STBRFS(1) LAPACK routine (version 3.2) STBRFS(1)NAME
STBRFS - provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band coeffi‐
cient matrix
SYNOPSIS
SUBROUTINE STBRFS( 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( * )
REAL AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR( * ),
WORK( * ), X( LDX, * )
PURPOSE
STBRFS provides error bounds and backward error estimates for the solu‐
tion to a system of linear equations with a triangular band coefficient
matrix. The solution matrix X must be computed by STBTRS or some other
means before entering this routine. STBRFS 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.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
AB (input) REAL 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) REAL 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) REAL array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL 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 (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution vec‐
tor X(j) (i.e., the smallest relative change in any element of
A or B that makes X(j) an exact solution).
WORK (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK routine (version 3.2) November 2008 STBRFS(1)