Home Man
Search
Today's Posts
Register

Linux & Unix Commands - Search Man Pages

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

ZLALSA(l)					)					ZLALSA(l)

NAME
       ZLALSA  -  i an itermediate step in solving the least squares problem by computing the SVD
       of the coefficient matrix in compact form (The singular vectors are computed  as  products
       of simple orthorgonal matrices.)

SYNOPSIS
       SUBROUTINE ZLALSA( ICOMPQ,  SMLSIZ,  N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR,
			  Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM,  C,  S,  RWORK,  IWORK,
			  INFO )

	   INTEGER	  ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ

	   INTEGER	  GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), K( * ), PERM( LDGCOL, * )

	   DOUBLE	  PRECISION  C(  *  ),	DIFL( LDU, * ), DIFR( LDU, * ), GIVNUM( LDU, * ),
			  POLES( LDU, * ), RWORK( * ), S( * ), U( LDU, * ), VT( LDU, * ), Z( LDU,
			  * )

	   COMPLEX*16	  B( LDB, * ), BX( LDBX, * )

PURPOSE
       ZLALSA is an itermediate step in solving the least squares problem by computing the SVD of
       the coefficient matrix in compact form (The singular vectors are computed as  products  of
       simple orthorgonal matrices.).  If ICOMPQ = 0, ZLALSA applies the inverse of the left sin-
       gular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ	=
       1,  ZLALSA  applies  the right singular vector matrix to the right hand side. The singular
       vector matrices were generated in compact form by ZLALSA.

ARGUMENTS
       ICOMPQ (input) INTEGER Specifies whether the left or the right singular vector  matrix  is
       involved.  = 0: Left singular vector matrix
       = 1: Right singular vector matrix

       SMLSIZ  (input)	INTEGER The maximum size of the subproblems at the bottom of the computa-
       tion tree.

       N      (input) INTEGER
	      The row and column dimensions of the upper bidiagonal matrix.

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

       B      (input) COMPLEX*16 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  in  the  calling	subprogram.  LDB must be at least
	      max(1,MAX( M, N ) ).

       BX     (output) COMPLEX*16 array, dimension ( LDBX, NRHS )
	      On exit, the result of applying the left or right singular vector matrix to B.

       LDBX   (input) INTEGER
	      The leading dimension of BX.

       U      (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
	      On entry, U contains the left singular vector matrices of all  subproblems  at  the
	      bottom level.

       LDU    (input) INTEGER, LDU = > N.
	      The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.

       VT     (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
	      On entry, VT' contains the right singular vector matrices of all subproblems at the
	      bottom level.

       K      (input) INTEGER array, dimension ( N ).

       DIFL   (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
	      where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.

       DIFR   (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
	      On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record distances between singular values
	      on  the  I-th  level and singular values on the (I -1)-th level, and DIFR(*, 2 * I)
	      record the normalizing factors of the right singular vectors matrices  of  subprob-
	      lems on I-th level.

       Z      (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
	      On  entry,  Z(1, I) contains the components of the deflation- adjusted updating row
	      vector for subproblems on the I-th level.

       POLES  (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
	      On entry, POLES(*, 2 * I -1: 2 * I)  contains  the  new  and  old  singular  values
	      involved in the secular equations on the I-th level.

	      GIVPTR  (input)  INTEGER array, dimension ( N ).	On entry, GIVPTR( I ) records the
	      number of Givens rotations performed on the I-th problem on the computation tree.

	      GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).  On entry,	for  each
	      I,  GIVCOL(*, 2 * I - 1: 2 * I) records the locations of Givens rotations performed
	      on the I-th level on the computation tree.

	      LDGCOL (input) INTEGER, LDGCOL = > N.  The leading dimension of arrays  GIVCOL  and
	      PERM.

       PERM   (input) INTEGER array, dimension ( LDGCOL, NLVL ).
	      On entry, PERM(*, I) records permutations done on the I-th level of the computation
	      tree.

	      GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2  *  NLVL  ).   On  entry,
	      GIVNUM(*,  2  *I	-1 : 2 * I) records the C- and S- values of Givens rotations per-
	      formed on the I-th level on the computation tree.

       C      (input) DOUBLE PRECISION array, dimension ( N ).
	      On entry, if the I-th subproblem is not square, C( I ) contains the  C-value  of	a
	      Givens rotation related to the right null space of the I-th subproblem.

       S      (input) DOUBLE PRECISION array, dimension ( N ).
	      On  entry,  if  the I-th subproblem is not square, S( I ) contains the S-value of a
	      Givens rotation related to the right null space of the I-th subproblem.

       RWORK  (workspace) DOUBLE PRECISION array, dimension at least
	      max ( N, (SMLSZ+1)*NRHS*3 ).

       IWORK  (workspace) INTEGER array.
	      The dimension must be at least 3 * N

       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 				ZLALSA(l)


All times are GMT -4. The time now is 08:19 AM.

Unix & Linux Forums Content Copyrightę1993-2018. All Rights Reserved.
UNIX.COM Login
Username:
Password:  
Show Password