TESTING/LIN/sppt05.f(3) | Library Functions Manual | TESTING/LIN/sppt05.f(3) |
NAME
TESTING/LIN/sppt05.f
SYNOPSIS
Functions/Subroutines
subroutine sppt05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact,
ldxact, ferr, berr, reslts)
SPPT05
Function/Subroutine Documentation
subroutine sppt05 (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) reslts)
SPPT05
Purpose:
SPPT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric matrix in packed storage format. RESLTS(1) = test of the error bound = norm(X - XACT) / ( norm(X) * FERR ) A large value is returned if this ratio is not less than one. RESLTS(2) = residual from the iterative refinement routine = the maximum of BERR / ( (n+1)*EPS + (*) ), where (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
Parameters
UPLO
UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular
N
N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
AP
AP is REAL array, dimension (N*(N+1)/2) The upper or lower triangle of the symmetric 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.
B
B is REAL array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.
LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
X
X is REAL array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.
LDX
LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
XACT
XACT is REAL array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.
LDXACT
LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR
FERR is REAL array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
BERR
BERR is REAL array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
RESLTS
RESLTS is REAL array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 154 of file sppt05.f.
Author
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