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

CPPRFS(l)					)					CPPRFS(l)

NAME
       CPPRFS  -  improve  the computed solution to a system of linear equations when the coeffi-
       cient matrix is Hermitian positive definite and packed,	and  provides  error  bounds  and
       backward error estimates for the solution

SYNOPSIS
       SUBROUTINE CPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   REAL 	  BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX	  AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE
       CPPRFS improves the computed solution to a system of linear equations when the coefficient
       matrix is Hermitian positive definite and packed, and provides error bounds  and  backward
       error estimates for the solution.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       NRHS    (input) INTEGER
	       The  number of right hand sides, i.e., the number of columns of the matrices B and
	       X.  NRHS >= 0.

       AP      (input) COMPLEX array, dimension (N*(N+1)/2)
	       The upper or lower triangle of the Hermitian matrix A, packed columnwise in a lin-
	       ear  array.   The j-th column of A is stored in the array AP as follows: if UPLO =
	       'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2)
	       = A(i,j) for j<=i<=n.

       AFP     (input) COMPLEX array, dimension (N*(N+1)/2)
	       The  triangular	factor	U  or L from the Cholesky factorization A = U**H*U or A =
	       L*L**H, as computed by SPPTRF/CPPTRF, packed columnwise in a linear array  in  the
	       same format as A (see AP).

       B       (input) COMPLEX array, dimension (LDB,NRHS)
	       The right hand side matrix B.

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= max(1,N).

       X       (input/output) COMPLEX array, dimension (LDX,NRHS)
	       On  entry,  the	solution  matrix X, as computed by CPPTRS.  On exit, the improved
	       solution matrix X.

       LDX     (input) INTEGER
	       The leading dimension of the array X.  LDX >= max(1,N).

       FERR    (output) REAL array, dimension (NRHS)
	       The estimated forward error bound for each solution vector X(j) (the  j-th  column
	       of  the	solution matrix X).  If XTRUE is the true solution corresponding to X(j),
	       FERR(j) is an estimated upper bound for the magnitude of the  largest  element  in
	       (X(j) - XTRUE) divided by the magnitude of the largest element in X(j).	The esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate of the true error.

       BERR    (output) REAL array, dimension (NRHS)
	       The  componentwise relative backward error of each solution vector X(j) (i.e., the
	       smallest relative change in any element of A or B that makes X(j) an  exact  solu-
	       tion).

       WORK    (workspace) COMPLEX array, dimension (2*N)

       RWORK   (workspace) REAL array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS
       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0			   15 June 2000 				CPPRFS(l)


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