cgesdd(3S)

NAME
     CGESDD - compute the singular value decomposition (SVD) of a complex M-
     by-N matrix A, optionally computing the left and/or right singular
     vectors, by using divide-and-conquer method

SYNOPSIS
     SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK,
                        RWORK, IWORK, INFO )

         CHARACTER      JOBZ

         INTEGER        INFO, LDA, LDU, LDVT, LWORK, M, N

         INTEGER        IWORK( * )

         REAL           RWORK( * ), S( * )

         COMPLEX        A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CGESDD computes the singular value decomposition (SVD) of a complex M-
     by-N matrix A, optionally computing the left and/or right singular
     vectors, by using divide-and-conquer method. 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 VT = V**H, not V.

     The divide and conquer algorithm makes very mild assumptions about
     floating point arithmetic. It will work on machines with a guard digit in
     add/subtract, or on those binary machines without guard digits which
     subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
     conceivably fail on hexadecimal or decimal machines without guard digits,
     but we know of none.


ARGUMENTS
     JOBZ    (input) CHARACTER*1
             Specifies options for computing all or part of the matrix U:
             = 'A':  all M columns of U and all N rows of V**H are returned in
             the arrays U and VT; = 'S':  the first min(M,N) columns of U and
             the first min(M,N) rows of V**H are returned in the arrays U and
             VT; = 'O':  If M >= N, the first N columns of U are overwritten
             on the array A and all rows of V**H are returned in the array VT;
             otherwise, all columns of U are returned in the array U and the
             first M rows of V**H are overwritten in the array VT; = 'N':  no
             columns of U or rows of V**H are computed.

     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 array, dimension (LDA,N)
             On entry, the M-by-N matrix A.  On exit, if JOBZ = 'O',  A is
             overwritten with the first N columns of U (the left singular
             vectors, stored columnwise) if M >= N; A is overwritten with the
             first M rows of V**H (the right singular vectors, stored rowwise)
             otherwise.  if JOBZ .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) COMPLEX array, dimension (LDU,UCOL)
             UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N)
             if JOBZ = 'S'.  If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains
             the M-by-M unitary matrix U; if JOBZ = 'S', U contains the first
             min(M,N) columns of U (the left singular vectors, stored
             columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not
             referenced.

     LDU     (input) INTEGER
             The leading dimension of the array U.  LDU >= 1; if JOBZ = 'S' or
             'A' or JOBZ = 'O' and M < N, LDU >= M.

     VT      (output) COMPLEX array, dimension (LDVT,N)
             If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N
             unitary matrix V**H; if JOBZ = 'S', VT contains the first
             min(M,N) rows of V**H (the right singular vectors, stored
             rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not
             referenced.
     LDVT    (input) INTEGER
             The leading dimension of the array VT.  LDVT >= 1; if JOBZ = 'A'
             or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >=
             min(M,N).

     WORK    (workspace/output) COMPLEX array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The dimension of the array WORK. LWORK >= 1.  if JOBZ = 'N',
             LWORK >= 2*min(M,N)+max(M,N).  if JOBZ = 'O', LWORK >=
             2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).  if JOBZ = 'S' or 'A',
             LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).  For good
             performance, LWORK should generally be larger.  If LWORK < 0 but
             other input arguments are legal, WORK(1) returns the optimal
             LWORK.

     RWORK   (workspace) REAL array, dimension (LRWORK)
             If JOBZ = 'N', LRWORK >= 7*min(M,N).  Otherwise, LRWORK >=
             5*min(M,N)*min(M,N) + 5*min(M,N)

     IWORK   (workspace) INTEGER array, dimension (8*min(M,N))

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.
             > 0:  The updating process of SBDSDC did not converge.

FURTHER DETAILS
     Based on contributions by
        Ming Gu and Huan Ren, Computer Science Division, University of
        California at Berkeley, USA


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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