ZHscIc0 ZHscIcSolve ZHscSsorSolve ZHsrIc0 ZHsrIcSolve ZHsrSsorSolve

ZHscSsorSolve() Sub ZHscSsorSolve ( Uplo 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 (Hermitian matrices) (CSC) Purpose This routine is the symmetric successive over-relaxation (SSOR) preconditioner for the Hermitian coefficient matrix A of the sparse linear equations. It solves the equation M*x = b, where M is the preconditioner matrix. Only the upper or lower trianglar part of A is referred for calculation. Parameters [in] Uplo = "U": Matrix A is stored in upper triangle. = "L": Matrix A is stored in lower triangle. [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 CG method with IC(0) preconditioner, where ( 1.4 -1.5+0.46i 0.16+0.23i ) A = ( -1.5-0.46i 1.44 -0.12+0.04i ) ( 0.16-0.23i -0.12-0.04i 0.05 ) ( -2.3215-1.1316i ) B = ( 1.7972+2.0692i ) ( -0.4042-0.0049i ) Sub Ex_ZCg_Ssor_Csc() Const N = 3, Nnz = 6, 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 A(0) = Cmplx(1.4): A(1) = Cmplx(-1.5, -0.46): A(2) = Cmplx(0.16, -0.23): A(3) = Cmplx(1.44): A(4) = Cmplx(-0.12, -0.04): A(5) = Cmplx(0.05) Ia(0) = 0: Ia(1) = 3: Ia(2) = 5: Ia(3) = 6 Ja(0) = 0: Ja(1) = 1: Ja(2) = 2: Ja(3) = 1: Ja(4) = 2: Ja(5) = 2 B(0) = Cmplx(-2.3215, -1.1316): B(1) = Cmplx(1.7972, 2.0692): B(2) = Cmplx(-0.4042, -0.0049) 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 ZCg_r(N, B(), X(), Info, XX(), YY(), IRev, Iter, Res) If IRev = 1 Then '- Matvec Call HscZusmv("L", N, Cmplx(1), A(), Ia(), Ja(), XX(), Cmplx(0), YY()) ElseIf IRev = 3 Then '- Psolve Call ZHscSsorSolve("L", 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 = (-0.820000000000034,-0.940000000000015) (0.739999999999993,0.199999999999984) (0.480000000000025,0.209999999999931) Iter = 3, Res = 4.45597478633465E-14, Info = 0