SGTRFS(1) LAPACK routine (version 3.2) SGTRFS(1)NAME
SGTRFS - 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
SYNOPSIS
SUBROUTINE SGTRFS( 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( * )
REAL B( LDB, * ), BERR( * ), D( * ), DF( * ), DL( * ),
DLF( * ), DU( * ), DU2( * ), DUF( * ), FERR( * ),
WORK( * ), X( LDX, * )
PURPOSE
SGTRFS 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) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of A.
D (input) REAL array, dimension (N)
The diagonal elements of A.
DU (input) REAL array, dimension (N-1)
The (n-1) superdiagonal elements of A.
DLF (input) REAL array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the LU fac‐
torization of A as computed by SGTTRF.
DF (input) REAL array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DUF (input) REAL array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.
DU2 (input) REAL 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) 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 SGTTRS. 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) REAL 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 refinement.
LAPACK routine (version 3.2) November 2008 SGTRFS(1)
