Abdelrahman Said
712 lines
22 KiB
C
712 lines
22 KiB
C
/* -- 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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/* > \brief \b DLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using th
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e double-shift/single-shift QR algorithm.
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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 DLAHQR + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahqr.
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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/dlahqr.
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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/dlahqr.
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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 DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
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ILOZ, IHIZ, Z, LDZ, INFO )
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INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
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LOGICAL WANTT, WANTZ
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DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), 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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> DLAHQR is an auxiliary routine called by DHSEQR to update the
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> eigenvalues and Schur decomposition already computed by DHSEQR, by
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> dealing with the Hessenberg submatrix in rows and columns ILO to
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> IHI.
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> \endverbatim
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Arguments:
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==========
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> \param[in] WANTT
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> \verbatim
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> WANTT is LOGICAL
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> = .TRUE. : the full Schur form T is required;
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> = .FALSE.: only eigenvalues are required.
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> \endverbatim
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>
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> \param[in] WANTZ
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> \verbatim
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> WANTZ is LOGICAL
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> = .TRUE. : the matrix of Schur vectors Z is required;
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> = .FALSE.: Schur vectors are not required.
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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 H. N >= 0.
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> \endverbatim
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>
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> \param[in] 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[in] IHI
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> \verbatim
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> IHI is INTEGER
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> It is assumed that H is already upper quasi-triangular in
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> rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless
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> ILO = 1). DLAHQR works primarily with the Hessenberg
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> submatrix in rows and columns ILO to IHI, but applies
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> transformations to all of H if WANTT is .TRUE..
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> 1 <= ILO <= max(1,IHI); IHI <= N.
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> \endverbatim
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>
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> \param[in,out] H
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> \verbatim
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> H is DOUBLE PRECISION array, dimension (LDH,N)
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> On entry, the upper Hessenberg matrix H.
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> On exit, if INFO is zero and if WANTT is .TRUE., H is upper
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> quasi-triangular in rows and columns ILO:IHI, with any
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> 2-by-2 diagonal blocks in standard form. If INFO is zero
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> and WANTT is .FALSE., the contents of H are unspecified on
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> exit. The output state of H if INFO is nonzero is given
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> below under the description of INFO.
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> \endverbatim
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>
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> \param[in] LDH
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> \verbatim
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> LDH is INTEGER
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> The leading dimension of the array H. LDH >= 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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> The real and imaginary parts, respectively, of the computed
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> eigenvalues ILO to IHI are stored in the corresponding
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> elements of WR and WI. If two eigenvalues are computed as a
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> complex conjugate pair, they are stored in consecutive
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> elements of WR and WI, say the i-th and (i+1)th, with
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> WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the
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> eigenvalues are stored in the same order as on the diagonal
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> of the Schur form returned in H, with WR(i) = H(i,i), and, if
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> H(i:i+1,i:i+1) is a 2-by-2 diagonal block,
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> WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).
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> \endverbatim
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>
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> \param[in] ILOZ
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> \verbatim
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> ILOZ is INTEGER
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> \endverbatim
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>
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> \param[in] IHIZ
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> \verbatim
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> IHIZ is INTEGER
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> Specify the rows of Z to which transformations must be
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> applied if WANTZ is .TRUE..
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> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
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> \endverbatim
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>
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> \param[in,out] Z
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> \verbatim
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> Z is DOUBLE PRECISION array, dimension (LDZ,N)
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> If WANTZ is .TRUE., on entry Z must contain the current
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> matrix Z of transformations accumulated by DHSEQR, and on
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> exit Z has been updated; transformations are applied only to
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> the submatrix Z(ILOZ:IHIZ,ILO:IHI).
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> If WANTZ is .FALSE., Z is not referenced.
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> \endverbatim
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>
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> \param[in] LDZ
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> \verbatim
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> LDZ is INTEGER
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> The leading dimension of the array Z. LDZ >= max(1,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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> .GT. 0: If INFO = i, DLAHQR failed to compute all the
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> eigenvalues ILO to IHI in a total of 30 iterations
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> per eigenvalue; elements i+1:ihi of WR and WI
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> contain those eigenvalues which have been
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> successfully computed.
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>
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> If INFO .GT. 0 and WANTT is .FALSE., then on exit,
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> the remaining unconverged eigenvalues are the
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> eigenvalues of the upper Hessenberg matrix rows
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> and columns ILO thorugh INFO of the final, output
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> value of H.
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>
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> If INFO .GT. 0 and WANTT is .TRUE., then on exit
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> (*) (initial value of H)*U = U*(final value of H)
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> where U is an orthognal matrix. The final
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> value of H is upper Hessenberg and triangular in
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> rows and columns INFO+1 through IHI.
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>
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> If INFO .GT. 0 and WANTZ is .TRUE., then on exit
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> (final value of Z) = (initial value of Z)*U
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> where U is the orthogonal matrix in (*)
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> (regardless of the value of WANTT.)
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> \endverbatim
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Authors:
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========
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> \author Univ. of Tennessee
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> \author Univ. of California Berkeley
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> \author Univ. of Colorado Denver
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> \author NAG Ltd.
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> \date September 2012
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> \ingroup doubleOTHERauxiliary
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> \par Further Details:
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=====================
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>
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> \verbatim
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>
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> 02-96 Based on modifications by
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> David Day, Sandia National Laboratory, USA
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>
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> 12-04 Further modifications by
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> Ralph Byers, University of Kansas, USA
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> This is a modified version of DLAHQR from LAPACK version 3.0.
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> It is (1) more robust against overflow and underflow and
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> (2) adopts the more conservative Ahues & Tisseur stopping
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> criterion (LAWN 122, 1997).
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> \endverbatim
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>
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=====================================================================
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Subroutine */ int igraphdlahqr_(logical *wantt, logical *wantz, integer *n,
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integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal
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*wr, doublereal *wi, integer *iloz, integer *ihiz, doublereal *z__,
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integer *ldz, integer *info)
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{
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/* System generated locals */
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integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3;
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doublereal d__1, d__2, d__3, d__4;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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integer i__, j, k, l, m;
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doublereal s, v[3];
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integer i1, i2;
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doublereal t1, t2, t3, v2, v3, aa, ab, ba, bb, h11, h12, h21, h22, cs;
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integer nh;
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doublereal sn;
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integer nr;
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doublereal tr;
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integer nz;
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doublereal det, h21s;
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integer its;
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doublereal ulp, sum, tst, rt1i, rt2i, rt1r, rt2r;
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extern /* Subroutine */ int igraphdrot_(integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, doublereal *), igraphdcopy_(
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integer *, doublereal *, integer *, doublereal *, integer *),
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igraphdlanv2_(doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *), igraphdlabad_(doublereal *, doublereal *);
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extern doublereal igraphdlamch_(char *);
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extern /* Subroutine */ int igraphdlarfg_(integer *, doublereal *, doublereal *,
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integer *, doublereal *);
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doublereal safmin, safmax, rtdisc, smlnum;
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/* -- LAPACK auxiliary routine (version 3.4.2) --
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-- LAPACK is a software package provided by Univ. of Tennessee, --
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-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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September 2012
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=========================================================
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Parameter adjustments */
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h_dim1 = *ldh;
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h_offset = 1 + h_dim1;
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h__ -= h_offset;
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--wr;
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--wi;
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z_dim1 = *ldz;
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z_offset = 1 + z_dim1;
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z__ -= z_offset;
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/* Function Body */
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*info = 0;
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/* Quick return if possible */
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if (*n == 0) {
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return 0;
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}
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if (*ilo == *ihi) {
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wr[*ilo] = h__[*ilo + *ilo * h_dim1];
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wi[*ilo] = 0.;
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return 0;
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}
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/* ==== clear out the trash ==== */
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i__1 = *ihi - 3;
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for (j = *ilo; j <= i__1; ++j) {
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h__[j + 2 + j * h_dim1] = 0.;
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h__[j + 3 + j * h_dim1] = 0.;
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/* L10: */
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}
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if (*ilo <= *ihi - 2) {
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h__[*ihi + (*ihi - 2) * h_dim1] = 0.;
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}
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nh = *ihi - *ilo + 1;
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nz = *ihiz - *iloz + 1;
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/* Set machine-dependent constants for the stopping criterion. */
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safmin = igraphdlamch_("SAFE MINIMUM");
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safmax = 1. / safmin;
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igraphdlabad_(&safmin, &safmax);
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ulp = igraphdlamch_("PRECISION");
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smlnum = safmin * ((doublereal) nh / ulp);
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/* I1 and I2 are the indices of the first row and last column of H
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to which transformations must be applied. If eigenvalues only are
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being computed, I1 and I2 are set inside the main loop. */
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if (*wantt) {
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i1 = 1;
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i2 = *n;
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}
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/* The main loop begins here. I is the loop index and decreases from
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IHI to ILO in steps of 1 or 2. Each iteration of the loop works
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with the active submatrix in rows and columns L to I.
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Eigenvalues I+1 to IHI have already converged. Either L = ILO or
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H(L,L-1) is negligible so that the matrix splits. */
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i__ = *ihi;
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L20:
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l = *ilo;
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if (i__ < *ilo) {
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goto L160;
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}
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/* Perform QR iterations on rows and columns ILO to I until a
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submatrix of order 1 or 2 splits off at the bottom because a
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subdiagonal element has become negligible. */
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for (its = 0; its <= 30; ++its) {
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/* Look for a single small subdiagonal element. */
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i__1 = l + 1;
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for (k = i__; k >= i__1; --k) {
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if ((d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)) <= smlnum) {
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goto L40;
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}
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tst = (d__1 = h__[k - 1 + (k - 1) * h_dim1], abs(d__1)) + (d__2 =
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h__[k + k * h_dim1], abs(d__2));
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if (tst == 0.) {
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if (k - 2 >= *ilo) {
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tst += (d__1 = h__[k - 1 + (k - 2) * h_dim1], abs(d__1));
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}
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if (k + 1 <= *ihi) {
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tst += (d__1 = h__[k + 1 + k * h_dim1], abs(d__1));
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}
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}
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/* ==== The following is a conservative small subdiagonal
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. deflation criterion due to Ahues & Tisseur (LAWN 122,
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. 1997). It has better mathematical foundation and
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. improves accuracy in some cases. ==== */
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if ((d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)) <= ulp * tst) {
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/* Computing MAX */
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d__3 = (d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)), d__4 = (
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d__2 = h__[k - 1 + k * h_dim1], abs(d__2));
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ab = max(d__3,d__4);
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/* Computing MIN */
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d__3 = (d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)), d__4 = (
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d__2 = h__[k - 1 + k * h_dim1], abs(d__2));
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ba = min(d__3,d__4);
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/* Computing MAX */
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d__3 = (d__1 = h__[k + k * h_dim1], abs(d__1)), d__4 = (d__2 =
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h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1],
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abs(d__2));
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aa = max(d__3,d__4);
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/* Computing MIN */
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d__3 = (d__1 = h__[k + k * h_dim1], abs(d__1)), d__4 = (d__2 =
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h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1],
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abs(d__2));
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bb = min(d__3,d__4);
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s = aa + ab;
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/* Computing MAX */
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d__1 = smlnum, d__2 = ulp * (bb * (aa / s));
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if (ba * (ab / s) <= max(d__1,d__2)) {
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goto L40;
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}
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}
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/* L30: */
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}
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L40:
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l = k;
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if (l > *ilo) {
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/* H(L,L-1) is negligible */
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h__[l + (l - 1) * h_dim1] = 0.;
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}
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/* Exit from loop if a submatrix of order 1 or 2 has split off. */
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if (l >= i__ - 1) {
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goto L150;
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}
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/* Now the active submatrix is in rows and columns L to I. If
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eigenvalues only are being computed, only the active submatrix
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need be transformed. */
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if (! (*wantt)) {
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i1 = l;
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i2 = i__;
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}
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if (its == 10) {
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/* Exceptional shift. */
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s = (d__1 = h__[l + 1 + l * h_dim1], abs(d__1)) + (d__2 = h__[l +
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2 + (l + 1) * h_dim1], abs(d__2));
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h11 = s * .75 + h__[l + l * h_dim1];
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h12 = s * -.4375;
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h21 = s;
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h22 = h11;
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} else if (its == 20) {
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/* Exceptional shift. */
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s = (d__1 = h__[i__ + (i__ - 1) * h_dim1], abs(d__1)) + (d__2 =
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h__[i__ - 1 + (i__ - 2) * h_dim1], abs(d__2));
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h11 = s * .75 + h__[i__ + i__ * h_dim1];
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h12 = s * -.4375;
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h21 = s;
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h22 = h11;
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} else {
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/* Prepare to use Francis' double shift
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(i.e. 2nd degree generalized Rayleigh quotient) */
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h11 = h__[i__ - 1 + (i__ - 1) * h_dim1];
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h21 = h__[i__ + (i__ - 1) * h_dim1];
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h12 = h__[i__ - 1 + i__ * h_dim1];
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h22 = h__[i__ + i__ * h_dim1];
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}
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s = abs(h11) + abs(h12) + abs(h21) + abs(h22);
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if (s == 0.) {
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rt1r = 0.;
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rt1i = 0.;
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rt2r = 0.;
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rt2i = 0.;
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} else {
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h11 /= s;
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h21 /= s;
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h12 /= s;
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h22 /= s;
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tr = (h11 + h22) / 2.;
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det = (h11 - tr) * (h22 - tr) - h12 * h21;
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rtdisc = sqrt((abs(det)));
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if (det >= 0.) {
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/* ==== complex conjugate shifts ==== */
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rt1r = tr * s;
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rt2r = rt1r;
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rt1i = rtdisc * s;
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rt2i = -rt1i;
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} else {
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/* ==== real shifts (use only one of them) ==== */
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rt1r = tr + rtdisc;
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rt2r = tr - rtdisc;
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if ((d__1 = rt1r - h22, abs(d__1)) <= (d__2 = rt2r - h22, abs(
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d__2))) {
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rt1r *= s;
|
|
rt2r = rt1r;
|
|
} else {
|
|
rt2r *= s;
|
|
rt1r = rt2r;
|
|
}
|
|
rt1i = 0.;
|
|
rt2i = 0.;
|
|
}
|
|
}
|
|
|
|
/* Look for two consecutive small subdiagonal elements. */
|
|
|
|
i__1 = l;
|
|
for (m = i__ - 2; m >= i__1; --m) {
|
|
/* Determine the effect of starting the double-shift QR
|
|
iteration at row M, and see if this would make H(M,M-1)
|
|
negligible. (The following uses scaling to avoid
|
|
overflows and most underflows.) */
|
|
|
|
h21s = h__[m + 1 + m * h_dim1];
|
|
s = (d__1 = h__[m + m * h_dim1] - rt2r, abs(d__1)) + abs(rt2i) +
|
|
abs(h21s);
|
|
h21s = h__[m + 1 + m * h_dim1] / s;
|
|
v[0] = h21s * h__[m + (m + 1) * h_dim1] + (h__[m + m * h_dim1] -
|
|
rt1r) * ((h__[m + m * h_dim1] - rt2r) / s) - rt1i * (rt2i
|
|
/ s);
|
|
v[1] = h21s * (h__[m + m * h_dim1] + h__[m + 1 + (m + 1) * h_dim1]
|
|
- rt1r - rt2r);
|
|
v[2] = h21s * h__[m + 2 + (m + 1) * h_dim1];
|
|
s = abs(v[0]) + abs(v[1]) + abs(v[2]);
|
|
v[0] /= s;
|
|
v[1] /= s;
|
|
v[2] /= s;
|
|
if (m == l) {
|
|
goto L60;
|
|
}
|
|
if ((d__1 = h__[m + (m - 1) * h_dim1], abs(d__1)) * (abs(v[1]) +
|
|
abs(v[2])) <= ulp * abs(v[0]) * ((d__2 = h__[m - 1 + (m -
|
|
1) * h_dim1], abs(d__2)) + (d__3 = h__[m + m * h_dim1],
|
|
abs(d__3)) + (d__4 = h__[m + 1 + (m + 1) * h_dim1], abs(
|
|
d__4)))) {
|
|
goto L60;
|
|
}
|
|
/* L50: */
|
|
}
|
|
L60:
|
|
|
|
/* Double-shift QR step */
|
|
|
|
i__1 = i__ - 1;
|
|
for (k = m; k <= i__1; ++k) {
|
|
|
|
/* The first iteration of this loop determines a reflection G
|
|
from the vector V and applies it from left and right to H,
|
|
thus creating a nonzero bulge below the subdiagonal.
|
|
|
|
Each subsequent iteration determines a reflection G to
|
|
restore the Hessenberg form in the (K-1)th column, and thus
|
|
chases the bulge one step toward the bottom of the active
|
|
submatrix. NR is the order of G.
|
|
|
|
Computing MIN */
|
|
i__2 = 3, i__3 = i__ - k + 1;
|
|
nr = min(i__2,i__3);
|
|
if (k > m) {
|
|
igraphdcopy_(&nr, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1);
|
|
}
|
|
igraphdlarfg_(&nr, v, &v[1], &c__1, &t1);
|
|
if (k > m) {
|
|
h__[k + (k - 1) * h_dim1] = v[0];
|
|
h__[k + 1 + (k - 1) * h_dim1] = 0.;
|
|
if (k < i__ - 1) {
|
|
h__[k + 2 + (k - 1) * h_dim1] = 0.;
|
|
}
|
|
} else if (m > l) {
|
|
/* ==== Use the following instead of
|
|
. H( K, K-1 ) = -H( K, K-1 ) to
|
|
. avoid a bug when v(2) and v(3)
|
|
. underflow. ==== */
|
|
h__[k + (k - 1) * h_dim1] *= 1. - t1;
|
|
}
|
|
v2 = v[1];
|
|
t2 = t1 * v2;
|
|
if (nr == 3) {
|
|
v3 = v[2];
|
|
t3 = t1 * v3;
|
|
|
|
/* Apply G from the left to transform the rows of the matrix
|
|
in columns K to I2. */
|
|
|
|
i__2 = i2;
|
|
for (j = k; j <= i__2; ++j) {
|
|
sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1]
|
|
+ v3 * h__[k + 2 + j * h_dim1];
|
|
h__[k + j * h_dim1] -= sum * t1;
|
|
h__[k + 1 + j * h_dim1] -= sum * t2;
|
|
h__[k + 2 + j * h_dim1] -= sum * t3;
|
|
/* L70: */
|
|
}
|
|
|
|
/* Apply G from the right to transform the columns of the
|
|
matrix in rows I1 to min(K+3,I).
|
|
|
|
Computing MIN */
|
|
i__3 = k + 3;
|
|
i__2 = min(i__3,i__);
|
|
for (j = i1; j <= i__2; ++j) {
|
|
sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1]
|
|
+ v3 * h__[j + (k + 2) * h_dim1];
|
|
h__[j + k * h_dim1] -= sum * t1;
|
|
h__[j + (k + 1) * h_dim1] -= sum * t2;
|
|
h__[j + (k + 2) * h_dim1] -= sum * t3;
|
|
/* L80: */
|
|
}
|
|
|
|
if (*wantz) {
|
|
|
|
/* Accumulate transformations in the matrix Z */
|
|
|
|
i__2 = *ihiz;
|
|
for (j = *iloz; j <= i__2; ++j) {
|
|
sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) *
|
|
z_dim1] + v3 * z__[j + (k + 2) * z_dim1];
|
|
z__[j + k * z_dim1] -= sum * t1;
|
|
z__[j + (k + 1) * z_dim1] -= sum * t2;
|
|
z__[j + (k + 2) * z_dim1] -= sum * t3;
|
|
/* L90: */
|
|
}
|
|
}
|
|
} else if (nr == 2) {
|
|
|
|
/* Apply G from the left to transform the rows of the matrix
|
|
in columns K to I2. */
|
|
|
|
i__2 = i2;
|
|
for (j = k; j <= i__2; ++j) {
|
|
sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1];
|
|
h__[k + j * h_dim1] -= sum * t1;
|
|
h__[k + 1 + j * h_dim1] -= sum * t2;
|
|
/* L100: */
|
|
}
|
|
|
|
/* Apply G from the right to transform the columns of the
|
|
matrix in rows I1 to min(K+3,I). */
|
|
|
|
i__2 = i__;
|
|
for (j = i1; j <= i__2; ++j) {
|
|
sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1]
|
|
;
|
|
h__[j + k * h_dim1] -= sum * t1;
|
|
h__[j + (k + 1) * h_dim1] -= sum * t2;
|
|
/* L110: */
|
|
}
|
|
|
|
if (*wantz) {
|
|
|
|
/* Accumulate transformations in the matrix Z */
|
|
|
|
i__2 = *ihiz;
|
|
for (j = *iloz; j <= i__2; ++j) {
|
|
sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) *
|
|
z_dim1];
|
|
z__[j + k * z_dim1] -= sum * t1;
|
|
z__[j + (k + 1) * z_dim1] -= sum * t2;
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
/* L130: */
|
|
}
|
|
|
|
/* L140: */
|
|
}
|
|
|
|
/* Failure to converge in remaining number of iterations */
|
|
|
|
*info = i__;
|
|
return 0;
|
|
|
|
L150:
|
|
|
|
if (l == i__) {
|
|
|
|
/* H(I,I-1) is negligible: one eigenvalue has converged. */
|
|
|
|
wr[i__] = h__[i__ + i__ * h_dim1];
|
|
wi[i__] = 0.;
|
|
} else if (l == i__ - 1) {
|
|
|
|
/* H(I-1,I-2) is negligible: a pair of eigenvalues have converged.
|
|
|
|
Transform the 2-by-2 submatrix to standard Schur form,
|
|
and compute and store the eigenvalues. */
|
|
|
|
igraphdlanv2_(&h__[i__ - 1 + (i__ - 1) * h_dim1], &h__[i__ - 1 + i__ *
|
|
h_dim1], &h__[i__ + (i__ - 1) * h_dim1], &h__[i__ + i__ *
|
|
h_dim1], &wr[i__ - 1], &wi[i__ - 1], &wr[i__], &wi[i__], &cs,
|
|
&sn);
|
|
|
|
if (*wantt) {
|
|
|
|
/* Apply the transformation to the rest of H. */
|
|
|
|
if (i2 > i__) {
|
|
i__1 = i2 - i__;
|
|
igraphdrot_(&i__1, &h__[i__ - 1 + (i__ + 1) * h_dim1], ldh, &h__[
|
|
i__ + (i__ + 1) * h_dim1], ldh, &cs, &sn);
|
|
}
|
|
i__1 = i__ - i1 - 1;
|
|
igraphdrot_(&i__1, &h__[i1 + (i__ - 1) * h_dim1], &c__1, &h__[i1 + i__ *
|
|
h_dim1], &c__1, &cs, &sn);
|
|
}
|
|
if (*wantz) {
|
|
|
|
/* Apply the transformation to Z. */
|
|
|
|
igraphdrot_(&nz, &z__[*iloz + (i__ - 1) * z_dim1], &c__1, &z__[*iloz +
|
|
i__ * z_dim1], &c__1, &cs, &sn);
|
|
}
|
|
}
|
|
|
|
/* return to start of the main loop with new value of I. */
|
|
|
|
i__ = l - 1;
|
|
goto L20;
|
|
|
|
L160:
|
|
return 0;
|
|
|
|
/* End of DLAHQR */
|
|
|
|
} /* igraphdlahqr_ */
|
|
|