SPORFS - improve the computed solution to a system of lin
ear equations when the coefficient matrix is symmetric
positive definite,
SYNOPSIS
SUBROUTINE SPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B,
LDB, X, LDX, FERR, BERR, WORK, IWORK,
INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IWORK( * )
REAL A( LDA, * ), AF( LDAF, * ), B( LDB, *
), BERR( * ), FERR( * ), WORK( * ), X(
LDX, * )
PURPOSE
SPORFS improves the computed solution to a system of lin
ear equations when the coefficient matrix is symmetric
positive definite, and provides error bounds and backward
error estimates for the solution.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 matrices B and X. NRHS >= 0.
A (input) REAL array, dimension (LDA,N)
The symmetric matrix A. If UPLO = 'U', the lead
ing N-by-N upper triangular part of A contains the
upper triangular part of the matrix A, and the
strictly lower triangular part of A is not refer
enced. If UPLO = 'L', the leading N-by-N lower
triangular part of A contains the lower triangular
part of the matrix A, and the strictly upper tri
angular part of A is not referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
The triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, as com
puted by SPOTRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
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
SPOTRS. 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).
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 ille
gal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refine
ment.
Man(1) output converted with
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