clals0 man page on YellowDog

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

CLALS0(l)			       )			     CLALS0(l)

NAME
       CLALS0  - 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 CLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,	 PERM,
			  GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL,
			  DIFR, Z, K, C, S, RWORK, INFO )

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

	   REAL		  C, S

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

	   REAL		  DIFL(	 *  ), DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ),
			  POLES( LDGNUM, * ), RWORK( * ), Z( * )

	   COMPLEX	  B( LDB, * ), BX( LDBX, * )

PURPOSE
       CLALS0 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) COMPLEX 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) COMPLEX 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)  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	(unde‐
	      flated)  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) 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) 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 rota‐
	      tion 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	 rota‐
	      tion related to the right null space if SQRE = 1.

       RWORK  (workspace) REAL array, dimension
	      ( K*(1+NRHS) + 2*NRHS )

       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			     CLALS0(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