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

DLASDQ(l)					)					DLASDQ(l)

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

SYNOPSIS
       SUBROUTINE DLASDQ( 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

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

PURPOSE
       DLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiago-
       nal 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 bidi-
	     agonal, 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) DOUBLE PRECISION 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 values in ascending order.

       E     (input/output) DOUBLE PRECISION array.
	     dimension is (N-1) if SQRE = 0 and N if SQRE = 1.	On entry, the entries of  E  con-
	     tain  the offdiagonal entries of the bidiagonal matrix whose SVD is desired. On nor-
	     mal 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 equiva-
	     lent to the one given as input.

       VT    (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 				DLASDQ(l)


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