version 1.10, 2012/07/31 11:06:38
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version 1.17, 2017/06/17 10:54:16
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* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download ZHGEQZ + dependencies |
*> Download ZHGEQZ + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhgeqz.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhgeqz.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhgeqz.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhgeqz.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhgeqz.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhgeqz.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
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* SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, |
* SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, |
* ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, |
* ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, |
* RWORK, INFO ) |
* RWORK, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER COMPQ, COMPZ, JOB |
* CHARACTER COMPQ, COMPZ, JOB |
* INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N |
* INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N |
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* $ Q( LDQ, * ), T( LDT, * ), WORK( * ), |
* $ Q( LDQ, * ), T( LDT, * ), WORK( * ), |
* $ Z( LDZ, * ) |
* $ Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> using the single-shift QZ method. |
*> using the single-shift QZ method. |
*> Matrix pairs of this type are produced by the reduction to |
*> Matrix pairs of this type are produced by the reduction to |
*> generalized upper Hessenberg form of a complex matrix pair (A,B): |
*> generalized upper Hessenberg form of a complex matrix pair (A,B): |
*> |
*> |
*> A = Q1*H*Z1**H, B = Q1*T*Z1**H, |
*> A = Q1*H*Z1**H, B = Q1*T*Z1**H, |
*> |
*> |
*> as computed by ZGGHRD. |
*> as computed by ZGGHRD. |
*> |
*> |
*> If JOB='S', then the Hessenberg-triangular pair (H,T) is |
*> If JOB='S', then the Hessenberg-triangular pair (H,T) is |
*> also reduced to generalized Schur form, |
*> also reduced to generalized Schur form, |
*> |
*> |
*> H = Q*S*Z**H, T = Q*P*Z**H, |
*> H = Q*S*Z**H, T = Q*P*Z**H, |
*> |
*> |
*> where Q and Z are unitary matrices and S and P are upper triangular. |
*> where Q and Z are unitary matrices and S and P are upper triangular. |
*> |
*> |
*> Optionally, the unitary matrix Q from the generalized Schur |
*> Optionally, the unitary matrix Q from the generalized Schur |
*> factorization may be postmultiplied into an input matrix Q1, and the |
*> factorization may be postmultiplied into an input matrix Q1, and the |
*> unitary matrix Z may be postmultiplied into an input matrix Z1. |
*> unitary matrix Z may be postmultiplied into an input matrix Z1. |
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*> the matrix pair (A,B) to generalized Hessenberg form, then the output |
*> the matrix pair (A,B) to generalized Hessenberg form, then the output |
*> matrices Q1*Q and Z1*Z are the unitary factors from the generalized |
*> matrices Q1*Q and Z1*Z are the unitary factors from the generalized |
*> Schur factorization of (A,B): |
*> Schur factorization of (A,B): |
*> |
*> |
*> A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. |
*> A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. |
*> |
*> |
*> To avoid overflow, eigenvalues of the matrix pair (H,T) |
*> To avoid overflow, eigenvalues of the matrix pair (H,T) |
*> (equivalently, of (A,B)) are computed as a pair of complex values |
*> (equivalently, of (A,B)) are computed as a pair of complex values |
*> (alpha,beta). If beta is nonzero, lambda = alpha / beta is an |
*> (alpha,beta). If beta is nonzero, lambda = alpha / beta is an |
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*> \param[in,out] Q |
*> \param[in,out] Q |
*> \verbatim |
*> \verbatim |
*> Q is COMPLEX*16 array, dimension (LDQ, N) |
*> Q is COMPLEX*16 array, dimension (LDQ, N) |
*> On entry, if COMPZ = 'V', the unitary matrix Q1 used in the |
*> On entry, if COMPQ = 'V', the unitary matrix Q1 used in the |
*> reduction of (A,B) to generalized Hessenberg form. |
*> reduction of (A,B) to generalized Hessenberg form. |
*> On exit, if COMPZ = 'I', the unitary matrix of left Schur |
*> On exit, if COMPQ = 'I', the unitary matrix of left Schur |
*> vectors of (H,T), and if COMPZ = 'V', the unitary matrix of |
*> vectors of (H,T), and if COMPQ = 'V', the unitary matrix of |
*> left Schur vectors of (A,B). |
*> left Schur vectors of (A,B). |
*> Not referenced if COMPZ = 'N'. |
*> Not referenced if COMPQ = 'N'. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDQ |
*> \param[in] LDQ |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date April 2012 |
*> \date April 2012 |
* |
* |
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$ ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, |
$ ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, |
$ RWORK, INFO ) |
$ RWORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.1) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* April 2012 |
* April 2012 |
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CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 ) |
CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 ) |
CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 ) |
CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 ) |
ELSE |
ELSE |
H( J, J ) = H( J, J )*SIGNBC |
CALL ZSCAL( 1, SIGNBC, H( J, J ), 1 ) |
END IF |
END IF |
IF( ILZ ) |
IF( ILZ ) |
$ CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 ) |
$ CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 ) |
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CALL ZSCAL( ILAST+1-IFRSTM, SIGNBC, H( IFRSTM, ILAST ), |
CALL ZSCAL( ILAST+1-IFRSTM, SIGNBC, H( IFRSTM, ILAST ), |
$ 1 ) |
$ 1 ) |
ELSE |
ELSE |
H( ILAST, ILAST ) = H( ILAST, ILAST )*SIGNBC |
CALL ZSCAL( 1, SIGNBC, H( ILAST, ILAST ), 1 ) |
END IF |
END IF |
IF( ILZ ) |
IF( ILZ ) |
$ CALL ZSCAL( N, SIGNBC, Z( 1, ILAST ), 1 ) |
$ CALL ZSCAL( N, SIGNBC, Z( 1, ILAST ), 1 ) |
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CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 ) |
CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 ) |
CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 ) |
CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 ) |
ELSE |
ELSE |
H( J, J ) = H( J, J )*SIGNBC |
CALL ZSCAL( 1, SIGNBC, H( J, J ), 1 ) |
END IF |
END IF |
IF( ILZ ) |
IF( ILZ ) |
$ CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 ) |
$ CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 ) |