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RedHat 9 (Linux i386) - man page for dgesdd (redhat section l)

DGESDD(l)					)					DGESDD(l)

NAME
       DGESDD - compute the singular value decomposition (SVD) of a real M-by-N matrix A, option-
       ally computing the left and right singular vectors

SYNOPSIS
       SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO )

	   CHARACTER	  JOBZ

	   INTEGER	  INFO, LDA, LDU, LDVT, LWORK, M, N

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION A( LDA, * ), S( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE
       DGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A,  option-
       ally  computing	the  left and right singular vectors. If singular vectors are desired, it
       uses a divide-and-conquer algorithm.

       The SVD is written

	    A = U * SIGMA * 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 orthogonal matrix, and V is an N-by-N orthogonal matrix.	The diagonal ele-
       ments 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**T, not V.

       The divide and conquer algorithm makes very mild assumptions about floating  point  arith-
       metic.  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.

ARGUMENTS
       JOBZ    (input) 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**T 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**T
	       are returned in the arrays U and VT; = 'O':  If M >= N, the first N columns  of	U
	       are  overwritten on the array A and all rows of V**T are returned in the array VT;
	       otherwise, all columns of U are returned in the array U and the first  M  rows  of
	       V**T  are overwritten in the array VT; = 'N':  no columns of U or rows of V**T are
	       computed.

       M       (input) INTEGER
	       The number of rows of the input matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the input matrix A.  N >= 0.

       A       (input/output) DOUBLE PRECISION 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**T (the right singular  vectors,  stored
	       rowwise) otherwise.  if JOBZ .ne. 'O', the contents of A are destroyed.

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

       S       (output) DOUBLE PRECISION array, dimension (min(M,N))
	       The singular values of A, sorted so that S(i) >= S(i+1).

       U       (output) DOUBLE PRECISION 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 orthogonal 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     (input) INTEGER
	       The leading dimension of the array U.  LDU >= 1; if JOBZ = 'S' or 'A'  or  JOBZ	=
	       'O' and M < N, LDU >= M.

       VT      (output) DOUBLE PRECISION array, dimension (LDVT,N)
	       If  JOBZ  = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N orthogonal matrix
	       V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (the right singu-
	       lar  vectors,  stored  rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not
	       referenced.

       LDVT    (input) 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    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK;

       LWORK   (input) INTEGER
	       The dimension of the array WORK. LWORK >= 1.  If JOBZ = 'N', LWORK >= 3*min(M,N) +
	       max(max(M,N),6*min(M,N)).   If  JOBZ  =	'O',  LWORK  >=   3*min(M,N)*min(M,N)	+
	       max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).   If  JOBZ  =  'S'  or  'A' LWORK >=
	       3*min(M,N)*min(M,N) + max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)).  For good per-
	       formance,  LWORK  should  generally be larger.  If LWORK < 0 but other input argu-
	       ments are legal, WORK(1) returns the optimal LWORK.

       IWORK   (workspace) INTEGER array, dimension (8*min(M,N))

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       > 0:  DBDSDC did not converge, updating process failed.

FURTHER DETAILS
       Based on contributions by
	  Ming Gu and Huan Ren, Computer Science Division, University of
	  California at Berkeley, USA

LAPACK version 3.0			   15 June 2000 				DGESDD(l)


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