ZBicg ZBicg_r ZBicg_s ZCgs ZCgs_r ZCgs_s ZCocg ZCocg_r ZCocg_s ZCocr ZCocr_r ZCocr_s ZDiom ZDiom_r ZDiom_s ZDqgmres ZDqgmres_r ZDqgmres_s ZFgmres ZFgmres_r ZFgmres_s ZFom ZFom_r ZFom_s ZGcr ZGcr_r ZGcr_s ZGpbicg ZGpbicg_r ZGpbicg_s ZOrthomin ZOrthomin_r ZOrthomin_s ZQmr ZQmr_r ZQmr_s ZSor ZSor_r ZSor_s ZTfqmr ZTfqmr_r ZTfqmr_s

ZCocg_r() Sub ZCocg_r ( N As  Long, B() As  Complex, X() As  Complex, Info As  Long, XX() As  Complex, YY() As  Complex, IRev As  Long, Optional Iter As  Long, Optional Res As  Double, Optional MaxIter As  Long = 500  ) Solution of linear system Ax = b using conjugate orthogonal conjugate gradient (COCG) method (Complex symmetric matrices) (Reverse communication version) Purpose This routine solves the linear system Ax = b with complex symmetric coefficient matrix using the conjugate orthogonal conjugate gradient (COCG) method with preconditioning. Cg_r is the reverse communication version of Cg so that the storage format of matrix A and the use of preconditioner can be flexibly selected. 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 < 0: The (-Info)-th argument is invalid. = 1: (Warning) Matrix A is not positive definite (computation continued). = 2: (Warning) Preconditioner matrix M is not positive definite (computation continued). = 11: Maximum number of iterations exceeded. = 12: Matrix A is singular (zero diagonal element). [in,out] XX() Array XX(LXX - 1) (LXX >= N) Vector XX for Matvec and Psolve operations. [in,out] YY() Array YY(LYY - 1) (LYY >= N) Vector YY for Matvec and Psolve 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] MaxIter (Optional) Maximum number of iterations. (MaxIter > 0) (default = 500) Example Program Solve the system of linear equations Ax = B, where ( 0.31+0.77i 0.25+0.23i -0.81-0.83i ) A = ( 0.25+0.23i 0.26-0.26i -0.58-0.08i ) ( -0.81-0.83i -0.56-0.08i 2.09+0.6i ) ( 0.3941-1.2711i ) B = ( 0.0036-0.72i ) ( 0.3628+1.9977i ) Sub Ex_ZCocg_r() Const N = 3, Nnz = 6, 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(0.31, 0.77): A(1) = Cmplx(0.25, 0.23): A(2) = Cmplx(0.26, -0.26): A(3) = Cmplx(-0.81, -0.83): A(4) = Cmplx(-0.56, -0.08): A(5) = Cmplx(2.09, 0.6) Ia(0) = 0: Ia(1) = 1: Ia(2) = 3: Ia(3) = 6 Ja(0) = 0: Ja(1) = 0: Ja(2) = 1: Ja(3) = 0: Ja(4) = 1: Ja(5) = 2 B(0) = Cmplx(0.3941, -1.2711): B(1) = Cmplx(0.0036, -0.72): B(2) = Cmplx(0.3628, 1.9977) IRev = 0 Do Call ZCocg_r(N, B(), X(), Info, XX(), YY(), IRev, Iter, Res) If IRev = 1 Then '- Matvec Call SsrZusmv("L", N, Cmplx(1), A(), Ia(), Ja(), XX(), Cmplx(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 =" 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 = (-0.820000000000002,-0.940000000000001) (0.739999999999999,0.199999999999999) (0.480000000000005,0.209999999999999) Iter = 3, Res = 1.44872095635518E-14, Info = 0