CGTRFS(l) ) CGTRFS(l)NAME
CGTRFS - 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 CGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV,
B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
CHARACTER TRANS
INTEGER INFO, LDB, LDX, N, NRHS
INTEGER IPIV( * )
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX B( LDB, * ), D( * ), DF( * ), DL( * ), DLF( * ), DU(
* ), DU2( * ), DUF( * ), WORK( * ), X( LDX, * )
PURPOSE
CGTRFS 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)
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) COMPLEX array, dimension (N-1)
The (n-1) subdiagonal elements of A.
D (input) COMPLEX array, dimension (N)
The diagonal elements of A.
DU (input) COMPLEX array, dimension (N-1)
The (n-1) superdiagonal elements of A.
DLF (input) COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the LU fac‐
torization of A as computed by CGTTRF.
DF (input) COMPLEX array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DUF (input) COMPLEX array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.
DU2 (input) COMPLEX 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 indicates a row interchange was not
required.
B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CGTTRS. 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 vec‐
tor X(j) (i.e., the smallest relative change in any element of
A or B that makes X(j) an exact solution).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL 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 refinement.
LAPACK version 3.0 15 June 2000 CGTRFS(l)
