ZTRT05
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZTRT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
triangular 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
triangular 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 matrix A is upper or lower triangular.
= 'U': Upper triangular = 'L': Lower triangular |
| TRANS |
(input) CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose) = 'T': A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) |
| DIAG |
(input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular = 'U': Unit 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 triangular matrix A. If UPLO = 'U', the leading n by n
upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. |
| 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 + (*) ) |