Add graph references
This commit is contained in:
Abdelrahman Said
+811
@@ -0,0 +1,811 @@
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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__0 = 0;
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static integer c_n1 = -1;
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/* > \brief <b> DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE mat
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rices</b>
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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 DGEEVX + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeevx.
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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/dgeevx.
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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/dgeevx.
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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 DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,
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VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,
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RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )
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CHARACTER BALANC, JOBVL, JOBVR, SENSE
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INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
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DOUBLE PRECISION ABNRM
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INTEGER IWORK( * )
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DOUBLE PRECISION A( LDA, * ), RCONDE( * ), RCONDV( * ),
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$ SCALE( * ), VL( LDVL, * ), VR( LDVR, * ),
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$ WI( * ), WORK( * ), WR( * )
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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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> DGEEVX computes for an N-by-N real nonsymmetric matrix A, the
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> eigenvalues and, optionally, the left and/or right eigenvectors.
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>
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> Optionally also, it computes a balancing transformation to improve
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> the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
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> SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
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> (RCONDE), and reciprocal condition numbers for the right
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> eigenvectors (RCONDV).
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>
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> The right eigenvector v(j) of A satisfies
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> A * v(j) = lambda(j) * v(j)
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> where lambda(j) is its eigenvalue.
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> The left eigenvector u(j) of A satisfies
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> u(j)**H * A = lambda(j) * u(j)**H
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> where u(j)**H denotes the conjugate-transpose of u(j).
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>
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> The computed eigenvectors are normalized to have Euclidean norm
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> equal to 1 and largest component real.
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>
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> Balancing a matrix means permuting the rows and columns to make it
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> more nearly upper triangular, and applying a diagonal similarity
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> transformation D * A * D**(-1), where D is a diagonal matrix, to
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> make its rows and columns closer in norm and the condition numbers
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> of its eigenvalues and eigenvectors smaller. The computed
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> reciprocal condition numbers correspond to the balanced matrix.
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> Permuting rows and columns will not change the condition numbers
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> (in exact arithmetic) but diagonal scaling will. For further
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> explanation of balancing, see section 4.10.2 of the LAPACK
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> Users' Guide.
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> \endverbatim
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Arguments:
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==========
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> \param[in] BALANC
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> \verbatim
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> BALANC is CHARACTER*1
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> Indicates how the input matrix should be diagonally scaled
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> and/or permuted to improve the conditioning of its
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> eigenvalues.
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> = 'N': Do not diagonally scale or permute;
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> = 'P': Perform permutations to make the matrix more nearly
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> upper triangular. Do not diagonally scale;
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> = 'S': Diagonally scale the matrix, i.e. replace A by
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> D*A*D**(-1), where D is a diagonal matrix chosen
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> to make the rows and columns of A more equal in
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> norm. Do not permute;
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> = 'B': Both diagonally scale and permute A.
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>
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> Computed reciprocal condition numbers will be for the matrix
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> after balancing and/or permuting. Permuting does not change
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> condition numbers (in exact arithmetic), but balancing does.
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> \endverbatim
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>
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> \param[in] JOBVL
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> \verbatim
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> JOBVL is CHARACTER*1
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> = 'N': left eigenvectors of A are not computed;
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> = 'V': left eigenvectors of A are computed.
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> If SENSE = 'E' or 'B', JOBVL must = 'V'.
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> \endverbatim
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>
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> \param[in] JOBVR
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> \verbatim
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> JOBVR is CHARACTER*1
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> = 'N': right eigenvectors of A are not computed;
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> = 'V': right eigenvectors of A are computed.
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> If SENSE = 'E' or 'B', JOBVR must = 'V'.
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> \endverbatim
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>
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> \param[in] SENSE
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> \verbatim
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> SENSE is CHARACTER*1
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> Determines which reciprocal condition numbers are computed.
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> = 'N': None are computed;
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> = 'E': Computed for eigenvalues only;
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> = 'V': Computed for right eigenvectors only;
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> = 'B': Computed for eigenvalues and right eigenvectors.
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>
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> If SENSE = 'E' or 'B', both left and right eigenvectors
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> must also be computed (JOBVL = 'V' and JOBVR = 'V').
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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 A. N >= 0.
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> \endverbatim
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>
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> \param[in,out] A
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> \verbatim
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> A is DOUBLE PRECISION array, dimension (LDA,N)
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> On entry, the N-by-N matrix A.
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> On exit, A has been overwritten. If JOBVL = 'V' or
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> JOBVR = 'V', A contains the real Schur form of the balanced
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> version of the input matrix A.
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> \endverbatim
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>
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> \param[in] LDA
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> \verbatim
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> LDA is INTEGER
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> The leading dimension of the array A. LDA >= max(1,N).
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> \endverbatim
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>
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> \param[out] WR
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> \verbatim
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> WR is DOUBLE PRECISION array, dimension (N)
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> \endverbatim
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>
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> \param[out] WI
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> \verbatim
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> WI is DOUBLE PRECISION array, dimension (N)
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> WR and WI contain the real and imaginary parts,
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> respectively, of the computed eigenvalues. Complex
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> conjugate pairs of eigenvalues will appear consecutively
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> with the eigenvalue having the positive imaginary part
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> first.
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> \endverbatim
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>
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> \param[out] VL
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> \verbatim
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> VL is DOUBLE PRECISION array, dimension (LDVL,N)
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> If JOBVL = 'V', the left eigenvectors u(j) are stored one
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> after another in the columns of VL, in the same order
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> as their eigenvalues.
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> If JOBVL = 'N', VL is not referenced.
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> If the j-th eigenvalue is real, then u(j) = VL(:,j),
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> the j-th column of VL.
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> If the j-th and (j+1)-st eigenvalues form a complex
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> conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
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> u(j+1) = VL(:,j) - i*VL(:,j+1).
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> \endverbatim
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>
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> \param[in] LDVL
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> \verbatim
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> LDVL is INTEGER
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> The leading dimension of the array VL. LDVL >= 1; if
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> JOBVL = 'V', LDVL >= N.
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> \endverbatim
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>
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> \param[out] VR
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> \verbatim
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> VR is DOUBLE PRECISION array, dimension (LDVR,N)
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> If JOBVR = 'V', the right eigenvectors v(j) are stored one
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> after another in the columns of VR, in the same order
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> as their eigenvalues.
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> If JOBVR = 'N', VR is not referenced.
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> If the j-th eigenvalue is real, then v(j) = VR(:,j),
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> the j-th column of VR.
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> If the j-th and (j+1)-st eigenvalues form a complex
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> conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
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> v(j+1) = VR(:,j) - i*VR(:,j+1).
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> \endverbatim
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>
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> \param[in] LDVR
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> \verbatim
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> LDVR is INTEGER
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> The leading dimension of the array VR. LDVR >= 1, and if
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> JOBVR = 'V', LDVR >= N.
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> \endverbatim
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>
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> \param[out] ILO
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> \verbatim
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> ILO is INTEGER
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> \endverbatim
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>
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> \param[out] IHI
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> \verbatim
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> IHI is INTEGER
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> ILO and IHI are integer values determined when A was
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> balanced. The balanced A(i,j) = 0 if I > J and
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> J = 1,...,ILO-1 or I = IHI+1,...,N.
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> \endverbatim
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>
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> \param[out] SCALE
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> \verbatim
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> SCALE is DOUBLE PRECISION array, dimension (N)
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> Details of the permutations and scaling factors applied
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> when balancing A. If P(j) is the index of the row and column
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> interchanged with row and column j, and D(j) is the scaling
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> factor applied to row and column j, then
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> SCALE(J) = P(J), for J = 1,...,ILO-1
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> = D(J), for J = ILO,...,IHI
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> = P(J) for J = IHI+1,...,N.
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> The order in which the interchanges are made is N to IHI+1,
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> then 1 to ILO-1.
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> \endverbatim
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>
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> \param[out] ABNRM
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> \verbatim
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> ABNRM is DOUBLE PRECISION
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> The one-norm of the balanced matrix (the maximum
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> of the sum of absolute values of elements of any column).
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> \endverbatim
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>
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> \param[out] RCONDE
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> \verbatim
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> RCONDE is DOUBLE PRECISION array, dimension (N)
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> RCONDE(j) is the reciprocal condition number of the j-th
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> eigenvalue.
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> \endverbatim
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>
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> \param[out] RCONDV
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> \verbatim
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> RCONDV is DOUBLE PRECISION array, dimension (N)
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> RCONDV(j) is the reciprocal condition number of the j-th
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> right eigenvector.
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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,LWORK))
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> On exit, if INFO = 0, WORK(1) returns the optimal 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. If SENSE = 'N' or 'E',
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> LWORK >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V',
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> LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6).
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> For good performance, LWORK must generally be larger.
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>
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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 (2*N-2)
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> If SENSE = 'N' or 'E', 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: if INFO = i, the QR algorithm failed to compute all the
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> eigenvalues, and no eigenvectors or condition numbers
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> have been computed; elements 1:ILO-1 and i+1:N of WR
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> and WI contain eigenvalues which have converged.
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> \endverbatim
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Authors:
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========
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> \author Univ. of Tennessee
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> \author Univ. of California Berkeley
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> \author Univ. of Colorado Denver
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> \author NAG Ltd.
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> \date September 2012
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> \ingroup doubleGEeigen
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||||
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=====================================================================
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Subroutine */ int igraphdgeevx_(char *balanc, char *jobvl, char *jobvr, char *
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sense, integer *n, doublereal *a, integer *lda, doublereal *wr,
|
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doublereal *wi, doublereal *vl, integer *ldvl, doublereal *vr,
|
||||
integer *ldvr, integer *ilo, integer *ihi, doublereal *scale,
|
||||
doublereal *abnrm, doublereal *rconde, doublereal *rcondv, doublereal
|
||||
*work, integer *lwork, integer *iwork, integer *info)
|
||||
{
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||||
/* System generated locals */
|
||||
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
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||||
i__2, i__3;
|
||||
doublereal d__1, d__2;
|
||||
|
||||
/* Builtin functions */
|
||||
double sqrt(doublereal);
|
||||
|
||||
/* Local variables */
|
||||
integer i__, k;
|
||||
doublereal r__, cs, sn;
|
||||
char job[1];
|
||||
doublereal scl, dum[1], eps;
|
||||
char side[1];
|
||||
doublereal anrm;
|
||||
integer ierr, itau;
|
||||
extern /* Subroutine */ int igraphdrot_(integer *, doublereal *, integer *,
|
||||
doublereal *, integer *, doublereal *, doublereal *);
|
||||
integer iwrk, nout;
|
||||
extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
|
||||
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
|
||||
integer *);
|
||||
integer icond;
|
||||
extern logical igraphlsame_(char *, char *);
|
||||
extern doublereal igraphdlapy2_(doublereal *, doublereal *);
|
||||
extern /* Subroutine */ int igraphdlabad_(doublereal *, doublereal *), igraphdgebak_(
|
||||
char *, char *, integer *, integer *, integer *, doublereal *,
|
||||
integer *, doublereal *, integer *, integer *),
|
||||
igraphdgebal_(char *, integer *, doublereal *, integer *, integer *,
|
||||
integer *, doublereal *, integer *);
|
||||
logical scalea;
|
||||
extern doublereal igraphdlamch_(char *);
|
||||
doublereal cscale;
|
||||
extern doublereal igraphdlange_(char *, integer *, integer *, doublereal *,
|
||||
integer *, doublereal *);
|
||||
extern /* Subroutine */ int igraphdgehrd_(integer *, integer *, integer *,
|
||||
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
||||
integer *), igraphdlascl_(char *, integer *, integer *, doublereal *,
|
||||
doublereal *, integer *, integer *, doublereal *, integer *,
|
||||
integer *);
|
||||
extern integer igraphidamax_(integer *, doublereal *, integer *);
|
||||
extern /* Subroutine */ int igraphdlacpy_(char *, integer *, integer *,
|
||||
doublereal *, integer *, doublereal *, integer *),
|
||||
igraphdlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
|
||||
doublereal *), igraphxerbla_(char *, integer *, ftnlen);
|
||||
logical select[1];
|
||||
extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
|
||||
integer *, integer *, ftnlen, ftnlen);
|
||||
doublereal bignum;
|
||||
extern /* Subroutine */ int igraphdorghr_(integer *, integer *, integer *,
|
||||
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
||||
integer *), igraphdhseqr_(char *, char *, integer *, integer *, integer
|
||||
*, doublereal *, integer *, doublereal *, doublereal *,
|
||||
doublereal *, integer *, doublereal *, integer *, integer *), igraphdtrevc_(char *, char *, logical *, integer *,
|
||||
doublereal *, integer *, doublereal *, integer *, doublereal *,
|
||||
integer *, integer *, integer *, doublereal *, integer *), igraphdtrsna_(char *, char *, logical *, integer *, doublereal
|
||||
*, integer *, doublereal *, integer *, doublereal *, integer *,
|
||||
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
||||
integer *, integer *, integer *);
|
||||
integer minwrk, maxwrk;
|
||||
logical wantvl, wntsnb;
|
||||
integer hswork;
|
||||
logical wntsne;
|
||||
doublereal smlnum;
|
||||
logical lquery, wantvr, wntsnn, wntsnv;
|
||||
|
||||
|
||||
/* -- LAPACK driver routine (version 3.4.2) --
|
||||
-- LAPACK is a software package provided by Univ. of Tennessee, --
|
||||
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
September 2012
|
||||
|
||||
|
||||
=====================================================================
|
||||
|
||||
|
||||
Test the input arguments
|
||||
|
||||
Parameter adjustments */
|
||||
a_dim1 = *lda;
|
||||
a_offset = 1 + a_dim1;
|
||||
a -= a_offset;
|
||||
--wr;
|
||||
--wi;
|
||||
vl_dim1 = *ldvl;
|
||||
vl_offset = 1 + vl_dim1;
|
||||
vl -= vl_offset;
|
||||
vr_dim1 = *ldvr;
|
||||
vr_offset = 1 + vr_dim1;
|
||||
vr -= vr_offset;
|
||||
--scale;
|
||||
--rconde;
|
||||
--rcondv;
|
||||
--work;
|
||||
--iwork;
|
||||
|
||||
/* Function Body */
|
||||
*info = 0;
|
||||
lquery = *lwork == -1;
|
||||
wantvl = igraphlsame_(jobvl, "V");
|
||||
wantvr = igraphlsame_(jobvr, "V");
|
||||
wntsnn = igraphlsame_(sense, "N");
|
||||
wntsne = igraphlsame_(sense, "E");
|
||||
wntsnv = igraphlsame_(sense, "V");
|
||||
wntsnb = igraphlsame_(sense, "B");
|
||||
if (! (igraphlsame_(balanc, "N") || igraphlsame_(balanc, "S") || igraphlsame_(balanc, "P")
|
||||
|| igraphlsame_(balanc, "B"))) {
|
||||
*info = -1;
|
||||
} else if (! wantvl && ! igraphlsame_(jobvl, "N")) {
|
||||
*info = -2;
|
||||
} else if (! wantvr && ! igraphlsame_(jobvr, "N")) {
|
||||
*info = -3;
|
||||
} else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb)
|
||||
&& ! (wantvl && wantvr)) {
|
||||
*info = -4;
|
||||
} else if (*n < 0) {
|
||||
*info = -5;
|
||||
} else if (*lda < max(1,*n)) {
|
||||
*info = -7;
|
||||
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
|
||||
*info = -11;
|
||||
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
|
||||
*info = -13;
|
||||
}
|
||||
|
||||
/* Compute workspace
|
||||
(Note: Comments in the code beginning "Workspace:" describe the
|
||||
minimal amount of workspace needed at that point in the code,
|
||||
as well as the preferred amount for good performance.
|
||||
NB refers to the optimal block size for the immediately
|
||||
following subroutine, as returned by ILAENV.
|
||||
HSWORK refers to the workspace preferred by DHSEQR, as
|
||||
calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
|
||||
the worst case.) */
|
||||
|
||||
if (*info == 0) {
|
||||
if (*n == 0) {
|
||||
minwrk = 1;
|
||||
maxwrk = 1;
|
||||
} else {
|
||||
maxwrk = *n + *n * igraphilaenv_(&c__1, "DGEHRD", " ", n, &c__1, n, &
|
||||
c__0, (ftnlen)6, (ftnlen)1);
|
||||
|
||||
if (wantvl) {
|
||||
igraphdhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
|
||||
1], &vl[vl_offset], ldvl, &work[1], &c_n1, info);
|
||||
} else if (wantvr) {
|
||||
igraphdhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
|
||||
1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
|
||||
} else {
|
||||
if (wntsnn) {
|
||||
igraphdhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &wr[1],
|
||||
&wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1,
|
||||
info);
|
||||
} else {
|
||||
igraphdhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &wr[1],
|
||||
&wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1,
|
||||
info);
|
||||
}
|
||||
}
|
||||
hswork = (integer) work[1];
|
||||
|
||||
if (! wantvl && ! wantvr) {
|
||||
minwrk = *n << 1;
|
||||
if (! wntsnn) {
|
||||
/* Computing MAX */
|
||||
i__1 = minwrk, i__2 = *n * *n + *n * 6;
|
||||
minwrk = max(i__1,i__2);
|
||||
}
|
||||
maxwrk = max(maxwrk,hswork);
|
||||
if (! wntsnn) {
|
||||
/* Computing MAX */
|
||||
i__1 = maxwrk, i__2 = *n * *n + *n * 6;
|
||||
maxwrk = max(i__1,i__2);
|
||||
}
|
||||
} else {
|
||||
minwrk = *n * 3;
|
||||
if (! wntsnn && ! wntsne) {
|
||||
/* Computing MAX */
|
||||
i__1 = minwrk, i__2 = *n * *n + *n * 6;
|
||||
minwrk = max(i__1,i__2);
|
||||
}
|
||||
maxwrk = max(maxwrk,hswork);
|
||||
/* Computing MAX */
|
||||
i__1 = maxwrk, i__2 = *n + (*n - 1) * igraphilaenv_(&c__1, "DORGHR",
|
||||
" ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
|
||||
maxwrk = max(i__1,i__2);
|
||||
if (! wntsnn && ! wntsne) {
|
||||
/* Computing MAX */
|
||||
i__1 = maxwrk, i__2 = *n * *n + *n * 6;
|
||||
maxwrk = max(i__1,i__2);
|
||||
}
|
||||
/* Computing MAX */
|
||||
i__1 = maxwrk, i__2 = *n * 3;
|
||||
maxwrk = max(i__1,i__2);
|
||||
}
|
||||
maxwrk = max(maxwrk,minwrk);
|
||||
}
|
||||
work[1] = (doublereal) maxwrk;
|
||||
|
||||
if (*lwork < minwrk && ! lquery) {
|
||||
*info = -21;
|
||||
}
|
||||
}
|
||||
|
||||
if (*info != 0) {
|
||||
i__1 = -(*info);
|
||||
igraphxerbla_("DGEEVX", &i__1, (ftnlen)6);
|
||||
return 0;
|
||||
} else if (lquery) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Quick return if possible */
|
||||
|
||||
if (*n == 0) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Get machine constants */
|
||||
|
||||
eps = igraphdlamch_("P");
|
||||
smlnum = igraphdlamch_("S");
|
||||
bignum = 1. / smlnum;
|
||||
igraphdlabad_(&smlnum, &bignum);
|
||||
smlnum = sqrt(smlnum) / eps;
|
||||
bignum = 1. / smlnum;
|
||||
|
||||
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
|
||||
|
||||
icond = 0;
|
||||
anrm = igraphdlange_("M", n, n, &a[a_offset], lda, dum);
|
||||
scalea = FALSE_;
|
||||
if (anrm > 0. && anrm < smlnum) {
|
||||
scalea = TRUE_;
|
||||
cscale = smlnum;
|
||||
} else if (anrm > bignum) {
|
||||
scalea = TRUE_;
|
||||
cscale = bignum;
|
||||
}
|
||||
if (scalea) {
|
||||
igraphdlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
|
||||
ierr);
|
||||
}
|
||||
|
||||
/* Balance the matrix and compute ABNRM */
|
||||
|
||||
igraphdgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
|
||||
*abnrm = igraphdlange_("1", n, n, &a[a_offset], lda, dum);
|
||||
if (scalea) {
|
||||
dum[0] = *abnrm;
|
||||
igraphdlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
|
||||
ierr);
|
||||
*abnrm = dum[0];
|
||||
}
|
||||
|
||||
/* Reduce to upper Hessenberg form
|
||||
(Workspace: need 2*N, prefer N+N*NB) */
|
||||
|
||||
itau = 1;
|
||||
iwrk = itau + *n;
|
||||
i__1 = *lwork - iwrk + 1;
|
||||
igraphdgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &
|
||||
ierr);
|
||||
|
||||
if (wantvl) {
|
||||
|
||||
/* Want left eigenvectors
|
||||
Copy Householder vectors to VL */
|
||||
|
||||
*(unsigned char *)side = 'L';
|
||||
igraphdlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
|
||||
;
|
||||
|
||||
/* Generate orthogonal matrix in VL
|
||||
(Workspace: need 2*N-1, prefer N+(N-1)*NB) */
|
||||
|
||||
i__1 = *lwork - iwrk + 1;
|
||||
igraphdorghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
|
||||
i__1, &ierr);
|
||||
|
||||
/* Perform QR iteration, accumulating Schur vectors in VL
|
||||
(Workspace: need 1, prefer HSWORK (see comments) ) */
|
||||
|
||||
iwrk = itau;
|
||||
i__1 = *lwork - iwrk + 1;
|
||||
igraphdhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vl[
|
||||
vl_offset], ldvl, &work[iwrk], &i__1, info);
|
||||
|
||||
if (wantvr) {
|
||||
|
||||
/* Want left and right eigenvectors
|
||||
Copy Schur vectors to VR */
|
||||
|
||||
*(unsigned char *)side = 'B';
|
||||
igraphdlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
|
||||
}
|
||||
|
||||
} else if (wantvr) {
|
||||
|
||||
/* Want right eigenvectors
|
||||
Copy Householder vectors to VR */
|
||||
|
||||
*(unsigned char *)side = 'R';
|
||||
igraphdlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
|
||||
;
|
||||
|
||||
/* Generate orthogonal matrix in VR
|
||||
(Workspace: need 2*N-1, prefer N+(N-1)*NB) */
|
||||
|
||||
i__1 = *lwork - iwrk + 1;
|
||||
igraphdorghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
|
||||
i__1, &ierr);
|
||||
|
||||
/* Perform QR iteration, accumulating Schur vectors in VR
|
||||
(Workspace: need 1, prefer HSWORK (see comments) ) */
|
||||
|
||||
iwrk = itau;
|
||||
i__1 = *lwork - iwrk + 1;
|
||||
igraphdhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vr[
|
||||
vr_offset], ldvr, &work[iwrk], &i__1, info);
|
||||
|
||||
} else {
|
||||
|
||||
/* Compute eigenvalues only
|
||||
If condition numbers desired, compute Schur form */
|
||||
|
||||
if (wntsnn) {
|
||||
*(unsigned char *)job = 'E';
|
||||
} else {
|
||||
*(unsigned char *)job = 'S';
|
||||
}
|
||||
|
||||
/* (Workspace: need 1, prefer HSWORK (see comments) ) */
|
||||
|
||||
iwrk = itau;
|
||||
i__1 = *lwork - iwrk + 1;
|
||||
igraphdhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vr[
|
||||
vr_offset], ldvr, &work[iwrk], &i__1, info);
|
||||
}
|
||||
|
||||
/* If INFO > 0 from DHSEQR, then quit */
|
||||
|
||||
if (*info > 0) {
|
||||
goto L50;
|
||||
}
|
||||
|
||||
if (wantvl || wantvr) {
|
||||
|
||||
/* Compute left and/or right eigenvectors
|
||||
(Workspace: need 3*N) */
|
||||
|
||||
igraphdtrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
|
||||
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &ierr);
|
||||
}
|
||||
|
||||
/* Compute condition numbers if desired
|
||||
(Workspace: need N*N+6*N unless SENSE = 'E') */
|
||||
|
||||
if (! wntsnn) {
|
||||
igraphdtrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset],
|
||||
ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout,
|
||||
&work[iwrk], n, &iwork[1], &icond);
|
||||
}
|
||||
|
||||
if (wantvl) {
|
||||
|
||||
/* Undo balancing of left eigenvectors */
|
||||
|
||||
igraphdgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl,
|
||||
&ierr);
|
||||
|
||||
/* Normalize left eigenvectors and make largest component real */
|
||||
|
||||
i__1 = *n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if (wi[i__] == 0.) {
|
||||
scl = 1. / igraphdnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
|
||||
igraphdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
|
||||
} else if (wi[i__] > 0.) {
|
||||
d__1 = igraphdnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
|
||||
d__2 = igraphdnrm2_(n, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
|
||||
scl = 1. / igraphdlapy2_(&d__1, &d__2);
|
||||
igraphdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
|
||||
igraphdscal_(n, &scl, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
|
||||
i__2 = *n;
|
||||
for (k = 1; k <= i__2; ++k) {
|
||||
/* Computing 2nd power */
|
||||
d__1 = vl[k + i__ * vl_dim1];
|
||||
/* Computing 2nd power */
|
||||
d__2 = vl[k + (i__ + 1) * vl_dim1];
|
||||
work[k] = d__1 * d__1 + d__2 * d__2;
|
||||
/* L10: */
|
||||
}
|
||||
k = igraphidamax_(n, &work[1], &c__1);
|
||||
igraphdlartg_(&vl[k + i__ * vl_dim1], &vl[k + (i__ + 1) * vl_dim1],
|
||||
&cs, &sn, &r__);
|
||||
igraphdrot_(n, &vl[i__ * vl_dim1 + 1], &c__1, &vl[(i__ + 1) *
|
||||
vl_dim1 + 1], &c__1, &cs, &sn);
|
||||
vl[k + (i__ + 1) * vl_dim1] = 0.;
|
||||
}
|
||||
/* L20: */
|
||||
}
|
||||
}
|
||||
|
||||
if (wantvr) {
|
||||
|
||||
/* Undo balancing of right eigenvectors */
|
||||
|
||||
igraphdgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr,
|
||||
&ierr);
|
||||
|
||||
/* Normalize right eigenvectors and make largest component real */
|
||||
|
||||
i__1 = *n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if (wi[i__] == 0.) {
|
||||
scl = 1. / igraphdnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
|
||||
igraphdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
|
||||
} else if (wi[i__] > 0.) {
|
||||
d__1 = igraphdnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
|
||||
d__2 = igraphdnrm2_(n, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
|
||||
scl = 1. / igraphdlapy2_(&d__1, &d__2);
|
||||
igraphdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
|
||||
igraphdscal_(n, &scl, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
|
||||
i__2 = *n;
|
||||
for (k = 1; k <= i__2; ++k) {
|
||||
/* Computing 2nd power */
|
||||
d__1 = vr[k + i__ * vr_dim1];
|
||||
/* Computing 2nd power */
|
||||
d__2 = vr[k + (i__ + 1) * vr_dim1];
|
||||
work[k] = d__1 * d__1 + d__2 * d__2;
|
||||
/* L30: */
|
||||
}
|
||||
k = igraphidamax_(n, &work[1], &c__1);
|
||||
igraphdlartg_(&vr[k + i__ * vr_dim1], &vr[k + (i__ + 1) * vr_dim1],
|
||||
&cs, &sn, &r__);
|
||||
igraphdrot_(n, &vr[i__ * vr_dim1 + 1], &c__1, &vr[(i__ + 1) *
|
||||
vr_dim1 + 1], &c__1, &cs, &sn);
|
||||
vr[k + (i__ + 1) * vr_dim1] = 0.;
|
||||
}
|
||||
/* L40: */
|
||||
}
|
||||
}
|
||||
|
||||
/* Undo scaling if necessary */
|
||||
|
||||
L50:
|
||||
if (scalea) {
|
||||
i__1 = *n - *info;
|
||||
/* Computing MAX */
|
||||
i__3 = *n - *info;
|
||||
i__2 = max(i__3,1);
|
||||
igraphdlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[*info +
|
||||
1], &i__2, &ierr);
|
||||
i__1 = *n - *info;
|
||||
/* Computing MAX */
|
||||
i__3 = *n - *info;
|
||||
i__2 = max(i__3,1);
|
||||
igraphdlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[*info +
|
||||
1], &i__2, &ierr);
|
||||
if (*info == 0) {
|
||||
if ((wntsnv || wntsnb) && icond == 0) {
|
||||
igraphdlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[
|
||||
1], n, &ierr);
|
||||
}
|
||||
} else {
|
||||
i__1 = *ilo - 1;
|
||||
igraphdlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[1],
|
||||
n, &ierr);
|
||||
i__1 = *ilo - 1;
|
||||
igraphdlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[1],
|
||||
n, &ierr);
|
||||
}
|
||||
}
|
||||
|
||||
work[1] = (doublereal) maxwrk;
|
||||
return 0;
|
||||
|
||||
/* End of DGEEVX */
|
||||
|
||||
} /* igraphdgeevx_ */
|
||||
|
||||
Reference in New Issue
Block a user