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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
commit8c8d2f518968ce7057eec6aa5cd5aec8faab861a (patch)
tree3dd1788b71d6a3ce2b73d2d475a3133580e17530 /src/lib/lapack/zgesvd.f
parent9f652ffc16a310ac6641a9766c5b9e2671e0e9cb (diff)
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Moving lapack to right place
Diffstat (limited to 'src/lib/lapack/zgesvd.f')
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diff --git a/src/lib/lapack/zgesvd.f b/src/lib/lapack/zgesvd.f
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- 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