parent
acdff55a6a
commit
26b3b3a3e6
|
@ -51,8 +51,7 @@ float LAPACKE_clantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
}
|
||||
#endif
|
||||
/* Allocate memory for working array(s) */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
work = (float*)LAPACKE_malloc( sizeof(float) * MAX(1,MAX(m,n)) );
|
||||
if( work == NULL ) {
|
||||
info = LAPACK_WORK_MEMORY_ERROR;
|
||||
|
@ -63,8 +62,7 @@ float LAPACKE_clantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
res = LAPACKE_clantr_work( matrix_layout, norm, uplo, diag, m, n, a, lda,
|
||||
work );
|
||||
/* Release memory and exit */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
LAPACKE_free( work );
|
||||
}
|
||||
exit_level_0:
|
||||
|
|
|
@ -51,8 +51,7 @@ double LAPACKE_dlantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
}
|
||||
#endif
|
||||
/* Allocate memory for working array(s) */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
work = (double*)LAPACKE_malloc( sizeof(double) * MAX(1,MAX(m,n)) );
|
||||
if( work == NULL ) {
|
||||
info = LAPACK_WORK_MEMORY_ERROR;
|
||||
|
@ -63,8 +62,7 @@ double LAPACKE_dlantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
res = LAPACKE_dlantr_work( matrix_layout, norm, uplo, diag, m, n, a, lda,
|
||||
work );
|
||||
/* Release memory and exit */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
LAPACKE_free( work );
|
||||
}
|
||||
exit_level_0:
|
||||
|
|
|
@ -38,10 +38,10 @@ double LAPACKE_dlantr_work( int matrix_layout, char norm, char uplo,
|
|||
const double* a, lapack_int lda, double* work )
|
||||
{
|
||||
lapack_int info = 0;
|
||||
double res = 0.;
|
||||
double res = 0.;
|
||||
if( matrix_layout == LAPACK_COL_MAJOR ) {
|
||||
/* Call LAPACK function and adjust info */
|
||||
LAPACK_dlantr( &norm, &uplo, &diag, &m, &n, a, &lda, work );
|
||||
res = LAPACK_dlantr( &norm, &uplo, &diag, &m, &n, a, &lda, work );
|
||||
if( info < 0 ) {
|
||||
info = info - 1;
|
||||
}
|
||||
|
|
|
@ -74,11 +74,10 @@ lapack_int LAPACKE_dormbr_work( int matrix_layout, char vect, char side,
|
|||
}
|
||||
/* Allocate memory for temporary array(s) */
|
||||
if( LAPACKE_lsame( vect, 'q' ) ) {
|
||||
a_t = (double*)LAPACKE_malloc( sizeof(double) * lda_t * k );
|
||||
a_t = (double*)LAPACKE_malloc( sizeof(double) * lda_t * MAX(1,k) );
|
||||
} else {
|
||||
a_t = (double*)LAPACKE_malloc( sizeof(double) * lda_t * nq );
|
||||
a_t = (double*)LAPACKE_malloc( sizeof(double) * lda_t * MAX(1,nq) );
|
||||
}
|
||||
|
||||
if( a_t == NULL ) {
|
||||
info = LAPACK_TRANSPOSE_MEMORY_ERROR;
|
||||
goto exit_level_0;
|
||||
|
@ -89,11 +88,7 @@ lapack_int LAPACKE_dormbr_work( int matrix_layout, char vect, char side,
|
|||
goto exit_level_1;
|
||||
}
|
||||
/* Transpose input matrices */
|
||||
if( LAPACKE_lsame( vect, 'q' ) ) {
|
||||
LAPACKE_dge_trans( matrix_layout, nq, k, a, lda, a_t, lda_t );
|
||||
} else {
|
||||
LAPACKE_dge_trans( matrix_layout, k, nq, a, lda, a_t, lda_t );
|
||||
}
|
||||
LAPACKE_dge_trans( matrix_layout, r, MIN(nq,k), a, lda, a_t, lda_t );
|
||||
LAPACKE_dge_trans( matrix_layout, m, n, c, ldc, c_t, ldc_t );
|
||||
/* Call LAPACK function and adjust info */
|
||||
LAPACK_dormbr( &vect, &side, &trans, &m, &n, &k, a_t, &lda_t, tau, c_t,
|
||||
|
|
|
@ -87,12 +87,7 @@ lapack_int LAPACKE_dormlq_work( int matrix_layout, char side, char trans,
|
|||
goto exit_level_1;
|
||||
}
|
||||
/* Transpose input matrices */
|
||||
if( LAPACKE_lsame( side, 'l' ) ){
|
||||
LAPACKE_dge_trans( matrix_layout, k, m, a, lda, a_t, lda_t );
|
||||
} else {
|
||||
LAPACKE_dge_trans( matrix_layout, k, n, a, lda, a_t, lda_t );
|
||||
}
|
||||
|
||||
LAPACKE_dge_trans( matrix_layout, k, m, a, lda, a_t, lda_t );
|
||||
LAPACKE_dge_trans( matrix_layout, m, n, c, ldc, c_t, ldc_t );
|
||||
/* Call LAPACK function and adjust info */
|
||||
LAPACK_dormlq( &side, &trans, &m, &n, &k, a_t, &lda_t, tau, c_t, &ldc_t,
|
||||
|
|
|
@ -51,8 +51,7 @@ float LAPACKE_slantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
}
|
||||
#endif
|
||||
/* Allocate memory for working array(s) */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
work = (float*)LAPACKE_malloc( sizeof(float) * MAX(1,MAX(m,n)) );
|
||||
if( work == NULL ) {
|
||||
info = LAPACK_WORK_MEMORY_ERROR;
|
||||
|
@ -63,8 +62,7 @@ float LAPACKE_slantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
res = LAPACKE_slantr_work( matrix_layout, norm, uplo, diag, m, n, a, lda,
|
||||
work );
|
||||
/* Release memory and exit */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
LAPACKE_free( work );
|
||||
}
|
||||
exit_level_0:
|
||||
|
|
|
@ -41,7 +41,7 @@ float LAPACKE_slantr_work( int matrix_layout, char norm, char uplo,
|
|||
float res = 0.;
|
||||
if( matrix_layout == LAPACK_COL_MAJOR ) {
|
||||
/* Call LAPACK function and adjust info */
|
||||
LAPACK_slantr( &norm, &uplo, &diag, &m, &n, a, &lda, work );
|
||||
res = LAPACK_slantr( &norm, &uplo, &diag, &m, &n, a, &lda, work );
|
||||
if( info < 0 ) {
|
||||
info = info - 1;
|
||||
}
|
||||
|
|
|
@ -73,8 +73,11 @@ lapack_int LAPACKE_sormbr_work( int matrix_layout, char vect, char side,
|
|||
return (info < 0) ? (info - 1) : info;
|
||||
}
|
||||
/* Allocate memory for temporary array(s) */
|
||||
a_t = (float*)
|
||||
LAPACKE_malloc( sizeof(float) * lda_t * MAX(1,MIN(nq,k)) );
|
||||
if( LAPACKE_lsame( vect, 'q' ) ) {
|
||||
a_t = (float*)LAPACKE_malloc( sizeof(float) * lda_t * MAX(1,k) );
|
||||
} else {
|
||||
a_t = (float*)LAPACKE_malloc( sizeof(float) * lda_t * MAX(1,nq) );
|
||||
}
|
||||
if( a_t == NULL ) {
|
||||
info = LAPACK_TRANSPOSE_MEMORY_ERROR;
|
||||
goto exit_level_0;
|
||||
|
|
|
@ -72,7 +72,11 @@ lapack_int LAPACKE_sormlq_work( int matrix_layout, char side, char trans,
|
|||
return (info < 0) ? (info - 1) : info;
|
||||
}
|
||||
/* Allocate memory for temporary array(s) */
|
||||
a_t = (float*)LAPACKE_malloc( sizeof(float) * lda_t * MAX(1,m) );
|
||||
if( LAPACKE_lsame( side, 'l' ) ) {
|
||||
a_t = (float*)LAPACKE_malloc( sizeof(float) * lda_t * MAX(1,m) );
|
||||
} else {
|
||||
a_t = (float*)LAPACKE_malloc( sizeof(float) * lda_t * MAX(1,n) );
|
||||
}
|
||||
if( a_t == NULL ) {
|
||||
info = LAPACK_TRANSPOSE_MEMORY_ERROR;
|
||||
goto exit_level_0;
|
||||
|
|
|
@ -51,8 +51,7 @@ double LAPACKE_zlantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
}
|
||||
#endif
|
||||
/* Allocate memory for working array(s) */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
work = (double*)LAPACKE_malloc( sizeof(double) * MAX(1,MAX(m,n)) );
|
||||
if( work == NULL ) {
|
||||
info = LAPACK_WORK_MEMORY_ERROR;
|
||||
|
@ -63,8 +62,7 @@ double LAPACKE_zlantr( int matrix_layout, char norm, char uplo, char diag,
|
|||
res = LAPACKE_zlantr_work( matrix_layout, norm, uplo, diag, m, n, a, lda,
|
||||
work );
|
||||
/* Release memory and exit */
|
||||
if( LAPACKE_lsame( norm, 'i' ) || LAPACKE_lsame( norm, '1' ) ||
|
||||
LAPACKE_lsame( norm, 'O' ) ) {
|
||||
if( LAPACKE_lsame( norm, 'i' ) ) {
|
||||
LAPACKE_free( work );
|
||||
}
|
||||
exit_level_0:
|
||||
|
|
|
@ -39,7 +39,7 @@ double LAPACKE_zlantr_work( int matrix_layout, char norm, char uplo,
|
|||
double* work )
|
||||
{
|
||||
lapack_int info = 0;
|
||||
double res = 0.;
|
||||
double res = 0.;
|
||||
if( matrix_layout == LAPACK_COL_MAJOR ) {
|
||||
/* Call LAPACK function and adjust info */
|
||||
res = LAPACK_zlantr( &norm, &uplo, &diag, &m, &n, a, &lda, work );
|
||||
|
|
|
@ -405,9 +405,9 @@
|
|||
$ WORK( IWRK ), LWORK-IWRK+1, INFO )
|
||||
END IF
|
||||
*
|
||||
* If INFO > 0 from CHSEQR, then quit
|
||||
* If INFO .NE. 0 from CHSEQR, then quit
|
||||
*
|
||||
IF( INFO.GT.0 )
|
||||
IF( INFO.NE.0 )
|
||||
$ GO TO 50
|
||||
*
|
||||
IF( WANTVL .OR. WANTVR ) THEN
|
||||
|
|
|
@ -170,7 +170,7 @@
|
|||
*> 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 ILQFin advance and an upper
|
||||
*> the exact value of NS is not known in advance and an upper
|
||||
*> bound must be used.
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
@ -294,8 +294,8 @@
|
|||
CHARACTER JOBZ, RNGTGK
|
||||
LOGICAL ALLS, INDS, LQUERY, VALS, WANTU, WANTVT
|
||||
INTEGER I, ID, IE, IERR, ILQF, ILTGK, IQRF, ISCL,
|
||||
$ ITAU, ITAUP, ITAUQ, ITEMP, ITGKZ, IUTGK,
|
||||
$ J, K, MAXWRK, MINMN, MINWRK, MNTHR
|
||||
$ ITAU, ITAUP, ITAUQ, ITEMP, ITEMPR, ITGKZ,
|
||||
$ IUTGK, J, K, MAXWRK, MINMN, MINWRK, MNTHR
|
||||
REAL ABSTOL, ANRM, BIGNUM, EPS, SMLNUM
|
||||
* ..
|
||||
* .. Local Arrays ..
|
||||
|
@ -367,8 +367,14 @@
|
|||
IF( INFO.EQ.0 ) THEN
|
||||
IF( WANTU .AND. LDU.LT.M ) THEN
|
||||
INFO = -15
|
||||
ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
|
||||
INFO = -16
|
||||
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
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -390,18 +396,24 @@
|
|||
*
|
||||
* Path 1 (M much larger than N)
|
||||
*
|
||||
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)
|
||||
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
|
||||
ELSE
|
||||
*
|
||||
* Path 2 (M at least N, but not much larger)
|
||||
*
|
||||
MAXWRK = 2*N + ( M+N )*
|
||||
$ ILAENV( 1, 'CGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = 2*N + M
|
||||
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
|
||||
END IF
|
||||
ELSE
|
||||
MNTHR = ILAENV( 6, 'CGESVD', JOBU // JOBVT, M, N, 0, 0 )
|
||||
|
@ -409,18 +421,25 @@
|
|||
*
|
||||
* Path 1t (N much larger than M)
|
||||
*
|
||||
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)
|
||||
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
|
||||
ELSE
|
||||
*
|
||||
* Path 2t (N greater than M, but not much larger)
|
||||
*
|
||||
MAXWRK = M*(M*2+19) + ( M+N )*
|
||||
$ ILAENV( 1, 'CGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = 2*M + N
|
||||
*
|
||||
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
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -518,14 +537,14 @@
|
|||
CALL CGEBRD( N, N, WORK( IQRF ), N, RWORK( ID ),
|
||||
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
|
||||
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + N*(N*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -539,7 +558,7 @@
|
|||
END DO
|
||||
K = K + N
|
||||
END DO
|
||||
CALL CLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
|
||||
CALL CLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
|
||||
*
|
||||
* Call CUNMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -594,14 +613,14 @@
|
|||
CALL CGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
|
||||
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
|
||||
$ LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + N*(N*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -615,7 +634,7 @@
|
|||
END DO
|
||||
K = K + N
|
||||
END DO
|
||||
CALL CLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
|
||||
CALL CLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
|
||||
*
|
||||
* Call CUNMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -681,14 +700,14 @@
|
|||
CALL CGEBRD( M, M, WORK( ILQF ), M, RWORK( ID ),
|
||||
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
|
||||
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + M*(M*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -722,7 +741,7 @@
|
|||
END DO
|
||||
K = K + M
|
||||
END DO
|
||||
CALL CLASET( 'A', M, N-M, CZERO, CZERO,
|
||||
CALL CLASET( 'A', NS, N-M, CZERO, CZERO,
|
||||
$ VT( 1,M+1 ), LDVT )
|
||||
*
|
||||
* Call CUNMBR to compute (VB**T)*(PB**T)
|
||||
|
@ -758,14 +777,14 @@
|
|||
CALL CGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
|
||||
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
|
||||
$ LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + M*(M*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -799,7 +818,7 @@
|
|||
END DO
|
||||
K = K + M
|
||||
END DO
|
||||
CALL CLASET( 'A', M, N-M, CZERO, CZERO,
|
||||
CALL CLASET( 'A', NS, N-M, CZERO, CZERO,
|
||||
$ VT( 1,M+1 ), LDVT )
|
||||
*
|
||||
* Call CUNMBR to compute VB**T * PB**T
|
||||
|
|
|
@ -145,15 +145,33 @@
|
|||
INTRINSIC ABS, CMPLX, MAX
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
INFO = 0
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Set constants to control overflow
|
||||
*
|
||||
INFO = 0
|
||||
EPS = SLAMCH( 'P' )
|
||||
SMLNUM = SLAMCH( 'S' ) / EPS
|
||||
BIGNUM = ONE / SMLNUM
|
||||
CALL SLABAD( SMLNUM, BIGNUM )
|
||||
*
|
||||
* Handle the case N=1 by itself
|
||||
*
|
||||
IF( N.EQ.1 ) THEN
|
||||
IPIV( 1 ) = 1
|
||||
JPIV( 1 ) = 1
|
||||
IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
|
||||
INFO = 1
|
||||
A( 1, 1 ) = CMPLX( SMLNUM, ZERO )
|
||||
END IF
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Factorize A using complete pivoting.
|
||||
* Set pivots less than SMIN to SMIN
|
||||
*
|
||||
|
|
|
@ -339,16 +339,16 @@
|
|||
$ LDVL, VR, LDVR, WORK, -1, IERR )
|
||||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
CALL CHGEQZ( 'S', JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB,
|
||||
$ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK,
|
||||
$ -1, WORK, IERR )
|
||||
$ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, -1,
|
||||
$ RWORK, IERR )
|
||||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
ELSE
|
||||
CALL CGGHD3( 'N', 'N', N, 1, N, A, LDA, B, LDB, VL, LDVL,
|
||||
$ VR, LDVR, WORK, -1, IERR )
|
||||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
CALL CHGEQZ( 'E', JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB,
|
||||
$ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK,
|
||||
$ -1, WORK, IERR )
|
||||
$ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, -1,
|
||||
$ RWORK, IERR )
|
||||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
END IF
|
||||
WORK( 1 ) = CMPLX( LWKOPT )
|
||||
|
|
|
@ -418,9 +418,9 @@
|
|||
$ WORK( IWRK ), LWORK-IWRK+1, INFO )
|
||||
END IF
|
||||
*
|
||||
* If INFO > 0 from DHSEQR, then quit
|
||||
* If INFO .NE. 0 from DHSEQR, then quit
|
||||
*
|
||||
IF( INFO.GT.0 )
|
||||
IF( INFO.NE.0 )
|
||||
$ GO TO 50
|
||||
*
|
||||
IF( WANTVL .OR. WANTVR ) THEN
|
||||
|
|
|
@ -169,7 +169,7 @@
|
|||
*> 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 ILQFin advance and an upper
|
||||
*> the exact value of NS is not known in advance and an upper
|
||||
*> bound must be used.
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
@ -357,8 +357,14 @@
|
|||
IF( INFO.EQ.0 ) THEN
|
||||
IF( WANTU .AND. LDU.LT.M ) THEN
|
||||
INFO = -15
|
||||
ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
|
||||
INFO = -16
|
||||
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
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -380,18 +386,34 @@
|
|||
*
|
||||
* Path 1 (M much larger than N)
|
||||
*
|
||||
MAXWRK = N*(N*2+16) +
|
||||
MAXWRK = N +
|
||||
$ N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
|
||||
MAXWRK = MAX( MAXWRK, N*(N*2+20) + 2*N*
|
||||
MAXWRK = MAX( MAXWRK, N*(N+5) + 2*N*
|
||||
$ ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
|
||||
MINWRK = N*(N*2+21)
|
||||
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)
|
||||
ELSE
|
||||
*
|
||||
* Path 2 (M at least N, but not much larger)
|
||||
*
|
||||
MAXWRK = N*(N*2+19) + ( M+N )*
|
||||
MAXWRK = 4*N + ( M+N )*
|
||||
$ ILAENV( 1, 'DGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = N*(N*2+20) + M
|
||||
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)
|
||||
END IF
|
||||
ELSE
|
||||
MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 )
|
||||
|
@ -399,18 +421,34 @@
|
|||
*
|
||||
* Path 1t (N much larger than M)
|
||||
*
|
||||
MAXWRK = M*(M*2+16) +
|
||||
MAXWRK = M +
|
||||
$ M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
|
||||
MAXWRK = MAX( MAXWRK, M*(M*2+20) + 2*M*
|
||||
MAXWRK = MAX( MAXWRK, M*(M+5) + 2*M*
|
||||
$ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
|
||||
MINWRK = M*(M*2+21)
|
||||
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)
|
||||
ELSE
|
||||
*
|
||||
* Path 2t (N greater than M, but not much larger)
|
||||
* Path 2t (N at least M, but not much larger)
|
||||
*
|
||||
MAXWRK = M*(M*2+19) + ( M+N )*
|
||||
MAXWRK = 4*M + ( M+N )*
|
||||
$ ILAENV( 1, 'DGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = M*(M*2+20) + N
|
||||
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)
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -522,7 +560,7 @@
|
|||
CALL DCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
|
||||
J = J + N*2
|
||||
END DO
|
||||
CALL DLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
CALL DLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
*
|
||||
* Call DORMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -591,7 +629,7 @@
|
|||
CALL DCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
|
||||
J = J + N*2
|
||||
END DO
|
||||
CALL DLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
CALL DLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
*
|
||||
* Call DORMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -687,7 +725,7 @@
|
|||
CALL DCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
|
||||
J = J + M*2
|
||||
END DO
|
||||
CALL DLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
|
||||
CALL DLASET( 'A', NS, 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)
|
||||
|
@ -756,7 +794,7 @@
|
|||
CALL DCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
|
||||
J = J + M*2
|
||||
END DO
|
||||
CALL DLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
|
||||
CALL DLASET( 'A', NS, 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)
|
||||
|
|
|
@ -145,15 +145,33 @@
|
|||
INTRINSIC ABS, MAX
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
INFO = 0
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Set constants to control overflow
|
||||
*
|
||||
INFO = 0
|
||||
EPS = DLAMCH( 'P' )
|
||||
SMLNUM = DLAMCH( 'S' ) / EPS
|
||||
BIGNUM = ONE / SMLNUM
|
||||
CALL DLABAD( SMLNUM, BIGNUM )
|
||||
*
|
||||
* Handle the case N=1 by itself
|
||||
*
|
||||
IF( N.EQ.1 ) THEN
|
||||
IPIV( 1 ) = 1
|
||||
JPIV( 1 ) = 1
|
||||
IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
|
||||
INFO = 1
|
||||
A( 1, 1 ) = SMLNUM
|
||||
END IF
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Factorize A using complete pivoting.
|
||||
* Set pivots less than SMIN to SMIN.
|
||||
*
|
||||
|
|
|
@ -418,9 +418,9 @@
|
|||
$ WORK( IWRK ), LWORK-IWRK+1, INFO )
|
||||
END IF
|
||||
*
|
||||
* If INFO > 0 from SHSEQR, then quit
|
||||
* If INFO .NE. 0 from SHSEQR, then quit
|
||||
*
|
||||
IF( INFO.GT.0 )
|
||||
IF( INFO.NE.0 )
|
||||
$ GO TO 50
|
||||
*
|
||||
IF( WANTVL .OR. WANTVR ) THEN
|
||||
|
|
|
@ -169,7 +169,7 @@
|
|||
*> 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 ILQFin advance and an upper
|
||||
*> the exact value of NS is not known in advance and an upper
|
||||
*> bound must be used.
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
@ -357,8 +357,14 @@
|
|||
IF( INFO.EQ.0 ) THEN
|
||||
IF( WANTU .AND. LDU.LT.M ) THEN
|
||||
INFO = -15
|
||||
ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
|
||||
INFO = -16
|
||||
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
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -380,18 +386,34 @@
|
|||
*
|
||||
* Path 1 (M much larger than N)
|
||||
*
|
||||
MAXWRK = N*(N*2+16) +
|
||||
MAXWRK = N +
|
||||
$ N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
|
||||
MAXWRK = MAX( MAXWRK, N*(N*2+20) + 2*N*
|
||||
MAXWRK = MAX( MAXWRK, N*(N+5) + 2*N*
|
||||
$ ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
|
||||
MINWRK = N*(N*2+21)
|
||||
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)
|
||||
ELSE
|
||||
*
|
||||
* Path 2 (M at least N, but not much larger)
|
||||
*
|
||||
MAXWRK = N*(N*2+19) + ( M+N )*
|
||||
MAXWRK = 4*N + ( M+N )*
|
||||
$ ILAENV( 1, 'SGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = N*(N*2+20) + M
|
||||
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)
|
||||
END IF
|
||||
ELSE
|
||||
MNTHR = ILAENV( 6, 'SGESVD', JOBU // JOBVT, M, N, 0, 0 )
|
||||
|
@ -399,18 +421,34 @@
|
|||
*
|
||||
* Path 1t (N much larger than M)
|
||||
*
|
||||
MAXWRK = M*(M*2+16) +
|
||||
MAXWRK = M +
|
||||
$ M*ILAENV( 1, 'SGELQF', ' ', M, N, -1, -1 )
|
||||
MAXWRK = MAX( MAXWRK, M*(M*2+20) + 2*M*
|
||||
MAXWRK = MAX( MAXWRK, M*(M+5) + 2*M*
|
||||
$ ILAENV( 1, 'SGEBRD', ' ', M, M, -1, -1 ) )
|
||||
MINWRK = M*(M*2+21)
|
||||
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)
|
||||
ELSE
|
||||
*
|
||||
* Path 2t (N greater than M, but not much larger)
|
||||
* Path 2t (N at least M, but not much larger)
|
||||
*
|
||||
MAXWRK = M*(M*2+19) + ( M+N )*
|
||||
MAXWRK = 4*M + ( M+N )*
|
||||
$ ILAENV( 1, 'SGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = M*(M*2+20) + N
|
||||
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)
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -522,7 +560,7 @@
|
|||
CALL SCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
|
||||
J = J + N*2
|
||||
END DO
|
||||
CALL SLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
CALL SLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
*
|
||||
* Call SORMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -591,7 +629,7 @@
|
|||
CALL SCOPY( N, WORK( J ), 1, U( 1,I ), 1 )
|
||||
J = J + N*2
|
||||
END DO
|
||||
CALL SLASET( 'A', M-N, N, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
CALL SLASET( 'A', M-N, NS, ZERO, ZERO, U( N+1,1 ), LDU )
|
||||
*
|
||||
* Call SORMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -687,7 +725,7 @@
|
|||
CALL SCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
|
||||
J = J + M*2
|
||||
END DO
|
||||
CALL SLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
|
||||
CALL SLASET( 'A', NS, 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)
|
||||
|
@ -756,7 +794,7 @@
|
|||
CALL SCOPY( M, WORK( J ), 1, VT( I,1 ), LDVT )
|
||||
J = J + M*2
|
||||
END DO
|
||||
CALL SLASET( 'A', M, N-M, ZERO, ZERO, VT( 1,M+1 ), LDVT )
|
||||
CALL SLASET( 'A', NS, 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)
|
||||
|
|
|
@ -145,15 +145,33 @@
|
|||
INTRINSIC ABS, MAX
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
INFO = 0
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Set constants to control overflow
|
||||
*
|
||||
INFO = 0
|
||||
EPS = SLAMCH( 'P' )
|
||||
SMLNUM = SLAMCH( 'S' ) / EPS
|
||||
BIGNUM = ONE / SMLNUM
|
||||
CALL SLABAD( SMLNUM, BIGNUM )
|
||||
*
|
||||
* Handle the case N=1 by itself
|
||||
*
|
||||
IF( N.EQ.1 ) THEN
|
||||
IPIV( 1 ) = 1
|
||||
JPIV( 1 ) = 1
|
||||
IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
|
||||
INFO = 1
|
||||
A( 1, 1 ) = SMLNUM
|
||||
END IF
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Factorize A using complete pivoting.
|
||||
* Set pivots less than SMIN to SMIN.
|
||||
*
|
||||
|
|
|
@ -404,9 +404,9 @@
|
|||
$ WORK( IWRK ), LWORK-IWRK+1, INFO )
|
||||
END IF
|
||||
*
|
||||
* If INFO > 0 from ZHSEQR, then quit
|
||||
* If INFO .NE. 0 from ZHSEQR, then quit
|
||||
*
|
||||
IF( INFO.GT.0 )
|
||||
IF( INFO.NE.0 )
|
||||
$ GO TO 50
|
||||
*
|
||||
IF( WANTVL .OR. WANTVR ) THEN
|
||||
|
|
|
@ -36,27 +36,30 @@
|
|||
* ..
|
||||
*
|
||||
*
|
||||
* 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.
|
||||
*> \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
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
|
@ -107,7 +110,7 @@
|
|||
*>
|
||||
*> \param[in,out] A
|
||||
*> \verbatim
|
||||
*> A is COMPLEX array, dimension (LDA,N)
|
||||
*> A is COMPLEX*16 array, dimension (LDA,N)
|
||||
*> On entry, the M-by-N matrix A.
|
||||
*> On exit, the contents of A are destroyed.
|
||||
*> \endverbatim
|
||||
|
@ -167,7 +170,7 @@
|
|||
*> 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 ILQFin advance and an upper
|
||||
*> the exact value of NS is not known in advance and an upper
|
||||
*> bound must be used.
|
||||
*> \endverbatim
|
||||
*>
|
||||
|
@ -291,8 +294,8 @@
|
|||
CHARACTER JOBZ, RNGTGK
|
||||
LOGICAL ALLS, INDS, LQUERY, VALS, WANTU, WANTVT
|
||||
INTEGER I, ID, IE, IERR, ILQF, ILTGK, IQRF, ISCL,
|
||||
$ ITAU, ITAUP, ITAUQ, ITEMP, ITGKZ, IUTGK,
|
||||
$ J, K, MAXWRK, MINMN, MINWRK, MNTHR
|
||||
$ ITAU, ITAUP, ITAUQ, ITEMP, ITEMPR, ITGKZ,
|
||||
$ IUTGK, J, K, MAXWRK, MINMN, MINWRK, MNTHR
|
||||
DOUBLE PRECISION ABSTOL, ANRM, BIGNUM, EPS, SMLNUM
|
||||
* ..
|
||||
* .. Local Arrays ..
|
||||
|
@ -364,8 +367,14 @@
|
|||
IF( INFO.EQ.0 ) THEN
|
||||
IF( WANTU .AND. LDU.LT.M ) THEN
|
||||
INFO = -15
|
||||
ELSE IF( WANTVT .AND. LDVT.LT.MINMN ) THEN
|
||||
INFO = -16
|
||||
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
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -387,18 +396,24 @@
|
|||
*
|
||||
* Path 1 (M much larger than N)
|
||||
*
|
||||
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)
|
||||
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
|
||||
ELSE
|
||||
*
|
||||
* Path 2 (M at least N, but not much larger)
|
||||
*
|
||||
MAXWRK = 2*N + ( M+N )*
|
||||
$ ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = 2*N + M
|
||||
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
|
||||
END IF
|
||||
ELSE
|
||||
MNTHR = ILAENV( 6, 'ZGESVD', JOBU // JOBVT, M, N, 0, 0 )
|
||||
|
@ -406,18 +421,25 @@
|
|||
*
|
||||
* Path 1t (N much larger than M)
|
||||
*
|
||||
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)
|
||||
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
|
||||
ELSE
|
||||
*
|
||||
* Path 2t (N greater than M, but not much larger)
|
||||
*
|
||||
MAXWRK = M*(M*2+19) + ( M+N )*
|
||||
$ ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 )
|
||||
MINWRK = 2*M + N
|
||||
*
|
||||
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
|
||||
END IF
|
||||
END IF
|
||||
END IF
|
||||
|
@ -515,14 +537,14 @@
|
|||
CALL ZGEBRD( N, N, WORK( IQRF ), N, RWORK( ID ),
|
||||
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
|
||||
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + N*(N*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -536,7 +558,7 @@
|
|||
END DO
|
||||
K = K + N
|
||||
END DO
|
||||
CALL ZLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
|
||||
CALL ZLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
|
||||
*
|
||||
* Call ZUNMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -591,14 +613,14 @@
|
|||
CALL ZGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
|
||||
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
|
||||
$ LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + N*(N*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), N*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -612,7 +634,7 @@
|
|||
END DO
|
||||
K = K + N
|
||||
END DO
|
||||
CALL ZLASET( 'A', M-N, N, CZERO, CZERO, U( N+1,1 ), LDU )
|
||||
CALL ZLASET( 'A', M-N, NS, CZERO, CZERO, U( N+1,1 ), LDU)
|
||||
*
|
||||
* Call ZUNMBR to compute QB*UB.
|
||||
* (Workspace in WORK( ITEMP ): need N, prefer N*NB)
|
||||
|
@ -678,14 +700,14 @@
|
|||
CALL ZGEBRD( M, M, WORK( ILQF ), M, RWORK( ID ),
|
||||
$ RWORK( IE ), WORK( ITAUQ ), WORK( ITAUP ),
|
||||
$ WORK( ITEMP ), LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + M*(M*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -719,7 +741,7 @@
|
|||
END DO
|
||||
K = K + M
|
||||
END DO
|
||||
CALL ZLASET( 'A', M, N-M, CZERO, CZERO,
|
||||
CALL ZLASET( 'A', NS, N-M, CZERO, CZERO,
|
||||
$ VT( 1,M+1 ), LDVT )
|
||||
*
|
||||
* Call ZUNMBR to compute (VB**T)*(PB**T)
|
||||
|
@ -755,14 +777,14 @@
|
|||
CALL ZGEBRD( M, N, A, LDA, RWORK( ID ), RWORK( IE ),
|
||||
$ WORK( ITAUQ ), WORK( ITAUP ), WORK( ITEMP ),
|
||||
$ LWORK-ITEMP+1, INFO )
|
||||
ITEMP = ITGKZ + M*(M*2+1)
|
||||
ITEMPR = 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( ITEMP ),
|
||||
$ RWORK( ITGKZ ), M*2, RWORK( ITEMPR ),
|
||||
$ IWORK, INFO)
|
||||
*
|
||||
* If needed, compute left singular vectors.
|
||||
|
@ -796,7 +818,7 @@
|
|||
END DO
|
||||
K = K + M
|
||||
END DO
|
||||
CALL ZLASET( 'A', M, N-M, CZERO, CZERO,
|
||||
CALL ZLASET( 'A', NS, N-M, CZERO, CZERO,
|
||||
$ VT( 1,M+1 ), LDVT )
|
||||
*
|
||||
* Call ZUNMBR to compute VB**T * PB**T
|
||||
|
|
|
@ -145,15 +145,33 @@
|
|||
INTRINSIC ABS, DCMPLX, MAX
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
INFO = 0
|
||||
*
|
||||
* Quick return if possible
|
||||
*
|
||||
IF( N.EQ.0 )
|
||||
$ RETURN
|
||||
*
|
||||
* Set constants to control overflow
|
||||
*
|
||||
INFO = 0
|
||||
EPS = DLAMCH( 'P' )
|
||||
SMLNUM = DLAMCH( 'S' ) / EPS
|
||||
BIGNUM = ONE / SMLNUM
|
||||
CALL DLABAD( SMLNUM, BIGNUM )
|
||||
*
|
||||
* Handle the case N=1 by itself
|
||||
*
|
||||
IF( N.EQ.1 ) THEN
|
||||
IPIV( 1 ) = 1
|
||||
JPIV( 1 ) = 1
|
||||
IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
|
||||
INFO = 1
|
||||
A( 1, 1 ) = DCMPLX( SMLNUM, ZERO )
|
||||
END IF
|
||||
RETURN
|
||||
END IF
|
||||
*
|
||||
* Factorize A using complete pivoting.
|
||||
* Set pivots less than SMIN to SMIN
|
||||
*
|
||||
|
|
|
@ -340,7 +340,7 @@
|
|||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
CALL ZHGEQZ( 'S', JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB,
|
||||
$ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, -1,
|
||||
$ WORK, IERR )
|
||||
$ RWORK, IERR )
|
||||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
ELSE
|
||||
CALL ZGGHD3( JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB, VL,
|
||||
|
@ -348,7 +348,7 @@
|
|||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
CALL ZHGEQZ( 'E', JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB,
|
||||
$ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, -1,
|
||||
$ WORK, IERR )
|
||||
$ RWORK, IERR )
|
||||
LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
|
||||
END IF
|
||||
WORK( 1 ) = DCMPLX( LWKOPT )
|
||||
|
|
Loading…
Reference in New Issue