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NAME DPTRFS - improve 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 SYNOPSIS SUBROUTINE DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO ) INTEGER INFO, LDB, LDX, N, NRHS DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF( * ), FERR( * ), WORK( * ), X( LDX, * ) PURPOSE DPTRFS 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) DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A. E (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A. DF (input) DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization computed by DPTTRF. EF (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the unit bidiago- nal factor L from the factorization computed by DPTTRF. B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). (LDX,NRHS) X (input/output) DOUBLE PRECISION array, dimension On entry, the solution matrix X, as computed by DPTTRS. On exit, the improved solution matrix X. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). FERR (output) DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution, FERR(j) bounds the magnitude of the largest entry in (X(j) - XTRUE) divided by the magnitude of the largest entry in X(j). The quality of the error bound depends on the quality of the estimate of norm(inv(A)) computed in the code; if the estimate of norm(inv(A)) is accu- rate, the error bound is guaranteed. BERR (output) DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any entry of A or B that makes X(j) an exact solution). WORK (workspace) DOUBLE PRECISION 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 refine- ment.