--- rpl/lapack/lapack/dorcsd.f 2010/12/21 13:53:34 1.2
+++ rpl/lapack/lapack/dorcsd.f 2023/08/07 08:39:01 1.16
@@ -1,17 +1,306 @@
+*> \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 (LDU1,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 (LDU2,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 (LDV1T,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 (LDV2T,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.
+*
+*> \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 3.3.0) --
-*
-* -- Contributed by Brian Sutton of the Randolph-Macon College --
-* -- November 2010
*
+* -- LAPACK computational routine --
* -- 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..--
*
* .. Scalar Arguments ..
CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
@@ -27,145 +316,11 @@
$ * )
* ..
*
-* 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-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 ..
- DOUBLE PRECISION REALONE
- PARAMETER ( REALONE = 1.0D0 )
- DOUBLE PRECISION NEGONE, ONE, PIOVER2, ZERO
- PARAMETER ( NEGONE = -1.0D0, ONE = 1.0D0,
- $ PIOVER2 = 1.57079632679489662D0,
+ DOUBLE PRECISION ONE, ZERO
+ PARAMETER ( ONE = 1.0D0,
$ ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
@@ -182,7 +337,7 @@
$ WANTV1T, WANTV2T
* ..
* .. External Subroutines ..
- EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT, DLASCL, DLASET,
+ EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT,
$ DORBDB, DORGLQ, DORGQR, XERBLA
* ..
* .. External Functions ..
@@ -190,7 +345,7 @@
EXTERNAL LSAME
* ..
* .. Intrinsic Functions
- INTRINSIC COS, INT, MAX, MIN, SIN
+ INTRINSIC INT, MAX, MIN
* ..
* .. Executable Statements ..
*
@@ -210,17 +365,30 @@
INFO = -8
ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
INFO = -9
- ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR.
- $ ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN
- INFO = -11
+ ELSE IF ( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
+ INFO = -11
+ ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
+ INFO = -11
+ ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
+ INFO = -13
+ ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
+ INFO = -13
+ ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
+ INFO = -15
+ ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
+ INFO = -15
+ ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
+ INFO = -17
+ ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
+ INFO = -17
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
@@ -269,19 +437,19 @@
ITAUQ1 = ITAUP2 + MAX( 1, M - P )
ITAUQ2 = ITAUQ1 + MAX( 1, Q )
IORGQR = ITAUQ2 + MAX( 1, M - Q )
- CALL DORGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
+ CALL DORGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
$ CHILDINFO )
LORGQRWORKOPT = INT( WORK(1) )
LORGQRWORKMIN = MAX( 1, M - Q )
IORGLQ = ITAUQ2 + MAX( 1, M - Q )
- CALL DORGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
+ CALL DORGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
$ CHILDINFO )
LORGLQWORKOPT = INT( WORK(1) )
LORGLQWORKMIN = MAX( 1, M - Q )
IORBDB = ITAUQ2 + MAX( 1, M - Q )
CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
- $ X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK,
- $ -1, CHILDINFO )
+ $ X21, LDX21, X22, LDX22, THETA, V1T, U1, U2, V1T,
+ $ V2T, WORK, -1, CHILDINFO )
LORBDBWORKOPT = INT( WORK(1) )
LORBDBWORKMIN = LORBDBWORKOPT
IB11D = ITAUQ2 + MAX( 1, M - Q )
@@ -293,16 +461,17 @@
IB22D = IB21E + MAX( 1, Q - 1 )
IB22E = IB22D + MAX( 1, Q )
IBBCSD = IB22E + MAX( 1, Q - 1 )
- CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0,
- $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0,
- $ 0, 0, 0, 0, 0, 0, 0, WORK, -1, CHILDINFO )
+ CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
+ $ THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
+ $ LDV2T, U1, U1, U1, U1, U1, U1, U1, U1, WORK, -1,
+ $ CHILDINFO )
LBBCSDWORKOPT = INT( WORK(1) )
LBBCSDWORKMIN = LBBCSDWORKOPT
LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
$ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKOPT ) - 1
LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN,
$ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKMIN ) - 1
- WORK(1) = LWORKOPT
+ WORK(1) = MAX(LWORKOPT,LWORKMIN)
*
IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
INFO = -22
@@ -356,10 +525,14 @@
END IF
IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
- CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
- $ V2T(P+1,P+1), LDV2T )
- CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
- $ WORK(IORGLQ), LORGLQWORK, INFO )
+ IF (M-P .GT. Q) Then
+ CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
+ $ V2T(P+1,P+1), LDV2T )
+ END IF
+ IF (M .GT. Q) THEN
+ CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
+ $ WORK(IORGLQ), LORGLQWORK, INFO )
+ END IF
END IF
ELSE
IF( WANTU1 .AND. P .GT. 0 ) THEN
@@ -403,7 +576,7 @@
* Permute rows and columns to place identity submatrices in top-
* left corner of (1,1)-block and/or bottom-right corner of (1,2)-
* block and/or bottom-right corner of (2,1)-block and/or top-left
-* corner of (2,2)-block
+* corner of (2,2)-block
*
IF( Q .GT. 0 .AND. WANTU2 ) THEN
DO I = 1, Q