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zgesdd.f(3) LAPACK zgesdd.f(3)

zgesdd.f -


subroutine zgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)
 
ZGESDD

ZGESDD
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.
The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
Parameters:
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.
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 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.
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)
          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.
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.
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.
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).
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 >= 1.
          if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).
          if JOBZ = 'O',
                LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
          if JOBZ = 'S' or 'A',
                LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
          For good performance, LWORK should generally be larger.
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.
RWORK
          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
          If JOBZ = 'N', LRWORK >= 5*min(M,N).
          Otherwise,
          LRWORK >= min(M,N)*max(5*min(M,N)+7,2*max(M,N)+2*min(M,N)+1)
IWORK
          IWORK is INTEGER array, dimension (8*min(M,N))
INFO
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  The updating process of DBDSDC did not converge.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
Definition at line 222 of file zgesdd.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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