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cpbrfs.f(3) LAPACK cpbrfs.f(3)

NAME

cpbrfs.f

SYNOPSIS

Functions/Subroutines


subroutine cpbrfs (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CPBRFS

Function/Subroutine Documentation

subroutine cpbrfs (character UPLO, integer N, integer KD, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldafb, * ) AFB, integer LDAFB, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, real, dimension( * ) FERR, real, dimension( * ) BERR, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

CPBRFS

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.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N


N is INTEGER
The order of the matrix A. N >= 0.

KD


KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.

NRHS


NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.

AB


AB is 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 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


LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

AFB


AFB is 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


LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

B


B is COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB


LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X


X is COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CPBTRS.
On exit, the improved solution matrix X.

LDX


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

FERR


FERR is 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


BERR is 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


WORK is COMPLEX array, dimension (2*N)

RWORK


RWORK is REAL array, dimension (N)

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters:


ITMAX is the maximum number of steps of iterative refinement.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 191 of file cpbrfs.f.

Author

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Tue Nov 14 2017 Version 3.8.0