DTBRFS - provide error bounds and backward error estimates
for the solution to a system of linear equations with a
triangular band coefficient matrix
SYNOPSIS
SUBROUTINE DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
LDAB, B, LDB, X, LDX, FERR, BERR, WORK,
IWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
INTEGER IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ),
BERR( * ), FERR( * ), WORK( * ), X(
LDX, * )
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.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS (input) 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 (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals or subdiagonals of
the triangular band matrix A. KD >= 0.
The number of right hand sides, i.e., the number
of columns of the matrices B and X. NRHS >= 0.
AB (input) 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 (input) INTEGER
The leading dimension of the array AB. LDAB >=
KD+1.
B (input) DOUBLE PRECISION array, dimension
(LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X (input) DOUBLE PRECISION array, dimension
(LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bound for each solu
tion vector X(j) (the j-th column of the solution
matrix X). If XTRUE is the true solution corre
sponding 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 reli
able as the estimate for RCOND, and is almost
always a slight overestimate of the true error.
BERR (output) 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 (workspace) DOUBLE PRECISION array, dimension
(3*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
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