CGBT05
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
CGBT05 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 band matrix of order n with kl subdiagonals and ku
superdiagonals 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 / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
computed solution to a system of equations op(A)*X = B, where A is a
general band matrix of order n with kl subdiagonals and ku
superdiagonals 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 / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1
Arguments
| TRANS |
(input) 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 |
(input) INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0. |
| KL |
(input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
|
| KU |
(input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
|
| NRHS |
(input) INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0. |
| AB |
(input) COMPLEX array, dimension (LDAB,N)
The original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). |
| LDAB |
(input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
|
| B |
(input) COMPLEX 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 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 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) REAL 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) REAL 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) REAL 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 + (*) ) |