ZPOT05
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZPOT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
Hermitian n by n matrix.
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 )
computed solution to a system of equations A*X = B, where A is a
Hermitian n by n matrix.
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 )
Arguments
| UPLO |
(input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular |
| N |
(input) INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0. |
| NRHS |
(input) INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0. |
| A |
(input) COMPLEX*16 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).
|
| B |
(input) COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations. |
| LDB |
(input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
|
| X |
(input) COMPLEX*16 array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X. |
| LDX |
(input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
|
| XACT |
(input) COMPLEX*16 array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT. |
| LDXACT |
(input) INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N).
|
| FERR |
(input) DOUBLE PRECISION 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 |
(input) DOUBLE PRECISION 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 |
(output) DOUBLE PRECISION 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 + (*) ) |