CHPRFS (3) Linux Manual Page

chprfs.f –

Synopsis

Functions/Subroutines

subroutine chprfs (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CHPRFS

Function/Subroutine Documentation

subroutine chprfs (characterUPLO, integerN, integerNRHS, complex, dimension( * )AP, complex, dimension( * )AFP, integer, dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CHPRFS

Purpose:

 CHPRFS improves the computed solution to a system of linear

 equations when the coefficient matrix is Hermitian indefinite

 and packed, 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.

AP

 AP is COMPLEX array, dimension (N*(N+1)/2)

 The upper or lower triangle of the Hermitian matrix A, packed

 columnwise in a linear 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

 AFP is COMPLEX array, dimension (N*(N+1)/2)

 The factored form of the matrix A. AFP contains the block

 diagonal matrix D and the multipliers used to obtain the

 factor U or L from the factorization A = U*D*U**H or

 A = L*D*L**H as computed by CHPTRF, stored as a packed

 triangular matrix.

IPIV

 IPIV is INTEGER array, dimension (N)

 Details of the interchanges and the block structure of D

 as determined by CHPTRF.

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 CHPTRS.

 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 180 of file chprfs.f.

Author

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