version 1.1, 2010/01/26 15:22:45
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version 1.20, 2018/05/29 07:17:54
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*> \brief \b DHGEQZ |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DHGEQZ + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dhgeqz.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/dhgeqz.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/dhgeqz.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, |
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* ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK, |
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* LWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER COMPQ, COMPZ, JOB |
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* INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION ALPHAI( * ), ALPHAR( * ), BETA( * ), |
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* $ H( LDH, * ), Q( LDQ, * ), T( LDT, * ), |
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* $ WORK( * ), Z( LDZ, * ) |
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* .. |
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* |
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* |
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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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*> DHGEQZ computes the eigenvalues of a real matrix pair (H,T), |
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*> where H is an upper Hessenberg matrix and T is upper triangular, |
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*> using the double-shift QZ method. |
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*> Matrix pairs of this type are produced by the reduction to |
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*> generalized upper Hessenberg form of a real matrix pair (A,B): |
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*> |
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*> A = Q1*H*Z1**T, B = Q1*T*Z1**T, |
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*> |
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*> as computed by DGGHRD. |
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*> |
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*> If JOB='S', then the Hessenberg-triangular pair (H,T) is |
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*> also reduced to generalized Schur form, |
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*> |
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*> H = Q*S*Z**T, T = Q*P*Z**T, |
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*> |
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*> where Q and Z are orthogonal matrices, P is an upper triangular |
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*> matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2 |
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*> diagonal blocks. |
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*> |
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*> The 1-by-1 blocks correspond to real eigenvalues of the matrix pair |
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*> (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of |
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*> eigenvalues. |
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*> |
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*> Additionally, the 2-by-2 upper triangular diagonal blocks of P |
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*> corresponding to 2-by-2 blocks of S are reduced to positive diagonal |
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*> form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0, |
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*> P(j,j) > 0, and P(j+1,j+1) > 0. |
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*> |
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*> Optionally, the orthogonal matrix Q from the generalized Schur |
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*> factorization may be postmultiplied into an input matrix Q1, and the |
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*> orthogonal matrix Z may be postmultiplied into an input matrix Z1. |
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*> If Q1 and Z1 are the orthogonal matrices from DGGHRD that reduced |
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*> the matrix pair (A,B) to generalized upper Hessenberg form, then the |
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*> output matrices Q1*Q and Z1*Z are the orthogonal factors from the |
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*> generalized Schur factorization of (A,B): |
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*> |
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*> A = (Q1*Q)*S*(Z1*Z)**T, B = (Q1*Q)*P*(Z1*Z)**T. |
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*> |
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*> To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently, |
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*> of (A,B)) are computed as a pair of values (alpha,beta), where alpha is |
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*> complex and beta real. |
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*> If beta is nonzero, lambda = alpha / beta is an eigenvalue of the |
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*> generalized nonsymmetric eigenvalue problem (GNEP) |
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*> A*x = lambda*B*x |
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*> and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the |
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*> alternate form of the GNEP |
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*> mu*A*y = B*y. |
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*> Real eigenvalues can be read directly from the generalized Schur |
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*> form: |
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*> alpha = S(i,i), beta = P(i,i). |
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*> |
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*> Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix |
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*> Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), |
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*> pp. 241--256. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] JOB |
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*> \verbatim |
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*> JOB is CHARACTER*1 |
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*> = 'E': Compute eigenvalues only; |
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*> = 'S': Compute eigenvalues and the Schur form. |
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*> \endverbatim |
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*> |
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*> \param[in] COMPQ |
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*> \verbatim |
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*> COMPQ is CHARACTER*1 |
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*> = 'N': Left Schur vectors (Q) are not computed; |
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*> = 'I': Q is initialized to the unit matrix and the matrix Q |
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*> of left Schur vectors of (H,T) is returned; |
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*> = 'V': Q must contain an orthogonal matrix Q1 on entry and |
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*> the product Q1*Q is returned. |
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*> \endverbatim |
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*> |
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*> \param[in] COMPZ |
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*> \verbatim |
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*> COMPZ is CHARACTER*1 |
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*> = 'N': Right Schur vectors (Z) are not computed; |
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*> = 'I': Z is initialized to the unit matrix and the matrix Z |
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*> of right Schur vectors of (H,T) is returned; |
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*> = 'V': Z must contain an orthogonal matrix Z1 on entry and |
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*> the product Z1*Z is returned. |
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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 matrices H, T, Q, and Z. 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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*> ILO and IHI mark the rows and columns of H which are in |
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*> Hessenberg form. It is assumed that A is already upper |
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*> triangular in rows and columns 1:ILO-1 and IHI+1:N. |
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*> If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0. |
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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 N-by-N upper Hessenberg matrix H. |
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*> On exit, if JOB = 'S', H contains the upper quasi-triangular |
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*> matrix S from the generalized Schur factorization. |
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*> If JOB = 'E', the diagonal blocks of H match those of S, but |
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*> the rest of H is unspecified. |
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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[in,out] T |
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*> \verbatim |
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*> T is DOUBLE PRECISION array, dimension (LDT, N) |
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*> On entry, the N-by-N upper triangular matrix T. |
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*> On exit, if JOB = 'S', T contains the upper triangular |
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*> matrix P from the generalized Schur factorization; |
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*> 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S |
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*> are reduced to positive diagonal form, i.e., if H(j+1,j) is |
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*> non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and |
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*> T(j+1,j+1) > 0. |
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*> If JOB = 'E', the diagonal blocks of T match those of P, but |
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*> the rest of T is unspecified. |
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*> \endverbatim |
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*> |
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*> \param[in] LDT |
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*> \verbatim |
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*> LDT is INTEGER |
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*> The leading dimension of the array T. LDT >= max( 1, N ). |
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*> \endverbatim |
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*> |
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*> \param[out] ALPHAR |
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*> \verbatim |
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*> ALPHAR is DOUBLE PRECISION array, dimension (N) |
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*> The real parts of each scalar alpha defining an eigenvalue |
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*> of GNEP. |
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*> \endverbatim |
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*> |
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*> \param[out] ALPHAI |
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*> \verbatim |
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*> ALPHAI is DOUBLE PRECISION array, dimension (N) |
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*> The imaginary parts of each scalar alpha defining an |
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*> eigenvalue of GNEP. |
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*> If ALPHAI(j) is zero, then the j-th eigenvalue is real; if |
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*> positive, then the j-th and (j+1)-st eigenvalues are a |
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*> complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j). |
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*> \endverbatim |
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*> |
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*> \param[out] BETA |
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*> \verbatim |
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*> BETA is DOUBLE PRECISION array, dimension (N) |
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*> The scalars beta that define the eigenvalues of GNEP. |
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*> Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and |
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*> beta = BETA(j) represent the j-th eigenvalue of the matrix |
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*> pair (A,B), in one of the forms lambda = alpha/beta or |
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*> mu = beta/alpha. Since either lambda or mu may overflow, |
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*> they should not, in general, be computed. |
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*> \endverbatim |
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*> |
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*> \param[in,out] Q |
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*> \verbatim |
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*> Q is DOUBLE PRECISION array, dimension (LDQ, N) |
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*> On entry, if COMPQ = 'V', the orthogonal matrix Q1 used in |
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*> the reduction of (A,B) to generalized Hessenberg form. |
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*> On exit, if COMPQ = 'I', the orthogonal matrix of left Schur |
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*> vectors of (H,T), and if COMPQ = 'V', the orthogonal matrix |
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*> of left Schur vectors of (A,B). |
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*> Not referenced if COMPQ = 'N'. |
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*> \endverbatim |
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*> |
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*> \param[in] LDQ |
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*> \verbatim |
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*> LDQ is INTEGER |
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*> The leading dimension of the array Q. LDQ >= 1. |
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*> If COMPQ='V' or 'I', then LDQ >= 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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*> On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in |
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*> the reduction of (A,B) to generalized Hessenberg form. |
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*> On exit, if COMPZ = 'I', the orthogonal matrix of |
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*> right Schur vectors of (H,T), and if COMPZ = 'V', the |
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*> orthogonal matrix of right Schur vectors of (A,B). |
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*> Not referenced if COMPZ = 'N'. |
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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 >= 1. |
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*> If COMPZ='V' or 'I', then LDZ >= N. |
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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. LWORK >= max(1,N). |
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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] 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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*> = 1,...,N: the QZ iteration did not converge. (H,T) is not |
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*> in Schur form, but ALPHAR(i), ALPHAI(i), and |
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*> BETA(i), i=INFO+1,...,N should be correct. |
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*> = N+1,...,2*N: the shift calculation failed. (H,T) is not |
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*> in Schur form, but ALPHAR(i), ALPHAI(i), and |
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*> BETA(i), i=INFO-N+1,...,N should be correct. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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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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* |
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*> \date June 2016 |
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* |
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*> \ingroup doubleGEcomputational |
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* |
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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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*> Iteration counters: |
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*> |
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*> JITER -- counts iterations. |
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*> IITER -- counts iterations run since ILAST was last |
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*> changed. This is therefore reset only when a 1-by-1 or |
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*> 2-by-2 block deflates off the bottom. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, |
SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, |
$ ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK, |
$ ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK, |
$ LWORK, INFO ) |
$ LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2.1) -- |
* -- 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 2009 -- |
* June 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER COMPQ, COMPZ, JOB |
CHARACTER COMPQ, COMPZ, JOB |
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$ WORK( * ), Z( LDZ, * ) |
$ WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
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* |
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* DHGEQZ computes the eigenvalues of a real matrix pair (H,T), |
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* where H is an upper Hessenberg matrix and T is upper triangular, |
|
* using the double-shift QZ method. |
|
* Matrix pairs of this type are produced by the reduction to |
|
* generalized upper Hessenberg form of a real matrix pair (A,B): |
|
* |
|
* A = Q1*H*Z1**T, B = Q1*T*Z1**T, |
|
* |
|
* as computed by DGGHRD. |
|
* |
|
* If JOB='S', then the Hessenberg-triangular pair (H,T) is |
|
* also reduced to generalized Schur form, |
|
* |
|
* H = Q*S*Z**T, T = Q*P*Z**T, |
|
* |
|
* where Q and Z are orthogonal matrices, P is an upper triangular |
|
* matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2 |
|
* diagonal blocks. |
|
* |
|
* The 1-by-1 blocks correspond to real eigenvalues of the matrix pair |
|
* (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of |
|
* eigenvalues. |
|
* |
|
* Additionally, the 2-by-2 upper triangular diagonal blocks of P |
|
* corresponding to 2-by-2 blocks of S are reduced to positive diagonal |
|
* form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0, |
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* P(j,j) > 0, and P(j+1,j+1) > 0. |
|
* |
|
* Optionally, the orthogonal matrix Q from the generalized Schur |
|
* factorization may be postmultiplied into an input matrix Q1, and the |
|
* orthogonal matrix Z may be postmultiplied into an input matrix Z1. |
|
* If Q1 and Z1 are the orthogonal matrices from DGGHRD that reduced |
|
* the matrix pair (A,B) to generalized upper Hessenberg form, then the |
|
* output matrices Q1*Q and Z1*Z are the orthogonal factors from the |
|
* generalized Schur factorization of (A,B): |
|
* |
|
* A = (Q1*Q)*S*(Z1*Z)**T, B = (Q1*Q)*P*(Z1*Z)**T. |
|
* |
|
* To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently, |
|
* of (A,B)) are computed as a pair of values (alpha,beta), where alpha is |
|
* complex and beta real. |
|
* If beta is nonzero, lambda = alpha / beta is an eigenvalue of the |
|
* generalized nonsymmetric eigenvalue problem (GNEP) |
|
* A*x = lambda*B*x |
|
* and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the |
|
* alternate form of the GNEP |
|
* mu*A*y = B*y. |
|
* Real eigenvalues can be read directly from the generalized Schur |
|
* form: |
|
* alpha = S(i,i), beta = P(i,i). |
|
* |
|
* Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix |
|
* Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), |
|
* pp. 241--256. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
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* JOB (input) CHARACTER*1 |
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* = 'E': Compute eigenvalues only; |
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* = 'S': Compute eigenvalues and the Schur form. |
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* |
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* COMPQ (input) CHARACTER*1 |
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* = 'N': Left Schur vectors (Q) are not computed; |
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* = 'I': Q is initialized to the unit matrix and the matrix Q |
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* of left Schur vectors of (H,T) is returned; |
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* = 'V': Q must contain an orthogonal matrix Q1 on entry and |
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* the product Q1*Q is returned. |
|
* |
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* COMPZ (input) CHARACTER*1 |
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* = 'N': Right Schur vectors (Z) are not computed; |
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* = 'I': Z is initialized to the unit matrix and the matrix Z |
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* of right Schur vectors of (H,T) is returned; |
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* = 'V': Z must contain an orthogonal matrix Z1 on entry and |
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* the product Z1*Z is returned. |
|
* |
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* N (input) INTEGER |
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* The order of the matrices H, T, Q, and Z. N >= 0. |
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* |
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* ILO (input) INTEGER |
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* IHI (input) INTEGER |
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* ILO and IHI mark the rows and columns of H which are in |
|
* Hessenberg form. It is assumed that A is already upper |
|
* triangular in rows and columns 1:ILO-1 and IHI+1:N. |
|
* If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0. |
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* |
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* H (input/output) DOUBLE PRECISION array, dimension (LDH, N) |
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* On entry, the N-by-N upper Hessenberg matrix H. |
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* On exit, if JOB = 'S', H contains the upper quasi-triangular |
|
* matrix S from the generalized Schur factorization; |
|
* 2-by-2 diagonal blocks (corresponding to complex conjugate |
|
* pairs of eigenvalues) are returned in standard form, with |
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* H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0. |
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* If JOB = 'E', the diagonal blocks of H match those of S, but |
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* the rest of H is unspecified. |
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* |
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* LDH (input) INTEGER |
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* The leading dimension of the array H. LDH >= max( 1, N ). |
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* |
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* T (input/output) DOUBLE PRECISION array, dimension (LDT, N) |
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* On entry, the N-by-N upper triangular matrix T. |
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* On exit, if JOB = 'S', T contains the upper triangular |
|
* matrix P from the generalized Schur factorization; |
|
* 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S |
|
* are reduced to positive diagonal form, i.e., if H(j+1,j) is |
|
* non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and |
|
* T(j+1,j+1) > 0. |
|
* If JOB = 'E', the diagonal blocks of T match those of P, but |
|
* the rest of T is unspecified. |
|
* |
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* LDT (input) INTEGER |
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* The leading dimension of the array T. LDT >= max( 1, N ). |
|
* |
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* ALPHAR (output) DOUBLE PRECISION array, dimension (N) |
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* The real parts of each scalar alpha defining an eigenvalue |
|
* of GNEP. |
|
* |
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* ALPHAI (output) DOUBLE PRECISION array, dimension (N) |
|
* The imaginary parts of each scalar alpha defining an |
|
* eigenvalue of GNEP. |
|
* If ALPHAI(j) is zero, then the j-th eigenvalue is real; if |
|
* positive, then the j-th and (j+1)-st eigenvalues are a |
|
* complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j). |
|
* |
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* BETA (output) DOUBLE PRECISION array, dimension (N) |
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* The scalars beta that define the eigenvalues of GNEP. |
|
* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and |
|
* beta = BETA(j) represent the j-th eigenvalue of the matrix |
|
* pair (A,B), in one of the forms lambda = alpha/beta or |
|
* mu = beta/alpha. Since either lambda or mu may overflow, |
|
* they should not, in general, be computed. |
|
* |
|
* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) |
|
* On entry, if COMPZ = 'V', the orthogonal matrix Q1 used in |
|
* the reduction of (A,B) to generalized Hessenberg form. |
|
* On exit, if COMPZ = 'I', the orthogonal matrix of left Schur |
|
* vectors of (H,T), and if COMPZ = 'V', the orthogonal matrix |
|
* of left Schur vectors of (A,B). |
|
* Not referenced if COMPZ = 'N'. |
|
* |
|
* LDQ (input) INTEGER |
|
* The leading dimension of the array Q. LDQ >= 1. |
|
* If COMPQ='V' or 'I', then LDQ >= N. |
|
* |
|
* Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N) |
|
* On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in |
|
* the reduction of (A,B) to generalized Hessenberg form. |
|
* On exit, if COMPZ = 'I', the orthogonal matrix of |
|
* right Schur vectors of (H,T), and if COMPZ = 'V', the |
|
* orthogonal matrix of right Schur vectors of (A,B). |
|
* Not referenced if COMPZ = 'N'. |
|
* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= 1. |
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* If COMPZ='V' or 'I', then LDZ >= N. |
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* |
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* WORK (workspace/output) 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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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. LWORK >= max(1,N). |
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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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* |
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* INFO (output) 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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* = 1,...,N: the QZ iteration did not converge. (H,T) is not |
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* in Schur form, but ALPHAR(i), ALPHAI(i), and |
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* BETA(i), i=INFO+1,...,N should be correct. |
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* = N+1,...,2*N: the shift calculation failed. (H,T) is not |
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* in Schur form, but ALPHAR(i), ALPHAI(i), and |
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* BETA(i), i=INFO-N+1,...,N should be correct. |
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* |
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* Further Details |
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* =============== |
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* |
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* Iteration counters: |
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* |
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* JITER -- counts iterations. |
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* IITER -- counts iterations run since ILAST was last |
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* changed. This is therefore reset only when a 1-by-1 or |
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* 2-by-2 block deflates off the bottom. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 627
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Line 739
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* Exceptional shift. Chosen for no particularly good reason. |
* Exceptional shift. Chosen for no particularly good reason. |
* (Single shift only.) |
* (Single shift only.) |
* |
* |
IF( ( DBLE( MAXIT )*SAFMIN )*ABS( H( ILAST-1, ILAST ) ).LT. |
IF( ( DBLE( MAXIT )*SAFMIN )*ABS( H( ILAST, ILAST-1 ) ).LT. |
$ ABS( T( ILAST-1, ILAST-1 ) ) ) THEN |
$ ABS( T( ILAST-1, ILAST-1 ) ) ) THEN |
ESHIFT = ESHIFT + H( ILAST-1, ILAST ) / |
ESHIFT = H( ILAST, ILAST-1 ) / |
$ T( ILAST-1, ILAST-1 ) |
$ T( ILAST-1, ILAST-1 ) |
ELSE |
ELSE |
ESHIFT = ESHIFT + ONE / ( SAFMIN*DBLE( MAXIT ) ) |
ESHIFT = ESHIFT + ONE / ( SAFMIN*DBLE( MAXIT ) ) |
Line 647
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Line 759
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$ T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1, |
$ T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1, |
$ S2, WR, WR2, WI ) |
$ S2, WR, WR2, WI ) |
* |
* |
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IF ( ABS( (WR/S1)*T( ILAST, ILAST ) - H( ILAST, ILAST ) ) |
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$ .GT. ABS( (WR2/S2)*T( ILAST, ILAST ) |
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$ - H( ILAST, ILAST ) ) ) THEN |
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TEMP = WR |
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WR = WR2 |
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WR2 = TEMP |
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TEMP = S1 |
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S1 = S2 |
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S2 = TEMP |
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END IF |
TEMP = MAX( S1, SAFMIN*MAX( ONE, ABS( WR ), ABS( WI ) ) ) |
TEMP = MAX( S1, SAFMIN*MAX( ONE, ABS( WR ), ABS( WI ) ) ) |
IF( WI.NE.ZERO ) |
IF( WI.NE.ZERO ) |
$ GO TO 200 |
$ GO TO 200 |
Line 808
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Line 930
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Z( J, ILAST ) = -Z( J, ILAST ) |
Z( J, ILAST ) = -Z( J, ILAST ) |
220 CONTINUE |
220 CONTINUE |
END IF |
END IF |
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B22 = -B22 |
END IF |
END IF |
* |
* |
* Step 2: Compute ALPHAR, ALPHAI, and BETA (see refs.) |
* Step 2: Compute ALPHAR, ALPHAI, and BETA (see refs.) |