SYNOPSIS
- SUBROUTINE SPTRFS(
- N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO )
- INTEGER INFO, LDB, LDX, N, NRHS
- REAL B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF( * ), FERR( * ), WORK( * ), X( LDX, * )
PURPOSE
SPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.ARGUMENTS
- 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 matrix B. NRHS >= 0.
- D (input) REAL array, dimension (N)
- The n diagonal elements of the tridiagonal matrix A.
- E (input) REAL array, dimension (N-1)
- The (n-1) subdiagonal elements of the tridiagonal matrix A.
- DF (input) REAL array, dimension (N)
- The n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF.
- EF (input) REAL array, dimension (N-1)
- The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by SPTTRF.
- 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 SPTTRS. 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 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).
- 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 (2*N)
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.