Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  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

SYNOPSIS

SUBROUTINE ZPBRFS( 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

DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( * )

COMPLEX*16     AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE

ZPBRFS 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 subdiagonals 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) DOUBLE PRECISION 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 j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,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*16 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
ZPBTRF, 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*16 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*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPBTRS.
On exit, the improved solution matrix X.

LDX     (input) INTEGER
The leading dimension of the array X.  LDX >= max(1,N).

FERR    (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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*16 array, dimension (2*N)

RWORK   (workspace) DOUBLE PRECISION 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 routine (version 3.2)               April 2011                            ZPBRFS(3lapack)