*> vectors, stored columnwise) as specified by RANGE; if
*> JOBU = 'N', U is not referenced.
*> Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
-*> the exact value of NS is not known in advance and an upper
+*> the exact value of NS is not known ILQFin advance and an upper
*> bound must be used.
*> \endverbatim
*>
CHARACTER JOBZ, RNGTGK
LOGICAL ALLS, INDS, LQUERY, VALS, WANTU, WANTVT
INTEGER I, ID, IE, IERR, ILQF, ILTGK, IQRF, ISCL,
- $ ITAU, ITAUP, ITAUQ, ITEMP, ITEMPR, ITGKZ,
- $ IUTGK, J, K, MAXWRK, MINMN, MINWRK, MNTHR
+ $ ITAU, ITAUP, ITAUQ, ITEMP, ITGKZ, IUTGK,
+ $ J, K, MAXWRK, MINMN, MINWRK, MNTHR
REAL ABSTOL, ANRM, BIGNUM, EPS, SMLNUM
* ..
* .. Local Arrays ..
IF( INFO.EQ.0 ) THEN
IF( WANTU .AND. LDU.LT.M ) THEN
INFO = -15
- ELSE IF( WANTVT ) THEN
- IF( INDS ) THEN
- IF( LDVT.LT.IU-IL+1 ) THEN
- INFO = -17
- END IF
- ELSE IF( LDVT.LT.MINMN ) THEN
- INFO = -17
- END IF
+ ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
+ INFO = -16
END IF
END IF
END IF
*
* Path 1 (M much larger than N)
*
- MINWRK = N*(N+5)
- MAXWRK = N + N*ILAENV(1,'CGEQRF',' ',M,N,-1,-1)
- MAXWRK = MAX(MAXWRK,
- $ N*N+2*N+2*N*ILAENV(1,'CGEBRD',' ',N,N,-1,-1))
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ N*N+2*N+N*ILAENV(1,'CUNMQR','LN',N,N,N,-1))
- END IF
+ MAXWRK = N + N*
+ $ ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
+ MAXWRK = MAX( MAXWRK, N*N + N + 2*N*
+ $ ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
+ MINWRK = N*(N+4)
ELSE
*
* Path 2 (M at least N, but not much larger)
*
- MINWRK = 3*N + M
- MAXWRK = 2*N + (M+N)*ILAENV(1,'CGEBRD',' ',M,N,-1,-1)
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ 2*N+N*ILAENV(1,'CUNMQR','LN',N,N,N,-1))
- END IF
+ MAXWRK = 2*N + ( M+N )*
+ $ ILAENV( 1, 'CGEBRD', ' ', M, N, -1, -1 )
+ MINWRK = 2*N + M
END IF
ELSE
MNTHR = ILAENV( 6, 'CGESVD', JOBU // JOBVT, M, N, 0, 0 )
*
* Path 1t (N much larger than M)
*
- MINWRK = M*(M+5)
- MAXWRK = M + M*ILAENV(1,'CGELQF',' ',M,N,-1,-1)
- MAXWRK = MAX(MAXWRK,
- $ M*M+2*M+2*M*ILAENV(1,'CGEBRD',' ',M,M,-1,-1))
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ M*M+2*M+M*ILAENV(1,'CUNMQR','LN',M,M,M,-1))
- END IF
+ MAXWRK = M + M*
+ $ ILAENV( 1, 'CGELQF', ' ', M, N, -1, -1 )
+ MAXWRK = MAX( MAXWRK, M*M + M + 2*M*
+ $ ILAENV( 1, 'CGEBRD', ' ', M, M, -1, -1 ) )
+ MINWRK = M*(M+4)
ELSE
*
* Path 2t (N greater than M, but not much larger)
*
-*
- MINWRK = 3*M + N
- MAXWRK = 2*M + (M+N)*ILAENV(1,'CGEBRD',' ',M,N,-1,-1)
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ 2*M+M*ILAENV(1,'CUNMQR','LN',M,M,M,-1))
- END IF
+ MAXWRK = M*(M*2+19) + ( M+N )*
+ $ ILAENV( 1, 'CGEBRD', ' ', M, N, -1, -1 )
+ MINWRK = 2*M + N
END IF
END IF
END IF
CALL CGEBRD( N, N, WORK( IQRF ), N, RWORK( ID ),
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + N*(N*2+1)
+ ITEMP = ITGKZ + N*(N*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*N*N+14*N)
*
CALL SBDSVDX( 'U', JOBZ, RNGTGK, N, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), N*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + N
END DO
- CALL CLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
+ CALL CLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
*
* Call CUNMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL CGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
$ LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + N*(N*2+1)
+ ITEMP = ITGKZ + N*(N*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*N*N+14*N)
*
CALL SBDSVDX( 'U', JOBZ, RNGTGK, N, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), N*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + N
END DO
- CALL CLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
+ CALL CLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
*
* Call CUNMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL CGEBRD( M, M, WORK( ILQF ), M, RWORK( ID ),
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + M*(M*2+1)
+ ITEMP = ITGKZ + M*(M*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*M*M+14*M)
*
CALL SBDSVDX( 'U', JOBZ, RNGTGK, M, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), M*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + M
END DO
- CALL CLASET( 'A', NS, N-M, CZERO, CZERO,
+ CALL CLASET( 'A', M, N-M, CZERO, CZERO,
$ VT( 1,M+1 ), LDVT )
*
* Call CUNMBR to compute (VB**T)*(PB**T)
CALL CGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
$ LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + M*(M*2+1)
+ ITEMP = ITGKZ + M*(M*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*M*M+14*M)
*
CALL SBDSVDX( 'L', JOBZ, RNGTGK, M, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), M*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + M
END DO
- CALL CLASET( 'A', NS, N-M, CZERO, CZERO,
+ CALL CLASET( 'A', M, N-M, CZERO, CZERO,
$ VT( 1,M+1 ), LDVT )
*
* Call CUNMBR to compute VB**T * PB**T
*> vectors, stored columnwise) as specified by RANGE; if
*> JOBU = 'N', U is not referenced.
*> Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
-*> the exact value of NS is not known in advance and an upper
+*> the exact value of NS is not known ILQFin advance and an upper
*> bound must be used.
*> \endverbatim
*>
IF( INFO.EQ.0 ) THEN
IF( WANTU .AND. LDU.LT.M ) THEN
INFO = -15
- ELSE IF( WANTVT ) THEN
- IF( INDS ) THEN
- IF( LDVT.LT.IU-IL+1 ) THEN
- INFO = -17
- END IF
- ELSE IF( LDVT.LT.MINMN ) THEN
- INFO = -17
- END IF
+ ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
+ INFO = -16
END IF
END IF
END IF
*
* Path 1 (M much larger than N)
*
- MAXWRK = N +
+ MAXWRK = N*(N*2+16) +
$ N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
- MAXWRK = MAX( MAXWRK, N*(N+5) + 2*N*
+ MAXWRK = MAX( MAXWRK, N*(N*2+20) + 2*N*
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,N*(N*3+6)+N*
- $ ILAENV( 1, 'DORMQR', ' ', N, N, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,N*(N*3+6)+N*
- $ ILAENV( 1, 'DORMLQ', ' ', N, N, -1, -1 ) )
- END IF
- MINWRK = N*(N*3+20)
+ MINWRK = N*(N*2+21)
ELSE
*
* Path 2 (M at least N, but not much larger)
*
- MAXWRK = 4*N + ( M+N )*
+ MAXWRK = N*(N*2+19) + ( M+N )*
$ ILAENV( 1, 'DGEBRD', ' ', M, N, -1, -1 )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,N*(N*2+5)+N*
- $ ILAENV( 1, 'DORMQR', ' ', N, N, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,N*(N*2+5)+N*
- $ ILAENV( 1, 'DORMLQ', ' ', N, N, -1, -1 ) )
- END IF
- MINWRK = MAX(N*(N*2+19),4*N+M)
+ MINWRK = N*(N*2+20) + M
END IF
ELSE
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 )
*
* Path 1t (N much larger than M)
*
- MAXWRK = M +
+ MAXWRK = M*(M*2+16) +
$ M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
- MAXWRK = MAX( MAXWRK, M*(M+5) + 2*M*
+ MAXWRK = MAX( MAXWRK, M*(M*2+20) + 2*M*
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,M*(M*3+6)+M*
- $ ILAENV( 1, 'DORMQR', ' ', M, M, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,M*(M*3+6)+M*
- $ ILAENV( 1, 'DORMLQ', ' ', M, M, -1, -1 ) )
- END IF
- MINWRK = M*(M*3+20)
+ MINWRK = M*(M*2+21)
ELSE
*
-* Path 2t (N at least M, but not much larger)
+* Path 2t (N greater than M, but not much larger)
*
- MAXWRK = 4*M + ( M+N )*
+ MAXWRK = M*(M*2+19) + ( M+N )*
$ ILAENV( 1, 'DGEBRD', ' ', M, N, -1, -1 )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,M*(M*2+5)+M*
- $ ILAENV( 1, 'DORMQR', ' ', M, M, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,M*(M*2+5)+M*
- $ ILAENV( 1, 'DORMLQ', ' ', M, M, -1, -1 ) )
- END IF
- MINWRK = MAX(M*(M*2+19),4*M+N)
+ MINWRK = M*(M*2+20) + N
END IF
END IF
END IF
CALL DCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
J = J + N*2
END DO
- CALL DLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
+ CALL DLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
*
* Call DORMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL DCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
J = J + N*2
END DO
- CALL DLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
+ CALL DLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
*
* Call DORMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL DCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
J = J + M*2
END DO
- CALL DLASET( 'A', NS, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT)
+ CALL DLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
*
* Call DORMBR to compute (VB**T)*(PB**T)
* (Workspace in WORK( ITEMP ): need M, prefer M*NB)
CALL DCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
J = J + M*2
END DO
- CALL DLASET( 'A', NS, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT)
+ CALL DLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
*
* Call DORMBR to compute VB**T * PB**T
* (Workspace in WORK( ITEMP ): need M, prefer M*NB)
*> vectors, stored columnwise) as specified by RANGE; if
*> JOBU = 'N', U is not referenced.
*> Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
-*> the exact value of NS is not known in advance and an upper
+*> the exact value of NS is not known ILQFin advance and an upper
*> bound must be used.
*> \endverbatim
*>
IF( INFO.EQ.0 ) THEN
IF( WANTU .AND. LDU.LT.M ) THEN
INFO = -15
- ELSE IF( WANTVT ) THEN
- IF( INDS ) THEN
- IF( LDVT.LT.IU-IL+1 ) THEN
- INFO = -17
- END IF
- ELSE IF( LDVT.LT.MINMN ) THEN
- INFO = -17
- END IF
+ ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
+ INFO = -16
END IF
END IF
END IF
*
* Path 1 (M much larger than N)
*
- MAXWRK = N +
+ MAXWRK = N*(N*2+16) +
$ N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
- MAXWRK = MAX( MAXWRK, N*(N+5) + 2*N*
+ MAXWRK = MAX( MAXWRK, N*(N*2+20) + 2*N*
$ ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,N*(N*3+6)+N*
- $ ILAENV( 1, 'SORMQR', ' ', N, N, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,N*(N*3+6)+N*
- $ ILAENV( 1, 'SORMLQ', ' ', N, N, -1, -1 ) )
- END IF
- MINWRK = N*(N*3+20)
+ MINWRK = N*(N*2+21)
ELSE
*
* Path 2 (M at least N, but not much larger)
*
- MAXWRK = 4*N + ( M+N )*
+ MAXWRK = N*(N*2+19) + ( M+N )*
$ ILAENV( 1, 'SGEBRD', ' ', M, N, -1, -1 )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,N*(N*2+5)+N*
- $ ILAENV( 1, 'SORMQR', ' ', N, N, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,N*(N*2+5)+N*
- $ ILAENV( 1, 'SORMLQ', ' ', N, N, -1, -1 ) )
- END IF
- MINWRK = MAX(N*(N*2+19),4*N+M)
+ MINWRK = N*(N*2+20) + M
END IF
ELSE
MNTHR = ILAENV( 6, 'SGESVD', JOBU // JOBVT, M, N, 0, 0 )
*
* Path 1t (N much larger than M)
*
- MAXWRK = M +
+ MAXWRK = M*(M*2+16) +
$ M*ILAENV( 1, 'SGELQF', ' ', M, N, -1, -1 )
- MAXWRK = MAX( MAXWRK, M*(M+5) + 2*M*
+ MAXWRK = MAX( MAXWRK, M*(M*2+20) + 2*M*
$ ILAENV( 1, 'SGEBRD', ' ', M, M, -1, -1 ) )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,M*(M*3+6)+M*
- $ ILAENV( 1, 'SORMQR', ' ', M, M, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,M*(M*3+6)+M*
- $ ILAENV( 1, 'SORMLQ', ' ', M, M, -1, -1 ) )
- END IF
- MINWRK = M*(M*3+20)
+ MINWRK = M*(M*2+21)
ELSE
*
-* Path 2t (N at least M, but not much larger)
+* Path 2t (N greater than M, but not much larger)
*
- MAXWRK = 4*M + ( M+N )*
+ MAXWRK = M*(M*2+19) + ( M+N )*
$ ILAENV( 1, 'SGEBRD', ' ', M, N, -1, -1 )
- IF (WANTU) THEN
- MAXWRK = MAX(MAXWRK,M*(M*2+5)+M*
- $ ILAENV( 1, 'SORMQR', ' ', M, M, -1, -1 ) )
- END IF
- IF (WANTVT) THEN
- MAXWRK = MAX(MAXWRK,M*(M*2+5)+M*
- $ ILAENV( 1, 'SORMLQ', ' ', M, M, -1, -1 ) )
- END IF
- MINWRK = MAX(M*(M*2+19),4*M+N)
+ MINWRK = M*(M*2+20) + N
END IF
END IF
END IF
CALL SCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
J = J + N*2
END DO
- CALL SLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
+ CALL SLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
*
* Call SORMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL SCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
J = J + N*2
END DO
- CALL SLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
+ CALL SLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
*
* Call SORMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL SCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
J = J + M*2
END DO
- CALL SLASET( 'A', NS, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT)
+ CALL SLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
*
* Call SORMBR to compute (VB**T)*(PB**T)
* (Workspace in WORK( ITEMP ): need M, prefer M*NB)
CALL SCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
J = J + M*2
END DO
- CALL SLASET( 'A', NS, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT)
+ CALL SLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
*
* Call SORMBR to compute VB**T * PB**T
* (Workspace in WORK( ITEMP ): need M, prefer M*NB)
* ..
*
*
-*> \par Purpose:
-* =============
-*>
-*> \verbatim
-*>
-*> ZGESVDX computes the singular value decomposition (SVD) of a complex
-*> M-by-N matrix A, optionally computing the left and/or right singular
-*> vectors. The SVD is written
-*>
-*> A = U * SIGMA * transpose(V)
-*>
-*> where SIGMA is an M-by-N matrix which is zero except for its
-*> min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
-*> V is an N-by-N unitary matrix. The diagonal elements of SIGMA
-*> are the singular values of A; they are real and non-negative, and
-*> are returned in descending order. The first min(m,n) columns of
-*> U and V are the left and right singular vectors of A.
-*>
-*> ZGESVDX uses an eigenvalue problem for obtaining the SVD, which
-*> allows for the computation of a subset of singular values and
-*> vectors. See DBDSVDX for details.
-*>
-*> Note that the routine returns V**T, not V.
-*> \endverbatim
+* Purpose
+* =======
+*
+* ZGESVDX computes the singular value decomposition (SVD) of a complex
+* M-by-N matrix A, optionally computing the left and/or right singular
+* vectors. The SVD is written
+*
+* A = U * SIGMA * transpose(V)
+*
+* where SIGMA is an M-by-N matrix which is zero except for its
+* min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
+* V is an N-by-N unitary matrix. The diagonal elements of SIGMA
+* are the singular values of A; they are real and non-negative, and
+* are returned in descending order. The first min(m,n) columns of
+* U and V are the left and right singular vectors of A.
+*
+* ZGESVDX uses an eigenvalue problem for obtaining the SVD, which
+* allows for the computation of a subset of singular values and
+* vectors. See DBDSVDX for details.
+*
+* Note that the routine returns V**T, not V.
*
* Arguments:
* ==========
*>
*> \param[in,out] A
*> \verbatim
-*> A is COMPLEX*16 array, dimension (LDA,N)
+*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the M-by-N matrix A.
*> On exit, the contents of A are destroyed.
*> \endverbatim
*> vectors, stored columnwise) as specified by RANGE; if
*> JOBU = 'N', U is not referenced.
*> Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
-*> the exact value of NS is not known in advance and an upper
+*> the exact value of NS is not known ILQFin advance and an upper
*> bound must be used.
*> \endverbatim
*>
CHARACTER JOBZ, RNGTGK
LOGICAL ALLS, INDS, LQUERY, VALS, WANTU, WANTVT
INTEGER I, ID, IE, IERR, ILQF, ILTGK, IQRF, ISCL,
- $ ITAU, ITAUP, ITAUQ, ITEMP, ITEMPR, ITGKZ,
- $ IUTGK, J, K, MAXWRK, MINMN, MINWRK, MNTHR
+ $ ITAU, ITAUP, ITAUQ, ITEMP, ITGKZ, IUTGK,
+ $ J, K, MAXWRK, MINMN, MINWRK, MNTHR
DOUBLE PRECISION ABSTOL, ANRM, BIGNUM, EPS, SMLNUM
* ..
* .. Local Arrays ..
IF( INFO.EQ.0 ) THEN
IF( WANTU .AND. LDU.LT.M ) THEN
INFO = -15
- ELSE IF( WANTVT ) THEN
- IF( INDS ) THEN
- IF( LDVT.LT.IU-IL+1 ) THEN
- INFO = -17
- END IF
- ELSE IF( LDVT.LT.MINMN ) THEN
- INFO = -17
- END IF
+ ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
+ INFO = -16
END IF
END IF
END IF
*
* Path 1 (M much larger than N)
*
- MINWRK = N*(N+5)
- MAXWRK = N + N*ILAENV(1,'ZGEQRF',' ',M,N,-1,-1)
- MAXWRK = MAX(MAXWRK,
- $ N*N+2*N+2*N*ILAENV(1,'ZGEBRD',' ',N,N,-1,-1))
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ N*N+2*N+N*ILAENV(1,'ZUNMQR','LN',N,N,N,-1))
- END IF
+ MAXWRK = N + N*
+ $ ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
+ MAXWRK = MAX( MAXWRK, N*N + N + 2*N*
+ $ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
+ MINWRK = N*(N+4)
ELSE
*
* Path 2 (M at least N, but not much larger)
*
- MINWRK = 3*N + M
- MAXWRK = 2*N + (M+N)*ILAENV(1,'ZGEBRD',' ',M,N,-1,-1)
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ 2*N+N*ILAENV(1,'ZUNMQR','LN',N,N,N,-1))
- END IF
+ MAXWRK = 2*N + ( M+N )*
+ $ ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 )
+ MINWRK = 2*N + M
END IF
ELSE
MNTHR = ILAENV( 6, 'ZGESVD', JOBU // JOBVT, M, N, 0, 0 )
*
* Path 1t (N much larger than M)
*
- MINWRK = M*(M+5)
- MAXWRK = M + M*ILAENV(1,'ZGELQF',' ',M,N,-1,-1)
- MAXWRK = MAX(MAXWRK,
- $ M*M+2*M+2*M*ILAENV(1,'ZGEBRD',' ',M,M,-1,-1))
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ M*M+2*M+M*ILAENV(1,'ZUNMQR','LN',M,M,M,-1))
- END IF
+ MAXWRK = M + M*
+ $ ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
+ MAXWRK = MAX( MAXWRK, M*M + M + 2*M*
+ $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
+ MINWRK = M*(M+4)
ELSE
*
* Path 2t (N greater than M, but not much larger)
*
-*
- MINWRK = 3*M + N
- MAXWRK = 2*M + (M+N)*ILAENV(1,'ZGEBRD',' ',M,N,-1,-1)
- IF (WANTU .OR. WANTVT) THEN
- MAXWRK = MAX(MAXWRK,
- $ 2*M+M*ILAENV(1,'ZUNMQR','LN',M,M,M,-1))
- END IF
+ MAXWRK = M*(M*2+19) + ( M+N )*
+ $ ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 )
+ MINWRK = 2*M + N
END IF
END IF
END IF
CALL ZGEBRD( N, N, WORK( IQRF ), N, RWORK( ID ),
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + N*(N*2+1)
+ ITEMP = ITGKZ + N*(N*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*N*N+14*N)
*
CALL DBDSVDX( 'U', JOBZ, RNGTGK, N, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), N*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + N
END DO
- CALL ZLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
+ CALL ZLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
*
* Call ZUNMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL ZGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
$ LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + N*(N*2+1)
+ ITEMP = ITGKZ + N*(N*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*N*N+14*N)
*
CALL DBDSVDX( 'U', JOBZ, RNGTGK, N, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), N*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + N
END DO
- CALL ZLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
+ CALL ZLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
*
* Call ZUNMBR to compute QB*UB.
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
CALL ZGEBRD( M, M, WORK( ILQF ), M, RWORK( ID ),
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + M*(M*2+1)
+ ITEMP = ITGKZ + M*(M*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*M*M+14*M)
*
CALL DBDSVDX( 'U', JOBZ, RNGTGK, M, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), M*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + M
END DO
- CALL ZLASET( 'A', NS, N-M, CZERO, CZERO,
+ CALL ZLASET( 'A', M, N-M, CZERO, CZERO,
$ VT( 1,M+1 ), LDVT )
*
* Call ZUNMBR to compute (VB**T)*(PB**T)
CALL ZGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
$ LWORK-ITEMP+1, INFO )
- ITEMPR = ITGKZ + M*(M*2+1)
+ ITEMP = ITGKZ + M*(M*2+1)
*
* Solve eigenvalue problem TGK*Z=Z*S.
* (Workspace: need 2*M*M+14*M)
*
CALL DBDSVDX( 'L', JOBZ, RNGTGK, M, RWORK( ID ),
$ RWORK( IE ), VL, VU, ILTGK, IUTGK, NS, S,
- $ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
+ $ RWORK( ITGKZ ), M*2, RWORK( ITEMP ),
$ IWORK, INFO)
*
* If needed, compute left singular vectors.
END DO
K = K + M
END DO
- CALL ZLASET( 'A', NS, N-M, CZERO, CZERO,
+ CALL ZLASET( 'A', M, N-M, CZERO, CZERO,
$ VT( 1,M+1 ), LDVT )
*
* Call ZUNMBR to compute VB**T * PB**T
projects / platform / upstream / openblas.git / commitdiff