08-03-2007
A plain unix commands solution would be lengthy.
Kahuna's solution is very short and easy to understand
even without knowledge of 'perl'.
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LEARN ABOUT REDHAT
spprfs
SPPRFS(l) ) SPPRFS(l)
NAME
SPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and
packed, and provides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE SPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
INTEGER IWORK( * )
REAL AFP( * ), AP( * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
PURPOSE
SPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and
packed, 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.
AP (input) REAL array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the
array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
j<=i<=n.
AFP (input) REAL array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF, packed column-
wise in a linear array in the same format as A (see AP).
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 SPPTRS. 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 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 illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
LAPACK version 3.0 15 June 2000 SPPRFS(l)