dlals0 man page on YellowDog

Man page or keyword search:  
man Server   18644 pages
apropos Keyword Search (all sections)
Output format
YellowDog logo
[printable version]

DLALS0(l)			       )			     DLALS0(l)

NAME
       DLALS0  - applie back the multiplying factors of either the left or the
       right singular vector matrix of a diagonal matrix appended by a row  to
       the right hand side matrix B in solving the least squares problem using
       the divide-and-conquer SVD approach

SYNOPSIS
       SUBROUTINE DLALS0( 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

	   DOUBLE	  PRECISION C, S

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

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

PURPOSE
       DLALS0  applies	back the multiplying factors of either the left or the
       right singular vector matrix of a diagonal matrix appended by a row  to
       the right hand side matrix B in solving 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 subproblem.

	      GIVCOL  (input) INTEGER array, dimension ( LDGCOL, 2 ) Each pair
	      of numbers indicates 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension ( K ).
	      On  entry,  DIFL(I)  is the distance between I-th updated (unde‐
	      flated) singular value and the I-th  (undeflated)	 old  singular
	      value.

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

       Z      (input) DOUBLE PRECISION 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) DOUBLE PRECISION
	      C contains garbage if SQRE =0 and the C-value of a Givens	 rota‐
	      tion related to the right null space if SQRE = 1.

       S      (input) DOUBLE PRECISION
	      S	 contains garbage if SQRE =0 and the S-value of a Givens rota‐
	      tion related to the right null space if SQRE = 1.

       WORK   (workspace) DOUBLE PRECISION 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			     DLALS0(l)
[top]

List of man pages available for YellowDog

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net