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author | jofret | 2009-04-28 07:17:00 +0000 |
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committer | jofret | 2009-04-28 07:17:00 +0000 |
commit | 8c8d2f518968ce7057eec6aa5cd5aec8faab861a (patch) | |
tree | 3dd1788b71d6a3ce2b73d2d475a3133580e17530 /src/lib/lapack/zgesvd.f | |
parent | 9f652ffc16a310ac6641a9766c5b9e2671e0e9cb (diff) | |
download | scilab2c-8c8d2f518968ce7057eec6aa5cd5aec8faab861a.tar.gz scilab2c-8c8d2f518968ce7057eec6aa5cd5aec8faab861a.tar.bz2 scilab2c-8c8d2f518968ce7057eec6aa5cd5aec8faab861a.zip |
Moving lapack to right place
Diffstat (limited to 'src/lib/lapack/zgesvd.f')
-rw-r--r-- | src/lib/lapack/zgesvd.f | 3602 |
1 files changed, 0 insertions, 3602 deletions
diff --git a/src/lib/lapack/zgesvd.f b/src/lib/lapack/zgesvd.f deleted file mode 100644 index 7b238d8b..00000000 --- a/src/lib/lapack/zgesvd.f +++ /dev/null @@ -1,3602 +0,0 @@ - SUBROUTINE ZGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, - $ WORK, LWORK, RWORK, INFO ) -* -* -- LAPACK driver routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - CHARACTER JOBU, JOBVT - INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION RWORK( * ), S( * ) - COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), - $ WORK( * ) -* .. -* -* Purpose -* ======= -* -* ZGESVD 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 * conjugate-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. -* -* Note that the routine returns V**H, not V. -* -* Arguments -* ========= -* -* JOBU (input) CHARACTER*1 -* Specifies options for computing all or part of the matrix U: -* = 'A': all M columns of U are returned in array U: -* = 'S': the first min(m,n) columns of U (the left singular -* vectors) are returned in the array U; -* = 'O': the first min(m,n) columns of U (the left singular -* vectors) are overwritten on the array A; -* = 'N': no columns of U (no left singular vectors) are -* computed. -* -* JOBVT (input) CHARACTER*1 -* Specifies options for computing all or part of the matrix -* V**H: -* = 'A': all N rows of V**H are returned in the array VT; -* = 'S': the first min(m,n) rows of V**H (the right singular -* vectors) are returned in the array VT; -* = 'O': the first min(m,n) rows of V**H (the right singular -* vectors) are overwritten on the array A; -* = 'N': no rows of V**H (no right singular vectors) are -* computed. -* -* JOBVT and JOBU cannot both be 'O'. -* -* M (input) INTEGER -* The number of rows of the input matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the input matrix A. N >= 0. -* -* A (input/output) COMPLEX*16 array, dimension (LDA,N) -* On entry, the M-by-N matrix A. -* On exit, -* if JOBU = 'O', A is overwritten with the first min(m,n) -* columns of U (the left singular vectors, -* stored columnwise); -* if JOBVT = 'O', A is overwritten with the first min(m,n) -* rows of V**H (the right singular vectors, -* stored rowwise); -* if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A -* are destroyed. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* S (output) DOUBLE PRECISION array, dimension (min(M,N)) -* The singular values of A, sorted so that S(i) >= S(i+1). -* -* U (output) COMPLEX*16 array, dimension (LDU,UCOL) -* (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. -* If JOBU = 'A', U contains the M-by-M unitary matrix U; -* if JOBU = 'S', U contains the first min(m,n) columns of U -* (the left singular vectors, stored columnwise); -* if JOBU = 'N' or 'O', U is not referenced. -* -* LDU (input) INTEGER -* The leading dimension of the array U. LDU >= 1; if -* JOBU = 'S' or 'A', LDU >= M. -* -* VT (output) COMPLEX*16 array, dimension (LDVT,N) -* If JOBVT = 'A', VT contains the N-by-N unitary matrix -* V**H; -* if JOBVT = 'S', VT contains the first min(m,n) rows of -* V**H (the right singular vectors, stored rowwise); -* if JOBVT = 'N' or 'O', VT is not referenced. -* -* LDVT (input) INTEGER -* The leading dimension of the array VT. LDVT >= 1; if -* JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). -* -* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -* -* LWORK (input) INTEGER -* The dimension of the array WORK. -* LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). -* For good performance, LWORK should generally be larger. -* -* 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. -* -* RWORK (workspace) DOUBLE PRECISION array, dimension (5*min(M,N)) -* On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the -* unconverged superdiagonal elements of an upper bidiagonal -* matrix B whose diagonal is in S (not necessarily sorted). -* B satisfies A = U * B * VT, so it has the same singular -* values as A, and singular vectors related by U and VT. -* -* INFO (output) INTEGER -* = 0: successful exit. -* < 0: if INFO = -i, the i-th argument had an illegal value. -* > 0: if ZBDSQR did not converge, INFO specifies how many -* superdiagonals of an intermediate bidiagonal form B -* did not converge to zero. See the description of RWORK -* above for details. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 CZERO, CONE - PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), - $ CONE = ( 1.0D0, 0.0D0 ) ) - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS, - $ WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS - INTEGER BLK, CHUNK, I, IE, IERR, IR, IRWORK, ISCL, - $ ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU, - $ MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU, - $ NRVT, WRKBL - DOUBLE PRECISION ANRM, BIGNUM, EPS, SMLNUM -* .. -* .. Local Arrays .. - DOUBLE PRECISION DUM( 1 ) - COMPLEX*16 CDUM( 1 ) -* .. -* .. External Subroutines .. - EXTERNAL DLASCL, XERBLA, ZBDSQR, ZGEBRD, ZGELQF, ZGEMM, - $ ZGEQRF, ZLACPY, ZLASCL, ZLASET, ZUNGBR, ZUNGLQ, - $ ZUNGQR, ZUNMBR -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, ZLANGE - EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - MINMN = MIN( M, N ) - WNTUA = LSAME( JOBU, 'A' ) - WNTUS = LSAME( JOBU, 'S' ) - WNTUAS = WNTUA .OR. WNTUS - WNTUO = LSAME( JOBU, 'O' ) - WNTUN = LSAME( JOBU, 'N' ) - WNTVA = LSAME( JOBVT, 'A' ) - WNTVS = LSAME( JOBVT, 'S' ) - WNTVAS = WNTVA .OR. WNTVS - WNTVO = LSAME( JOBVT, 'O' ) - WNTVN = LSAME( JOBVT, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* - IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN - INFO = -1 - ELSE IF( .NOT.( WNTVA .OR. WNTVS .OR. WNTVO .OR. WNTVN ) .OR. - $ ( WNTVO .AND. WNTUO ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -6 - ELSE IF( LDU.LT.1 .OR. ( WNTUAS .AND. LDU.LT.M ) ) THEN - INFO = -9 - ELSE IF( LDVT.LT.1 .OR. ( WNTVA .AND. LDVT.LT.N ) .OR. - $ ( WNTVS .AND. LDVT.LT.MINMN ) ) THEN - INFO = -11 - END IF -* -* Compute workspace -* (Note: Comments in the code beginning "Workspace:" describe the -* minimal amount of workspace needed at that point in the code, -* as well as the preferred amount for good performance. -* CWorkspace refers to complex workspace, and RWorkspace to -* real workspace. NB refers to the optimal block size for the -* immediately following subroutine, as returned by ILAENV.) -* - IF( INFO.EQ.0 ) THEN - MINWRK = 1 - MAXWRK = 1 - IF( M.GE.N .AND. MINMN.GT.0 ) THEN -* -* Space needed for ZBDSQR is BDSPAC = 5*N -* - MNTHR = ILAENV( 6, 'ZGESVD', JOBU // JOBVT, M, N, 0, 0 ) - IF( M.GE.MNTHR ) THEN - IF( WNTUN ) THEN -* -* Path 1 (M much larger than N, JOBU='N') -* - MAXWRK = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, - $ -1 ) - MAXWRK = MAX( MAXWRK, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - IF( WNTVO .OR. WNTVAS ) - $ MAXWRK = MAX( MAXWRK, 2*N+( N-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) ) - MINWRK = 3*N - ELSE IF( WNTUO .AND. WNTVN ) THEN -* -* Path 2 (M much larger than N, JOBU='O', JOBVT='N') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'ZUNGQR', ' ', M, - $ N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - MAXWRK = MAX( N*N+WRKBL, N*N+M*N ) - MINWRK = 2*N + M - ELSE IF( WNTUO .AND. WNTVAS ) THEN -* -* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or -* 'A') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'ZUNGQR', ' ', M, - $ N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+( N-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) ) - MAXWRK = MAX( N*N+WRKBL, N*N+M*N ) - MINWRK = 2*N + M - ELSE IF( WNTUS .AND. WNTVN ) THEN -* -* Path 4 (M much larger than N, JOBU='S', JOBVT='N') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'ZUNGQR', ' ', M, - $ N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - MAXWRK = N*N + WRKBL - MINWRK = 2*N + M - ELSE IF( WNTUS .AND. WNTVO ) THEN -* -* Path 5 (M much larger than N, JOBU='S', JOBVT='O') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'ZUNGQR', ' ', M, - $ N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+( N-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) ) - MAXWRK = 2*N*N + WRKBL - MINWRK = 2*N + M - ELSE IF( WNTUS .AND. WNTVAS ) THEN -* -* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or -* 'A') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'ZUNGQR', ' ', M, - $ N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+( N-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) ) - MAXWRK = N*N + WRKBL - MINWRK = 2*N + M - ELSE IF( WNTUA .AND. WNTVN ) THEN -* -* Path 7 (M much larger than N, JOBU='A', JOBVT='N') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'ZUNGQR', ' ', M, - $ M, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - MAXWRK = N*N + WRKBL - MINWRK = 2*N + M - ELSE IF( WNTUA .AND. WNTVO ) THEN -* -* Path 8 (M much larger than N, JOBU='A', JOBVT='O') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'ZUNGQR', ' ', M, - $ M, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+( N-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) ) - MAXWRK = 2*N*N + WRKBL - MINWRK = 2*N + M - ELSE IF( WNTUA .AND. WNTVAS ) THEN -* -* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or -* 'A') -* - WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'ZUNGQR', ' ', M, - $ M, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+2*N* - $ ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', N, N, N, -1 ) ) - WRKBL = MAX( WRKBL, 2*N+( N-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) ) - MAXWRK = N*N + WRKBL - MINWRK = 2*N + M - END IF - ELSE -* -* Path 10 (M at least N, but not much larger) -* - MAXWRK = 2*N + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N, - $ -1, -1 ) - IF( WNTUS .OR. WNTUO ) - $ MAXWRK = MAX( MAXWRK, 2*N+N* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, N, N, -1 ) ) - IF( WNTUA ) - $ MAXWRK = MAX( MAXWRK, 2*N+M* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, N, -1 ) ) - IF( .NOT.WNTVN ) - $ MAXWRK = MAX( MAXWRK, 2*N+( N-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) ) - MINWRK = 2*N + M - END IF - ELSE IF( MINMN.GT.0 ) THEN -* -* Space needed for ZBDSQR is BDSPAC = 5*M -* - MNTHR = ILAENV( 6, 'ZGESVD', JOBU // JOBVT, M, N, 0, 0 ) - IF( N.GE.MNTHR ) THEN - IF( WNTVN ) THEN -* -* Path 1t(N much larger than M, JOBVT='N') -* - MAXWRK = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, - $ -1 ) - MAXWRK = MAX( MAXWRK, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - IF( WNTUO .OR. WNTUAS ) - $ MAXWRK = MAX( MAXWRK, 2*M+M* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) ) - MINWRK = 3*M - ELSE IF( WNTVO .AND. WNTUN ) THEN -* -* Path 2t(N much larger than M, JOBU='N', JOBVT='O') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - MAXWRK = MAX( M*M+WRKBL, M*M+M*N ) - MINWRK = 2*M + N - ELSE IF( WNTVO .AND. WNTUAS ) THEN -* -* Path 3t(N much larger than M, JOBU='S' or 'A', -* JOBVT='O') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+M* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) ) - MAXWRK = MAX( M*M+WRKBL, M*M+M*N ) - MINWRK = 2*M + N - ELSE IF( WNTVS .AND. WNTUN ) THEN -* -* Path 4t(N much larger than M, JOBU='N', JOBVT='S') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - MAXWRK = M*M + WRKBL - MINWRK = 2*M + N - ELSE IF( WNTVS .AND. WNTUO ) THEN -* -* Path 5t(N much larger than M, JOBU='O', JOBVT='S') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+M* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) ) - MAXWRK = 2*M*M + WRKBL - MINWRK = 2*M + N - ELSE IF( WNTVS .AND. WNTUAS ) THEN -* -* Path 6t(N much larger than M, JOBU='S' or 'A', -* JOBVT='S') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+M* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) ) - MAXWRK = M*M + WRKBL - MINWRK = 2*M + N - ELSE IF( WNTVA .AND. WNTUN ) THEN -* -* Path 7t(N much larger than M, JOBU='N', JOBVT='A') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'ZUNGLQ', ' ', N, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - MAXWRK = M*M + WRKBL - MINWRK = 2*M + N - ELSE IF( WNTVA .AND. WNTUO ) THEN -* -* Path 8t(N much larger than M, JOBU='O', JOBVT='A') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'ZUNGLQ', ' ', N, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+M* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) ) - MAXWRK = 2*M*M + WRKBL - MINWRK = 2*M + N - ELSE IF( WNTVA .AND. WNTUAS ) THEN -* -* Path 9t(N much larger than M, JOBU='S' or 'A', -* JOBVT='A') -* - WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'ZUNGLQ', ' ', N, - $ N, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+2*M* - $ ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'P', M, M, M, -1 ) ) - WRKBL = MAX( WRKBL, 2*M+M* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) ) - MAXWRK = M*M + WRKBL - MINWRK = 2*M + N - END IF - ELSE -* -* Path 10t(N greater than M, but not much larger) -* - MAXWRK = 2*M + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N, - $ -1, -1 ) - IF( WNTVS .OR. WNTVO ) - $ MAXWRK = MAX( MAXWRK, 2*M+M* - $ ILAENV( 1, 'ZUNGBR', 'P', M, N, M, -1 ) ) - IF( WNTVA ) - $ MAXWRK = MAX( MAXWRK, 2*M+N* - $ ILAENV( 1, 'ZUNGBR', 'P', N, N, M, -1 ) ) - IF( .NOT.WNTUN ) - $ MAXWRK = MAX( MAXWRK, 2*M+( M-1 )* - $ ILAENV( 1, 'ZUNGBR', 'Q', M, M, M, -1 ) ) - MINWRK = 2*M + N - END IF - END IF - MAXWRK = MAX( MAXWRK, MINWRK ) - WORK( 1 ) = MAXWRK -* - IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN - INFO = -13 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZGESVD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - RETURN - END IF -* -* Get machine constants -* - EPS = DLAMCH( 'P' ) - SMLNUM = SQRT( DLAMCH( 'S' ) ) / EPS - BIGNUM = ONE / SMLNUM -* -* Scale A if max element outside range [SMLNUM,BIGNUM] -* - ANRM = ZLANGE( 'M', M, N, A, LDA, DUM ) - ISCL = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN - ISCL = 1 - CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, IERR ) - ELSE IF( ANRM.GT.BIGNUM ) THEN - ISCL = 1 - CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, IERR ) - END IF -* - IF( M.GE.N ) THEN -* -* A has at least as many rows as columns. If A has sufficiently -* more rows than columns, first reduce using the QR -* decomposition (if sufficient workspace available) -* - IF( M.GE.MNTHR ) THEN -* - IF( WNTUN ) THEN -* -* Path 1 (M much larger than N, JOBU='N') -* No left singular vectors to be computed -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: need 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Zero out below R -* - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ), - $ LDA ) - IE = 1 - ITAUQ = 1 - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in A -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - NCVT = 0 - IF( WNTVO .OR. WNTVAS ) THEN -* -* If right singular vectors desired, generate P'. -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - NCVT = N - END IF - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in A if desired -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, NCVT, 0, 0, S, RWORK( IE ), A, LDA, - $ CDUM, 1, CDUM, 1, RWORK( IRWORK ), INFO ) -* -* If right singular vectors desired in VT, copy them there -* - IF( WNTVAS ) - $ CALL ZLACPY( 'F', N, N, A, LDA, VT, LDVT ) -* - ELSE IF( WNTUO .AND. WNTVN ) THEN -* -* Path 2 (M much larger than N, JOBU='O', JOBVT='N') -* N left singular vectors to be overwritten on A and -* no right singular vectors to be computed -* - IF( LWORK.GE.N*N+3*N ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*N ) THEN -* -* WORK(IU) is LDA by N, WORK(IR) is LDA by N -* - LDWRKU = LDA - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+N*N ) THEN -* -* WORK(IU) is LDA by N, WORK(IR) is N by N -* - LDWRKU = LDA - LDWRKR = N - ELSE -* -* WORK(IU) is LDWRKU by N, WORK(IR) is N by N -* - LDWRKU = ( LWORK-N*N ) / N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IR) and zero out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR ) - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ WORK( IR+1 ), LDWRKR ) -* -* Generate Q in A -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IR) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing R -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) -* (RWorkspace: need 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) -* (CWorkspace: need N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, 0, N, 0, S, RWORK( IE ), CDUM, 1, - $ WORK( IR ), LDWRKR, CDUM, 1, - $ RWORK( IRWORK ), INFO ) - IU = ITAUQ -* -* Multiply Q in A by left singular vectors of R in -* WORK(IR), storing result in WORK(IU) and copying to A -* (CWorkspace: need N*N+N, prefer N*N+M*N) -* (RWorkspace: 0) -* - DO 10 I = 1, M, LDWRKU - CHUNK = MIN( M-I+1, LDWRKU ) - CALL ZGEMM( 'N', 'N', CHUNK, N, N, CONE, A( I, 1 ), - $ LDA, WORK( IR ), LDWRKR, CZERO, - $ WORK( IU ), LDWRKU ) - CALL ZLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU, - $ A( I, 1 ), LDA ) - 10 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - IE = 1 - ITAUQ = 1 - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize A -* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) -* (RWorkspace: N) -* - CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing A -* (CWorkspace: need 3*N, prefer 2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in A -* (CWorkspace: need 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, 0, M, 0, S, RWORK( IE ), CDUM, 1, - $ A, LDA, CDUM, 1, RWORK( IRWORK ), INFO ) -* - END IF -* - ELSE IF( WNTUO .AND. WNTVAS ) THEN -* -* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') -* N left singular vectors to be overwritten on A and -* N right singular vectors to be computed in VT -* - IF( LWORK.GE.N*N+3*N ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by N -* - LDWRKU = LDA - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+N*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is N by N -* - LDWRKU = LDA - LDWRKR = N - ELSE -* -* WORK(IU) is LDWRKU by N and WORK(IR) is N by N -* - LDWRKU = ( LWORK-N*N ) / N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to VT, zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ VT( 2, 1 ), LDVT ) -* -* Generate Q in A -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT, copying result to WORK(IR) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', N, N, VT, LDVT, WORK( IR ), LDWRKR ) -* -* Generate left vectors bidiagonalizing R in WORK(IR) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing R in VT -* (CWorkspace: need N*N+3*N-1, prefer N*N+2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) and computing right -* singular vectors of R in VT -* (CWorkspace: need N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), VT, - $ LDVT, WORK( IR ), LDWRKR, CDUM, 1, - $ RWORK( IRWORK ), INFO ) - IU = ITAUQ -* -* Multiply Q in A by left singular vectors of R in -* WORK(IR), storing result in WORK(IU) and copying to A -* (CWorkspace: need N*N+N, prefer N*N+M*N) -* (RWorkspace: 0) -* - DO 20 I = 1, M, LDWRKU - CHUNK = MIN( M-I+1, LDWRKU ) - CALL ZGEMM( 'N', 'N', CHUNK, N, N, CONE, A( I, 1 ), - $ LDA, WORK( IR ), LDWRKR, CZERO, - $ WORK( IU ), LDWRKU ) - CALL ZLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU, - $ A( I, 1 ), LDA ) - 20 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to VT, zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ VT( 2, 1 ), LDVT ) -* -* Generate Q in A -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: N) -* - CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in A by left vectors bidiagonalizing R -* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, - $ WORK( ITAUQ ), A, LDA, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing R in VT -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in A and computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), VT, - $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTUS ) THEN -* - IF( WNTVN ) THEN -* -* Path 4 (M much larger than N, JOBU='S', JOBVT='N') -* N left singular vectors to be computed in U and -* no right singular vectors to be computed -* - IF( LWORK.GE.N*N+3*N ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IR) is LDA by N -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is N by N -* - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IR), zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ WORK( IR+1 ), LDWRKR ) -* -* Generate Q in A -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IR) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing R in WORK(IR) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) -* (CWorkspace: need N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, 0, N, 0, S, RWORK( IE ), CDUM, - $ 1, WORK( IR ), LDWRKR, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply Q in A by left singular vectors of R in -* WORK(IR), storing result in U -* (CWorkspace: need N*N) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, N, CONE, A, LDA, - $ WORK( IR ), LDWRKR, CZERO, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ A( 2, 1 ), LDA ) -* -* Bidiagonalize R in A -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left vectors bidiagonalizing R -* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, 0, M, 0, S, RWORK( IE ), CDUM, - $ 1, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVO ) THEN -* -* Path 5 (M much larger than N, JOBU='S', JOBVT='O') -* N left singular vectors to be computed in U and -* N right singular vectors to be overwritten on A -* - IF( LWORK.GE.2*N*N+3*N ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is N by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = N - ELSE -* -* WORK(IU) is N by N and WORK(IR) is N by N -* - LDWRKU = N - IR = IU + LDWRKU*N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ WORK( IU+1 ), LDWRKU ) -* -* Generate Q in A -* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to -* WORK(IR) -* (CWorkspace: need 2*N*N+3*N, -* prefer 2*N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in WORK(IR) -* (CWorkspace: need 2*N*N+3*N-1, -* prefer 2*N*N+2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in WORK(IR) -* (CWorkspace: need 2*N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), - $ WORK( IR ), LDWRKR, WORK( IU ), - $ LDWRKU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* -* Multiply Q in A by left singular vectors of R in -* WORK(IU), storing result in U -* (CWorkspace: need N*N) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, N, CONE, A, LDA, - $ WORK( IU ), LDWRKU, CZERO, U, LDU ) -* -* Copy right singular vectors of R to A -* (CWorkspace: need N*N) -* (RWorkspace: 0) -* - CALL ZLACPY( 'F', N, N, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ A( 2, 1 ), LDA ) -* -* Bidiagonalize R in A -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left vectors bidiagonalizing R -* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing R in A -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in A -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), A, - $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVAS ) THEN -* -* Path 6 (M much larger than N, JOBU='S', JOBVT='S' -* or 'A') -* N left singular vectors to be computed in U and -* N right singular vectors to be computed in VT -* - IF( LWORK.GE.N*N+3*N ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IU) is LDA by N -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is N by N -* - LDWRKU = N - END IF - ITAU = IU + LDWRKU*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ WORK( IU+1 ), LDWRKU ) -* -* Generate Q in A -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to VT -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT, - $ LDVT ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (CWorkspace: need N*N+3*N-1, -* prefer N*N+2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in VT -* (CWorkspace: need N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), VT, - $ LDVT, WORK( IU ), LDWRKU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply Q in A by left singular vectors of R in -* WORK(IU), storing result in U -* (CWorkspace: need N*N) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, N, CONE, A, LDA, - $ WORK( IU ), LDWRKU, CZERO, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, N, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to VT, zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ VT( 2, 1 ), LDVT ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in VT -* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), VT, - $ LDVT, U, LDU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - END IF -* - ELSE IF( WNTUA ) THEN -* - IF( WNTVN ) THEN -* -* Path 7 (M much larger than N, JOBU='A', JOBVT='N') -* M left singular vectors to be computed in U and -* no right singular vectors to be computed -* - IF( LWORK.GE.N*N+MAX( N+M, 3*N ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IR) is LDA by N -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is N by N -* - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Copy R to WORK(IR), zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ WORK( IR+1 ), LDWRKR ) -* -* Generate Q in U -* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IR) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in WORK(IR) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) -* (CWorkspace: need N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, 0, N, 0, S, RWORK( IE ), CDUM, - $ 1, WORK( IR ), LDWRKR, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply Q in U by left singular vectors of R in -* WORK(IR), storing result in A -* (CWorkspace: need N*N) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, N, CONE, U, LDU, - $ WORK( IR ), LDWRKR, CZERO, A, LDA ) -* -* Copy left singular vectors of A from A to U -* - CALL ZLACPY( 'F', M, N, A, LDA, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need N+M, prefer N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ A( 2, 1 ), LDA ) -* -* Bidiagonalize R in A -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in A -* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, 0, M, 0, S, RWORK( IE ), CDUM, - $ 1, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVO ) THEN -* -* Path 8 (M much larger than N, JOBU='A', JOBVT='O') -* M left singular vectors to be computed in U and -* N right singular vectors to be overwritten on A -* - IF( LWORK.GE.2*N*N+MAX( N+M, 3*N ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is N by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = N - ELSE -* -* WORK(IU) is N by N and WORK(IR) is N by N -* - LDWRKU = N - IR = IU + LDWRKU*N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ WORK( IU+1 ), LDWRKU ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to -* WORK(IR) -* (CWorkspace: need 2*N*N+3*N, -* prefer 2*N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in WORK(IR) -* (CWorkspace: need 2*N*N+3*N-1, -* prefer 2*N*N+2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in WORK(IR) -* (CWorkspace: need 2*N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), - $ WORK( IR ), LDWRKR, WORK( IU ), - $ LDWRKU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* -* Multiply Q in U by left singular vectors of R in -* WORK(IU), storing result in A -* (CWorkspace: need N*N) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, N, CONE, U, LDU, - $ WORK( IU ), LDWRKU, CZERO, A, LDA ) -* -* Copy left singular vectors of A from A to U -* - CALL ZLACPY( 'F', M, N, A, LDA, U, LDU ) -* -* Copy right singular vectors of R from WORK(IR) to A -* - CALL ZLACPY( 'F', N, N, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need N+M, prefer N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ A( 2, 1 ), LDA ) -* -* Bidiagonalize R in A -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in A -* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in A -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in A -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), A, - $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVAS ) THEN -* -* Path 9 (M much larger than N, JOBU='A', JOBVT='S' -* or 'A') -* M left singular vectors to be computed in U and -* N right singular vectors to be computed in VT -* - IF( LWORK.GE.N*N+MAX( N+M, 3*N ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IU) is LDA by N -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is N by N -* - LDWRKU = N - END IF - ITAU = IU + LDWRKU*N - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ WORK( IU+1 ), LDWRKU ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to VT -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT, - $ LDVT ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (CWorkspace: need N*N+3*N-1, -* prefer N*N+2*N+(N-1)*NB) -* (RWorkspace: need 0) -* - CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in VT -* (CWorkspace: need N*N) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), VT, - $ LDVT, WORK( IU ), LDWRKU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply Q in U by left singular vectors of R in -* WORK(IU), storing result in A -* (CWorkspace: need N*N) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, N, CONE, U, LDU, - $ WORK( IU ), LDWRKU, CZERO, A, LDA ) -* -* Copy left singular vectors of A from A to U -* - CALL ZLACPY( 'F', M, N, A, LDA, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (CWorkspace: need 2*N, prefer N+N*NB) -* (RWorkspace: 0) -* - CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (CWorkspace: need N+M, prefer N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R from A to VT, zeroing out below it -* - CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, - $ VT( 2, 1 ), LDVT ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT -* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in VT -* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), VT, - $ LDVT, U, LDU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - END IF -* - END IF -* - ELSE -* -* M .LT. MNTHR -* -* Path 10 (M at least N, but not much larger) -* Reduce to bidiagonal form without QR decomposition -* - IE = 1 - ITAUQ = 1 - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize A -* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) -* (RWorkspace: need N) -* - CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - IF( WNTUAS ) THEN -* -* If left singular vectors desired in U, copy result to U -* and generate left bidiagonalizing vectors in U -* (CWorkspace: need 2*N+NCU, prefer 2*N+NCU*NB) -* (RWorkspace: 0) -* - CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) - IF( WNTUS ) - $ NCU = N - IF( WNTUA ) - $ NCU = M - CALL ZUNGBR( 'Q', M, NCU, N, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVAS ) THEN -* -* If right singular vectors desired in VT, copy result to -* VT and generate right bidiagonalizing vectors in VT -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) - CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTUO ) THEN -* -* If left singular vectors desired in A, generate left -* bidiagonalizing vectors in A -* (CWorkspace: need 3*N, prefer 2*N+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVO ) THEN -* -* If right singular vectors desired in A, generate right -* bidiagonalizing vectors in A -* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IRWORK = IE + N - IF( WNTUAS .OR. WNTUO ) - $ NRU = M - IF( WNTUN ) - $ NRU = 0 - IF( WNTVAS .OR. WNTVO ) - $ NCVT = N - IF( WNTVN ) - $ NCVT = 0 - IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, NCVT, NRU, 0, S, RWORK( IE ), VT, - $ LDVT, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) - ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in A -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, NCVT, NRU, 0, S, RWORK( IE ), A, - $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) - ELSE -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in A and computing right singular -* vectors in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', N, NCVT, NRU, 0, S, RWORK( IE ), VT, - $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ), - $ INFO ) - END IF -* - END IF -* - ELSE -* -* A has more columns than rows. If A has sufficiently more -* columns than rows, first reduce using the LQ decomposition (if -* sufficient workspace available) -* - IF( N.GE.MNTHR ) THEN -* - IF( WNTVN ) THEN -* -* Path 1t(N much larger than M, JOBVT='N') -* No right singular vectors to be computed -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Zero out above L -* - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, A( 1, 2 ), - $ LDA ) - IE = 1 - ITAUQ = 1 - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in A -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - IF( WNTUO .OR. WNTUAS ) THEN -* -* If left singular vectors desired, generate Q -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IRWORK = IE + M - NRU = 0 - IF( WNTUO .OR. WNTUAS ) - $ NRU = M -* -* Perform bidiagonal QR iteration, computing left singular -* vectors of A in A if desired -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, 0, NRU, 0, S, RWORK( IE ), CDUM, 1, - $ A, LDA, CDUM, 1, RWORK( IRWORK ), INFO ) -* -* If left singular vectors desired in U, copy them there -* - IF( WNTUAS ) - $ CALL ZLACPY( 'F', M, M, A, LDA, U, LDU ) -* - ELSE IF( WNTVO .AND. WNTUN ) THEN -* -* Path 2t(N much larger than M, JOBU='N', JOBVT='O') -* M right singular vectors to be overwritten on A and -* no left singular vectors to be computed -* - IF( LWORK.GE.M*M+3*M ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+M*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is M by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = M - ELSE -* -* WORK(IU) is M by CHUNK and WORK(IR) is M by M -* - LDWRKU = M - CHUNK = ( LWORK-M*M ) / M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IR) and zero out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, WORK( IR ), LDWRKR ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ WORK( IR+LDWRKR ), LDWRKR ) -* -* Generate Q in A -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IR) -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, WORK( IR ), LDWRKR, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing L -* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of L in WORK(IR) -* (CWorkspace: need M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, 0, 0, S, RWORK( IE ), - $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1, - $ RWORK( IRWORK ), INFO ) - IU = ITAUQ -* -* Multiply right singular vectors of L in WORK(IR) by Q -* in A, storing result in WORK(IU) and copying to A -* (CWorkspace: need M*M+M, prefer M*M+M*N) -* (RWorkspace: 0) -* - DO 30 I = 1, N, CHUNK - BLK = MIN( N-I+1, CHUNK ) - CALL ZGEMM( 'N', 'N', M, BLK, M, CONE, WORK( IR ), - $ LDWRKR, A( 1, I ), LDA, CZERO, - $ WORK( IU ), LDWRKU ) - CALL ZLACPY( 'F', M, BLK, WORK( IU ), LDWRKU, - $ A( 1, I ), LDA ) - 30 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - IE = 1 - ITAUQ = 1 - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize A -* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing A -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in A -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'L', M, N, 0, 0, S, RWORK( IE ), A, LDA, - $ CDUM, 1, CDUM, 1, RWORK( IRWORK ), INFO ) -* - END IF -* - ELSE IF( WNTVO .AND. WNTUAS ) THEN -* -* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') -* M right singular vectors to be overwritten on A and -* M left singular vectors to be computed in U -* - IF( LWORK.GE.M*M+3*M ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+M*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is M by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = M - ELSE -* -* WORK(IU) is M by CHUNK and WORK(IR) is M by M -* - LDWRKU = M - CHUNK = ( LWORK-M*M ) / M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing about above it -* - CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, U( 1, 2 ), - $ LDU ) -* -* Generate Q in A -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U, copying result to WORK(IR) -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, M, U, LDU, WORK( IR ), LDWRKR ) -* -* Generate right vectors bidiagonalizing L in WORK(IR) -* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing L in U -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in U, and computing right -* singular vectors of L in WORK(IR) -* (CWorkspace: need M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), - $ WORK( IR ), LDWRKR, U, LDU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) - IU = ITAUQ -* -* Multiply right singular vectors of L in WORK(IR) by Q -* in A, storing result in WORK(IU) and copying to A -* (CWorkspace: need M*M+M, prefer M*M+M*N)) -* (RWorkspace: 0) -* - DO 40 I = 1, N, CHUNK - BLK = MIN( N-I+1, CHUNK ) - CALL ZGEMM( 'N', 'N', M, BLK, M, CONE, WORK( IR ), - $ LDWRKR, A( 1, I ), LDA, CZERO, - $ WORK( IU ), LDWRKU ) - CALL ZLACPY( 'F', M, BLK, WORK( IU ), LDWRKU, - $ A( 1, I ), LDA ) - 40 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, U( 1, 2 ), - $ LDU ) -* -* Generate Q in A -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right vectors bidiagonalizing L by Q in A -* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'P', 'L', 'C', M, N, M, U, LDU, - $ WORK( ITAUP ), A, LDA, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing L in U -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in A -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), A, LDA, - $ U, LDU, CDUM, 1, RWORK( IRWORK ), INFO ) -* - END IF -* - ELSE IF( WNTVS ) THEN -* - IF( WNTUN ) THEN -* -* Path 4t(N much larger than M, JOBU='N', JOBVT='S') -* M right singular vectors to be computed in VT and -* no left singular vectors to be computed -* - IF( LWORK.GE.M*M+3*M ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IR) is LDA by M -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is M by M -* - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IR), zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ WORK( IR+LDWRKR ), LDWRKR ) -* -* Generate Q in A -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IR) -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, WORK( IR ), LDWRKR, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing L in -* WORK(IR) -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of L in WORK(IR) -* (CWorkspace: need M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, 0, 0, S, RWORK( IE ), - $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IR) by -* Q in A, storing result in VT -* (CWorkspace: need M*M) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IR ), - $ LDWRKR, A, LDA, CZERO, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy result to VT -* - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ A( 1, 2 ), LDA ) -* -* Bidiagonalize L in A -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right vectors bidiagonalizing L by Q in VT -* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, N, 0, 0, S, RWORK( IE ), VT, - $ LDVT, CDUM, 1, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - ELSE IF( WNTUO ) THEN -* -* Path 5t(N much larger than M, JOBU='O', JOBVT='S') -* M right singular vectors to be computed in VT and -* M left singular vectors to be overwritten on A -* - IF( LWORK.GE.2*M*M+3*M ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is LDA by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is M by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = M - ELSE -* -* WORK(IU) is M by M and WORK(IR) is M by M -* - LDWRKU = M - IR = IU + LDWRKU*M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out below it -* - CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) -* -* Generate Q in A -* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to -* WORK(IR) -* (CWorkspace: need 2*M*M+3*M, -* prefer 2*M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need 2*M*M+3*M-1, -* prefer 2*M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in WORK(IR) -* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in WORK(IR) and computing -* right singular vectors of L in WORK(IU) -* (CWorkspace: need 2*M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), - $ WORK( IU ), LDWRKU, WORK( IR ), - $ LDWRKR, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in A, storing result in VT -* (CWorkspace: need M*M) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), - $ LDWRKU, A, LDA, CZERO, VT, LDVT ) -* -* Copy left singular vectors of L to A -* (CWorkspace: need M*M) -* (RWorkspace: 0) -* - CALL ZLACPY( 'F', M, M, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ A( 1, 2 ), LDA ) -* -* Bidiagonalize L in A -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right vectors bidiagonalizing L by Q in VT -* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors of L in A -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in A and computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, - $ LDVT, A, LDA, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - ELSE IF( WNTUAS ) THEN -* -* Path 6t(N much larger than M, JOBU='S' or 'A', -* JOBVT='S') -* M right singular vectors to be computed in VT and -* M left singular vectors to be computed in U -* - IF( LWORK.GE.M*M+3*M ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IU) is LDA by N -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is LDA by M -* - LDWRKU = M - END IF - ITAU = IU + LDWRKU*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) -* -* Generate Q in A -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to U -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, U, - $ LDU ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need M*M+3*M-1, -* prefer M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in U and computing right -* singular vectors of L in WORK(IU) -* (CWorkspace: need M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), - $ WORK( IU ), LDWRKU, U, LDU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in A, storing result in VT -* (CWorkspace: need M*M) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), - $ LDWRKU, A, LDA, CZERO, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( M, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ U( 1, 2 ), LDU ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in U by Q -* in VT -* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'P', 'L', 'C', M, N, M, U, LDU, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, - $ LDVT, U, LDU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - END IF -* - ELSE IF( WNTVA ) THEN -* - IF( WNTUN ) THEN -* -* Path 7t(N much larger than M, JOBU='N', JOBVT='A') -* N right singular vectors to be computed in VT and -* no left singular vectors to be computed -* - IF( LWORK.GE.M*M+MAX( N+M, 3*M ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IR) is LDA by M -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is M by M -* - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Copy L to WORK(IR), zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ WORK( IR+LDWRKR ), LDWRKR ) -* -* Generate Q in VT -* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IR) -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, WORK( IR ), LDWRKR, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in WORK(IR) -* (CWorkspace: need M*M+3*M-1, -* prefer M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of L in WORK(IR) -* (CWorkspace: need M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, 0, 0, S, RWORK( IE ), - $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IR) by -* Q in VT, storing result in A -* (CWorkspace: need M*M) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IR ), - $ LDWRKR, VT, LDVT, CZERO, A, LDA ) -* -* Copy right singular vectors of A from A to VT -* - CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need M+N, prefer M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ A( 1, 2 ), LDA ) -* -* Bidiagonalize L in A -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in A by Q -* in VT -* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, N, 0, 0, S, RWORK( IE ), VT, - $ LDVT, CDUM, 1, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - ELSE IF( WNTUO ) THEN -* -* Path 8t(N much larger than M, JOBU='O', JOBVT='A') -* N right singular vectors to be computed in VT and -* M left singular vectors to be overwritten on A -* - IF( LWORK.GE.2*M*M+MAX( N+M, 3*M ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is LDA by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is M by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = M - ELSE -* -* WORK(IU) is M by M and WORK(IR) is M by M -* - LDWRKU = M - IR = IU + LDWRKU*M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to -* WORK(IR) -* (CWorkspace: need 2*M*M+3*M, -* prefer 2*M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need 2*M*M+3*M-1, -* prefer 2*M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in WORK(IR) -* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in WORK(IR) and computing -* right singular vectors of L in WORK(IU) -* (CWorkspace: need 2*M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), - $ WORK( IU ), LDWRKU, WORK( IR ), - $ LDWRKR, CDUM, 1, RWORK( IRWORK ), - $ INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in VT, storing result in A -* (CWorkspace: need M*M) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), - $ LDWRKU, VT, LDVT, CZERO, A, LDA ) -* -* Copy right singular vectors of A from A to VT -* - CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT ) -* -* Copy left singular vectors of A from WORK(IR) to A -* - CALL ZLACPY( 'F', M, M, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need M+N, prefer M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ A( 1, 2 ), LDA ) -* -* Bidiagonalize L in A -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in A by Q -* in VT -* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in A -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in A and computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, - $ LDVT, A, LDA, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - ELSE IF( WNTUAS ) THEN -* -* Path 9t(N much larger than M, JOBU='S' or 'A', -* JOBVT='A') -* N right singular vectors to be computed in VT and -* M left singular vectors to be computed in U -* - IF( LWORK.GE.M*M+MAX( N+M, 3*M ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IU) is LDA by M -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is M by M -* - LDWRKU = M - END IF - ITAU = IU + LDWRKU*M - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to U -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, U, - $ LDU ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in U and computing right -* singular vectors of L in WORK(IU) -* (CWorkspace: need M*M) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), - $ WORK( IU ), LDWRKU, U, LDU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in VT, storing result in A -* (CWorkspace: need M*M) -* (RWorkspace: 0) -* - CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), - $ LDWRKU, VT, LDVT, CZERO, A, LDA ) -* -* Copy right singular vectors of A from A to VT -* - CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (CWorkspace: need 2*M, prefer M+M*NB) -* (RWorkspace: 0) -* - CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (CWorkspace: need M+N, prefer M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing out above it -* - CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, - $ U( 1, 2 ), LDU ) - IE = 1 - ITAUQ = ITAU - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U -* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) -* (RWorkspace: need M) -* - CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in U by Q -* in VT -* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) -* (RWorkspace: 0) -* - CALL ZUNMBR( 'P', 'L', 'C', M, N, M, U, LDU, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IRWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, - $ LDVT, U, LDU, CDUM, 1, - $ RWORK( IRWORK ), INFO ) -* - END IF -* - END IF -* - END IF -* - ELSE -* -* N .LT. MNTHR -* -* Path 10t(N greater than M, but not much larger) -* Reduce to bidiagonal form without LQ decomposition -* - IE = 1 - ITAUQ = 1 - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize A -* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) -* (RWorkspace: M) -* - CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - IF( WNTUAS ) THEN -* -* If left singular vectors desired in U, copy result to U -* and generate left bidiagonalizing vectors in U -* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL ZUNGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVAS ) THEN -* -* If right singular vectors desired in VT, copy result to -* VT and generate right bidiagonalizing vectors in VT -* (CWorkspace: need 2*M+NRVT, prefer 2*M+NRVT*NB) -* (RWorkspace: 0) -* - CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) - IF( WNTVA ) - $ NRVT = N - IF( WNTVS ) - $ NRVT = M - CALL ZUNGBR( 'P', NRVT, N, M, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTUO ) THEN -* -* If left singular vectors desired in A, generate left -* bidiagonalizing vectors in A -* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'Q', M, M, N, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVO ) THEN -* -* If right singular vectors desired in A, generate right -* bidiagonalizing vectors in A -* (CWorkspace: need 3*M, prefer 2*M+M*NB) -* (RWorkspace: 0) -* - CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IRWORK = IE + M - IF( WNTUAS .OR. WNTUO ) - $ NRU = M - IF( WNTUN ) - $ NRU = 0 - IF( WNTVAS .OR. WNTVO ) - $ NCVT = N - IF( WNTVN ) - $ NCVT = 0 - IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'L', M, NCVT, NRU, 0, S, RWORK( IE ), VT, - $ LDVT, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) - ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in A -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'L', M, NCVT, NRU, 0, S, RWORK( IE ), A, - $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), - $ INFO ) - ELSE -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in A and computing right singular -* vectors in VT -* (CWorkspace: 0) -* (RWorkspace: need BDSPAC) -* - CALL ZBDSQR( 'L', M, NCVT, NRU, 0, S, RWORK( IE ), VT, - $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ), - $ INFO ) - END IF -* - END IF -* - END IF -* -* Undo scaling if necessary -* - IF( ISCL.EQ.1 ) THEN - IF( ANRM.GT.BIGNUM ) - $ CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN, - $ IERR ) - IF( INFO.NE.0 .AND. ANRM.GT.BIGNUM ) - $ CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN-1, 1, - $ RWORK( IE ), MINMN, IERR ) - IF( ANRM.LT.SMLNUM ) - $ CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN, - $ IERR ) - IF( INFO.NE.0 .AND. ANRM.LT.SMLNUM ) - $ CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN-1, 1, - $ RWORK( IE ), MINMN, IERR ) - END IF -* -* Return optimal workspace in WORK(1) -* - WORK( 1 ) = MAXWRK -* - RETURN -* -* End of ZGESVD -* - END |