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

Diom_s() Sub Diom_s ( N As  Long, Matvec As  LongPtr, Psolve As  LongPtr, ChkConv As  LongPtr, B() As  Double, X() As  Double, Optional Info As  Long, Optional Iter As  Long, Optional Res As  Double, Optional M As  Long = 0, Optional MaxIter As  Long = 500  ) Solution of linear system Ax = b using direct incomplete orthogonalization method (DIOM) (Subroutine version) Purpose This routine solves the linear system Ax = b using the direct incomplete orthogonalization method (DIOM) with preconditioning. 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] Psolve User supplied subroutine which perform the preconditioner solve routine for the linear system M*x = b as follows, where M is a preconditioner metrix. Sub Psolve(N As Long, B() As Double, X() As Double) Solve M*x = b, and return solution 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: Breakdown occurred. [out] Iter (Optional) Actual number of iterations performed for convergence. [out] Res (Optional) Final residual norm value norm(b - A*x). [in] M (Optional) Truncation parameter. (0 < M <= N) (default = min(64, N)) [in] MaxIter (Optional) Maximum number of iterations. (MaxIter > 0) (default = 500) 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, 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 Psolve(N As Long, B() As Double, X() As Double) Dim I As Long For I = 0 To N - 1 X(I) = B(I) Next 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_Diom_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 Diom_s(N, AddressOf Matvec, AddressOf Psolve, 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 = 0.860000000000001 0.639999999999999 0.51 Iter = 3, Res = 2.94792821573918E-16, Info = 0