DGBRFS 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.
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 = Transpose)
N is INTEGER The order of the matrix A. N >= 0.
KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
AB is 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-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 is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB is 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 is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
IPIV is 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 is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B.
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
X is DOUBLE PRECISION array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by DGBTRS. On exit, the improved solution matrix X.
LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
FERR is 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 is DOUBLE PRECISION 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 is DOUBLE PRECISION array, dimension (3*N)
IWORK is INTEGER array, dimension (N)
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
Univ. of California Berkeley
Univ. of Colorado Denver
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