subroutine dgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DGTRFS
DGTRFS
Purpose:
DGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, 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 = Transpose)
N
N is INTEGER The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DL
DL is DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of A.
D
D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.
DU
DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) superdiagonal elements of A.
DLF
DLF is DOUBLE PRECISION array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF.
DF
DF is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUF
DUF is DOUBLE PRECISION array, dimension (N-1) The (n-1) elements of the first superdiagonal of U.
DU2
DU2 is DOUBLE PRECISION array, dimension (N-2) The (n-2) elements of the second superdiagonal of U.
IPIV
IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
B
B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by DGTTRS. 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 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
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
WORK is DOUBLE PRECISION array, dimension (3*N)
IWORK
IWORK is INTEGER 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 211 of file dgtrfs.f.
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