2;
|
||||
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
|
||||
+ 1], abs(d__2)) + safmin) {
|
||||
goto L60;
|
||||
}
|
||||
/* L50: */
|
||||
}
|
||||
}
|
||||
|
||||
m = lend;
|
||||
|
||||
L60:
|
||||
if (m < lend) {
|
||||
e[m] = 0.;
|
||||
}
|
||||
p = d__[l];
|
||||
if (m == l) {
|
||||
goto L80;
|
||||
}
|
||||
|
||||
/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
|
||||
to compute its eigensystem. */
|
||||
|
||||
if (m == l + 1) {
|
||||
if (icompz > 0) {
|
||||
igraphdlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
|
||||
work[l] = c__;
|
||||
work[*n - 1 + l] = s;
|
||||
igraphdlasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
|
||||
z__[l * z_dim1 + 1], ldz);
|
||||
} else {
|
||||
igraphdlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
|
||||
}
|
||||
d__[l] = rt1;
|
||||
d__[l + 1] = rt2;
|
||||
e[l] = 0.;
|
||||
l += 2;
|
||||
if (l <= lend) {
|
||||
goto L40;
|
||||
}
|
||||
goto L140;
|
||||
}
|
||||
|
||||
if (jtot == nmaxit) {
|
||||
goto L140;
|
||||
}
|
||||
++jtot;
|
||||
|
||||
/* Form shift. */
|
||||
|
||||
g = (d__[l + 1] - p) / (e[l] * 2.);
|
||||
r__ = igraphdlapy2_(&g, &c_b10);
|
||||
g = d__[m] - p + e[l] / (g + d_sign(&r__, &g));
|
||||
|
||||
s = 1.;
|
||||
c__ = 1.;
|
||||
p = 0.;
|
||||
|
||||
/* Inner loop */
|
||||
|
||||
mm1 = m - 1;
|
||||
i__1 = l;
|
||||
for (i__ = mm1; i__ >= i__1; --i__) {
|
||||
f = s * e[i__];
|
||||
b = c__ * e[i__];
|
||||
igraphdlartg_(&g, &f, &c__, &s, &r__);
|
||||
if (i__ != m - 1) {
|
||||
e[i__ + 1] = r__;
|
||||
}
|
||||
g = d__[i__ + 1] - p;
|
||||
r__ = (d__[i__] - g) * s + c__ * 2. * b;
|
||||
p = s * r__;
|
||||
d__[i__ + 1] = g + p;
|
||||
g = c__ * r__ - b;
|
||||
|
||||
/* If eigenvectors are desired, then save rotations. */
|
||||
|
||||
if (icompz > 0) {
|
||||
work[i__] = c__;
|
||||
work[*n - 1 + i__] = -s;
|
||||
}
|
||||
|
||||
/* L70: */
|
||||
}
|
||||
|
||||
/* If eigenvectors are desired, then apply saved rotations. */
|
||||
|
||||
if (icompz > 0) {
|
||||
mm = m - l + 1;
|
||||
igraphdlasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l
|
||||
* z_dim1 + 1], ldz);
|
||||
}
|
||||
|
||||
d__[l] -= p;
|
||||
e[l] = g;
|
||||
goto L40;
|
||||
|
||||
/* Eigenvalue found. */
|
||||
|
||||
L80:
|
||||
d__[l] = p;
|
||||
|
||||
++l;
|
||||
if (l <= lend) {
|
||||
goto L40;
|
||||
}
|
||||
goto L140;
|
||||
|
||||
} else {
|
||||
|
||||
/* QR Iteration
|
||||
|
||||
Look for small superdiagonal element. */
|
||||
|
||||
L90:
|
||||
if (l != lend) {
|
||||
lendp1 = lend + 1;
|
||||
i__1 = lendp1;
|
||||
for (m = l; m >= i__1; --m) {
|
||||
/* Computing 2nd power */
|
||||
d__2 = (d__1 = e[m - 1], abs(d__1));
|
||||
tst = d__2 * d__2;
|
||||
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
|
||||
- 1], abs(d__2)) + safmin) {
|
||||
goto L110;
|
||||
}
|
||||
/* L100: */
|
||||
}
|
||||
}
|
||||
|
||||
m = lend;
|
||||
|
||||
L110:
|
||||
if (m > lend) {
|
||||
e[m - 1] = 0.;
|
||||
}
|
||||
p = d__[l];
|
||||
if (m == l) {
|
||||
goto L130;
|
||||
}
|
||||
|
||||
/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
|
||||
to compute its eigensystem. */
|
||||
|
||||
if (m == l - 1) {
|
||||
if (icompz > 0) {
|
||||
igraphdlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
|
||||
;
|
||||
work[m] = c__;
|
||||
work[*n - 1 + m] = s;
|
||||
igraphdlasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
|
||||
z__[(l - 1) * z_dim1 + 1], ldz);
|
||||
} else {
|
||||
igraphdlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
|
||||
}
|
||||
d__[l - 1] = rt1;
|
||||
d__[l] = rt2;
|
||||
e[l - 1] = 0.;
|
||||
l += -2;
|
||||
if (l >= lend) {
|
||||
goto L90;
|
||||
}
|
||||
goto L140;
|
||||
}
|
||||
|
||||
if (jtot == nmaxit) {
|
||||
goto L140;
|
||||
}
|
||||
++jtot;
|
||||
|
||||
/* Form shift. */
|
||||
|
||||
g = (d__[l - 1] - p) / (e[l - 1] * 2.);
|
||||
r__ = igraphdlapy2_(&g, &c_b10);
|
||||
g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g));
|
||||
|
||||
s = 1.;
|
||||
c__ = 1.;
|
||||
p = 0.;
|
||||
|
||||
/* Inner loop */
|
||||
|
||||
lm1 = l - 1;
|
||||
i__1 = lm1;
|
||||
for (i__ = m; i__ <= i__1; ++i__) {
|
||||
f = s * e[i__];
|
||||
b = c__ * e[i__];
|
||||
igraphdlartg_(&g, &f, &c__, &s, &r__);
|
||||
if (i__ != m) {
|
||||
e[i__ - 1] = r__;
|
||||
}
|
||||
g = d__[i__] - p;
|
||||
r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b;
|
||||
p = s * r__;
|
||||
d__[i__] = g + p;
|
||||
g = c__ * r__ - b;
|
||||
|
||||
/* If eigenvectors are desired, then save rotations. */
|
||||
|
||||
if (icompz > 0) {
|
||||
work[i__] = c__;
|
||||
work[*n - 1 + i__] = s;
|
||||
}
|
||||
|
||||
/* L120: */
|
||||
}
|
||||
|
||||
/* If eigenvectors are desired, then apply saved rotations. */
|
||||
|
||||
if (icompz > 0) {
|
||||
mm = l - m + 1;
|
||||
igraphdlasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m
|
||||
* z_dim1 + 1], ldz);
|
||||
}
|
||||
|
||||
d__[l] -= p;
|
||||
e[lm1] = g;
|
||||
goto L90;
|
||||
|
||||
/* Eigenvalue found. */
|
||||
|
||||
L130:
|
||||
d__[l] = p;
|
||||
|
||||
--l;
|
||||
if (l >= lend) {
|
||||
goto L90;
|
||||
}
|
||||
goto L140;
|
||||
|
||||
}
|
||||
|
||||
/* Undo scaling if necessary */
|
||||
|
||||
L140:
|
||||
if (iscale == 1) {
|
||||
i__1 = lendsv - lsv + 1;
|
||||
igraphdlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
|
||||
n, info);
|
||||
i__1 = lendsv - lsv;
|
||||
igraphdlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n,
|
||||
info);
|
||||
} else if (iscale == 2) {
|
||||
i__1 = lendsv - lsv + 1;
|
||||
igraphdlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
|
||||
n, info);
|
||||
i__1 = lendsv - lsv;
|
||||
igraphdlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n,
|
||||
info);
|
||||
}
|
||||
|
||||
/* Check for no convergence to an eigenvalue after a total
|
||||
of N*MAXIT iterations. */
|
||||
|
||||
if (jtot < nmaxit) {
|
||||
goto L10;
|
||||
}
|
||||
i__1 = *n - 1;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if (e[i__] != 0.) {
|
||||
++(*info);
|
||||
}
|
||||
/* L150: */
|
||||
}
|
||||
goto L190;
|
||||
|
||||
/* Order eigenvalues and eigenvectors. */
|
||||
|
||||
L160:
|
||||
if (icompz == 0) {
|
||||
|
||||
/* Use Quick Sort */
|
||||
|
||||
igraphdlasrt_("I", n, &d__[1], info);
|
||||
|
||||
} else {
|
||||
|
||||
/* Use Selection Sort to minimize swaps of eigenvectors */
|
||||
|
||||
i__1 = *n;
|
||||
for (ii = 2; ii <= i__1; ++ii) {
|
||||
i__ = ii - 1;
|
||||
k = i__;
|
||||
p = d__[i__];
|
||||
i__2 = *n;
|
||||
for (j = ii; j <= i__2; ++j) {
|
||||
if (d__[j] < p) {
|
||||
k = j;
|
||||
p = d__[j];
|
||||
}
|
||||
/* L170: */
|
||||
}
|
||||
if (k != i__) {
|
||||
d__[k] = d__[i__];
|
||||
d__[i__] = p;
|
||||
igraphdswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
|
||||
&c__1);
|
||||
}
|
||||
/* L180: */
|
||||
}
|
||||
}
|
||||
|
||||
L190:
|
||||
return 0;
|
||||
|
||||
/* End of DSTEQR */
|
||||
|
||||
} /* igraphdsteqr_ */
|
||||
|
||||
Reference in New Issue
Block a user