SRC/zgesvd.f(3)

NAME
SRC/zgesvd.f

SYNOPSIS

  Functions/Subroutines
subroutine zgesvd (jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, info)
ZGESVD computes the singular value decomposition (SVD) for GE matrices

Function/Subroutine Documentation

  subroutine zgesvd (character jobu, character jobvt, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt, integer ldvt, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer info)

ZGESVD computes the singular value decomposition (SVD) for GE matrices

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.
    !>

Parameters
    JOBU

    !>          JOBU is 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

    !>          JOBVT is 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

    !>          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 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

    !>          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)
    !>          (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

    !>          LDU is INTEGER
    !>          The leading dimension of the array U.  LDU >= 1; if
    !>          JOBU = 'S' or 'A', LDU >= M.
    !>

    VT

    !>          VT is 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

    !>          LDVT is INTEGER
    !>          The leading dimension of the array VT.  LDVT >= 1; if
    !>          JOBVT = 'A', LDVT >= N; if JOBVT = '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 >=  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

    !>          RWORK is 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

    !>          INFO is 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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 212 of file zgesvd.f.

Author

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