- SUBROUTINE SGERFS(
- TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
- CHARACTER TRANS
- INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
- INTEGER IPIV( * ), IWORK( * )
- REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
PURPOSESGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution.
- 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
PARAMETERSITMAX is the maximum number of steps of iterative refinement.