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RedHat 9 (Linux i386) - man page for slals0 (redhat section l)

SLALS0(l)					)					SLALS0(l)

NAME
       SLALS0 - applie back the multiplying factors of either the left or the right singular vec-
       tor matrix of a diagonal matrix appended by a row to the right hand side matrix B in solv-
       ing the least squares problem using the divide-and-conquer SVD approach

SYNOPSIS
       SUBROUTINE SLALS0( ICOMPQ,  NL,	NR,  SQRE,  NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL,
			  LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO )

	   INTEGER	  GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, LDGNUM, NL, NR, NRHS, SQRE

	   REAL 	  C, S

	   INTEGER	  GIVCOL( LDGCOL, * ), PERM( * )

	   REAL 	  B( LDB, * ), BX( LDBX, * ), DIFL( *  ),  DIFR(  LDGNUM,  *  ),  GIVNUM(
			  LDGNUM, * ), POLES( LDGNUM, * ), WORK( * ), Z( * )

PURPOSE
       SLALS0  applies back the multiplying factors of either the left or the right singular vec-
       tor matrix of a diagonal matrix appended by a row to the right hand side matrix B in solv-
       ing  the  least	squares  problem using the divide-and-conquer SVD approach.  For the left
       singular vector matrix, three types of orthogonal matrices are involved:

       (1L) Givens rotations: the number of such rotations is GIVPTR; the
	    pairs of columns/rows they were applied to are stored in GIVCOL;
	    and the C- and S-values of these rotations are stored in GIVNUM.

       (2L) Permutation. The (NL+1)-st row of B is to be moved to the first
	    row, and for J=2:N, PERM(J)-th row of B is to be moved to the
	    J-th row.

       (3L) The left singular vector matrix of the remaining matrix.

       For the right singular vector matrix, four types of orthogonal matrices are involved:

       (1R) The right singular vector matrix of the remaining matrix.

       (2R) If SQRE = 1, one extra Givens rotation to generate the right
	    null space.

       (3R) The inverse transformation of (2L).

       (4R) The inverse transformation of (1L).

ARGUMENTS
       ICOMPQ (input) INTEGER Specifies whether singular vectors are to be computed  in  factored
       form:
       = 0: Left singular vector matrix.
       = 1: Right singular vector matrix.

       NL     (input) INTEGER
	      The row dimension of the upper block. NL >= 1.

       NR     (input) INTEGER
	      The row dimension of the lower block. NR >= 1.

       SQRE   (input) INTEGER
	      = 0: the lower block is an NR-by-NR square matrix.
	      = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

	      The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N
	      + SQRE.

       NRHS   (input) INTEGER
	      The number of columns of B and BX. NRHS must be at least 1.

       B      (input/output) REAL array, dimension ( LDB, NRHS )
	      On input, B contains the right hand sides of the least squares problem  in  rows	1
	      through M. On output, B contains the solution X in rows 1 through N.

       LDB    (input) INTEGER
	      The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).

       BX     (workspace) REAL array, dimension ( LDBX, NRHS )

       LDBX   (input) INTEGER
	      The leading dimension of BX.

       PERM   (input) INTEGER array, dimension ( N )
	      The permutations (from deflation and sorting) applied to the two blocks.

	      GIVPTR (input) INTEGER The number of Givens rotations which took place in this sub-
	      problem.

	      GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 ) Each pair  of  numbers  indi-
	      cates a pair of rows/columns involved in a Givens rotation.

	      LDGCOL (input) INTEGER The leading dimension of GIVCOL, must be at least N.

	      GIVNUM (input) REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C or S
	      value used in the corresponding Givens rotation.

	      LDGNUM (input) INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must
	      be at least K.

       POLES  (input) REAL array, dimension ( LDGNUM, 2 )
	      On  entry, POLES(1:K, 1) contains the new singular values obtained from solving the
	      secular equation, and POLES(1:K, 2) is an array containing the poles in the secular
	      equation.

       DIFL   (input) REAL array, dimension ( K ).
	      On  entry, DIFL(I) is the distance between I-th updated (undeflated) singular value
	      and the I-th (undeflated) old singular value.

       DIFR   (input) REAL array, dimension ( LDGNUM, 2 ).
	      On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated)  sin-
	      gular  value  and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the
	      normalizing factor for the I-th right singular vector.

       Z      (input) REAL array, dimension ( K )
	      Contain the components of the deflation-adjusted updating row vector.

       K      (input) INTEGER
	      Contains the dimension of the non-deflated matrix, This is the order of the related
	      secular equation. 1 <= K <=N.

       C      (input) REAL
	      C  contains  garbage if SQRE =0 and the C-value of a Givens rotation related to the
	      right null space if SQRE = 1.

       S      (input) REAL
	      S contains garbage if SQRE =0 and the S-value of a Givens rotation related  to  the
	      right null space if SQRE = 1.

       WORK   (workspace) REAL array, dimension ( K )

       INFO   (output) INTEGER
	      = 0:  successful exit.
	      < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS
       Based on contributions by
	  Ming Gu and Ren-Cang Li, Computer Science Division, University of
	    California at Berkeley, USA
	  Osni Marques, LBNL/NERSC, USA

LAPACK version 3.0			   15 June 2000 				SLALS0(l)


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