cporfs-f(3)

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 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 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 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 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 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

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