CscIlu CscIlu0 CscIluSolve CscSsorSolve CsrIlu CsrIlu0 CsrIluSolve CsrSsorSolve CsxDs CsxDsSolve CsxSsor

CscIlu0() Sub CscIlu0 ( N As  Long, Val() As  Double, Colptr() As  Long, Rowind() As  Long, Val2() As  Double, D() As  Double, Optional Info As  Long, Optional Base As  Long = -1  ) Initialize incomplete LU decomposition without fill-in (ILU0) preconditioner (CSC) Purpose This routine computes the incomplete LU decomposition, without fill-in, of the coefficient matrix A of the sparse linear equations. A = L * U + R where R is the difference from the complete LU decomposition. Assuming that R is small, the following preconditioner matrix is obtained by solving the equations using this decomposition. M = L * U This routine outputs the lower triangular matrix L and the upper triangular matrix U in Val2(). And the diagonal elements of U are copied to D(). Val2() and D() will be used by CscIluSolve(). Parameters [in] N Dimension of the matrix A. (N >= 0) (if N = 0, returns without computation) [in] Val() Array Val(LVal - 1) (LVal >= Nnz) (Nnz is number of non-zero elements) Values of non-zero elements of matrix A. [in] Colptr() Array Colptr(LColptr - 1) (LColptr >= N + 1) Column pointers of matrix A. [in] Rowind() Array Rowind(LRowind - 1) (LRowind >= Nnz) Row indices of matrix A. [out] Val2() Array Val2(LVal2 - 1) (LVal2 >= Nnz) Values of non-zero elements of the lower triangular matrix L and the upper triangular matrix U. (Values to be stored in the same location of lower and upper triangular elements of A) [out] D() Array D(LD) (LD >= N) The diagonal elements of upper triangular matrix U. [out] Info (Optional) = 0: Successful exit. = i < 0: The (-i)-th argument is invalid. = j > 0: Matrix is singular (j-th diagonal element is zero). [in] Base (Optional) Indexing of Colptr() and Rowind(). = 0: Zero-based (C style) indexing: Starting index is 0. = 1: One-based (Fortran style) indexing: Starting index is 1. (default: Assumes 1 if Colptr(0) = 1, 0 otherwise) Example Program Solve the system of linear equations Ax = B by FGMRES method with ILU(0) preconditioner, where ( 0.2 -0.11 -0.93 ) ( -0.3727 ) A = ( -0.32 0.81 0.37 ), B = ( 0.4319 ) ( -0.8 -0.92 -0.29 ) ( -1.4247 ) Sub Ex_Fgmres_Ilu0_Csc() Const N = 3, Nnz = N * N, Tol = 0.0000000001 '1.0e-10 Dim A(Nnz - 1) As Double, Ia(N) As Long, Ja(Nnz - 1) As Long Dim B(N - 1) As Double, X(N - 1) As Double Dim XX(N - 1) As Double, YY(N - 1) As Double Dim Iter As Long, Res As Double, IRev As Long, Info As Long A(0) = 0.2: A(1) = -0.32: A(2) = -0.8: A(3) = -0.11: A(4) = 0.81: A(5) = -0.92: A(6) = -0.93: A(7) = 0.37: A(8) = -0.29 Ia(0) = 0: Ia(1) = 3: Ia(2) = 6: Ia(3) = 9 Ja(0) = 0: Ja(1) = 1: Ja(2) = 2: Ja(3) = 0: Ja(4) = 1: Ja(5) = 2: Ja(6) = 0: Ja(7) = 1: Ja(8) = 2 B(0) = -0.3727: B(1) = 0.4319: B(2) = -1.4247 Dim M(Nnz - 1) As Double, D(N - 1) As Double Call CscIlu0(N, A(), Ia(), Ja(), M(), D(), Info) If Info <> 0 Then Debug.Print "Ilu0 Info =" + Str(Info) IRev = 0 Do Call Fgmres_r(N, B(), X(), Info, XX(), YY(), IRev, Iter, Res) If IRev = 1 Then '- Matvec Call CscDusmv("N", N, N, 1, A(), Ia(), Ja(), XX(), 0, YY()) ElseIf IRev = 3 Then '- Psolve Call CscIluSolve("N", N, M(), Ia(), Ja(), D(), YY(), XX(), Info) If Info <> 0 Then Debug.Print "IluSolve Info =" + Str(Info) ElseIf IRev = 10 Then '- Check convergence If Res < Tol Then IRev = 11 End If Loop While IRev <> 0 Debug.Print "X =", X(0), X(1), X(2) Debug.Print "Iter = " + CStr(Iter) + ", Res = " + CStr(Res) + ", Info = " + CStr(Info) End Sub Example Results X = 0.86 0.64 0.51 Iter = 1, Res = 3.40151402401104E-16, Info = 0