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## cgesvd()

subroutine cgesvd | ( | character | jobu,
|  | character | jobvt,
|  | integer | m,
|  | integer | n,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | real, dimension( * ) | s,
|  | complex, dimension( ldu, * ) | u,
|  | integer | ldu,
|  | complex, dimension( ldvt, * ) | vt,
|  | integer | ldvt,
|  | complex, dimension( * ) | work,
|  | integer | lwork,
|  | real, dimension( * ) | rwork,
|  | integer | info )

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

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

Purpose:

      !>
      !> CGESVD 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

  [in]

  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.
      !>

  [in]

  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'.
      !>

  [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 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.
      !>

  [in]

  LDA

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

  [out]

  S

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

  [out]

  U

      !>          U is COMPLEX 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.
      !>

  [in]

  LDU

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

  [out]

  VT

      !>          VT is COMPLEX 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.
      !>

  [in]

  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).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX 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 >=  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.
      !>

  [out]

  RWORK

      !>          RWORK is REAL 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.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit.
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
      !>          > 0:  if CBDSQR 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.