SLASDQ(l)								 )								 SLASDQ(l)

NAME

       SLASDQ  -  compute  the	singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E,
       accumulating the transformations if desired

SYNOPSIS

       SUBROUTINE SLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE

	   REAL 	  C( LDC, * ), D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE

       SLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with  diagonal  D  and  offdiagonal	E,
       accumulating the transformations if desired. Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and
       P such that B = Q * S * P' (P' denotes the transpose of P). The singular values S are overwritten on D.

       The input matrix U  is changed to U  * Q  if desired.
       The input matrix VT is changed to P' * VT if desired.
       The input matrix C  is changed to Q' * C  if desired.

       See "Computing  Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy," by J. Demmel  and	W.  Kahan,  LAPACK
       Working Note #3, for a detailed description of the algorithm.

ARGUMENTS

       UPLO  (input) CHARACTER*1
	     On  entry,  UPLO specifies whether the input bidiagonal matrix is upper or lower bidiagonal, and wether it is square are not.  UPLO =
	     'U' or 'u'   B is upper bidiagonal.  UPLO = 'L' or 'l'   B is lower bidiagonal.

       SQRE  (input) INTEGER
	     = 0: then the input matrix is N-by-N.
	     = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and (N+1)-by-N if UPLU = 'L'.

	     The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.

       N     (input) INTEGER
	     On entry, N specifies the number of rows and columns in the matrix. N must be at least 0.

       NCVT  (input) INTEGER
	     On entry, NCVT specifies the number of columns of the matrix VT. NCVT must be at least 0.

       NRU   (input) INTEGER
	     On entry, NRU specifies the number of rows of the matrix U. NRU must be at least 0.

       NCC   (input) INTEGER
	     On entry, NCC specifies the number of columns of the matrix C. NCC must be at least 0.

       D     (input/output) REAL array, dimension (N)
	     On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular val-
	     ues in ascending order.

       E     (input/output) REAL array.
	     dimension	is  (N-1)  if  SQRE  =	0 and N if SQRE = 1.  On entry, the entries of E contain the offdiagonal entries of the bidiagonal
	     matrix whose SVD is desired. On normal exit, E will contain 0. If the algorithm does not converge, D and E will contain the  diagonal
	     and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input.

       VT    (input/output) REAL array, dimension (LDVT, NCVT)
	     On entry, contains a matrix which on exit has been premultiplied by P', dimension N-by-NCVT if SQRE = 0 and (N+1)-by-NCVT if SQRE = 1
	     (not referenced if NCVT=0).

       LDVT  (input) INTEGER
	     On entry, LDVT specifies the leading dimension of VT as declared in the calling (sub) program. LDVT must be at least 1.  If  NCVT	is
	     nonzero LDVT must also be at least N.

       U     (input/output) REAL array, dimension (LDU, N)
	     On  entry, contains a  matrix which on exit has been postmultiplied by Q, dimension NRU-by-N if SQRE = 0 and NRU-by-(N+1) if SQRE = 1
	     (not referenced if NRU=0).

       LDU   (input) INTEGER
	     On entry, LDU  specifies the leading dimension of U as declared in the calling (sub) program. LDU must be at least max( 1, NRU ) .

       C     (input/output) REAL array, dimension (LDC, NCC)
	     On entry, contains an N-by-NCC matrix which on exit has been premultiplied by Q'  dimension N-by-NCC if SQRE = 0 and (N+1)-by-NCC	if
	     SQRE = 1 (not referenced if NCC=0).

       LDC   (input) INTEGER
	     On  entry,  LDC   specifies  the  leading	dimension of C as declared in the calling (sub) program. LDC must be at least 1. If NCC is
	     nonzero, LDC must also be at least N.

       WORK  (workspace) REAL array, dimension (4*N)
	     Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at least 2.

       INFO  (output) INTEGER
	     On exit, a value of 0 indicates a successful exit.  If INFO < 0, argument number -INFO is illegal.  If INFO > 0,  the  algorithm  did
	     not converge, and INFO specifies how many superdiagonals did not converge.

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 							 SLASDQ(l)