SGERFS
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
SGERFS improves the computed solution to a system of linear
equations and provides error bounds and backward error estimates for
the solution.
equations 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.
|
| NRHS |
(input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0. |
| A |
(input) REAL array, dimension (LDA,N)
The original N-by-N matrix A.
|
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
|
| AF |
(input) REAL array, dimension (LDAF,N)
The factors L and U from the factorization A = P*L*U
as computed by SGETRF. |
| LDAF |
(input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
|
| IPIV |
(input) INTEGER array, dimension (N)
The pivot indices from SGETRF; 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 SGETRS.
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.