SGBRFS
November 2006
Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH.
Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH.
Purpose
SGBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is banded, and provides
error bounds and backward error estimates for the solution.
equations when the coefficient matrix is banded, and provides
error bounds and backward error estimates for the solution.
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 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 right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0. |
| AB |
(input) REAL 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.
|
| AFB |
(input) REAL array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
| LDAFB |
(input) INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
|
| IPIV |
(input) INTEGER array, dimension (N)
The pivot indices from SGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i). |
| B |
(input) REAL 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/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SGBTRS.
On exit, the improved 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) REAL array, dimension (3*N)
|
| IWORK |
(workspace) INTEGER array, dimension (N)
|
| INFO |
(output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
Internal Parameters
ITMAX is the maximum number of steps of iterative refinement.