Add graph references
This commit is contained in:
Abdelrahman Said
+831
@@ -0,0 +1,831 @@
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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 doublereal c_b18 = .001;
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/* > \brief \b DSTEMR
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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 DSTEMR + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstemr.
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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/dstemr.
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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/dstemr.
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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 DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
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M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
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IWORK, LIWORK, INFO )
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CHARACTER JOBZ, RANGE
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LOGICAL TRYRAC
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INTEGER IL, INFO, IU, LDZ, NZC, LIWORK, LWORK, M, N
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DOUBLE PRECISION VL, VU
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INTEGER ISUPPZ( * ), IWORK( * )
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DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
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DOUBLE PRECISION 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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> DSTEMR computes selected eigenvalues and, optionally, eigenvectors
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> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
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> a well defined set of pairwise different real eigenvalues, the corresponding
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> real eigenvectors are pairwise orthogonal.
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>
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> The spectrum may be computed either completely or partially by specifying
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> either an interval (VL,VU] or a range of indices IL:IU for the desired
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> eigenvalues.
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>
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> Depending on the number of desired eigenvalues, these are computed either
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> by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are
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> computed by the use of various suitable L D L^T factorizations near clusters
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> of close eigenvalues (referred to as RRRs, Relatively Robust
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> Representations). An informal sketch of the algorithm follows.
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>
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> For each unreduced block (submatrix) of T,
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> (a) Compute T - sigma I = L D L^T, so that L and D
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> define all the wanted eigenvalues to high relative accuracy.
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> This means that small relative changes in the entries of D and L
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> cause only small relative changes in the eigenvalues and
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> eigenvectors. The standard (unfactored) representation of the
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> tridiagonal matrix T does not have this property in general.
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> (b) Compute the eigenvalues to suitable accuracy.
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> If the eigenvectors are desired, the algorithm attains full
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> accuracy of the computed eigenvalues only right before
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> the corresponding vectors have to be computed, see steps c) and d).
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> (c) For each cluster of close eigenvalues, select a new
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> shift close to the cluster, find a new factorization, and refine
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> the shifted eigenvalues to suitable accuracy.
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> (d) For each eigenvalue with a large enough relative separation compute
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> the corresponding eigenvector by forming a rank revealing twisted
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> factorization. Go back to (c) for any clusters that remain.
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>
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> For more details, see:
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> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
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> to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
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> Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
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> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
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> Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
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> 2004. Also LAPACK Working Note 154.
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> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
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> tridiagonal eigenvalue/eigenvector problem",
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> Computer Science Division Technical Report No. UCB/CSD-97-971,
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> UC Berkeley, May 1997.
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>
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> Further Details
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> 1.DSTEMR works only on machines which follow IEEE-754
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> floating-point standard in their handling of infinities and NaNs.
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> This permits the use of efficient inner loops avoiding a check for
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> zero divisors.
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> \endverbatim
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Arguments:
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==========
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> \param[in] JOBZ
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> \verbatim
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> JOBZ is CHARACTER*1
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> = 'N': Compute eigenvalues only;
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> = 'V': Compute eigenvalues and eigenvectors.
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> \endverbatim
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>
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> \param[in] RANGE
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> \verbatim
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> RANGE is CHARACTER*1
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> = 'A': all eigenvalues will be found.
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> = 'V': all eigenvalues in the half-open interval (VL,VU]
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> will be found.
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> = 'I': the IL-th through IU-th eigenvalues will be found.
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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 N diagonal elements of the tridiagonal matrix
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> T. On exit, D is overwritten.
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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)
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> On entry, the (N-1) subdiagonal elements of the tridiagonal
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> matrix T in elements 1 to N-1 of E. E(N) need not be set on
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> input, but is used internally as workspace.
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> On exit, E is overwritten.
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> \endverbatim
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>
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> \param[in] VL
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> \verbatim
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> VL is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in] VU
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> \verbatim
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> VU is DOUBLE PRECISION
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>
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> If RANGE='V', the lower and upper bounds of the interval to
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> be searched for eigenvalues. VL < VU.
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> Not referenced if RANGE = 'A' or 'I'.
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> \endverbatim
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>
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> \param[in] IL
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> \verbatim
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> IL is INTEGER
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> \endverbatim
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>
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> \param[in] IU
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> \verbatim
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> IU is INTEGER
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>
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> If RANGE='I', the indices (in ascending order) of the
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> smallest and largest eigenvalues to be returned.
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> 1 <= IL <= IU <= N, if N > 0.
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> Not referenced if RANGE = 'A' or 'V'.
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> \endverbatim
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>
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> \param[out] M
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> \verbatim
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> M is INTEGER
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> The total number of eigenvalues found. 0 <= M <= N.
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> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
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> \endverbatim
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>
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> \param[out] W
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> \verbatim
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> W is DOUBLE PRECISION array, dimension (N)
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> The first M elements contain the selected eigenvalues in
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> ascending order.
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> \endverbatim
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>
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> \param[out] Z
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> \verbatim
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> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
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> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
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> contain the orthonormal eigenvectors of the matrix T
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> corresponding to the selected eigenvalues, with the i-th
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> column of Z holding the eigenvector associated with W(i).
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> If JOBZ = 'N', then Z is not referenced.
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> Note: the user must ensure that at least max(1,M) columns are
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> supplied in the array Z; if RANGE = 'V', the exact value of M
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> is not known in advance and can be computed with a workspace
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> query by setting NZC = -1, see below.
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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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> JOBZ = 'V', then LDZ >= max(1,N).
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> \endverbatim
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>
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> \param[in] NZC
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> \verbatim
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> NZC is INTEGER
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> The number of eigenvectors to be held in the array Z.
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> If RANGE = 'A', then NZC >= max(1,N).
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> If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,VU].
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> If RANGE = 'I', then NZC >= IU-IL+1.
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> If NZC = -1, then a workspace query is assumed; the
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> routine calculates the number of columns of the array Z that
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> are needed to hold the eigenvectors.
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> This value is returned as the first entry of the Z array, and
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> no error message related to NZC is issued by XERBLA.
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> \endverbatim
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>
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> \param[out] ISUPPZ
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> \verbatim
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> ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) )
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> The support of the eigenvectors in Z, i.e., the indices
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> indicating the nonzero elements in Z. The i-th computed eigenvector
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> is nonzero only in elements ISUPPZ( 2*i-1 ) through
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> ISUPPZ( 2*i ). This is relevant in the case when the matrix
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> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
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> \endverbatim
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>
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> \param[in,out] TRYRAC
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> \verbatim
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> TRYRAC is LOGICAL
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> If TRYRAC.EQ..TRUE., indicates that the code should check whether
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> the tridiagonal matrix defines its eigenvalues to high relative
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> accuracy. If so, the code uses relative-accuracy preserving
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> algorithms that might be (a bit) slower depending on the matrix.
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> If the matrix does not define its eigenvalues to high relative
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> accuracy, the code can uses possibly faster algorithms.
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> If TRYRAC.EQ..FALSE., the code is not required to guarantee
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> relatively accurate eigenvalues and can use the fastest possible
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> techniques.
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> On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix
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> does not define its eigenvalues to high relative accuracy.
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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 (LWORK)
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> On exit, if INFO = 0, WORK(1) returns the optimal
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||||
> (and minimal) LWORK.
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||||
> \endverbatim
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||||
>
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> \param[in] LWORK
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> \verbatim
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> LWORK is INTEGER
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> The dimension of the array WORK. LWORK >= max(1,18*N)
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> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
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> If LWORK = -1, then a workspace query is assumed; the routine
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> only calculates the optimal size of the WORK array, returns
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> this value as the first entry of the WORK array, and no error
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> message related to LWORK is issued by XERBLA.
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> \endverbatim
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>
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> \param[out] IWORK
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> \verbatim
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> IWORK is INTEGER array, dimension (LIWORK)
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> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
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||||
> \endverbatim
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||||
>
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> \param[in] LIWORK
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> \verbatim
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||||
> LIWORK is INTEGER
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> The dimension of the array IWORK. LIWORK >= max(1,10*N)
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||||
> if the eigenvectors are desired, and LIWORK >= max(1,8*N)
|
||||
> if only the eigenvalues are to be computed.
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> If LIWORK = -1, then a workspace query is assumed; the
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||||
> routine only calculates the optimal size of the IWORK array,
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> returns this value as the first entry of the IWORK array, and
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> no error message related to LIWORK is issued by XERBLA.
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||||
> \endverbatim
|
||||
>
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||||
> \param[out] INFO
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||||
> \verbatim
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||||
> INFO is INTEGER
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||||
> On exit, INFO
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> = 0: successful exit
|
||||
> < 0: if INFO = -i, the i-th argument had an illegal value
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||||
> > 0: if INFO = 1X, internal error in DLARRE,
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||||
> if INFO = 2X, internal error in DLARRV.
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||||
> Here, the digit X = ABS( IINFO ) < 10, where IINFO is
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||||
> the nonzero error code returned by DLARRE or
|
||||
> DLARRV, respectively.
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||||
> \endverbatim
|
||||
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Authors:
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||||
========
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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 2013
|
||||
|
||||
> \ingroup doubleOTHERcomputational
|
||||
|
||||
> \par Contributors:
|
||||
==================
|
||||
>
|
||||
> Beresford Parlett, University of California, Berkeley, USA \n
|
||||
> Jim Demmel, University of California, Berkeley, USA \n
|
||||
> Inderjit Dhillon, University of Texas, Austin, USA \n
|
||||
> Osni Marques, LBNL/NERSC, USA \n
|
||||
> Christof Voemel, University of California, Berkeley, USA
|
||||
|
||||
=====================================================================
|
||||
Subroutine */ int igraphdstemr_(char *jobz, char *range, integer *n, doublereal *
|
||||
d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il,
|
||||
integer *iu, integer *m, doublereal *w, doublereal *z__, integer *ldz,
|
||||
integer *nzc, integer *isuppz, logical *tryrac, doublereal *work,
|
||||
integer *lwork, integer *iwork, integer *liwork, integer *info)
|
||||
{
|
||||
/* System generated locals */
|
||||
integer z_dim1, z_offset, i__1, i__2;
|
||||
doublereal d__1, d__2;
|
||||
|
||||
/* Builtin functions */
|
||||
double sqrt(doublereal);
|
||||
|
||||
/* Local variables */
|
||||
integer i__, j;
|
||||
doublereal r1, r2;
|
||||
integer jj;
|
||||
doublereal cs;
|
||||
integer in;
|
||||
doublereal sn, wl, wu;
|
||||
integer iil, iiu;
|
||||
doublereal eps, tmp;
|
||||
integer indd, iend, jblk, wend;
|
||||
doublereal rmin, rmax;
|
||||
integer itmp;
|
||||
doublereal tnrm;
|
||||
extern /* Subroutine */ int igraphdlae2_(doublereal *, doublereal *, doublereal
|
||||
*, doublereal *, doublereal *);
|
||||
integer inde2, itmp2;
|
||||
doublereal rtol1, rtol2;
|
||||
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
|
||||
integer *);
|
||||
doublereal scale;
|
||||
integer indgp;
|
||||
extern logical igraphlsame_(char *, char *);
|
||||
integer iinfo, iindw, ilast;
|
||||
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
|
||||
doublereal *, integer *), igraphdswap_(integer *, doublereal *, integer
|
||||
*, doublereal *, integer *);
|
||||
integer lwmin;
|
||||
logical wantz;
|
||||
extern /* Subroutine */ int igraphdlaev2_(doublereal *, doublereal *,
|
||||
doublereal *, doublereal *, doublereal *, doublereal *,
|
||||
doublereal *);
|
||||
extern doublereal igraphdlamch_(char *);
|
||||
logical alleig;
|
||||
integer ibegin;
|
||||
logical indeig;
|
||||
integer iindbl;
|
||||
logical valeig;
|
||||
extern /* Subroutine */ int igraphdlarrc_(char *, integer *, doublereal *,
|
||||
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
|
||||
integer *, integer *, integer *), igraphdlarre_(char *,
|
||||
integer *, doublereal *, doublereal *, integer *, integer *,
|
||||
doublereal *, doublereal *, doublereal *, doublereal *,
|
||||
doublereal *, doublereal *, integer *, integer *, integer *,
|
||||
doublereal *, doublereal *, doublereal *, integer *, integer *,
|
||||
doublereal *, doublereal *, doublereal *, integer *, integer *);
|
||||
integer wbegin;
|
||||
doublereal safmin;
|
||||
extern /* Subroutine */ int igraphdlarrj_(integer *, doublereal *, doublereal *,
|
||||
integer *, integer *, doublereal *, integer *, doublereal *,
|
||||
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
|
||||
integer *), igraphxerbla_(char *, integer *, ftnlen);
|
||||
doublereal bignum;
|
||||
integer inderr, iindwk, indgrs, offset;
|
||||
extern doublereal igraphdlanst_(char *, integer *, doublereal *, doublereal *);
|
||||
extern /* Subroutine */ int igraphdlarrr_(integer *, doublereal *, doublereal *,
|
||||
integer *), igraphdlarrv_(integer *, doublereal *, doublereal *,
|
||||
doublereal *, doublereal *, doublereal *, integer *, integer *,
|
||||
integer *, integer *, doublereal *, doublereal *, doublereal *,
|
||||
doublereal *, doublereal *, doublereal *, integer *, integer *,
|
||||
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
||||
integer *, integer *), igraphdlasrt_(char *, integer *, doublereal *,
|
||||
integer *);
|
||||
doublereal thresh;
|
||||
integer iinspl, ifirst, indwrk, liwmin, nzcmin;
|
||||
doublereal pivmin;
|
||||
integer nsplit;
|
||||
doublereal smlnum;
|
||||
logical lquery, zquery;
|
||||
|
||||
|
||||
/* -- LAPACK computational routine (version 3.5.0) --
|
||||
-- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
November 2013
|
||||
|
||||
|
||||
=====================================================================
|
||||
|
||||
|
||||
Test the input parameters.
|
||||
|
||||
Parameter adjustments */
|
||||
--d__;
|
||||
--e;
|
||||
--w;
|
||||
z_dim1 = *ldz;
|
||||
z_offset = 1 + z_dim1;
|
||||
z__ -= z_offset;
|
||||
--isuppz;
|
||||
--work;
|
||||
--iwork;
|
||||
|
||||
/* Function Body */
|
||||
wantz = igraphlsame_(jobz, "V");
|
||||
alleig = igraphlsame_(range, "A");
|
||||
valeig = igraphlsame_(range, "V");
|
||||
indeig = igraphlsame_(range, "I");
|
||||
|
||||
lquery = *lwork == -1 || *liwork == -1;
|
||||
zquery = *nzc == -1;
|
||||
/* DSTEMR needs WORK of size 6*N, IWORK of size 3*N.
|
||||
In addition, DLARRE needs WORK of size 6*N, IWORK of size 5*N.
|
||||
Furthermore, DLARRV needs WORK of size 12*N, IWORK of size 7*N. */
|
||||
if (wantz) {
|
||||
lwmin = *n * 18;
|
||||
liwmin = *n * 10;
|
||||
} else {
|
||||
/* need less workspace if only the eigenvalues are wanted */
|
||||
lwmin = *n * 12;
|
||||
liwmin = *n << 3;
|
||||
}
|
||||
wl = 0.;
|
||||
wu = 0.;
|
||||
iil = 0;
|
||||
iiu = 0;
|
||||
nsplit = 0;
|
||||
if (valeig) {
|
||||
/* We do not reference VL, VU in the cases RANGE = 'I','A'
|
||||
The interval (WL, WU] contains all the wanted eigenvalues.
|
||||
It is either given by the user or computed in DLARRE. */
|
||||
wl = *vl;
|
||||
wu = *vu;
|
||||
} else if (indeig) {
|
||||
/* We do not reference IL, IU in the cases RANGE = 'V','A' */
|
||||
iil = *il;
|
||||
iiu = *iu;
|
||||
}
|
||||
|
||||
*info = 0;
|
||||
if (! (wantz || igraphlsame_(jobz, "N"))) {
|
||||
*info = -1;
|
||||
} else if (! (alleig || valeig || indeig)) {
|
||||
*info = -2;
|
||||
} else if (*n < 0) {
|
||||
*info = -3;
|
||||
} else if (valeig && *n > 0 && wu <= wl) {
|
||||
*info = -7;
|
||||
} else if (indeig && (iil < 1 || iil > *n)) {
|
||||
*info = -8;
|
||||
} else if (indeig && (iiu < iil || iiu > *n)) {
|
||||
*info = -9;
|
||||
} else if (*ldz < 1 || wantz && *ldz < *n) {
|
||||
*info = -13;
|
||||
} else if (*lwork < lwmin && ! lquery) {
|
||||
*info = -17;
|
||||
} else if (*liwork < liwmin && ! lquery) {
|
||||
*info = -19;
|
||||
}
|
||||
|
||||
/* Get machine constants. */
|
||||
|
||||
safmin = igraphdlamch_("Safe minimum");
|
||||
eps = igraphdlamch_("Precision");
|
||||
smlnum = safmin / eps;
|
||||
bignum = 1. / smlnum;
|
||||
rmin = sqrt(smlnum);
|
||||
/* Computing MIN */
|
||||
d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin));
|
||||
rmax = min(d__1,d__2);
|
||||
|
||||
if (*info == 0) {
|
||||
work[1] = (doublereal) lwmin;
|
||||
iwork[1] = liwmin;
|
||||
|
||||
if (wantz && alleig) {
|
||||
nzcmin = *n;
|
||||
} else if (wantz && valeig) {
|
||||
igraphdlarrc_("T", n, vl, vu, &d__[1], &e[1], &safmin, &nzcmin, &itmp, &
|
||||
itmp2, info);
|
||||
} else if (wantz && indeig) {
|
||||
nzcmin = iiu - iil + 1;
|
||||
} else {
|
||||
/* WANTZ .EQ. FALSE. */
|
||||
nzcmin = 0;
|
||||
}
|
||||
if (zquery && *info == 0) {
|
||||
z__[z_dim1 + 1] = (doublereal) nzcmin;
|
||||
} else if (*nzc < nzcmin && ! zquery) {
|
||||
*info = -14;
|
||||
}
|
||||
}
|
||||
if (*info != 0) {
|
||||
|
||||
i__1 = -(*info);
|
||||
igraphxerbla_("DSTEMR", &i__1, (ftnlen)6);
|
||||
|
||||
return 0;
|
||||
} else if (lquery || zquery) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Handle N = 0, 1, and 2 cases immediately */
|
||||
|
||||
*m = 0;
|
||||
if (*n == 0) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
if (*n == 1) {
|
||||
if (alleig || indeig) {
|
||||
*m = 1;
|
||||
w[1] = d__[1];
|
||||
} else {
|
||||
if (wl < d__[1] && wu >= d__[1]) {
|
||||
*m = 1;
|
||||
w[1] = d__[1];
|
||||
}
|
||||
}
|
||||
if (wantz && ! zquery) {
|
||||
z__[z_dim1 + 1] = 1.;
|
||||
isuppz[1] = 1;
|
||||
isuppz[2] = 1;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
if (*n == 2) {
|
||||
if (! wantz) {
|
||||
igraphdlae2_(&d__[1], &e[1], &d__[2], &r1, &r2);
|
||||
} else if (wantz && ! zquery) {
|
||||
igraphdlaev2_(&d__[1], &e[1], &d__[2], &r1, &r2, &cs, &sn);
|
||||
}
|
||||
if (alleig || valeig && r2 > wl && r2 <= wu || indeig && iil == 1) {
|
||||
++(*m);
|
||||
w[*m] = r2;
|
||||
if (wantz && ! zquery) {
|
||||
z__[*m * z_dim1 + 1] = -sn;
|
||||
z__[*m * z_dim1 + 2] = cs;
|
||||
/* Note: At most one of SN and CS can be zero. */
|
||||
if (sn != 0.) {
|
||||
if (cs != 0.) {
|
||||
isuppz[(*m << 1) - 1] = 1;
|
||||
isuppz[*m * 2] = 2;
|
||||
} else {
|
||||
isuppz[(*m << 1) - 1] = 1;
|
||||
isuppz[*m * 2] = 1;
|
||||
}
|
||||
} else {
|
||||
isuppz[(*m << 1) - 1] = 2;
|
||||
isuppz[*m * 2] = 2;
|
||||
}
|
||||
}
|
||||
}
|
||||
if (alleig || valeig && r1 > wl && r1 <= wu || indeig && iiu == 2) {
|
||||
++(*m);
|
||||
w[*m] = r1;
|
||||
if (wantz && ! zquery) {
|
||||
z__[*m * z_dim1 + 1] = cs;
|
||||
z__[*m * z_dim1 + 2] = sn;
|
||||
/* Note: At most one of SN and CS can be zero. */
|
||||
if (sn != 0.) {
|
||||
if (cs != 0.) {
|
||||
isuppz[(*m << 1) - 1] = 1;
|
||||
isuppz[*m * 2] = 2;
|
||||
} else {
|
||||
isuppz[(*m << 1) - 1] = 1;
|
||||
isuppz[*m * 2] = 1;
|
||||
}
|
||||
} else {
|
||||
isuppz[(*m << 1) - 1] = 2;
|
||||
isuppz[*m * 2] = 2;
|
||||
}
|
||||
}
|
||||
}
|
||||
} else {
|
||||
/* Continue with general N */
|
||||
indgrs = 1;
|
||||
inderr = (*n << 1) + 1;
|
||||
indgp = *n * 3 + 1;
|
||||
indd = (*n << 2) + 1;
|
||||
inde2 = *n * 5 + 1;
|
||||
indwrk = *n * 6 + 1;
|
||||
|
||||
iinspl = 1;
|
||||
iindbl = *n + 1;
|
||||
iindw = (*n << 1) + 1;
|
||||
iindwk = *n * 3 + 1;
|
||||
|
||||
/* Scale matrix to allowable range, if necessary.
|
||||
The allowable range is related to the PIVMIN parameter; see the
|
||||
comments in DLARRD. The preference for scaling small values
|
||||
up is heuristic; we expect users' matrices not to be close to the
|
||||
RMAX threshold. */
|
||||
|
||||
scale = 1.;
|
||||
tnrm = igraphdlanst_("M", n, &d__[1], &e[1]);
|
||||
if (tnrm > 0. && tnrm < rmin) {
|
||||
scale = rmin / tnrm;
|
||||
} else if (tnrm > rmax) {
|
||||
scale = rmax / tnrm;
|
||||
}
|
||||
if (scale != 1.) {
|
||||
igraphdscal_(n, &scale, &d__[1], &c__1);
|
||||
i__1 = *n - 1;
|
||||
igraphdscal_(&i__1, &scale, &e[1], &c__1);
|
||||
tnrm *= scale;
|
||||
if (valeig) {
|
||||
/* If eigenvalues in interval have to be found,
|
||||
scale (WL, WU] accordingly */
|
||||
wl *= scale;
|
||||
wu *= scale;
|
||||
}
|
||||
}
|
||||
|
||||
/* Compute the desired eigenvalues of the tridiagonal after splitting
|
||||
into smaller subblocks if the corresponding off-diagonal elements
|
||||
are small
|
||||
THRESH is the splitting parameter for DLARRE
|
||||
A negative THRESH forces the old splitting criterion based on the
|
||||
size of the off-diagonal. A positive THRESH switches to splitting
|
||||
which preserves relative accuracy. */
|
||||
|
||||
if (*tryrac) {
|
||||
/* Test whether the matrix warrants the more expensive relative approach. */
|
||||
igraphdlarrr_(n, &d__[1], &e[1], &iinfo);
|
||||
} else {
|
||||
/* The user does not care about relative accurately eigenvalues */
|
||||
iinfo = -1;
|
||||
}
|
||||
/* Set the splitting criterion */
|
||||
if (iinfo == 0) {
|
||||
thresh = eps;
|
||||
} else {
|
||||
thresh = -eps;
|
||||
/* relative accuracy is desired but T does not guarantee it */
|
||||
*tryrac = FALSE_;
|
||||
}
|
||||
|
||||
if (*tryrac) {
|
||||
/* Copy original diagonal, needed to guarantee relative accuracy */
|
||||
igraphdcopy_(n, &d__[1], &c__1, &work[indd], &c__1);
|
||||
}
|
||||
/* Store the squares of the offdiagonal values of T */
|
||||
i__1 = *n - 1;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
/* Computing 2nd power */
|
||||
d__1 = e[j];
|
||||
work[inde2 + j - 1] = d__1 * d__1;
|
||||
/* L5: */
|
||||
}
|
||||
/* Set the tolerance parameters for bisection */
|
||||
if (! wantz) {
|
||||
/* DLARRE computes the eigenvalues to full precision. */
|
||||
rtol1 = eps * 4.;
|
||||
rtol2 = eps * 4.;
|
||||
} else {
|
||||
/* DLARRE computes the eigenvalues to less than full precision.
|
||||
DLARRV will refine the eigenvalue approximations, and we can
|
||||
need less accurate initial bisection in DLARRE.
|
||||
Note: these settings do only affect the subset case and DLARRE */
|
||||
rtol1 = sqrt(eps);
|
||||
/* Computing MAX */
|
||||
d__1 = sqrt(eps) * .005, d__2 = eps * 4.;
|
||||
rtol2 = max(d__1,d__2);
|
||||
}
|
||||
igraphdlarre_(range, n, &wl, &wu, &iil, &iiu, &d__[1], &e[1], &work[inde2],
|
||||
&rtol1, &rtol2, &thresh, &nsplit, &iwork[iinspl], m, &w[1], &
|
||||
work[inderr], &work[indgp], &iwork[iindbl], &iwork[iindw], &
|
||||
work[indgrs], &pivmin, &work[indwrk], &iwork[iindwk], &iinfo);
|
||||
if (iinfo != 0) {
|
||||
*info = abs(iinfo) + 10;
|
||||
return 0;
|
||||
}
|
||||
/* Note that if RANGE .NE. 'V', DLARRE computes bounds on the desired
|
||||
part of the spectrum. All desired eigenvalues are contained in
|
||||
(WL,WU] */
|
||||
if (wantz) {
|
||||
|
||||
/* Compute the desired eigenvectors corresponding to the computed
|
||||
eigenvalues */
|
||||
|
||||
igraphdlarrv_(n, &wl, &wu, &d__[1], &e[1], &pivmin, &iwork[iinspl], m, &
|
||||
c__1, m, &c_b18, &rtol1, &rtol2, &w[1], &work[inderr], &
|
||||
work[indgp], &iwork[iindbl], &iwork[iindw], &work[indgrs],
|
||||
&z__[z_offset], ldz, &isuppz[1], &work[indwrk], &iwork[
|
||||
iindwk], &iinfo);
|
||||
if (iinfo != 0) {
|
||||
*info = abs(iinfo) + 20;
|
||||
return 0;
|
||||
}
|
||||
} else {
|
||||
/* DLARRE computes eigenvalues of the (shifted) root representation
|
||||
DLARRV returns the eigenvalues of the unshifted matrix.
|
||||
However, if the eigenvectors are not desired by the user, we need
|
||||
to apply the corresponding shifts from DLARRE to obtain the
|
||||
eigenvalues of the original matrix. */
|
||||
i__1 = *m;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
itmp = iwork[iindbl + j - 1];
|
||||
w[j] += e[iwork[iinspl + itmp - 1]];
|
||||
/* L20: */
|
||||
}
|
||||
}
|
||||
|
||||
if (*tryrac) {
|
||||
/* Refine computed eigenvalues so that they are relatively accurate
|
||||
with respect to the original matrix T. */
|
||||
ibegin = 1;
|
||||
wbegin = 1;
|
||||
i__1 = iwork[iindbl + *m - 1];
|
||||
for (jblk = 1; jblk <= i__1; ++jblk) {
|
||||
iend = iwork[iinspl + jblk - 1];
|
||||
in = iend - ibegin + 1;
|
||||
wend = wbegin - 1;
|
||||
/* check if any eigenvalues have to be refined in this block */
|
||||
L36:
|
||||
if (wend < *m) {
|
||||
if (iwork[iindbl + wend] == jblk) {
|
||||
++wend;
|
||||
goto L36;
|
||||
}
|
||||
}
|
||||
if (wend < wbegin) {
|
||||
ibegin = iend + 1;
|
||||
goto L39;
|
||||
}
|
||||
offset = iwork[iindw + wbegin - 1] - 1;
|
||||
ifirst = iwork[iindw + wbegin - 1];
|
||||
ilast = iwork[iindw + wend - 1];
|
||||
rtol2 = eps * 4.;
|
||||
igraphdlarrj_(&in, &work[indd + ibegin - 1], &work[inde2 + ibegin -
|
||||
1], &ifirst, &ilast, &rtol2, &offset, &w[wbegin], &
|
||||
work[inderr + wbegin - 1], &work[indwrk], &iwork[
|
||||
iindwk], &pivmin, &tnrm, &iinfo);
|
||||
ibegin = iend + 1;
|
||||
wbegin = wend + 1;
|
||||
L39:
|
||||
;
|
||||
}
|
||||
}
|
||||
|
||||
/* If matrix was scaled, then rescale eigenvalues appropriately. */
|
||||
|
||||
if (scale != 1.) {
|
||||
d__1 = 1. / scale;
|
||||
igraphdscal_(m, &d__1, &w[1], &c__1);
|
||||
}
|
||||
}
|
||||
|
||||
/* If eigenvalues are not in increasing order, then sort them,
|
||||
possibly along with eigenvectors. */
|
||||
|
||||
if (nsplit > 1 || *n == 2) {
|
||||
if (! wantz) {
|
||||
igraphdlasrt_("I", m, &w[1], &iinfo);
|
||||
if (iinfo != 0) {
|
||||
*info = 3;
|
||||
return 0;
|
||||
}
|
||||
} else {
|
||||
i__1 = *m - 1;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
i__ = 0;
|
||||
tmp = w[j];
|
||||
i__2 = *m;
|
||||
for (jj = j + 1; jj <= i__2; ++jj) {
|
||||
if (w[jj] < tmp) {
|
||||
i__ = jj;
|
||||
tmp = w[jj];
|
||||
}
|
||||
/* L50: */
|
||||
}
|
||||
if (i__ != 0) {
|
||||
w[i__] = w[j];
|
||||
w[j] = tmp;
|
||||
if (wantz) {
|
||||
igraphdswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j *
|
||||
z_dim1 + 1], &c__1);
|
||||
itmp = isuppz[(i__ << 1) - 1];
|
||||
isuppz[(i__ << 1) - 1] = isuppz[(j << 1) - 1];
|
||||
isuppz[(j << 1) - 1] = itmp;
|
||||
itmp = isuppz[i__ * 2];
|
||||
isuppz[i__ * 2] = isuppz[j * 2];
|
||||
isuppz[j * 2] = itmp;
|
||||
}
|
||||
}
|
||||
/* L60: */
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
work[1] = (doublereal) lwmin;
|
||||
iwork[1] = liwmin;
|
||||
return 0;
|
||||
|
||||
/* End of DSTEMR */
|
||||
|
||||
} /* igraphdstemr_ */
|
||||
|
||||
Reference in New Issue
Block a user