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

SLALSD(l)					)					SLALSD(l)

NAME
       SLALSD  -  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 SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, IWORK, INFO )

	   CHARACTER	  UPLO

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

	   REAL 	  RCOND

	   INTEGER	  IWORK( * )

	   REAL 	  B( LDB, * ), D( * ), E( * ), WORK( * )

PURPOSE
       SLALSD  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) REAL 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) REAL array, dimension at least
	      (9*N  +  2*N*SMLSIZ  +  8*N*NLVL	+  N*NRHS  +  (SMLSIZ+1)**2), where NLVL = max(0,
	      INT(log_2 (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 				SLALSD(l)


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