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 !> 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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