CGBRFS - 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 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 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)
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-
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 computed 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 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) 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).
RWORK (workspace) REAL 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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