DGBRFS - improve the computed solution to a system of lin
ear equations when the coefficient matrix is banded, and
provides error bounds and backward error estimates for the
solution
SYNOPSIS
SUBROUTINE DGBRFS( 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 lin
ear equations when the coefficient matrix is banded, and
provides error bounds and backward error estimates for the
solution.
ARGUMENTS
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)
N (input) INTEGER
The order of the matrix A. N >= 0.
KL (input) INTEGER
The number of subdiagonals within the band of A.
KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A.
KU >= 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) DOUBLE PRECISION array, dimension (LDAB,N)
The original band matrix A, stored in rows 1 to
KL+KU+1. The j-th column of A is stored in the j-
j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >=
KL+KU+1.
AFB (input) DOUBLE PRECISION array, dimension
(LDAFB,N)
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.
LDAFB (input) INTEGER
The leading dimension of the array AFB. LDAFB >=
2*KL*KU+1.
IPIV (input) INTEGER array, dimension (N)
The pivot indices from DGBTRF; for 1<=i<=N, row i
of the matrix was interchanged with row IPIV(i).
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/output) DOUBLE PRECISION array,
dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by
DGBTRS. On exit, the improved 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
change in any element of A or B that makes X(j) an
exact solution).
WORK (workspace) DOUBLE PRECISION 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 ille
gal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refine
ment.
Man(1) output converted with
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