SPTRFS - improve the computed solution to a system of lin
ear equations when the coefficient matrix is symmetric
positive definite and tridiagonal, and provides error
bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE SPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
FERR, BERR, WORK, INFO )
INTEGER INFO, LDB, LDX, N, NRHS
REAL B( LDB, * ), BERR( * ), D( * ), DF( *
), E( * ), EF( * ), FERR( * ), WORK( *
), X( LDX, * )
PURPOSE
SPTRFS improves the computed solution to a system of lin
ear equations when the coefficient matrix is symmetric
positive definite and tridiagonal, and provides error
bounds and backward error estimates for the solution.
ARGUMENTS
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.
D (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix
A.
E (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal
matrix A.
DF (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D
from the factorization computed by SPTTRF.
EF (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the unit bidiag
onal factor L from the factorization computed by
SPTTRF.
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).
On entry, the solution matrix X, as computed by
SPTTRS. 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 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).
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).
WORK (workspace) REAL array, dimension (2*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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