CTBRFS
November 2006
Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH.
Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH.
Purpose
CTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.
The solution matrix X must be computed by CTBTRS or some other
means before entering this routine. CTBRFS does not do iterative
refinement because doing so cannot improve the backward error.
solution to a system of linear equations with a triangular band
coefficient matrix.
The solution matrix X must be computed by CTBTRS or some other
means before entering this routine. CTBRFS does not do iterative
refinement because doing so cannot improve the backward error.
Arguments
| UPLO |
(input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular. |
| 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) |
| DIAG |
(input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular. |
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| KD |
(input) INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0. |
| NRHS |
(input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0. |
| AB |
(input) COMPLEX 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 |
(input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
|
| B |
(input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
|
| LDB |
(input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
|
| X |
(input) COMPLEX array, dimension (LDX,NRHS)
The solution matrix X.
|
| LDX |
(input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
|
| FERR |
(output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error. |
| BERR |
(output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution). |
| WORK |
(workspace) COMPLEX array, dimension (2*N)
|
| RWORK |
(workspace) REAL array, dimension (N)
|
| INFO |
(output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |