dpbrfs.f man page

dpbrfs.f —

Synopsis

Functions/Subroutines

subroutine dpbrfs (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DPBRFS

Function/Subroutine Documentation

subroutine dpbrfs (characterUPLO, integerN, integerKD, integerNRHS, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldafb, * )AFB, integerLDAFB, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

DPBRFS

Purpose:

DPBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric 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 DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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 DOUBLE PRECISION array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T of the band matrix A as computed by
DPBTRF, 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DPBTRS.
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 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

BERR is 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

WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK

IWORK is INTEGER 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:

November 2011

Definition at line 189 of file dpbrfs.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dpbrfs(3) is an alias of dpbrfs.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK