
DGTRFS(l) ) DGTRFS(l)
NAME
DGTRFS  improve the computed solution to a system of linear equations when the coeffi
cient 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 = 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 matrix B. NRHS
>= 0.
DL (input) DOUBLE PRECISION array, dimension (N1)
The (n1) subdiagonal elements of A.
D (input) DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.
DU (input) DOUBLE PRECISION array, dimension (N1)
The (n1) superdiagonal elements of A.
DLF (input) DOUBLE PRECISION array, dimension (N1)
The (n1) 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 (N1)
The (n1) elements of the first superdiagonal of U.
DU2 (input) DOUBLE PRECISION array, dimension (N2)
The (n2) 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 indicates 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).
X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
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 bound for each solution vector X(j) (the jth 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 esti
mate is as reliable as the estimate for RCOND, and is almost always a slight over
estimate of the true error.
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 element of A or B that makes X(j) an exact solu
tion).
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 ith argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
LAPACK version 3.0 15 June 2000 DGTRFS(l) 
