ZGBRFS(1) LAPACK routine (version 3.2) ZGBRFS(1)NAME
ZGBRFS - 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 ZGBRFS( 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( * )
DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( *
), X( LDX, * )
PURPOSE
ZGBRFS 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*16 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*16 array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as com‐
puted by ZGBTRF. 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 ZGBTRF; for 1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).
B (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZGBTRS. 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 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) DOUBLE PRECISION 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*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION 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 ZGBRFS(1)
