dpbrfs.f (3) Linux Manual 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.