TESTING/LIN/zget07.f(3) | Library Functions Manual | TESTING/LIN/zget07.f(3) |
NAME
TESTING/LIN/zget07.f
SYNOPSIS
Functions/Subroutines
subroutine zget07 (trans, n, nrhs, a, lda, b, ldb, x, ldx,
xact, ldxact, ferr, chkferr, berr, reslts)
ZGET07
Function/Subroutine Documentation
subroutine zget07 (character trans, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, logical chkferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)
ZGET07
Purpose:
ZGET07 tests the error bounds from iterative refinement for the computed solution to a system of equations op(A)*X = B, where A is a general n by n matrix and op(A) = A or A**T, depending on TRANS. 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(op(A))*abs(X) +abs(b))_i )
Parameters
TRANS
TRANS is CHARACTER*1 Specifies the form of the system of equations. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose)
N
N is INTEGER The number of rows of the matrices X and XACT. N >= 0.
NRHS
NRHS is INTEGER The number of columns of the matrices X and XACT. NRHS >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N) The original n by n matrix A.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
B
B is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 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.
CHKFERR
CHKFERR is LOGICAL Set to .TRUE. to check FERR, .FALSE. not to check FERR. When the test system is ill-conditioned, the 'true' solution in XACT may be incorrect.
BERR
BERR is 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
RESLTS is 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 + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 164 of file zget07.f.
Author
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