CGBRFS(1) LAPACK routine (version 3.2) CGBRFS(1)NAME
CGBRFS - 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
SUBROUTINE CGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV,
B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
CHARACTER TRANS
INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
INTEGER IPIV( * )
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( *
), X( LDX, * )
PURPOSE
CGBRFS 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
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)
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) COMPLEX 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-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).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB (input) COMPLEX array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as com‐
puted by CGBTRF. 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 CGBTRF; for 1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).
B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CGBTRS. On
exit, the improved 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) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 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.
LAPACK routine (version 3.2) November 2008 CGBRFS(1)