Add graph references
This commit is contained in:
Abdelrahman Said
+867
@@ -0,0 +1,867 @@
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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_n1 = -1;
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static integer c__3 = 3;
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static integer c__2 = 2;
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static integer c__0 = 0;
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/* > \brief \b DSTEBZ
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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 DSTEBZ + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstebz.
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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/dstebz.
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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/dstebz.
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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 DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E,
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M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK,
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INFO )
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CHARACTER ORDER, RANGE
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INTEGER IL, INFO, IU, M, N, NSPLIT
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DOUBLE PRECISION ABSTOL, VL, VU
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INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * )
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DOUBLE PRECISION D( * ), E( * ), W( * ), 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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> DSTEBZ computes the eigenvalues of a symmetric tridiagonal
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> matrix T. The user may ask for all eigenvalues, all eigenvalues
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> in the half-open interval (VL, VU], or the IL-th through IU-th
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> eigenvalues.
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>
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> To avoid overflow, the matrix must be scaled so that its
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> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
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> accuracy, it should not be much smaller than that.
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>
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> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
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> Matrix", Report CS41, Computer Science Dept., Stanford
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> University, July 21, 1966.
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> \endverbatim
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Arguments:
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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") all eigenvalues will be found.
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> = 'V': ("Value") all eigenvalues in the half-open interval
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> (VL, VU] will be found.
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> = 'I': ("Index") the IL-th through IU-th eigenvalues (of the
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> entire matrix) will be found.
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> \endverbatim
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>
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> \param[in] ORDER
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> \verbatim
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> ORDER is CHARACTER*1
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> = 'B': ("By Block") the eigenvalues will be grouped by
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> split-off block (see IBLOCK, ISPLIT) and
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> ordered from smallest to largest within
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> the block.
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> = 'E': ("Entire matrix")
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> the eigenvalues for the entire matrix
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> will be ordered from smallest to
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> largest.
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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 tridiagonal matrix T. N >= 0.
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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. Eigenvalues less than or equal
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> to VL, or greater than VU, will not be returned. 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; IL = 1 and IU = 0 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[in] ABSTOL
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> \verbatim
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> ABSTOL is DOUBLE PRECISION
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> The absolute tolerance for the eigenvalues. An eigenvalue
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> (or cluster) is considered to be located if it has been
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> determined to lie in an interval whose width is ABSTOL or
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> less. If ABSTOL is less than or equal to zero, then ULP*|T|
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> will be used, where |T| means the 1-norm of T.
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>
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> Eigenvalues will be computed most accurately when ABSTOL is
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> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
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> \endverbatim
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>
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> \param[in] D
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> \verbatim
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> D is DOUBLE PRECISION array, dimension (N)
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> The n diagonal elements of the tridiagonal matrix T.
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> \endverbatim
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>
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> \param[in] E
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> \verbatim
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> E is DOUBLE PRECISION array, dimension (N-1)
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> The (n-1) off-diagonal elements of the tridiagonal matrix T.
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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 actual number of eigenvalues found. 0 <= M <= N.
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> (See also the description of INFO=2,3.)
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> \endverbatim
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>
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> \param[out] NSPLIT
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> \verbatim
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> NSPLIT is INTEGER
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> The number of diagonal blocks in the matrix T.
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> 1 <= NSPLIT <= N.
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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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> On exit, the first M elements of W will contain the
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> eigenvalues. (DSTEBZ may use the remaining N-M elements as
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> workspace.)
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> \endverbatim
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>
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> \param[out] IBLOCK
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> \verbatim
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> IBLOCK is INTEGER array, dimension (N)
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> At each row/column j where E(j) is zero or small, the
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> matrix T is considered to split into a block diagonal
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> matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which
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> block (from 1 to the number of blocks) the eigenvalue W(i)
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> belongs. (DSTEBZ may use the remaining N-M elements as
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> workspace.)
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> \endverbatim
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>
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> \param[out] ISPLIT
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> \verbatim
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> ISPLIT is INTEGER array, dimension (N)
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> The splitting points, at which T breaks up into submatrices.
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> The first submatrix consists of rows/columns 1 to ISPLIT(1),
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> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
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> etc., and the NSPLIT-th consists of rows/columns
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> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
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> (Only the first NSPLIT elements will actually be used, but
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> since the user cannot know a priori what value NSPLIT will
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> have, N words must be reserved for ISPLIT.)
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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 (4*N)
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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 (3*N)
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> \endverbatim
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>
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> \param[out] INFO
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> \verbatim
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> INFO is INTEGER
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> = 0: successful exit
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> < 0: if INFO = -i, the i-th argument had an illegal value
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> > 0: some or all of the eigenvalues failed to converge or
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> were not computed:
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> =1 or 3: Bisection failed to converge for some
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> eigenvalues; these eigenvalues are flagged by a
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> negative block number. The effect is that the
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> eigenvalues may not be as accurate as the
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> absolute and relative tolerances. This is
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> generally caused by unexpectedly inaccurate
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> arithmetic.
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> =2 or 3: RANGE='I' only: Not all of the eigenvalues
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> IL:IU were found.
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> Effect: M < IU+1-IL
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> Cause: non-monotonic arithmetic, causing the
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> Sturm sequence to be non-monotonic.
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> Cure: recalculate, using RANGE='A', and pick
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> out eigenvalues IL:IU. In some cases,
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> increasing the PARAMETER "FUDGE" may
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> make things work.
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> = 4: RANGE='I', and the Gershgorin interval
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> initially used was too small. No eigenvalues
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> were computed.
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> Probable cause: your machine has sloppy
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> floating-point arithmetic.
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> Cure: Increase the PARAMETER "FUDGE",
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> recompile, and try again.
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> \endverbatim
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> \par Internal Parameters:
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=========================
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>
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> \verbatim
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> RELFAC DOUBLE PRECISION, default = 2.0e0
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> The relative tolerance. An interval (a,b] lies within
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> "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|),
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> where "ulp" is the machine precision (distance from 1 to
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> the next larger floating point number.)
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>
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> FUDGE DOUBLE PRECISION, default = 2
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> A "fudge factor" to widen the Gershgorin intervals. Ideally,
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> a value of 1 should work, but on machines with sloppy
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> arithmetic, this needs to be larger. The default for
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> publicly released versions should be large enough to handle
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> the worst machine around. Note that this has no effect
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> on accuracy of the solution.
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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 igraphdstebz_(char *range, char *order, integer *n, doublereal
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*vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol,
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doublereal *d__, doublereal *e, integer *m, integer *nsplit,
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doublereal *w, integer *iblock, integer *isplit, doublereal *work,
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integer *iwork, integer *info)
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{
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/* System generated locals */
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integer i__1, i__2, i__3;
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doublereal d__1, d__2, d__3, d__4, d__5;
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/* Builtin functions */
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double sqrt(doublereal), log(doublereal);
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/* Local variables */
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integer j, ib, jb, ie, je, nb;
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doublereal gl;
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integer im, in;
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doublereal gu;
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integer iw;
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doublereal wl, wu;
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integer nwl;
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doublereal ulp, wlu, wul;
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integer nwu;
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doublereal tmp1, tmp2;
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integer iend, ioff, iout, itmp1, jdisc;
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extern logical igraphlsame_(char *, char *);
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integer iinfo;
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doublereal atoli;
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integer iwoff;
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doublereal bnorm;
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integer itmax;
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doublereal wkill, rtoli, tnorm;
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extern doublereal igraphdlamch_(char *);
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integer ibegin;
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extern /* Subroutine */ int igraphdlaebz_(integer *, integer *, integer *,
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||||
integer *, integer *, integer *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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||||
doublereal *, doublereal *, integer *, integer *, doublereal *,
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integer *, integer *);
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integer irange, idiscl;
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||||
doublereal safemn;
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integer idumma[1];
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extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
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||||
extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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integer idiscu, iorder;
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||||
logical ncnvrg;
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||||
doublereal pivmin;
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||||
logical toofew;
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||||
|
||||
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/* -- LAPACK computational routine (version 3.4.0) --
|
||||
-- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
November 2011
|
||||
|
||||
|
||||
=====================================================================
|
||||
|
||||
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||||
Parameter adjustments */
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||||
--iwork;
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||||
--work;
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--isplit;
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||||
--iblock;
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||||
--w;
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||||
--e;
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||||
--d__;
|
||||
|
||||
/* Function Body */
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||||
*info = 0;
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||||
|
||||
/* Decode RANGE */
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||||
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||||
if (igraphlsame_(range, "A")) {
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||||
irange = 1;
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||||
} else if (igraphlsame_(range, "V")) {
|
||||
irange = 2;
|
||||
} else if (igraphlsame_(range, "I")) {
|
||||
irange = 3;
|
||||
} else {
|
||||
irange = 0;
|
||||
}
|
||||
|
||||
/* Decode ORDER */
|
||||
|
||||
if (igraphlsame_(order, "B")) {
|
||||
iorder = 2;
|
||||
} else if (igraphlsame_(order, "E")) {
|
||||
iorder = 1;
|
||||
} else {
|
||||
iorder = 0;
|
||||
}
|
||||
|
||||
/* Check for Errors */
|
||||
|
||||
if (irange <= 0) {
|
||||
*info = -1;
|
||||
} else if (iorder <= 0) {
|
||||
*info = -2;
|
||||
} else if (*n < 0) {
|
||||
*info = -3;
|
||||
} else if (irange == 2) {
|
||||
if (*vl >= *vu) {
|
||||
*info = -5;
|
||||
}
|
||||
} else if (irange == 3 && (*il < 1 || *il > max(1,*n))) {
|
||||
*info = -6;
|
||||
} else if (irange == 3 && (*iu < min(*n,*il) || *iu > *n)) {
|
||||
*info = -7;
|
||||
}
|
||||
|
||||
if (*info != 0) {
|
||||
i__1 = -(*info);
|
||||
igraphxerbla_("DSTEBZ", &i__1, (ftnlen)6);
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Initialize error flags */
|
||||
|
||||
*info = 0;
|
||||
ncnvrg = FALSE_;
|
||||
toofew = FALSE_;
|
||||
|
||||
/* Quick return if possible */
|
||||
|
||||
*m = 0;
|
||||
if (*n == 0) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Simplifications: */
|
||||
|
||||
if (irange == 3 && *il == 1 && *iu == *n) {
|
||||
irange = 1;
|
||||
}
|
||||
|
||||
/* Get machine constants
|
||||
NB is the minimum vector length for vector bisection, or 0
|
||||
if only scalar is to be done. */
|
||||
|
||||
safemn = igraphdlamch_("S");
|
||||
ulp = igraphdlamch_("P");
|
||||
rtoli = ulp * 2.;
|
||||
nb = igraphilaenv_(&c__1, "DSTEBZ", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
|
||||
ftnlen)1);
|
||||
if (nb <= 1) {
|
||||
nb = 0;
|
||||
}
|
||||
|
||||
/* Special Case when N=1 */
|
||||
|
||||
if (*n == 1) {
|
||||
*nsplit = 1;
|
||||
isplit[1] = 1;
|
||||
if (irange == 2 && (*vl >= d__[1] || *vu < d__[1])) {
|
||||
*m = 0;
|
||||
} else {
|
||||
w[1] = d__[1];
|
||||
iblock[1] = 1;
|
||||
*m = 1;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Compute Splitting Points */
|
||||
|
||||
*nsplit = 1;
|
||||
work[*n] = 0.;
|
||||
pivmin = 1.;
|
||||
|
||||
i__1 = *n;
|
||||
for (j = 2; j <= i__1; ++j) {
|
||||
/* Computing 2nd power */
|
||||
d__1 = e[j - 1];
|
||||
tmp1 = d__1 * d__1;
|
||||
/* Computing 2nd power */
|
||||
d__2 = ulp;
|
||||
if ((d__1 = d__[j] * d__[j - 1], abs(d__1)) * (d__2 * d__2) + safemn
|
||||
> tmp1) {
|
||||
isplit[*nsplit] = j - 1;
|
||||
++(*nsplit);
|
||||
work[j - 1] = 0.;
|
||||
} else {
|
||||
work[j - 1] = tmp1;
|
||||
pivmin = max(pivmin,tmp1);
|
||||
}
|
||||
/* L10: */
|
||||
}
|
||||
isplit[*nsplit] = *n;
|
||||
pivmin *= safemn;
|
||||
|
||||
/* Compute Interval and ATOLI */
|
||||
|
||||
if (irange == 3) {
|
||||
|
||||
/* RANGE='I': Compute the interval containing eigenvalues
|
||||
IL through IU.
|
||||
|
||||
Compute Gershgorin interval for entire (split) matrix
|
||||
and use it as the initial interval */
|
||||
|
||||
gu = d__[1];
|
||||
gl = d__[1];
|
||||
tmp1 = 0.;
|
||||
|
||||
i__1 = *n - 1;
|
||||
for (j = 1; j <= i__1; ++j) {
|
||||
tmp2 = sqrt(work[j]);
|
||||
/* Computing MAX */
|
||||
d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
|
||||
gu = max(d__1,d__2);
|
||||
/* Computing MIN */
|
||||
d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
|
||||
gl = min(d__1,d__2);
|
||||
tmp1 = tmp2;
|
||||
/* L20: */
|
||||
}
|
||||
|
||||
/* Computing MAX */
|
||||
d__1 = gu, d__2 = d__[*n] + tmp1;
|
||||
gu = max(d__1,d__2);
|
||||
/* Computing MIN */
|
||||
d__1 = gl, d__2 = d__[*n] - tmp1;
|
||||
gl = min(d__1,d__2);
|
||||
/* Computing MAX */
|
||||
d__1 = abs(gl), d__2 = abs(gu);
|
||||
tnorm = max(d__1,d__2);
|
||||
gl = gl - tnorm * 2.1 * ulp * *n - pivmin * 4.2000000000000002;
|
||||
gu = gu + tnorm * 2.1 * ulp * *n + pivmin * 2.1;
|
||||
|
||||
/* Compute Iteration parameters */
|
||||
|
||||
itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.)) + 2;
|
||||
if (*abstol <= 0.) {
|
||||
atoli = ulp * tnorm;
|
||||
} else {
|
||||
atoli = *abstol;
|
||||
}
|
||||
|
||||
work[*n + 1] = gl;
|
||||
work[*n + 2] = gl;
|
||||
work[*n + 3] = gu;
|
||||
work[*n + 4] = gu;
|
||||
work[*n + 5] = gl;
|
||||
work[*n + 6] = gu;
|
||||
iwork[1] = -1;
|
||||
iwork[2] = -1;
|
||||
iwork[3] = *n + 1;
|
||||
iwork[4] = *n + 1;
|
||||
iwork[5] = *il - 1;
|
||||
iwork[6] = *iu;
|
||||
|
||||
igraphdlaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin,
|
||||
&d__[1], &e[1], &work[1], &iwork[5], &work[*n + 1], &work[*n
|
||||
+ 5], &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
|
||||
|
||||
if (iwork[6] == *iu) {
|
||||
wl = work[*n + 1];
|
||||
wlu = work[*n + 3];
|
||||
nwl = iwork[1];
|
||||
wu = work[*n + 4];
|
||||
wul = work[*n + 2];
|
||||
nwu = iwork[4];
|
||||
} else {
|
||||
wl = work[*n + 2];
|
||||
wlu = work[*n + 4];
|
||||
nwl = iwork[2];
|
||||
wu = work[*n + 3];
|
||||
wul = work[*n + 1];
|
||||
nwu = iwork[3];
|
||||
}
|
||||
|
||||
if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
|
||||
*info = 4;
|
||||
return 0;
|
||||
}
|
||||
} else {
|
||||
|
||||
/* RANGE='A' or 'V' -- Set ATOLI
|
||||
|
||||
Computing MAX */
|
||||
d__3 = abs(d__[1]) + abs(e[1]), d__4 = (d__1 = d__[*n], abs(d__1)) + (
|
||||
d__2 = e[*n - 1], abs(d__2));
|
||||
tnorm = max(d__3,d__4);
|
||||
|
||||
i__1 = *n - 1;
|
||||
for (j = 2; j <= i__1; ++j) {
|
||||
/* Computing MAX */
|
||||
d__4 = tnorm, d__5 = (d__1 = d__[j], abs(d__1)) + (d__2 = e[j - 1]
|
||||
, abs(d__2)) + (d__3 = e[j], abs(d__3));
|
||||
tnorm = max(d__4,d__5);
|
||||
/* L30: */
|
||||
}
|
||||
|
||||
if (*abstol <= 0.) {
|
||||
atoli = ulp * tnorm;
|
||||
} else {
|
||||
atoli = *abstol;
|
||||
}
|
||||
|
||||
if (irange == 2) {
|
||||
wl = *vl;
|
||||
wu = *vu;
|
||||
} else {
|
||||
wl = 0.;
|
||||
wu = 0.;
|
||||
}
|
||||
}
|
||||
|
||||
/* Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU.
|
||||
NWL accumulates the number of eigenvalues .le. WL,
|
||||
NWU accumulates the number of eigenvalues .le. WU */
|
||||
|
||||
*m = 0;
|
||||
iend = 0;
|
||||
*info = 0;
|
||||
nwl = 0;
|
||||
nwu = 0;
|
||||
|
||||
i__1 = *nsplit;
|
||||
for (jb = 1; jb <= i__1; ++jb) {
|
||||
ioff = iend;
|
||||
ibegin = ioff + 1;
|
||||
iend = isplit[jb];
|
||||
in = iend - ioff;
|
||||
|
||||
if (in == 1) {
|
||||
|
||||
/* Special Case -- IN=1 */
|
||||
|
||||
if (irange == 1 || wl >= d__[ibegin] - pivmin) {
|
||||
++nwl;
|
||||
}
|
||||
if (irange == 1 || wu >= d__[ibegin] - pivmin) {
|
||||
++nwu;
|
||||
}
|
||||
if (irange == 1 || wl < d__[ibegin] - pivmin && wu >= d__[ibegin]
|
||||
- pivmin) {
|
||||
++(*m);
|
||||
w[*m] = d__[ibegin];
|
||||
iblock[*m] = jb;
|
||||
}
|
||||
} else {
|
||||
|
||||
/* General Case -- IN > 1
|
||||
|
||||
Compute Gershgorin Interval
|
||||
and use it as the initial interval */
|
||||
|
||||
gu = d__[ibegin];
|
||||
gl = d__[ibegin];
|
||||
tmp1 = 0.;
|
||||
|
||||
i__2 = iend - 1;
|
||||
for (j = ibegin; j <= i__2; ++j) {
|
||||
tmp2 = (d__1 = e[j], abs(d__1));
|
||||
/* Computing MAX */
|
||||
d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
|
||||
gu = max(d__1,d__2);
|
||||
/* Computing MIN */
|
||||
d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
|
||||
gl = min(d__1,d__2);
|
||||
tmp1 = tmp2;
|
||||
/* L40: */
|
||||
}
|
||||
|
||||
/* Computing MAX */
|
||||
d__1 = gu, d__2 = d__[iend] + tmp1;
|
||||
gu = max(d__1,d__2);
|
||||
/* Computing MIN */
|
||||
d__1 = gl, d__2 = d__[iend] - tmp1;
|
||||
gl = min(d__1,d__2);
|
||||
/* Computing MAX */
|
||||
d__1 = abs(gl), d__2 = abs(gu);
|
||||
bnorm = max(d__1,d__2);
|
||||
gl = gl - bnorm * 2.1 * ulp * in - pivmin * 2.1;
|
||||
gu = gu + bnorm * 2.1 * ulp * in + pivmin * 2.1;
|
||||
|
||||
/* Compute ATOLI for the current submatrix */
|
||||
|
||||
if (*abstol <= 0.) {
|
||||
/* Computing MAX */
|
||||
d__1 = abs(gl), d__2 = abs(gu);
|
||||
atoli = ulp * max(d__1,d__2);
|
||||
} else {
|
||||
atoli = *abstol;
|
||||
}
|
||||
|
||||
if (irange > 1) {
|
||||
if (gu < wl) {
|
||||
nwl += in;
|
||||
nwu += in;
|
||||
goto L70;
|
||||
}
|
||||
gl = max(gl,wl);
|
||||
gu = min(gu,wu);
|
||||
if (gl >= gu) {
|
||||
goto L70;
|
||||
}
|
||||
}
|
||||
|
||||
/* Set Up Initial Interval */
|
||||
|
||||
work[*n + 1] = gl;
|
||||
work[*n + in + 1] = gu;
|
||||
igraphdlaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
|
||||
pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
|
||||
work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
|
||||
w[*m + 1], &iblock[*m + 1], &iinfo);
|
||||
|
||||
nwl += iwork[1];
|
||||
nwu += iwork[in + 1];
|
||||
iwoff = *m - iwork[1];
|
||||
|
||||
/* Compute Eigenvalues */
|
||||
|
||||
itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(2.)
|
||||
) + 2;
|
||||
igraphdlaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
|
||||
pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
|
||||
work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
|
||||
&w[*m + 1], &iblock[*m + 1], &iinfo);
|
||||
|
||||
/* Copy Eigenvalues Into W and IBLOCK
|
||||
Use -JB for block number for unconverged eigenvalues. */
|
||||
|
||||
i__2 = iout;
|
||||
for (j = 1; j <= i__2; ++j) {
|
||||
tmp1 = (work[j + *n] + work[j + in + *n]) * .5;
|
||||
|
||||
/* Flag non-convergence. */
|
||||
|
||||
if (j > iout - iinfo) {
|
||||
ncnvrg = TRUE_;
|
||||
ib = -jb;
|
||||
} else {
|
||||
ib = jb;
|
||||
}
|
||||
i__3 = iwork[j + in] + iwoff;
|
||||
for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
|
||||
w[je] = tmp1;
|
||||
iblock[je] = ib;
|
||||
/* L50: */
|
||||
}
|
||||
/* L60: */
|
||||
}
|
||||
|
||||
*m += im;
|
||||
}
|
||||
L70:
|
||||
;
|
||||
}
|
||||
|
||||
/* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU
|
||||
If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
|
||||
|
||||
if (irange == 3) {
|
||||
im = 0;
|
||||
idiscl = *il - 1 - nwl;
|
||||
idiscu = nwu - *iu;
|
||||
|
||||
if (idiscl > 0 || idiscu > 0) {
|
||||
i__1 = *m;
|
||||
for (je = 1; je <= i__1; ++je) {
|
||||
if (w[je] <= wlu && idiscl > 0) {
|
||||
--idiscl;
|
||||
} else if (w[je] >= wul && idiscu > 0) {
|
||||
--idiscu;
|
||||
} else {
|
||||
++im;
|
||||
w[im] = w[je];
|
||||
iblock[im] = iblock[je];
|
||||
}
|
||||
/* L80: */
|
||||
}
|
||||
*m = im;
|
||||
}
|
||||
if (idiscl > 0 || idiscu > 0) {
|
||||
|
||||
/* Code to deal with effects of bad arithmetic:
|
||||
Some low eigenvalues to be discarded are not in (WL,WLU],
|
||||
or high eigenvalues to be discarded are not in (WUL,WU]
|
||||
so just kill off the smallest IDISCL/largest IDISCU
|
||||
eigenvalues, by simply finding the smallest/largest
|
||||
eigenvalue(s).
|
||||
|
||||
(If N(w) is monotone non-decreasing, this should never
|
||||
happen.) */
|
||||
|
||||
if (idiscl > 0) {
|
||||
wkill = wu;
|
||||
i__1 = idiscl;
|
||||
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
|
||||
iw = 0;
|
||||
i__2 = *m;
|
||||
for (je = 1; je <= i__2; ++je) {
|
||||
if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
|
||||
iw = je;
|
||||
wkill = w[je];
|
||||
}
|
||||
/* L90: */
|
||||
}
|
||||
iblock[iw] = 0;
|
||||
/* L100: */
|
||||
}
|
||||
}
|
||||
if (idiscu > 0) {
|
||||
|
||||
wkill = wl;
|
||||
i__1 = idiscu;
|
||||
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
|
||||
iw = 0;
|
||||
i__2 = *m;
|
||||
for (je = 1; je <= i__2; ++je) {
|
||||
if (iblock[je] != 0 && (w[je] > wkill || iw == 0)) {
|
||||
iw = je;
|
||||
wkill = w[je];
|
||||
}
|
||||
/* L110: */
|
||||
}
|
||||
iblock[iw] = 0;
|
||||
/* L120: */
|
||||
}
|
||||
}
|
||||
im = 0;
|
||||
i__1 = *m;
|
||||
for (je = 1; je <= i__1; ++je) {
|
||||
if (iblock[je] != 0) {
|
||||
++im;
|
||||
w[im] = w[je];
|
||||
iblock[im] = iblock[je];
|
||||
}
|
||||
/* L130: */
|
||||
}
|
||||
*m = im;
|
||||
}
|
||||
if (idiscl < 0 || idiscu < 0) {
|
||||
toofew = TRUE_;
|
||||
}
|
||||
}
|
||||
|
||||
/* If ORDER='B', do nothing -- the eigenvalues are already sorted
|
||||
by block.
|
||||
If ORDER='E', sort the eigenvalues from smallest to largest */
|
||||
|
||||
if (iorder == 1 && *nsplit > 1) {
|
||||
i__1 = *m - 1;
|
||||
for (je = 1; je <= i__1; ++je) {
|
||||
ie = 0;
|
||||
tmp1 = w[je];
|
||||
i__2 = *m;
|
||||
for (j = je + 1; j <= i__2; ++j) {
|
||||
if (w[j] < tmp1) {
|
||||
ie = j;
|
||||
tmp1 = w[j];
|
||||
}
|
||||
/* L140: */
|
||||
}
|
||||
|
||||
if (ie != 0) {
|
||||
itmp1 = iblock[ie];
|
||||
w[ie] = w[je];
|
||||
iblock[ie] = iblock[je];
|
||||
w[je] = tmp1;
|
||||
iblock[je] = itmp1;
|
||||
}
|
||||
/* L150: */
|
||||
}
|
||||
}
|
||||
|
||||
*info = 0;
|
||||
if (ncnvrg) {
|
||||
++(*info);
|
||||
}
|
||||
if (toofew) {
|
||||
*info += 2;
|
||||
}
|
||||
return 0;
|
||||
|
||||
/* End of DSTEBZ */
|
||||
|
||||
} /* igraphdstebz_ */
|
||||
|
||||
Reference in New Issue
Block a user