Bicg Bicg1 Bicg_r Bicg_s Cgs Cgs_r Cgs_s Diom Diom_r Diom_s Dqgmres Dqgmres_r Dqgmres_s Fgmres Fgmres_r Fgmres_s Fom Fom_r Fom_s Gcr Gcr_r Gcr_s Gpbicg Gpbicg_r Gpbicg_s Orthomin Orthomin_r Orthomin_s Qmr Qmr_r Qmr_s Sor Sor_r Sor_s Tfqmr Tfqmr_r Tfqmr_s

Sor_s() Sub Sor_s ( N As  Long, Matvec As  LongPtr, Matsol As  LongPtr, ChkConv As  LongPtr, B() As  Double, X() As  Double, Optional Info As  Long, Optional Iter As  Long, Optional Res As  Double, Optional MaxIter As  Long = 500  ) Solution of linear system Ax = b using Successive over-relaxation (SOR) method (Subroutine version) Purpose This routine solves the linear system Ax = b using successive over-relaxation (SOR) iterative method. Parameters [in] N Dimension of the matrix A. (N >= 0) (if N = 0, returns without computation) [in] Matvec User supplied subroutine which calculates the product of matrix A and vector x as follows. Sub Matvec(N As Long, X() As Double, Y() As Double) Compute A*x, and return in Y(). End Sub [in] Matsol User supplied subroutine which computes (D/ω + L)^(-1)*b using diagonal and lower tridiagonal parts of matrix A as follows. Sub Matsol(N As Long, B() As Double, X() As Double) Compute x = (D/ω + L)^(-1)*b (or solve (D/ω + L)*x = b) and return solution x in X(). End Sub [in] ChkConv User supplied subroutine which is called on every iteration for the convergence test as follows, where X() is the current approximate solution, Res is the current residual norm norm(b - A*x), and Iter is the current number of iterations. This routine can also be used to output the intermediate results. Sub ChkConv(N As Long, X() As Double, Res As Double, Iter As Long, IChk As Long) Set IChk = 1 if converged. Otherwise, set IChk = 0. End Sub [in] B() Array B(LB - 1) (LB >= N) Right hand side vector b. [in,out] X() Array X(LX - 1) (LX >= N) [in] Initial guess of solution. [out] Obtained approximate solution. [out] Info (Optional) = 0: Successful exit = i < 0: The (-i)-th argument is invalid. = 11: Maximum number of iterations exceeded. = 12: Matrix is singular (zero diagonal element). [out] Iter (Optional) Actual number of iterations performed for convergence. [out] Res (Optional) Final residual norm value norm(b - A*x). [in] MaxIter (Optional) Maximum number of iterations. (MaxIter > 0) (default = 500) Note To calculate (D/ω + L)^(-1)*b, CscDussv or CsrDussv can be used. Example Program Solve the system of linear equations Ax = B, 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 ) Const N = 3, Nnz = N * N, Omega = 0.4, Tol = 0.0000000001 Dim A(Nnz - 1) As Double, Ia(N) As Long, Ja(Nnz - 1) As Long Sub Matvec(N As Long, X() As Double, Y() As Double) Call CsrDusmv("N", N, N, 1, A(), Ia(), Ja(), X(), 0, Y()) End Sub Sub Matsol(N As Long, B() As Double, X() As Double) Dim I As Long For I = 0 To N - 1 X(I) = B(I) Next Call CsrDussv("L", "N", "N", N, A(), Ia(), Ja(), X(), Omega:=Omega) End Sub Sub ChkConv(N As Long, X() As Double, Res As Double, Iter As Long, IChk As Long) If Res < Tol Then IChk = 1 Else IChk = 0 End If End Sub Sub Ex_Sor_s() Dim B(N - 1) As Double, X(N - 1) As Double Dim Iter As Long, Res As Double, Info As Long A(0) = 0.2: A(1) = -0.11: A(2) = -0.93: A(3) = -0.32: A(4) = 0.81: A(5) = 0.37: A(6) = -0.8: A(7) = -0.92: 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 Call Sor_s(N, AddressOf Matvec, AddressOf Matsol, AddressOf ChkConv, B(), X(), Info, Iter, Res) 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 = 0.859999999965658 0.640000000003731 0.509999999994652 Iter = 57, Res = 2.83730635879748E-11, Info = 0