STBRFS(3f)

NAME
STBRFS - error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient 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 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

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 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) 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