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

CLALSA(l)					)					CLALSA(l)

NAME
       CLALSA  -  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 CLALSA( 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, * )

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

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

PURPOSE
       CLALSA 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, CLALSA applies the inverse of the left sin-
       gular  vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ =
       1, CLALSA applies the right singular vector matrix to the right hand  side.  The  singular
       vector matrices were generated in compact form by CLALSA.

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 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 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) REAL 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) REAL 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) REAL array, dimension ( LDU, NLVL ).
	      where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.

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

       C      (input) REAL 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) REAL 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) REAL 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 				CLALSA(l)


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