_SVD(3F)							      _SVD(3F)

NAME    [Toc]    [Back]

     SVD, SSVD	   -  EISPACK routine.	This subroutine	determines the
     singular value decomposition
	T A=USV	 of a REAL M by	N rectangular matrix.  Householder
     bidiagonalization and a variant of	the QR algorithm are used.

SYNOPSYS    [Toc]    [Back]

	  subroutine  svd(nm, m, n, a, w, matu,	u, matv, v, ierr, rv1)
	  integer	   nm, m, n, ierr
	  double precision a(nm,n), w(n), u(nm,n), v(nm,n), rv1(n)
	  logical	   matu, matv

	  subroutine ssvd(nm, m, n, a, w, matu,	u, matv, v, ierr, rv1)
	  integer	   nm, m, n, ierr
	  real		   a(nm,n), w(n), u(nm,n), v(nm,n), rv1(n)
	  logical	   matu, matv

DESCRIPTION    [Toc]    [Back]

     On	Input

     NM	must be	set to the row dimension of two-dimensional array parameters
     as	declared in the	calling	program	dimension statement.  Note that	NM
     must be at	least as large as the maximum of M and N.

     M is the number of	rows of	A (and U).

     N is the number of	columns	of A (and U) and the order of V.

     A contains	the rectangular	input matrix to	be decomposed.

     MATU should be set	to .TRUE. if the U matrix in the decomposition is
     desired, and to .FALSE. otherwise.

     MATV should be set	to .TRUE. if the V matrix in the decomposition is
     desired, and to .FALSE. otherwise.	 On Output

     A is unaltered (unless overwritten	by U or	V).

     W contains	the N (non-negative) singular values of	A (the diagonal
     elements of S).  They are UNORDERED.  If an error exit is made, the
     singular values should be correct for indices IERR+1,IERR+2,...,N.

     U contains	the matrix U (orthogonal column	vectors) of the	decomposition
     if	MATU has been set to .TRUE.  Otherwise U is used as a temporary	array.
     U may coincide with A.  If	an error exit is made, the columns of U
     corresponding to indices of correct singular values should	be correct.

     V contains	the matrix V (orthogonal) of the decomposition if MATV has
     been set to .TRUE.	 Otherwise V is	not referenced.	 V may also coincide



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_SVD(3F)							      _SVD(3F)



     with A if U is not	needed.	 If an error exit is made, the columns of V
     corresponding to indices of correct singular values should	be correct.

     IERR is set to Zero       for normal return, K	     if	the K-th
     singular value has	not been
	determined after 30 iterations.

     RV1 is a temporary	storage	array. CALLS PYTHAG(A,B) for sqrt(A**2 +
     B**2).  Questions and comments should be directed to B. S.	Garbow,
     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY


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