SGESVD(l)	     LAPACK driver routine (version 1.1)	    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	vectors

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	vectors. 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)	diag-
  onal elements, U is an M-by-M	orthogonal matrix, and V is an N-by-N orthog-
  onal 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 vec-
	  tors)	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 vec-
	  tors,	stored columnwise); if JOBU = 'N' or 'O', U is not refer-
	  enced.

  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 elements
	  of an	upper bidiagonal matrix	B whose	diagonal is in S (not neces-
	  sarily 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)-4).  For good performance,	LWORK
	  should generally be larger.

  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 superdi-
	  agonals of an	intermediate bidiagonal	form B did not converge	to
	  zero.	See the	description of WORK above for details.