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

Gpbicg() Sub Gpbicg ( N As  Long, Val() As  Double, Ptr() As  Long, Ind() As  Long, B() As  Double, X() As  Double, Optional Info As  Long, Optional Iter As  Long, Optional Res As  Double, Optional Format As  Long = 0, Optional Mode As  Long = 0, Optional MaxIter As  Long = 500, Optional Tol As  Double = 1.0E-10, Optional Base As  Long = -1, Optional Precon As  Long = 0, Optional Omega As  Double = 1.7, Optional P As  Long = 3, Optional Nnz2 As  Long = -1, Optional Md As  Long = 0  ) Solution of linear system Ax = b using general product bi-conjugate gradient (GPBICG) method, bi-conjugate gradient stabilized (BICGSTAB) method or BICGSTAB2 method (driver) Purpose This routine solves the linear system Ax = b using the general product bi-conjugate gradient (GPBICG) method, bi-conjugate gradient stabilized (BICGSTAB) method or BICGSTAB2 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. = 11: Maximum number of iterations exceeded. = 12: Breakdown occurred. = 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] Mode (Optional) Specify method to be used. (default = 0) = 0: GPBICG. = 1: BICGSTAB. = 2: BICGSTAB2. [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] 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: ILU(0) preconditioner. = 4: ILU(p) preconditioner. [in] Omega (Optional) The relaxation parameter ω of SSOR preconditioner. (0 < ω < 2) (default = 1.7) Not used if Precon <> 2. [in] P (Optional) The value of level p of ILU(p) algorithm. (P >= 0) (default = 3) Not used if Precon <> 4. [in] Nnz2 (Optional) Maximum number of non-zero elements of matrix L*U. If the number of non-zero elements exceeds this, the routine will be terminated with error (info = 13). (Nnz2 > 0) (default = P*Nnz) Not used if Precon <> 4. [in] Md (Optional) Specify whether the diagonal compensation of the dropped elements are required. ILU with this compensation is called as MILU (modified ILU). = 0: ILU (no compensation). = 1: MILU (with diagonal compensation). Not used if Precon <> 4 or Format <> 0. 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_Gpbicg() Const N = 3, Nnz = N * N 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 Iter As Long, Res As Double, Info 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 Call Gpbicg(N, A(), Ia(), Ja(), B(), X(), Info, Iter, Res) 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 = 0.859999999999996 0.640000000000003 0.509999999999995 Iter = 3, Res = 4.09907879275695E-15, Info = 0