CLALS0 man page on IRIX

Man page or keyword search:  
man Server   31559 pages
apropos Keyword Search (all sections)
Output format
IRIX logo
[printable version]



CLALS0(3S)							    CLALS0(3S)

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, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

									Page 1

CLALS0(3S)							    CLALS0(3S)

     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.

									Page 2

CLALS0(3S)							    CLALS0(3S)

	    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
	    (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) singular 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.

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

									Page 3

CLALS0(3S)							    CLALS0(3S)

     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

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

									Page 4

[top]

List of man pages available for IRIX

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