
CPBRFS(l) ) CPBRFS(l)
NAME
CPBRFS  improve the computed solution to a system of linear equations when the coeffi
cient matrix is Hermitian positive definite and banded, and provides error bounds and
backward error estimates for the solution
SYNOPSIS
SUBROUTINE CPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR,
WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, KD, LDAB, LDAFB, LDB, LDX, N, NRHS
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )
PURPOSE
CPBRFS improves the computed solution to a system of linear equations when the coefficient
matrix is Hermitian positive definite and banded, 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.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub
diagonals if UPLO = 'L'. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrices B and
X. NRHS >= 0.
AB (input) COMPLEX array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian band matrix A, stored in the first
KD+1 rows of the array. The jth column of A is stored in the jth column of the
array AB as follows: if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = 'L', AB(1+ij,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
AFB (input) COMPLEX array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization A = U**H*U or A =
L*L**H of the band matrix A as computed by CPBTRF, in the same storage format as A
(see AB).
LDAFB (input) INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.
B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CPBTRS. 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 jth 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 esti
mate is as reliable as the estimate for RCOND, and is almost always a slight over
estimate 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 solu
tion).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
LAPACK version 3.0 15 June 2000 CPBRFS(l) 
