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

SLASDQ(l)					)					SLASDQ(l)

NAME
       SLASDQ - 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 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) 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) 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 values 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 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) 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)


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