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zgesvd.f(3) LAPACK zgesvd.f(3)

zgesvd.f -


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

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.
Date:
April 2012
Definition at line 214 of file zgesvd.f.

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Sat Nov 16 2013 Version 3.4.2

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