TESTING/LIN/ztbt05.f(3) | Library Functions Manual | TESTING/LIN/ztbt05.f(3) |
NAME
TESTING/LIN/ztbt05.f
SYNOPSIS
Functions/Subroutines
subroutine ztbt05 (uplo, trans, diag, n, kd, nrhs, ab,
ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
ZTBT05
Function/Subroutine Documentation
subroutine ztbt05 (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, 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, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)
ZTBT05
Purpose:
ZTBT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular band 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 / ( NZ*EPS + (*) ), where (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) and NZ = max. number of nonzeros in any row of A, plus 1
Parameters
UPLO
UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
TRANS
TRANS is 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
DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit 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.
KD
KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
NRHS
NRHS is INTEGER The number of columns of the matrices X, B, and XACT. NRHS >= 0.
AB
AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
LDAB
LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
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.
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 / ( NZ*EPS + (*) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 187 of file ztbt05.f.
Author
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