dgtrfs (l) - Linux Manuals
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
NAME
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 solutionSYNOPSIS
- SUBROUTINE DGTRFS(
- TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
- CHARACTER TRANS
- INTEGER INFO, LDB, LDX, N, NRHS
- INTEGER IPIV( * ), IWORK( * )
- DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ), DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ), FERR( * ), WORK( * ), X( LDX, * )
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.ARGUMENTS
- TRANS (input) CHARACTER*1
-
Specifies the form of the system of equations:
= aqNaq: A * X = B (No transpose)
= aqTaq: A**T * X = B (Transpose)
= aqCaq: A**H * X = B (Conjugate transpose = Transpose) - N (input) INTEGER
- The order of the matrix A. N >= 0.
- NRHS (input) INTEGER
- The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
- DL (input) DOUBLE PRECISION array, dimension (N-1)
- The (n-1) subdiagonal elements of A.
- D (input) DOUBLE PRECISION array, dimension (N)
- The diagonal elements of A.
- DU (input) DOUBLE PRECISION array, dimension (N-1)
- The (n-1) superdiagonal elements of A.
- DLF (input) 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 (input) DOUBLE PRECISION array, dimension (N)
- The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
- DUF (input) DOUBLE PRECISION array, dimension (N-1)
- The (n-1) elements of the first superdiagonal of U.
- DU2 (input) DOUBLE PRECISION array, dimension (N-2)
- The (n-2) elements of the second superdiagonal of U.
- IPIV (input) 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 (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
- On entry, the solution matrix X, as computed by DGTTRS. 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 vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
- WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
- IWORK (workspace) INTEGER 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.