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

ZSor() Sub ZSor ( N As  Long, Val() As  Complex, Ptr() As  Long, Ind() As  Long, B() As  Complex, X() As  Complex, Optional Info As  Long, Optional Iter As  Long, Optional Res As  Double, Optional Format As  Long = 0, Optional Omega As  Double = 1.5, Optional MaxIter As  Long = 500, Optional Tol As  Double = 1.0E-10, Optional Base As  Long = -1  ) Solution of linear system Ax = b using Successive over-relaxation (SOR) method (Complex matrices) (driver) Purpose This routine solves the linear system Ax = b using successive over-relaxation (SOR) iterative method. Matrix A is represented in CSR or CSC format. Parameters [in] N Dimension of the matrix A. (N >= 0) (if N = 0, returns without computation) [in] Val() Array Val(LVal - 1) (LVal >= Nnz) (Nnz is the number of nonzero elements of the matrix A) Values of nonzero elements of the matrix A. [in] Ptr() Array Ptr(LPtr - 1) (LPtr >= N + 1) Column pointers (if CSC) or row pointers (if CSR) of the matrix A. [in] Ind() Array Ind(LInd - 1) (LInd >= Nnz) Row indices (if CSC) or column indices (if CSR) of the matrix A. [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). = 15: Internal error. [out] Iter (Optional) Actual number of iterations performed for convergence. [out] Res (Optional) Final residual norm value norm(b - A*x). [in] Format (Optional) Sparse matrix format. (default = 0) = 0: CSR format. = 1: CSC format. [in] Omega (Optional) The relaxation parameter ω. (0 < ω < 2) (default = 1.5) [in] MaxIter (Optional) Maximum number of iterations. (MaxIter > 0) (default = 500) If MaxIter <= 0, the default value is assumed. [in] Tol (Optional) Tolerance for convergence test. (default = 1.0e-10) Assumed to be converged if norm(b - A*x) <= Tol*norm(b). If Tol < eps (machine epsilon), Tol = eps is assumed. [in] Base (Optional) Indexing of Ptr() and Ind(). = 0: Zero-based (C style) indexing: Starting index is 0. = 1: One-based (Fortran style) indexing: Starting index is 1. (default: Assumes 1 if Ptr(0) = 1, 0 otherwise) Example Program Solve the system of linear equations Ax = B, where ( 4 0 1 0.7 0 ) ( 2i 4 0 1 0.7 ) A = ( 0 2i 4 0 1 ) ( 0 0 2i 4 0 ) ( 0 0 0 2i 4 ) ( 5.7 ) ( 5.7 + 2i ) B = ( 5 + 2i ) ( 4 + 2i ) ( 4 + 2i ) Sub Ex_ZSor() Const N = 5, Nnz = 14, Omega = 1.05 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 Iter As Long, Res As Double, Info As Long A(0) = Cmplx(4): A(1) = Cmplx(1): A(2) = Cmplx(0.7): A(3) = Cmplx(0, 2): A(4) = Cmplx(4): A(5) = Cmplx(1): A(6) = Cmplx(0.7): A(7) = Cmplx(0, 2): A(8) = Cmplx(4): A(9) = Cmplx(1): A(10) = Cmplx(0, 2): A(11) = Cmplx(4): A(12) = Cmplx(0, 2): A(13) = Cmplx(4) Ia(0) = 0: Ia(1) = 3: Ia(2) = 7: Ia(3) = 10: Ia(4) = 12: Ia(5) = 14 Ja(0) = 0: Ja(1) = 2: Ja(2) = 3: Ja(3) = 0: Ja(4) = 1: Ja(5) = 3: Ja(6) = 4: Ja(7) = 1: Ja(8) = 2: Ja(9) = 4: Ja(10) = 2: Ja(11) = 3: Ja(12) = 3: Ja(13) = 4 B(0) = Cmplx(5.7): B(1) = Cmplx(5.7, 2): B(2) = Cmplx(5, 2): B(3) = Cmplx(4, 2): B(4) = Cmplx(4, 2) Call ZSor(N, A(), Ia(), Ja(), B(), X(), Info, Iter, Res, , Omega) 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 "(" + CStr(Creal(X(3))) + "," + CStr(Cimag(X(3))) + ")" Debug.Print "(" + CStr(Creal(X(4))) + "," + CStr(Cimag(X(4))) + ")" Debug.Print "Iter =" + Str(Iter) + ", Res =" + Str(Res) + ", Info =" + Str(Info) End Sub Example Results X = ( .999999999924489,-7.08452827945102E-11) ( .999999999965658, 7.93322103076301E-11) ( 1.00000000005495, 8.34202476797265E-12) ( .999999999994847,-2.33985620845386E-11) ( .999999999991225, 5.71383743476044E-12) Iter = 11, Res = 4.1830004025201E-10, Info = 0