--- rpl/lapack/lapack/zggsvp.f 2011/07/22 07:38:14 1.8
+++ rpl/lapack/lapack/zggsvp.f 2011/11/21 20:43:10 1.9
@@ -1,11 +1,272 @@
+*> \brief \b ZGGSVP
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGGSVP + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
+* TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
+* IWORK, RWORK, TAU, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBQ, JOBU, JOBV
+* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P
+* DOUBLE PRECISION TOLA, TOLB
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION RWORK( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
+* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGGSVP computes unitary matrices U, V and Q such that
+*>
+*> N-K-L K L
+*> U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
+*> L ( 0 0 A23 )
+*> M-K-L ( 0 0 0 )
+*>
+*> N-K-L K L
+*> = K ( 0 A12 A13 ) if M-K-L < 0;
+*> M-K ( 0 0 A23 )
+*>
+*> N-K-L K L
+*> V**H*B*Q = L ( 0 0 B13 )
+*> P-L ( 0 0 0 )
+*>
+*> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
+*> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
+*> otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
+*> numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.
+*>
+*> This decomposition is the preprocessing step for computing the
+*> Generalized Singular Value Decomposition (GSVD), see subroutine
+*> ZGGSVD.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBU
+*> \verbatim
+*> JOBU is CHARACTER*1
+*> = 'U': Unitary matrix U is computed;
+*> = 'N': U is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBV
+*> \verbatim
+*> JOBV is CHARACTER*1
+*> = 'V': Unitary matrix V is computed;
+*> = 'N': V is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBQ
+*> \verbatim
+*> JOBQ is CHARACTER*1
+*> = 'Q': Unitary matrix Q is computed;
+*> = 'N': Q is not computed.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix A. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*> P is INTEGER
+*> The number of rows of the matrix B. P >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrices A and B. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the M-by-N matrix A.
+*> On exit, A contains the triangular (or trapezoidal) matrix
+*> described in the Purpose section.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,N)
+*> On entry, the P-by-N matrix B.
+*> On exit, B contains the triangular matrix described in
+*> the Purpose section.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,P).
+*> \endverbatim
+*>
+*> \param[in] TOLA
+*> \verbatim
+*> TOLA is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in] TOLB
+*> \verbatim
+*> TOLB is DOUBLE PRECISION
+*>
+*> TOLA and TOLB are the thresholds to determine the effective
+*> numerical rank of matrix B and a subblock of A. Generally,
+*> they are set to
+*> TOLA = MAX(M,N)*norm(A)*MAZHEPS,
+*> TOLB = MAX(P,N)*norm(B)*MAZHEPS.
+*> The size of TOLA and TOLB may affect the size of backward
+*> errors of the decomposition.
+*> \endverbatim
+*>
+*> \param[out] K
+*> \verbatim
+*> K is INTEGER
+*> \endverbatim
+*>
+*> \param[out] L
+*> \verbatim
+*> L is INTEGER
+*>
+*> On exit, K and L specify the dimension of the subblocks
+*> described in Purpose section.
+*> K + L = effective numerical rank of (A**H,B**H)**H.
+*> \endverbatim
+*>
+*> \param[out] U
+*> \verbatim
+*> U is COMPLEX*16 array, dimension (LDU,M)
+*> If JOBU = 'U', U contains the unitary matrix U.
+*> If JOBU = 'N', U is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDU
+*> \verbatim
+*> LDU is INTEGER
+*> The leading dimension of the array U. LDU >= max(1,M) if
+*> JOBU = 'U'; LDU >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[out] V
+*> \verbatim
+*> V is COMPLEX*16 array, dimension (LDV,P)
+*> If JOBV = 'V', V contains the unitary matrix V.
+*> If JOBV = 'N', V is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDV
+*> \verbatim
+*> LDV is INTEGER
+*> The leading dimension of the array V. LDV >= max(1,P) if
+*> JOBV = 'V'; LDV >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[out] Q
+*> \verbatim
+*> Q is COMPLEX*16 array, dimension (LDQ,N)
+*> If JOBQ = 'Q', Q contains the unitary matrix Q.
+*> If JOBQ = 'N', Q is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDQ
+*> \verbatim
+*> LDQ is INTEGER
+*> The leading dimension of the array Q. LDQ >= max(1,N) if
+*> JOBQ = 'Q'; LDQ >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is COMPLEX*16 array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (max(3*N,M,P))
+*> \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.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization
+*> with column pivoting to detect the effective numerical rank of the
+*> a matrix. It may be replaced by a better rank determination strategy.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
$ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
$ IWORK, RWORK, TAU, WORK, INFO )
*
-* -- LAPACK routine (version 3.3.1) --
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBQ, JOBU, JOBV
@@ -19,132 +280,6 @@
$ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZGGSVP computes unitary matrices U, V and Q such that
-*
-* N-K-L K L
-* U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
-* L ( 0 0 A23 )
-* M-K-L ( 0 0 0 )
-*
-* N-K-L K L
-* = K ( 0 A12 A13 ) if M-K-L < 0;
-* M-K ( 0 0 A23 )
-*
-* N-K-L K L
-* V**H*B*Q = L ( 0 0 B13 )
-* P-L ( 0 0 0 )
-*
-* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
-* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
-* otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
-* numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.
-*
-* This decomposition is the preprocessing step for computing the
-* Generalized Singular Value Decomposition (GSVD), see subroutine
-* ZGGSVD.
-*
-* Arguments
-* =========
-*
-* JOBU (input) CHARACTER*1
-* = 'U': Unitary matrix U is computed;
-* = 'N': U is not computed.
-*
-* JOBV (input) CHARACTER*1
-* = 'V': Unitary matrix V is computed;
-* = 'N': V is not computed.
-*
-* JOBQ (input) CHARACTER*1
-* = 'Q': Unitary matrix Q is computed;
-* = 'N': Q is not computed.
-*
-* M (input) INTEGER
-* The number of rows of the matrix A. M >= 0.
-*
-* P (input) INTEGER
-* The number of rows of the matrix B. P >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrices A and B. N >= 0.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA,N)
-* On entry, the M-by-N matrix A.
-* On exit, A contains the triangular (or trapezoidal) matrix
-* described in the Purpose section.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* B (input/output) COMPLEX*16 array, dimension (LDB,N)
-* On entry, the P-by-N matrix B.
-* On exit, B contains the triangular matrix described in
-* the Purpose section.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,P).
-*
-* TOLA (input) DOUBLE PRECISION
-* TOLB (input) DOUBLE PRECISION
-* TOLA and TOLB are the thresholds to determine the effective
-* numerical rank of matrix B and a subblock of A. Generally,
-* they are set to
-* TOLA = MAX(M,N)*norm(A)*MAZHEPS,
-* TOLB = MAX(P,N)*norm(B)*MAZHEPS.
-* The size of TOLA and TOLB may affect the size of backward
-* errors of the decomposition.
-*
-* K (output) INTEGER
-* L (output) INTEGER
-* On exit, K and L specify the dimension of the subblocks
-* described in Purpose section.
-* K + L = effective numerical rank of (A**H,B**H)**H.
-*
-* U (output) COMPLEX*16 array, dimension (LDU,M)
-* If JOBU = 'U', U contains the unitary matrix U.
-* If JOBU = 'N', U is not referenced.
-*
-* LDU (input) INTEGER
-* The leading dimension of the array U. LDU >= max(1,M) if
-* JOBU = 'U'; LDU >= 1 otherwise.
-*
-* V (output) COMPLEX*16 array, dimension (LDV,P)
-* If JOBV = 'V', V contains the unitary matrix V.
-* If JOBV = 'N', V is not referenced.
-*
-* LDV (input) INTEGER
-* The leading dimension of the array V. LDV >= max(1,P) if
-* JOBV = 'V'; LDV >= 1 otherwise.
-*
-* Q (output) COMPLEX*16 array, dimension (LDQ,N)
-* If JOBQ = 'Q', Q contains the unitary matrix Q.
-* If JOBQ = 'N', Q is not referenced.
-*
-* LDQ (input) INTEGER
-* The leading dimension of the array Q. LDQ >= max(1,N) if
-* JOBQ = 'Q'; LDQ >= 1 otherwise.
-*
-* IWORK (workspace) INTEGER array, dimension (N)
-*
-* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
-*
-* TAU (workspace) COMPLEX*16 array, dimension (N)
-*
-* WORK (workspace) COMPLEX*16 array, dimension (max(3*N,M,P))
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-*
-* Further Details
-* ===============
-*
-* The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization
-* with column pivoting to detect the effective numerical rank of the
-* a matrix. It may be replaced by a better rank determination strategy.
-*
* =====================================================================
*
* .. Parameters ..