sgesvd.f

famous linear algebra library (LAPACK) ports to windows

      SUBROUTINE SGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
     $                   WORK, LWORK, 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 ..
      REAL               A( LDA, * ), S( * ), U( LDU, * ),
     $                   VT( LDVT, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  SGESVD computes the singular value decomposition (SVD) of a real
*  M-by-N matrix A, optionally computing the left and/or right singular
*  vectors. The SVD is written
*
*       A = U * SIGMA * transpose(V)
*
*  where SIGMA is an M-by-N matrix which is zero except for its
*  min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
*  V is an N-by-N orthogonal 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**T, 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**T:
*          = 'A':  all N rows of V**T are returned in the array VT;
*          = 'S':  the first min(m,n) rows of V**T (the right singular
*                  vectors) are returned in the array VT;
*          = 'O':  the first min(m,n) rows of V**T (the right singular
*                  vectors) are overwritten on the array A;
*          = 'N':  no rows of V**T (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) REAL 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**T (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) REAL array, dimension (min(M,N))
*          The singular values of A, sorted so that S(i) >= S(i+1).
*
*  U       (output) REAL 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 orthogonal 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) REAL array, dimension (LDVT,N)
*          If JOBVT = 'A', VT contains the N-by-N orthogonal matrix
*          V**T;
*          if JOBVT = 'S', VT contains the first min(m,n) rows of
*          V**T (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) REAL array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
*          if INFO > 0, WORK(2:MIN(M,N)) 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.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(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.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit.
*          < 0:  if INFO = -i, the i-th argument had an illegal value.
*          > 0:  if SBDSQR did not converge, INFO specifies how many
*                superdiagonals of an intermediate bidiagonal form B
*                did not converge to zero. See the description of WORK
*                above for details.
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
     $                   WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS
      INTEGER            BDSPAC, BLK, CHUNK, I, IE, IERR, IR, ISCL,
     $                   ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
     $                   MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
     $                   NRVT, WRKBL
      REAL               ANRM, BIGNUM, EPS, SMLNUM
*     ..
*     .. Local Arrays ..
      REAL               DUM( 1 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           SBDSQR, SGEBRD, SGELQF, SGEMM, SGEQRF, SLACPY,
     $                   SLASCL, SLASET, SORGBR, SORGLQ, SORGQR, SORMBR,
     $                   XERBLA
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      REAL               SLAMCH, SLANGE
      EXTERNAL           LSAME, ILAENV, SLAMCH, SLANGE
*     ..
*     .. 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.
*       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
*
*           Compute space needed for SBDSQR
*
            MNTHR = ILAENV( 6, 'SGESVD', JOBU // JOBVT, M, N, 0, 0 )
            BDSPAC = 5*N
            IF( M.GE.MNTHR ) THEN
               IF( WNTUN ) THEN
*
*                 Path 1 (M much larger than N, JOBU='N')
*
                  MAXWRK = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1,
     $                     -1 )
                  MAXWRK = MAX( MAXWRK, 3*N+2*N*
     $                     ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
                  IF( WNTVO .OR. WNTVAS )
     $               MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
     $                        ILAENV( 1, 'SORGBR', 'P', N, N, N, -1 ) )
                  MAXWRK = MAX( MAXWRK, BDSPAC )
                  MINWRK = MAX( 4*N, BDSPAC )
               ELSE IF( WNTUO .AND. WNTVN ) THEN
*
*                 Path 2 (M much larger than N, JOBU='O', JOBVT='N')
*
                  WRKBL = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'SORGQR', ' ', M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+2*N*
     $                    ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    ILAENV( 1, 'SORGBR', 'Q', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, BDSPAC )
                  MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N )
                  MINWRK = MAX( 3*N+M, BDSPAC )
               ELSE IF( WNTUO .AND. WNTVAS ) THEN
*
*                 Path 3 (M much larger than N, JOBU='O', JOBVT='S' or
*                 'A')
*
                  WRKBL = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'SORGQR', ' ', M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+2*N*
     $                    ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    ILAENV( 1, 'SORGBR', 'Q', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+( N-1 )*
     $                    ILAENV( 1, 'SORGBR', 'P', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, BDSPAC )
                  MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N )
                  MINWRK = MAX( 3*N+M, BDSPAC )
               ELSE IF( WNTUS .AND. WNTVN ) THEN
*
*                 Path 4 (M much larger than N, JOBU='S', JOBVT='N')
*
                  WRKBL = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'SORGQR', ' ', M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+2*N*
     $                    ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    ILAENV( 1, 'SORGBR', 'Q', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, BDSPAC )
                  MAXWRK = N*N + WRKBL
                  MINWRK = MAX( 3*N+M, BDSPAC )
               ELSE IF( WNTUS .AND. WNTVO ) THEN
*
*                 Path 5 (M much larger than N, JOBU='S', JOBVT='O')
*
                  WRKBL = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'SORGQR', ' ', M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+2*N*
     $                    ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    ILAENV( 1, 'SORGBR', 'Q', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+( N-1 )*
     $                    ILAENV( 1, 'SORGBR', 'P', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, BDSPAC )
                  MAXWRK = 2*N*N + WRKBL
                  MINWRK = MAX( 3*N+M, BDSPAC )
               ELSE IF( WNTUS .AND. WNTVAS ) THEN
*
*                 Path 6 (M much larger than N, JOBU='S', JOBVT='S' or
*                 'A')
*
                  WRKBL = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'SORGQR', ' ', M,
     $                    N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+2*N*
     $                    ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    ILAENV( 1, 'SORGBR', 'Q', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+( N-1 )*
     $                    ILAENV( 1, 'SORGBR', 'P', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, BDSPAC )
                  MAXWRK = N*N + WRKBL
                  MINWRK = MAX( 3*N+M, BDSPAC )
               ELSE IF( WNTUA .AND. WNTVN ) THEN
*
*                 Path 7 (M much larger than N, JOBU='A', JOBVT='N')
*
                  WRKBL = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
                  WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'SORGQR', ' ', M,
     $                    M, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+2*N*
     $                    ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    ILAENV( 1, 'SORGBR', 'Q', N, N, N, -1 ) )