SGESVD(l)								 )								 SGESVD(l)

NAME

       SGESVD - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vec-
       tors

SYNOPSIS

       SUBROUTINE SGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO )

	   CHARACTER	  JOBU, JOBVT

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

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

PURPOSE

       SGESVD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular  vec-
       tors. 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 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**T, not V.

ARGUMENTS

       JOBU    (input) 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   (input) CHARACTER*1
	       Specifies options for computing all or part of the matrix V**T:
	       = 'A':  all N rows of V**T are returned in the array VT;
	       = 'S':  the first min(m,n) rows of V**T (the right singular vectors) are returned in the array VT; = 'O':  the first min(m,n)  rows
	       of  V**T  (the right singular vectors) are overwritten on the array A; = 'N':  no rows of V**T (no right singular vectors) are com-
	       puted.

	       JOBVT and JOBU cannot both be 'O'.

       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) REAL 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**T (the right singular vectors,
	       stored rowwise); if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A are destroyed.

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

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

       U       (output) REAL 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 orthogonal 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     (input) INTEGER
	       The leading dimension of the array U.  LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.

       VT      (output) REAL array, dimension (LDVT,N)
	       If  JOBVT  =  'A',  VT contains the N-by-N orthogonal matrix V**T; if JOBVT = 'S', VT contains the first min(m,n) rows of V**T (the
	       right singular vectors, stored rowwise); if JOBVT = 'N' or 'O', VT is not referenced.

       LDVT    (input) INTEGER
	       The leading dimension of the array VT.  LDVT >= 1; if JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).

       WORK    (workspace/output) REAL array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK; if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged superdiagonal  ele-
	       ments  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.

       LWORK   (input) INTEGER
	       The dimension of the array WORK. LWORK >= 1.  LWORK >= MAX(3*MIN(M,N)+MAX(M,N),5*MIN(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.

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       > 0:  if SBDSQR did not converge, INFO specifies how many superdiagonals of an intermediate bidiagonal form B did not  converge	to
	       zero. See the description of WORK above for details.

LAPACK version 3.0						   15 June 2000 							 SGESVD(l)