subroutine cgbrfs (TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CGBRFS
CGBRFS
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.
Parameters:
TRANS is 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
N is INTEGER The order of the matrix A. N >= 0.
KL
KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
NRHS
NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
AB
AB is 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
LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB
AFB is 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
LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
IPIV
IPIV is 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
B is COMPLEX array, dimension (LDB,NRHS) The right hand side matrix B.
LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
X
X is COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CGBTRS. On exit, the improved solution matrix X.
LDX
LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
FERR
FERR is 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
BERR is 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).
WORK
WORK is COMPLEX array, dimension (2*N)
RWORK
RWORK is REAL array, dimension (N)
INFO
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Internal Parameters:
ITMAX is the maximum number of steps of iterative refinement.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 208 of file cgbrfs.f.
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