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

Dqgmres_r() Sub Dqgmres_r ( N As  Long, B() As  Double, X() As  Double, Info As  Long, XX() As  Double, YY() As  Double, IRev 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 quasi generalized minimum residual (DQGMRES) method (Reverse communication version) Purpose This routine solves the linear system Ax = b using the direct quasi generalized minimum residual (DQGMRES) method with preconditioning. Parameters [in] N Dimension of the matrix A. (N >= 0) (if N = 0, returns without computation) [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 = 0: Successful exit = i < 0: The (-i)-th argument is invalid. = 11: Maximum number of iterations exceeded. = 12: Breakdown occurred. [in,out] XX() Array XX(LXX - 1) (LXX >= N) Vector XX for Matvec, MatvecTrans, Psolve and PsolveTrans operations. [in,out] YY() Array YY(LYY - 1) (LYY >= N) Vector YY for Matvec, MatvecTrans, Psolve and PsolveTrans operations. [in,out] IRev Control variable for reverse communication. [in] Before first call, IRev should be initialized to zero. On succeeding calls, IRev should not be altered (except if converged). [out] If IRev is not zero, complete the following process and call this routine again. = 0: Computation finished. See return code in info. = 1: Matvec operation. User should set A*XX in YY. Do not alter any other variables. = 3: Psolve operation. User should set solution of M*XX = YY in XX. Do not alter any other variables. = 10: To be returned for the convergence test on every iteration . Set IRev = 11 if converged. Do not alter IRev otherwise. The latest values in X(), Iter and Res can be used to decide the convergence. Further, these values may be used to output the intermediate results. [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 ) Sub Ex_Dqgmres_r() 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, I 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 IRev = 0 Do Call Dqgmres_r(N, B(), X(), Info, XX(), YY(), IRev, Iter, Res) If IRev = 1 Then '- Matvec Call CsrDusmv("N", N, N, 1, A(), Ia(), Ja(), XX(), 0, YY()) ElseIf IRev = 3 Then '- Psolve For I = 0 To N - 1 XX(I) = YY(I) Next 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 = 3, Res = 2.94792821573918E-16, Info = 0