#### 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.
__TRANS__
TRANS 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)
__DIAG__
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
__N__
N is INTEGER
The order of the matrix A. N >= 0.
__KD__
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. 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 triangular 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).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
__LDAB__
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 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)
The 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
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
Generated automatically by Doxygen for LAPACK from the source code.
| |