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NAME DGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution SYNOPSIS SUBROUTINE DGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO ) CHARACTER TRANS INTEGER INFO, LDB, LDX, N, NRHS INTEGER IPIV( * ), IWORK( * ) DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ), DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ), FERR( * ), WORK( * ), X( LDX, * ) PURPOSE DGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, 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 = Tran- spose) 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. DL (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of A. D (input) DOUBLE PRECISION array, dimension (N) The diagonal elements of A. DU (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) superdiagonal elements of A. DLF (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF. DF (input) DOUBLE PRECISION array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. DUF (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. DU2 (input) DOUBLE PRECISION array, dimension (N-2) The (n-2) elements of the second superdiagonal of U. IPIV (input) INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indi- cates a row interchange was not required. 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 DGTTRS. 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 (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 PARAMETERS ITMAX is the maximum number of steps of iterative refine- ment.