CPPRFS - improve the computed solution to a system of lin
ear equations when the coefficient matrix is Hermitian
positive definite and packed, and provides error bounds
and backward error estimates for the solution
SYNOPSIS
SUBROUTINE CPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX AFP( * ), AP( * ), B( LDB, * ), WORK( *
), X( LDX, * )
PURPOSE
CPPRFS improves the computed solution to a system of lin
ear equations when the coefficient matrix is Hermitian
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) COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian
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) COMPLEX array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, as com
puted by SPPTRF/CPPTRF, packed columnwise in a
linear array in the same format as A (see AP).
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
The leading dimension of the array B. LDB >=
max(1,N).
X (input/output) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by
CPPTRS. 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) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL 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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