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

CLALSD(l)					)					CLALSD(l)

NAME
       CLALSD  -  use the singular value decomposition of A to solve the least squares problem of
       finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N  upper
       bidiagonal, and X and B are N-by-NRHS

SYNOPSIS
       SUBROUTINE CLALSD( UPLO,  SMLSIZ,  N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK,
			  INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDB, N, NRHS, RANK, SMLSIZ

	   REAL 	  RCOND

	   INTEGER	  IWORK( * )

	   REAL 	  D( * ), E( * ), RWORK( * )

	   COMPLEX	  B( LDB, * ), WORK( * )

PURPOSE
       CLALSD uses the singular value decomposition of A to solve the least  squares  problem  of
       finding	X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper
       bidiagonal, and X and B are N-by-NRHS. The solution X overwrites B.  The  singular  values
       of  A  smaller  than RCOND times the largest singular value are treated as zero in solving
       the least squares problem; in this case a minimum norm solution is returned.   The  actual
       singular values are returned in D in ascending order.

       This  code  makes  very	mild assumptions about floating point arithmetic. It will work on
       machines with a guard digit in add/subtract, or on those  binary  machines  without  guard
       digits  which  subtract	like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.  It could con-
       ceivably fail on hexadecimal or decimal machines without guard  digits,	but  we  know  of
       none.

ARGUMENTS
       UPLO   (input) CHARACTER*1
	      = 'U': D and E define an upper bidiagonal matrix.
	      = 'L': D and E define a  lower bidiagonal matrix.

	      SMLSIZ  (input)  INTEGER	The  maximum size of the subproblems at the bottom of the
	      computation tree.

       N      (input) INTEGER
	      The dimension of the  bidiagonal matrix.	N >= 0.

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

       D      (input/output) REAL array, dimension (N)
	      On entry D contains the main diagonal of the bidiagonal matrix. On exit, if INFO	=
	      0, D contains its singular values.

       E      (input) REAL array, dimension (N-1)
	      Contains	the super-diagonal entries of the bidiagonal matrix.  On exit, E has been
	      destroyed.

       B      (input/output) COMPLEX array, dimension (LDB,NRHS)
	      On input, B contains the right hand sides of the least squares problem. On  output,
	      B contains the solution X.

       LDB    (input) INTEGER
	      The  leading  dimension  of  B  in  the  calling	subprogram.  LDB must be at least
	      max(1,N).

       RCOND  (input) REAL
	      The singular values of A less than or equal to RCOND  times  the	largest  singular
	      value  are  treated as zero in solving the least squares problem. If RCOND is nega-
	      tive, machine precision is used instead.	For  example,  if  diag(S)*X=B	were  the
	      least  squares  problem, where diag(S) is a diagonal matrix of singular values, the
	      solution would be X(i) = B(i) / S(i) if S(i) is greater than RCOND*max(S), and X(i)
	      = 0 if S(i) is less than or equal to RCOND*max(S).

       RANK   (output) INTEGER
	      The  number  of  singular values of A greater than RCOND times the largest singular
	      value.

       WORK   (workspace) COMPLEX array, dimension at least
	      (N * NRHS).

       RWORK  (workspace) REAL array, dimension at least
	      (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + (SMLSIZ+1)**2), where NLVL = MAX( 0,
	      INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )

       IWORK  (workspace) INTEGER array, dimension at least
	      (3*N*NLVL + 11*N).

       INFO   (output) INTEGER
	      = 0:  successful exit.
	      < 0:  if INFO = -i, the i-th argument had an illegal value.
	      > 0:  The algorithm failed to compute an singular value while working on the subma-
	      trix lying in rows and columns INFO/(N+1) through MOD(INFO,N+1).

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 				CLALSD(l)


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