ZCg ZCg_r ZCg_s ZCr ZCr_r ZCr_s

ZCg() Sub ZCg ( 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 MaxIter As  Long = 500, Optional Tol As  Double = 1.0E-10, Optional Uplo As  String = "F", Optional Base As  Long = -1, Optional Precon As  Long = 0, Optional Omega As  Double = 1.5  ) Solution of linear system Ax = b using conjugate gradient (CG) method (Hermitian positive definite matrices) (driver) Purpose This routine solves the linear system Ax = b with Hermitian positive definite coefficient matrix using the conjugate gradient (CG) method with preconditioning. 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. = 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). = 13: Error during initializing preconditioner. = 14: Error during preconditioning. [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] MaxIter (Optional) Maximum number of iterations. (MaxIter > 0) (default = 500) [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] Uplo (Optional) Specifies whether the upper or lower triangular part of matrix A is stored. (default = "F") = "U": Upper triangular part is stored. = "L": Lower triangular part is stored. = "F": Full matrix (both upper and lower triangular parts) are stored. [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) [in] Precon (Optional) Specify preconditioner. (default = 0) = 0: No preconditioner. = 1: Diagonal scaling preconditioner. = 2: SSOR preconditioner. = 3: IC0 preconditioner. [in] Omega (Optional) The relaxation parameter ω of SSOR preconditioner. (0 < ω < 2) (default = 1.5) Not used if Precon <> 2. Example Program Solve the system of linear equations Ax = B, where ( 1.4 -1.5+0.46i 0.16+0.23i ) A = ( -1.5-0.46i 1.44 -0.12+0.04i ) ( 0.16-0.23i -0.12-0.04i 0.05 ) ( -2.3215-1.1316i ) B = ( 1.7972+2.0692i ) ( -0.4042-0.0049i ) Sub Ex_ZCg() Const N = 3, Nnz = 6 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(1.4): A(1) = Cmplx(-1.5, -0.46): A(2) = Cmplx(1.44): A(3) = Cmplx(0.16, -0.23): A(4) = Cmplx(-0.12, -0.04): A(5) = Cmplx(0.05) 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(-2.3215, -1.1316): B(1) = Cmplx(1.7972, 2.0692): B(2) = Cmplx(-0.4042, -0.0049) Call ZCg(N, A(), Ia(), Ja(), B(), X(), Info, Iter, Res, Uplo:="L") 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 = (-0.819999999999983,-0.939999999999992) (0.739999999999985,0.199999999999988) (0.480000000000001,0.209999999999999) Iter = 3, Res = 8.08057086495744E-14, Info = 0