zgesdd.f(3)

NAME
zgesdd.f -

SYNOPSIS

  Functions/Subroutines
subroutine zgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)
ZGESDD

Function/Subroutine Documentation

  subroutine zgesdd (characterJOBZ, integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, complex*16, dimension( ldu, * )U, integerLDU, complex*16, dimension( ldvt, * )VT, integerLDVT, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)

ZGESDD

Purpose:

     ZGESDD 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.

Parameters:
    JOBZ

              JOBZ is 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
                      in 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 A;
              = 'N':  no columns of U or rows of V**H are computed.

    M

              M is INTEGER
              The number of rows of the input matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the input matrix A.  N >= 0.

    A

              A is COMPLEX*16 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

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,M).

    S

              S is DOUBLE PRECISION array, dimension (min(M,N))
              The singular values of A, sorted so that S(i) >= S(i+1).

    U

              U is COMPLEX*16 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

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

    VT

              VT is COMPLEX*16 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

              LDVT is 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

              WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is 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 = -1, a workspace query is assumed.  The optimal
              size for the WORK array is calculated and stored in WORK(1),
              and no other work except argument checking is performed.

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
              If JOBZ = 'N', LRWORK >= 5*min(M,N).
              Otherwise,
              LRWORK >= min(M,N)*max(5*min(M,N)+7,2*max(M,N)+2*min(M,N)+1)

    IWORK

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

    INFO

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

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Contributors:
    Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 222 of file zgesdd.f.

Author

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