dtbrfs (3)  Linux Man Pages
NAME
dtbrfs.f 
SYNOPSIS
Functions/Subroutines
subroutine dtbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DTBRFS
Function/Subroutine Documentation
subroutine dtbrfs (characterUPLO, characterTRANS, characterDIAG, integerN, integerKD, integerNRHS, double precision, dimension( ldab, * )AB, integerLDAB, 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)
DTBRFS
Purpose:

DTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by DTBTRS or some other means before entering this routine. DTBRFS does not do iterative refinement because doing so cannot improve the backward error.
Parameters:

UPLO
UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.
TRANSTRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose)
DIAGDIAG is CHARACTER*1 = 'N': A is nonunit triangular; = 'U': A is unit triangular.
NN is INTEGER The order of the matrix A. N >= 0.
KDKD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
ABAB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular 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). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
LDABLDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
BB is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
XX is DOUBLE PRECISION array, dimension (LDX,NRHS) The solution matrix X.
LDXLDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
FERRFERR is DOUBLE PRECISION 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 estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
BERRBERR 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).
WORKWORK is DOUBLE PRECISION array, dimension (3*N)
IWORKIWORK is INTEGER array, dimension (N)
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Definition at line 188 of file dtbrfs.f.
Author
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