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DLASDQ(l)			       )			     DLASDQ(l)

NAME
       DLASDQ  -  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 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) bidiagonal matrix with diagonal D and offdiagonal E,  accumu‐
       lating the transformations if desired. Letting B denote the input bidi‐
       agonal matrix, the algorithm computes orthogonal matrices Q and P  such
       that  B = Q * S * P' (P' denotes the transpose of P). The singular val‐
       ues 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 Guar‐
       anteed High Relative Accuracy," by J. Demmel and W. Kahan, LAPACK Work‐
       ing 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) 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  sin‐
	     gular 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 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	diago‐
	     nal and superdiagonal entries of a bidiagonal matrix orthogonally
	     equivalent 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  postmulti‐
	     plied  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 pre‐
	     multiplied 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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