SGTRFS - improve the computed solution to a system of lin
ear 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 lin
ear 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
TRF.
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 indi
cates 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 solu
tion vector X(j) (the j-th column of the solution
matrix X). If XTRUE is the true solution corre
sponding 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 reli
able 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 vector X(j) (i.e., the smallest relative
change in any element of A or B that makes X(j) an
exact solution).
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refine
ment.
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