ZCscIlu ZCscIlu0 ZCscIluSolve ZCscSsorSolve ZCsrIlu ZCsrIlu0 ZCsrIluSolve ZCsrSsorSolve ZCsxDs ZCsxDsSolve ZCsxSsor ZSscSsorSolve ZSsrSsorSolve

ZCscSsorSolve() Sub ZCscSsorSolve ( Trans As  String, N As  Long, Omega As  Double, Val() As  Complex, Colptr() As  Long, Rowind() As  Long, D() As  Complex, B() As  Complex, X() As  Complex, Optional Info As  Long, Optional Base As  Long = -1  ) Symmetric successive over-relaxation (SSOR) preconditioner (Complex matrices) (CSC) Purpose This routine is the symmetric successive over-relaxation (SSOR) preconditioner for the coefficient matrix A of the sparse linear equations. It solves the equation M*x = b, M^T*x = b or M^H*x = b, where M is the preconditioner matrix. Parameters [in] Trans = "N": solve M*x = b. = "T": solve M^T*x = b. = "C": solve M^H*x = b. [in] N Dimension of preconditioner matrix. (N >= 0) (if N = 0, returns without computation) [in] Omega The relaxation parameter ω. (0 < ω < 2) [in] Val() Array Val(LVal - 1) (LVal >= Nnz) Values of non-zero elements of matrix A. (Nnz is number of non-zero elements) [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 (where Nnz is the number of nonzero elements). [in] D() Array D(LD) (LD >= N) Diagonal elements of preconditioner matrix M obtained by CSC_SSOR(). [in] B() Array B(LB - 1) (LB >= N) Right hand side vector b. [out] X() Array X(LX - 1) (LX >= N) Solution vector x. [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 SSOR preconditioner, where ( 0.78+0.16i -0.9-1.46i 0.48-1.08i ) A = ( 0.73+0.63i 1.58-1.24 -0.41-0.91i ) ( 0.23-1.37i 0.79+0.64i -0.73-1.5i ) ( 0.2126-0.2904i ) B = ( -0.3028+0.3346i ) ( -1.2905-1.0346i ) Sub Ex_ZFgmres_Ssor_Csc() Const N = 3, Nnz = N * N, Omega = 1.5, Tol = 0.0000000001 '1.0e-10 Dim A(Nnz - 1) As Complex, Ia(N) As Long, Ja(Nnz - 1) As Long Dim B(N - 1) As Complex, X(N - 1) As Complex Dim XX(N - 1) As Complex, YY(N - 1) As Complex Dim Iter As Long, Res As Double, IRev As Long, Info As Long, I As Long A(0) = Cmplx(0.78, 0.16): A(1) = Cmplx(0.73, 0.63): A(2) = Cmplx(0.23, -1.37): A(3) = Cmplx(-0.9, -1.46): A(4) = Cmplx(1.58, -1.24): A(5) = Cmplx(0.79, 0.64): A(6) = Cmplx(0.48, -1.08): A(7) = Cmplx(-0.41, -0.91): A(8) = Cmplx(-0.73, -1.5) 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) = Cmplx(0.2126, -0.2904): B(1) = Cmplx(-0.3028, 0.3346): B(2) = Cmplx(-1.2905, -1.0346) Dim D(N - 1) As Complex Call ZCsxSsor(N, Omega, A(), Ia(), Ja(), D(), Info) If Info <> 0 Then Debug.Print "Ssor Info =" + Str(Info) IRev = 0 Do Call ZFgmres_r(N, B(), X(), Info, XX(), YY(), IRev, Iter, Res) If IRev = 1 Then '- Matvec Call CscZusmv("N", N, N, Cmplx(1), A(), Ia(), Ja(), XX(), Cmplx(0), YY()) ElseIf IRev = 3 Then '- Psolve Call ZCscSsorSolve("N", N, Omega, A(), Ia(), Ja(), D(), YY(), XX(), Info) If Info <> 0 Then Debug.Print "SsorSolve Info =" + Str(Info) ElseIf IRev = 10 Then '- Check convergence If Res < Tol Then IRev = 11 End If Loop While IRev <> 0 Debug.Print "X =" Debug.Print "(" + CStr(Creal(X(0))) + "," + CStr(Cimag(X(0))) + ")" Debug.Print "(" + CStr(Creal(X(1))) + "," + CStr(Cimag(X(1))) + ")" Debug.Print "(" + CStr(Creal(X(2))) + "," + CStr(Cimag(X(2))) + ")" Debug.Print "Iter =" + Str(Iter) + ", Res =" + Str(Res) + ", Info =" + Str(Info) End Sub Example Results X = (0.590000000000001,-0.279999999999999) (-0.2,-3.99999999999995E-02) (0.24,-0.490000000000001) Iter = 3, Res = 8.1784563928974E-16, Info = 0