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## zgesdd()

subroutine zgesdd | ( | character | jobz,
|  | 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, dimension( * ) | iwork,
|  | integer | info )

ZGESDD

Download ZGESDD + dependencies [TGZ] [ZIP] [TXT]

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.
      !>
      !>

Parameters

  [in]

  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.
      !>

  [in]

  M

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

  [in]

  N

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

  [in,out]

  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.
      !>

  [in]

  LDA

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

  [out]

  S

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

  [out]

  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.
      !>

  [in]

  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.
      !>

  [out]

  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.
      !>

  [in]

  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).
      !>

  [out]

  WORK

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

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The dimension of the array WORK. LWORK >= 1.
      !>          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.
      !>
      !>          Let mx = max(M,N) and mn = min(M,N).
      !>          If JOBZ = 'N', LWORK >= 2*mn + mx.
      !>          If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx.
      !>          If JOBZ = 'S', LWORK >=   mn*mn + 3*mn.
      !>          If JOBZ = 'A', LWORK >=   mn*mn + 2*mn + mx.
      !>          These are not tight minimums in all cases; see comments inside code.
      !>          For good performance, LWORK should generally be larger;
      !>          a query is recommended.
      !>

  [out]

  RWORK

      !>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
      !>          Let mx = max(M,N) and mn = min(M,N).
      !>          If JOBZ = 'N',    LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn);
      !>          else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn;
      !>          else              LRWORK >= max( 5*mn*mn + 5*mn,
      !>                                           2*mx*mn + 2*mn*mn + mn ).
      !>

  [out]

  IWORK

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

  [out]

  INFO

      !>          INFO is INTEGER
      !>          <  0:  if INFO = -i, the i-th argument had an illegal value.
      !>          = -4:  if A had a NAN entry.
      !>          >  0:  The updating process of DBDSDC did not converge.
      !>          =  0:  successful exit.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

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