--- rpl/lapack/lapack/ztgevc.f 2010/08/07 13:22:45 1.5
+++ rpl/lapack/lapack/ztgevc.f 2023/08/07 08:39:40 1.17
@@ -1,10 +1,225 @@
+*> \brief \b ZTGEVC
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZTGEVC + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
+* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER HOWMNY, SIDE
+* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N
+* ..
+* .. Array Arguments ..
+* LOGICAL SELECT( * )
+* DOUBLE PRECISION RWORK( * )
+* COMPLEX*16 P( LDP, * ), S( LDS, * ), VL( LDVL, * ),
+* $ VR( LDVR, * ), WORK( * )
+* ..
+*
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZTGEVC computes some or all of the right and/or left eigenvectors of
+*> a pair of complex matrices (S,P), where S and P are upper triangular.
+*> Matrix pairs of this type are produced by the generalized Schur
+*> factorization of a complex matrix pair (A,B):
+*>
+*> A = Q*S*Z**H, B = Q*P*Z**H
+*>
+*> as computed by ZGGHRD + ZHGEQZ.
+*>
+*> The right eigenvector x and the left eigenvector y of (S,P)
+*> corresponding to an eigenvalue w are defined by:
+*>
+*> S*x = w*P*x, (y**H)*S = w*(y**H)*P,
+*>
+*> where y**H denotes the conjugate tranpose of y.
+*> The eigenvalues are not input to this routine, but are computed
+*> directly from the diagonal elements of S and P.
+*>
+*> This routine returns the matrices X and/or Y of right and left
+*> eigenvectors of (S,P), or the products Z*X and/or Q*Y,
+*> where Z and Q are input matrices.
+*> If Q and Z are the unitary factors from the generalized Schur
+*> factorization of a matrix pair (A,B), then Z*X and Q*Y
+*> are the matrices of right and left eigenvectors of (A,B).
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*> SIDE is CHARACTER*1
+*> = 'R': compute right eigenvectors only;
+*> = 'L': compute left eigenvectors only;
+*> = 'B': compute both right and left eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] HOWMNY
+*> \verbatim
+*> HOWMNY is CHARACTER*1
+*> = 'A': compute all right and/or left eigenvectors;
+*> = 'B': compute all right and/or left eigenvectors,
+*> backtransformed by the matrices in VR and/or VL;
+*> = 'S': compute selected right and/or left eigenvectors,
+*> specified by the logical array SELECT.
+*> \endverbatim
+*>
+*> \param[in] SELECT
+*> \verbatim
+*> SELECT is LOGICAL array, dimension (N)
+*> If HOWMNY='S', SELECT specifies the eigenvectors to be
+*> computed. The eigenvector corresponding to the j-th
+*> eigenvalue is computed if SELECT(j) = .TRUE..
+*> Not referenced if HOWMNY = 'A' or 'B'.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrices S and P. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] S
+*> \verbatim
+*> S is COMPLEX*16 array, dimension (LDS,N)
+*> The upper triangular matrix S from a generalized Schur
+*> factorization, as computed by ZHGEQZ.
+*> \endverbatim
+*>
+*> \param[in] LDS
+*> \verbatim
+*> LDS is INTEGER
+*> The leading dimension of array S. LDS >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*> P is COMPLEX*16 array, dimension (LDP,N)
+*> The upper triangular matrix P from a generalized Schur
+*> factorization, as computed by ZHGEQZ. P must have real
+*> diagonal elements.
+*> \endverbatim
+*>
+*> \param[in] LDP
+*> \verbatim
+*> LDP is INTEGER
+*> The leading dimension of array P. LDP >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] VL
+*> \verbatim
+*> VL is COMPLEX*16 array, dimension (LDVL,MM)
+*> On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
+*> contain an N-by-N matrix Q (usually the unitary matrix Q
+*> of left Schur vectors returned by ZHGEQZ).
+*> On exit, if SIDE = 'L' or 'B', VL contains:
+*> if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
+*> if HOWMNY = 'B', the matrix Q*Y;
+*> if HOWMNY = 'S', the left eigenvectors of (S,P) specified by
+*> SELECT, stored consecutively in the columns of
+*> VL, in the same order as their eigenvalues.
+*> Not referenced if SIDE = 'R'.
+*> \endverbatim
+*>
+*> \param[in] LDVL
+*> \verbatim
+*> LDVL is INTEGER
+*> The leading dimension of array VL. LDVL >= 1, and if
+*> SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.
+*> \endverbatim
+*>
+*> \param[in,out] VR
+*> \verbatim
+*> VR is COMPLEX*16 array, dimension (LDVR,MM)
+*> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
+*> contain an N-by-N matrix Q (usually the unitary matrix Z
+*> of right Schur vectors returned by ZHGEQZ).
+*> On exit, if SIDE = 'R' or 'B', VR contains:
+*> if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
+*> if HOWMNY = 'B', the matrix Z*X;
+*> if HOWMNY = 'S', the right eigenvectors of (S,P) specified by
+*> SELECT, stored consecutively in the columns of
+*> VR, in the same order as their eigenvalues.
+*> Not referenced if SIDE = 'L'.
+*> \endverbatim
+*>
+*> \param[in] LDVR
+*> \verbatim
+*> LDVR is INTEGER
+*> The leading dimension of the array VR. LDVR >= 1, and if
+*> SIDE = 'R' or 'B', LDVR >= N.
+*> \endverbatim
+*>
+*> \param[in] MM
+*> \verbatim
+*> MM is INTEGER
+*> The number of columns in the arrays VL and/or VR. MM >= M.
+*> \endverbatim
+*>
+*> \param[out] M
+*> \verbatim
+*> M is INTEGER
+*> The number of columns in the arrays VL and/or VR actually
+*> used to store the eigenvectors. If HOWMNY = 'A' or 'B', M
+*> is set to N. Each selected eigenvector occupies one column.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16GEcomputational
+*
+* =====================================================================
SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
$ LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER HOWMNY, SIDE
@@ -18,121 +233,6 @@
* ..
*
*
-* Purpose
-* =======
-*
-* ZTGEVC computes some or all of the right and/or left eigenvectors of
-* a pair of complex matrices (S,P), where S and P are upper triangular.
-* Matrix pairs of this type are produced by the generalized Schur
-* factorization of a complex matrix pair (A,B):
-*
-* A = Q*S*Z**H, B = Q*P*Z**H
-*
-* as computed by ZGGHRD + ZHGEQZ.
-*
-* The right eigenvector x and the left eigenvector y of (S,P)
-* corresponding to an eigenvalue w are defined by:
-*
-* S*x = w*P*x, (y**H)*S = w*(y**H)*P,
-*
-* where y**H denotes the conjugate tranpose of y.
-* The eigenvalues are not input to this routine, but are computed
-* directly from the diagonal elements of S and P.
-*
-* This routine returns the matrices X and/or Y of right and left
-* eigenvectors of (S,P), or the products Z*X and/or Q*Y,
-* where Z and Q are input matrices.
-* If Q and Z are the unitary factors from the generalized Schur
-* factorization of a matrix pair (A,B), then Z*X and Q*Y
-* are the matrices of right and left eigenvectors of (A,B).
-*
-* Arguments
-* =========
-*
-* SIDE (input) CHARACTER*1
-* = 'R': compute right eigenvectors only;
-* = 'L': compute left eigenvectors only;
-* = 'B': compute both right and left eigenvectors.
-*
-* HOWMNY (input) CHARACTER*1
-* = 'A': compute all right and/or left eigenvectors;
-* = 'B': compute all right and/or left eigenvectors,
-* backtransformed by the matrices in VR and/or VL;
-* = 'S': compute selected right and/or left eigenvectors,
-* specified by the logical array SELECT.
-*
-* SELECT (input) LOGICAL array, dimension (N)
-* If HOWMNY='S', SELECT specifies the eigenvectors to be
-* computed. The eigenvector corresponding to the j-th
-* eigenvalue is computed if SELECT(j) = .TRUE..
-* Not referenced if HOWMNY = 'A' or 'B'.
-*
-* N (input) INTEGER
-* The order of the matrices S and P. N >= 0.
-*
-* S (input) COMPLEX*16 array, dimension (LDS,N)
-* The upper triangular matrix S from a generalized Schur
-* factorization, as computed by ZHGEQZ.
-*
-* LDS (input) INTEGER
-* The leading dimension of array S. LDS >= max(1,N).
-*
-* P (input) COMPLEX*16 array, dimension (LDP,N)
-* The upper triangular matrix P from a generalized Schur
-* factorization, as computed by ZHGEQZ. P must have real
-* diagonal elements.
-*
-* LDP (input) INTEGER
-* The leading dimension of array P. LDP >= max(1,N).
-*
-* VL (input/output) COMPLEX*16 array, dimension (LDVL,MM)
-* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
-* contain an N-by-N matrix Q (usually the unitary matrix Q
-* of left Schur vectors returned by ZHGEQZ).
-* On exit, if SIDE = 'L' or 'B', VL contains:
-* if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
-* if HOWMNY = 'B', the matrix Q*Y;
-* if HOWMNY = 'S', the left eigenvectors of (S,P) specified by
-* SELECT, stored consecutively in the columns of
-* VL, in the same order as their eigenvalues.
-* Not referenced if SIDE = 'R'.
-*
-* LDVL (input) INTEGER
-* The leading dimension of array VL. LDVL >= 1, and if
-* SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.
-*
-* VR (input/output) COMPLEX*16 array, dimension (LDVR,MM)
-* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
-* contain an N-by-N matrix Q (usually the unitary matrix Z
-* of right Schur vectors returned by ZHGEQZ).
-* On exit, if SIDE = 'R' or 'B', VR contains:
-* if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
-* if HOWMNY = 'B', the matrix Z*X;
-* if HOWMNY = 'S', the right eigenvectors of (S,P) specified by
-* SELECT, stored consecutively in the columns of
-* VR, in the same order as their eigenvalues.
-* Not referenced if SIDE = 'L'.
-*
-* LDVR (input) INTEGER
-* The leading dimension of the array VR. LDVR >= 1, and if
-* SIDE = 'R' or 'B', LDVR >= N.
-*
-* MM (input) INTEGER
-* The number of columns in the arrays VL and/or VR. MM >= M.
-*
-* M (output) INTEGER
-* The number of columns in the arrays VL and/or VR actually
-* used to store the eigenvectors. If HOWMNY = 'A' or 'B', M
-* is set to N. Each selected eigenvector occupies one column.
-*
-* WORK (workspace) COMPLEX*16 array, dimension (2*N)
-*
-* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-*
* =====================================================================
*
* .. Parameters ..