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DGBRFS(1) LAPACK routine (version 3.2) DGBRFS(1)

NAME

DGBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution

SYNOPSIS

TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

CHARACTER TRANS INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS INTEGER IPIV( * ), IWORK( * ) DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

DGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.

ARGUMENTS

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)
The order of the matrix A. N >= 0.
The number of subdiagonals within the band of A. KL >= 0.
The number of superdiagonals within the band of A. KU >= 0.
The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
The original band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
The leading dimension of the array AB. LDAB >= KL+KU+1.
Details of the LU factorization of the band matrix A, as computed by DGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
The pivot indices from DGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
The right hand side matrix B.
The leading dimension of the array B. LDB >= max(1,N).
On entry, the solution matrix X, as computed by DGBTRS. On exit, the improved 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

PARAMETERS

ITMAX is the maximum number of steps of iterative refinement.

November 2008 LAPACK routine (version 3.2)