LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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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.