cporfs(l) [redhat man page]

CPORFS(l)								 )								 CPORFS(l)

NAME

       CPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,

SYNOPSIS

       SUBROUTINE CPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

	   CHARACTER	  UPLO

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

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

	   COMPLEX	  A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

       CPORFS  improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and pro-
       vides 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) COMPLEX array, dimension (LDA,N)
	       The Hermitian 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) COMPLEX array, dimension (LDAF,N)
	       The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.

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

       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 CPOTRS.	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 estimate is as reliable as the estimate  for  RCOND,  and	is  almost
	       always a slight overestimate 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 solution).

       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 							 CPORFS(l)

cporfs.f(3)							      LAPACK							       cporfs.f(3)

NAME

       cporfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cporfs (UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
	   CPORFS

Function/Subroutine Documentation
   subroutine cporfs (characterUPLO, integerN, integerNRHS, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldaf, * )AF,
       integerLDAF, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real,
       dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)
       CPORFS

       Purpose:

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

       Parameters:
	   UPLO

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

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   NRHS

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

	   A

		     A is COMPLEX array, dimension (LDA,N)
		     The Hermitian 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

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

	   AF

		     AF is COMPLEX array, dimension (LDAF,N)
		     The triangular factor U or L from the Cholesky factorization
		     A = U**H*U or A = L*L**H, as computed by CPOTRF.

	   LDAF

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

	   B

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

	   LDB

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

	   X

		     X is COMPLEX array, dimension (LDX,NRHS)
		     On entry, the solution matrix X, as computed by CPOTRS.
		     On exit, the improved solution matrix X.

	   LDX

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

	   FERR

		     FERR is 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 estimate is as reliable as
		     the estimate for RCOND, and is almost always a slight
		     overestimate of the true error.

	   BERR

		     BERR is 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 solution).

	   WORK

		     WORK is COMPLEX array, dimension (2*N)

	   RWORK

		     RWORK is REAL array, dimension (N)

	   INFO

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

       Internal Parameters:

	     ITMAX is the maximum number of steps of iterative refinement.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 183 of file cporfs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       cporfs.f(3)