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

ZCocr_s() Sub ZCocr_s ( N As  Long, Matvec As  LongPtr, Psolve As  LongPtr, ChkConv As  LongPtr, B() As  Complex, X() As  Complex, Optional Info As  Long, Optional Iter As  Long, Optional Res As  Double, Optional Mode As  Long = 0, Optional MaxIter As  Long = 500  ) Solution of linear system Ax = b using conjugate orthogonal conjugate residual (COCR) method (Complex symmetric matrices) (Subroutine version) Purpose This routine solves the linear system Ax = b with complex symmetric coefficient matrix using the conjugate orthogonal conjugate residual (COCR) method 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 Complex, Y() As Complex) 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 Complex, X() As Complex) 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 Complex, 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 < 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). [out] Iter (Optional) Actual number of iterations performed for convergence. [out] Res (Optional) Final residual norm value norm(b - A*x). [in] Mode (Optional) The residual norm returned via parameters chkcnv and res can be specified. (default = 0) = 0: norm(b - A*x) is returned. However, one additional matvec operation per one iteration is required. = 1: M^(-1)*norm(b - A*x) is returned. [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 ) Const N = 3, Nnz = N * N, Tol = 0.0000000001 Dim A(Nnz - 1) As Complex, Ia(N) As Long, Ja(Nnz - 1) As Long Sub Matvec(N As Long, X() As Complex, Y() As Complex) Call SsrZusmv("L", N, Cmplx(1), A(), Ia(), Ja(), X(), Cmplx(0), Y()) End Sub Sub Psolve(N As Long, B() As Complex, X() As Complex) Dim I As Long For I = 0 To N - 1 X(I) = B(I) Next End Sub Sub ChkConv(N As Long, X() As Complex, Res As Double, Iter As Long, IChk As Long) If Res < Tol Then IChk = 1 Else IChk = 0 End If End Sub Sub Ex_ZCocr_s() Dim B(N - 1) As Complex, X(N - 1) As Complex Dim Iter As Long, Res As Double, Info 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) Call ZCocr_s(N, AddressOf Matvec, AddressOf Psolve, AddressOf ChkConv, B(), X(), Info, Iter, Res) 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 = (-0.820000000000007,-0.940000000000006) (0.739999999999996,0.2) (0.480000000000016,0.210000000000004) Iter = 3, Res = 5.1647781609597E-14, Info = 0