--- rpl/lapack/lapack/dorcsd.f 2011/07/22 07:38:08 1.3
+++ rpl/lapack/lapack/dorcsd.f 2011/11/21 20:43:00 1.4
@@ -1,19 +1,309 @@
+*> \brief \b DORCSD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DORCSD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
+* SIGNS, M, P, Q, X11, LDX11, X12,
+* LDX12, X21, LDX21, X22, LDX22, THETA,
+* U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
+* LDV2T, WORK, LWORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
+* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
+* $ LDX21, LDX22, LWORK, M, P, Q
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION THETA( * )
+* DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
+* $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
+* $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
+* $ * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DORCSD computes the CS decomposition of an M-by-M partitioned
+*> orthogonal matrix X:
+*>
+*> [ I 0 0 | 0 0 0 ]
+*> [ 0 C 0 | 0 -S 0 ]
+*> [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T
+*> X = [-----------] = [---------] [---------------------] [---------] .
+*> [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ]
+*> [ 0 S 0 | 0 C 0 ]
+*> [ 0 0 I | 0 0 0 ]
+*>
+*> X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
+*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
+*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
+*> which R = MIN(P,M-P,Q,M-Q).
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBU1
+*> \verbatim
+*> JOBU1 is CHARACTER
+*> = 'Y': U1 is computed;
+*> otherwise: U1 is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBU2
+*> \verbatim
+*> JOBU2 is CHARACTER
+*> = 'Y': U2 is computed;
+*> otherwise: U2 is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBV1T
+*> \verbatim
+*> JOBV1T is CHARACTER
+*> = 'Y': V1T is computed;
+*> otherwise: V1T is not computed.
+*> \endverbatim
+*>
+*> \param[in] JOBV2T
+*> \verbatim
+*> JOBV2T is CHARACTER
+*> = 'Y': V2T is computed;
+*> otherwise: V2T is not computed.
+*> \endverbatim
+*>
+*> \param[in] TRANS
+*> \verbatim
+*> TRANS is CHARACTER
+*> = 'T': X, U1, U2, V1T, and V2T are stored in row-major
+*> order;
+*> otherwise: X, U1, U2, V1T, and V2T are stored in column-
+*> major order.
+*> \endverbatim
+*>
+*> \param[in] SIGNS
+*> \verbatim
+*> SIGNS is CHARACTER
+*> = 'O': The lower-left block is made nonpositive (the
+*> "other" convention);
+*> otherwise: The upper-right block is made nonpositive (the
+*> "default" convention).
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows and columns in X.
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*> P is INTEGER
+*> The number of rows in X11 and X12. 0 <= P <= M.
+*> \endverbatim
+*>
+*> \param[in] Q
+*> \verbatim
+*> Q is INTEGER
+*> The number of columns in X11 and X21. 0 <= Q <= M.
+*> \endverbatim
+*>
+*> \param[in,out] X11
+*> \verbatim
+*> X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
+*> On entry, part of the orthogonal matrix whose CSD is desired.
+*> \endverbatim
+*>
+*> \param[in] LDX11
+*> \verbatim
+*> LDX11 is INTEGER
+*> The leading dimension of X11. LDX11 >= MAX(1,P).
+*> \endverbatim
+*>
+*> \param[in,out] X12
+*> \verbatim
+*> X12 is DOUBLE PRECISION array, dimension (LDX12,M-Q)
+*> On entry, part of the orthogonal matrix whose CSD is desired.
+*> \endverbatim
+*>
+*> \param[in] LDX12
+*> \verbatim
+*> LDX12 is INTEGER
+*> The leading dimension of X12. LDX12 >= MAX(1,P).
+*> \endverbatim
+*>
+*> \param[in,out] X21
+*> \verbatim
+*> X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
+*> On entry, part of the orthogonal matrix whose CSD is desired.
+*> \endverbatim
+*>
+*> \param[in] LDX21
+*> \verbatim
+*> LDX21 is INTEGER
+*> The leading dimension of X11. LDX21 >= MAX(1,M-P).
+*> \endverbatim
+*>
+*> \param[in,out] X22
+*> \verbatim
+*> X22 is DOUBLE PRECISION array, dimension (LDX22,M-Q)
+*> On entry, part of the orthogonal matrix whose CSD is desired.
+*> \endverbatim
+*>
+*> \param[in] LDX22
+*> \verbatim
+*> LDX22 is INTEGER
+*> The leading dimension of X11. LDX22 >= MAX(1,M-P).
+*> \endverbatim
+*>
+*> \param[out] THETA
+*> \verbatim
+*> THETA is DOUBLE PRECISION array, dimension (R), in which R =
+*> MIN(P,M-P,Q,M-Q).
+*> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
+*> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
+*> \endverbatim
+*>
+*> \param[out] U1
+*> \verbatim
+*> U1 is DOUBLE PRECISION array, dimension (P)
+*> If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
+*> \endverbatim
+*>
+*> \param[in] LDU1
+*> \verbatim
+*> LDU1 is INTEGER
+*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
+*> MAX(1,P).
+*> \endverbatim
+*>
+*> \param[out] U2
+*> \verbatim
+*> U2 is DOUBLE PRECISION array, dimension (M-P)
+*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
+*> matrix U2.
+*> \endverbatim
+*>
+*> \param[in] LDU2
+*> \verbatim
+*> LDU2 is INTEGER
+*> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
+*> MAX(1,M-P).
+*> \endverbatim
+*>
+*> \param[out] V1T
+*> \verbatim
+*> V1T is DOUBLE PRECISION array, dimension (Q)
+*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
+*> matrix V1**T.
+*> \endverbatim
+*>
+*> \param[in] LDV1T
+*> \verbatim
+*> LDV1T is INTEGER
+*> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
+*> MAX(1,Q).
+*> \endverbatim
+*>
+*> \param[out] V2T
+*> \verbatim
+*> V2T is DOUBLE PRECISION array, dimension (M-Q)
+*> If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
+*> matrix V2**T.
+*> \endverbatim
+*>
+*> \param[in] LDV2T
+*> \verbatim
+*> LDV2T is INTEGER
+*> The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
+*> MAX(1,M-Q).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
+*> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
+*> define the matrix in intermediate bidiagonal-block form
+*> remaining after nonconvergence. INFO specifies the number
+*> of nonzero PHI's.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the work array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (M-MIN(P, M-P, Q, M-Q))
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> > 0: DBBCSD did not converge. See the description of WORK
+*> above for details.
+*> \endverbatim
+*
+*> \par References:
+* ================
+*>
+*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
+*> Algorithms, 50(1):33-65, 2009.
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doubleOTHERcomputational
+*
+* =====================================================================
RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
$ SIGNS, M, P, Q, X11, LDX11, X12,
$ LDX12, X21, LDX21, X22, LDX22, THETA,
$ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
$ LDV2T, WORK, LWORK, IWORK, INFO )
- IMPLICIT NONE
-*
-* -- LAPACK routine (version 3.3.1) --
-*
-* -- Contributed by Brian Sutton of the Randolph-Macon College --
-* -- November 2010
*
+* -- 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..--
-*
-* @precisions normal d -> s
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
@@ -29,137 +319,6 @@
$ * )
* ..
*
-* Purpose
-* =======
-*
-* DORCSD computes the CS decomposition of an M-by-M partitioned
-* orthogonal matrix X:
-*
-* [ I 0 0 | 0 0 0 ]
-* [ 0 C 0 | 0 -S 0 ]
-* [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T
-* X = [-----------] = [---------] [---------------------] [---------] .
-* [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ]
-* [ 0 S 0 | 0 C 0 ]
-* [ 0 0 I | 0 0 0 ]
-*
-* X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
-* (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
-* R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
-* which R = MIN(P,M-P,Q,M-Q).
-*
-* Arguments
-* =========
-*
-* JOBU1 (input) CHARACTER
-* = 'Y': U1 is computed;
-* otherwise: U1 is not computed.
-*
-* JOBU2 (input) CHARACTER
-* = 'Y': U2 is computed;
-* otherwise: U2 is not computed.
-*
-* JOBV1T (input) CHARACTER
-* = 'Y': V1T is computed;
-* otherwise: V1T is not computed.
-*
-* JOBV2T (input) CHARACTER
-* = 'Y': V2T is computed;
-* otherwise: V2T is not computed.
-*
-* TRANS (input) CHARACTER
-* = 'T': X, U1, U2, V1T, and V2T are stored in row-major
-* order;
-* otherwise: X, U1, U2, V1T, and V2T are stored in column-
-* major order.
-*
-* SIGNS (input) CHARACTER
-* = 'O': The lower-left block is made nonpositive (the
-* "other" convention);
-* otherwise: The upper-right block is made nonpositive (the
-* "default" convention).
-*
-* M (input) INTEGER
-* The number of rows and columns in X.
-*
-* P (input) INTEGER
-* The number of rows in X11 and X12. 0 <= P <= M.
-*
-* Q (input) INTEGER
-* The number of columns in X11 and X21. 0 <= Q <= M.
-*
-* X (input/workspace) DOUBLE PRECISION array, dimension (LDX,M)
-* On entry, the orthogonal matrix whose CSD is desired.
-*
-* LDX (input) INTEGER
-* The leading dimension of X. LDX >= MAX(1,M).
-*
-* THETA (output) DOUBLE PRECISION array, dimension (R), in which R =
-* MIN(P,M-P,Q,M-Q).
-* C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
-* S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
-*
-* U1 (output) DOUBLE PRECISION array, dimension (P)
-* If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
-*
-* LDU1 (input) INTEGER
-* The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
-* MAX(1,P).
-*
-* U2 (output) DOUBLE PRECISION array, dimension (M-P)
-* If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
-* matrix U2.
-*
-* LDU2 (input) INTEGER
-* The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
-* MAX(1,M-P).
-*
-* V1T (output) DOUBLE PRECISION array, dimension (Q)
-* If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
-* matrix V1**T.
-*
-* LDV1T (input) INTEGER
-* The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
-* MAX(1,Q).
-*
-* V2T (output) DOUBLE PRECISION array, dimension (M-Q)
-* If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
-* matrix V2**T.
-*
-* LDV2T (input) INTEGER
-* The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
-* MAX(1,M-Q).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-* If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
-* ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
-* define the matrix in intermediate bidiagonal-block form
-* remaining after nonconvergence. INFO specifies the number
-* of nonzero PHI's.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal size of the WORK array, returns
-* this value as the first entry of the work array, and no error
-* message related to LWORK is issued by XERBLA.
-*
-* IWORK (workspace) INTEGER array, dimension (M-MIN(P, M-P, Q, M-Q))
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: DBBCSD did not converge. See the description of WORK
-* above for details.
-*
-* Reference
-* =========
-*
-* [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
-* Algorithms, 50(1):33-65, 2009.
-*
* ===================================================================
*
* .. Parameters ..
@@ -192,7 +351,7 @@
EXTERNAL LSAME
* ..
* .. Intrinsic Functions
- INTRINSIC COS, INT, MAX, MIN, SIN
+ INTRINSIC INT, MAX, MIN
* ..
* .. Executable Statements ..
*
@@ -216,13 +375,13 @@
$ ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN
INFO = -11
ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
- INFO = -14
+ INFO = -20
ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
- INFO = -16
+ INFO = -22
ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
- INFO = -18
+ INFO = -24
ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
- INFO = -20
+ INFO = -26
END IF
*
* Work with transpose if convenient