zgesvd.f3

!>
!> 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.
!> 

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.
!> 

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