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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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* 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 3.6.1) -- |
* -- 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 |