DPORFS man page on IRIX

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DPORFS(3F)							    DPORFS(3F)

NAME
     DPORFS - improve the computed solution to a system of linear equations
     when the coefficient matrix is symmetric positive definite,

SYNOPSIS
     SUBROUTINE DPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR,
			BERR, WORK, IWORK, INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, LDA, LDAF, LDB, LDX, N, NRHS

	 INTEGER	IWORK( * )

	 DOUBLE		PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
			BERR( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE
     DPORFS improves the computed solution to a system of linear equations
     when the coefficient matrix is symmetric positive definite, 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.

     A	     (input) DOUBLE PRECISION array, dimension (LDA,N)
	     The symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper
	     triangular part of A contains the upper triangular part of the
	     matrix A, and the strictly lower triangular part of A is not
	     referenced.  If UPLO = 'L', the leading N-by-N lower triangular
	     part of A contains the lower triangular part of the matrix A, and
	     the strictly upper triangular part of A is not referenced.

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

     AF	     (input) DOUBLE PRECISION array, dimension (LDAF,N)
	     The triangular factor U or L from the Cholesky factorization A =
	     U**T*U or A = L*L**T, as computed by DPOTRF.

									Page 1

DPORFS(3F)							    DPORFS(3F)

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

     B	     (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
	     On entry, the solution matrix X, as computed by DPOTRS.  On exit,
	     the improved solution matrix X.

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

     FERR    (output) DOUBLE PRECISION 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
	     estimate is as reliable as the estimate for RCOND, and is almost
	     always a slight overestimate of the true error.

     BERR    (output) DOUBLE PRECISION 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 solution).

     WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

     IWORK   (workspace) INTEGER 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.

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