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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 coefficient matrix

SYNOPSIS

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 solution 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

= 'U': A is upper triangular;
= 'L': A is lower triangular.

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)

= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
The order of the matrix A. N >= 0.
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.
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.
The leading dimension of the array AB. LDAB >= KD+1.
The right hand side matrix B.
The leading dimension of the array B. LDB >= max(1,N).
The solution matrix X.
The leading dimension of the array X. LDX >= max(1,N).
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.
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).
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
November 2008 LAPACK routine (version 3.2)