cpprfs-f(3)

cpprfs.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

CPPRFS

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.

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.

 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)*(2n-j)/2) = A(i,j) for j<=i<=n.

AFP

 AFP is 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 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 CPPTRS.
 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 171 of file cpprfs.f.

Author

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