/* This Source Code Form is subject to the terms of the Mozilla Public * License, v. 2.0. If a copy of the MPL was not distributed with this * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ /** @file @author Trevor Irons @date 01/02/2010 @version $Id: hankeltransformgaussianquadrature.h 199 2014-12-29 19:25:20Z tirons $ **/ #ifndef _HANKELTRANSFORMGAUSSIANQUADRATURE_h_INC #define _HANKELTRANSFORMGAUSSIANQUADRATURE_h_INC #include "hankeltransform.h" #include "kernelem1dbase.h" #ifdef HAVEBOOSTCYLBESSEL #include "boost/math/special_functions.hpp" #endif namespace Lemma { // ======================================================================= // Class: HankelTransformGaussianQuadrature /// \brief Calculates hankel transform using gaussian quadrature. /// \details Accurate but slow, this is a port of Alan Chave's public domain /// fortran code // ======================================================================= class HankelTransformGaussianQuadrature : public HankelTransform { friend std::ostream &operator<<(std::ostream &stream, const HankelTransformGaussianQuadrature &ob); public: // ==================== LIFECYCLE =========================== /** * Returns pointer to new HankelTransformGaussianQuadrature. * Location is * initialized to (0,0,0) type and polarization are * initialized to nonworking values that will throw * exceptions if used. */ static HankelTransformGaussianQuadrature* New(); /** * @copybrief LemmaObject::Delete() * @copydetails LemmaObject::Delete() */ void Delete(); // ==================== OPERATORS =========================== // ==================== OPERATIONS =========================== /// Performs numerical integration using Gaussian quadrature /// ikk: type of kernel depending on source and receiver couple /// imode: a switch for TE(0) and TM(1) mode /// itype: order of Bessel function /// rho is argument to integral /// wavef is the propogation constant of free space /// = omega * sqrt( EP*AMU ) amu = 4 pi e-7 ep = 8.85e-12 //template <EMMODE T> Complex Zgauss(const int &ikk, const EMMODE &imode, const int &itype, const Real &rho, const Real &wavef, KernelEm1DBase *Kernel); // ==================== ACCESS ============================ // ==================== INQUIRY ============================ // ==================== DATA MEMBERS ============================ protected: // ==================== LIFECYCLE ============================ /// Default protected constructor. HankelTransformGaussianQuadrature (const std::string &name); /// Default protected constructor. ~HankelTransformGaussianQuadrature (); /** * @copybrief LemmaObject::Release() * @copydetails LemmaObject::Release() */ void Release(); // ==================== OPERATIONS ============================ /// Modified by Yoonho Song to branch cut, June, 1996 /// Separate Gaussian quarature integral by two interval /// first: integal from 0 to wavenumber of free space /// second: integral from wavenunmber of free space to infinity /// for large arguments, it uses continued fraction also /// It is recommended to use nl = 1 to 6, nu =7 /// PERFORMS AUTOMATIC CALCULATION OF BESSEL TRANSFORM TO SPECIFIED /// RELATIVportisheadE AND ABSOLUTE ERROR /// /// ARGUMENT LIST: /// /// BESR,BESI-REAL AND IMAGINARY PARTS RETURNED BY BESAUX /// iorder-ORDER OF THE BESSEL FUNCTION /// NL-LOWER LIMIT FOR GAUSS ORDER TO START COMPUTATION /// NU-UPPER LIMIT FOR GAUSS ORDER /// NU,NL=1,...7 SELECTS 3,7,15,31,63,127,AND 255 POINT GAUSS /// QUADRATURE BETWEEN THE ZERO CROSSINGS OF THE BESSEL FUNCTION /// R-ARGUMENT OF THE BESSEL FUNCTION /// RERR,AERR-RELATIVE AND ABSOLUTE ERROR FOR TERMINATION /// BESAUX TERMINATES WHEN INCREASING THE GAUSS ORDER DOES NOT /// CHANGE THE RESULT BY MORE THAN RERR OR WHEN THE ABSOLUTE ERROR /// IS LESS THAN AERR OR WHEN A GAUSS ORDER OF NU IS REACHED. /// NPCS-NUMBER OF PIECES INTO WHICH EACH PARTIAL INTEGRAND /// IS DIVIDED, /// ORDINARILY SET TO ONE. FOR VERY SMALL VALUES OF R WHERE /// THE KERNEL FUNCTION IS APPRECIABLE ONLY OVER THE FIRST FEW /// LOOPS OF THE BESSEL FUNCTION, NPCS MAY BE INCREASED TO ACHIEVE /// REASONABLE ACCURACY. /// NEW IF NEW=1, THE INTEGRANDS ARE COMPUTED AND SAVED AT EACH /// GAUSS /// ORDER. IF NEW=2, PREVIOUSLY COMPUTED INTEGRANDS ARE USED. NOTE /// THAT ORDER,R, AND NPCS MUST NOT BE CHANGED WHEN SETTING NEW=2. /// IERR-ERROR PARAMETER /// IERR=0--NORMAL RETURN /// IERR=1--RESULT NOT ACCURATE TO RERR DUE TO TOO LOW A GAUSS /// ORDER OR CONVERGENCE NOT ACHIEVED IN BESTRX //template <EMMODE T> void Besautn(Real &besr, Real &besi, const int &iorder, const int &nl, const int &nu, const Real &rho, const Real &rerr, const Real &aerr, const int &npcs, int &inew, const Real &aorb, KernelEm1DBase *Kernel); /// COMPUTES BESSEL TRANSFORM OF SPECIFIED ORDER DEFINED AS /// INTEGRAL(FUNCT(X)*J-SUB-ORDER(X*R)*DX) FROM X=0 TO INFINITY /// COMPUTATION IS ACHIEVED BY INTEGRATION BETWEEN THE ASYMPTOTIC /// ZERO CROSSINGS OF THE BESSEL FUNCTION USING GAUSS QUADRATURE. /// THE RESULTING SERIES OF PARTIAL INTEGRANDS IS SUMMED BY /// CALCULATING THE PADE APPROXIMANTS TO SPEED UP CONVERGENCE. /// ARGUMENT LIST: /// BESR,BESI REAL AND IMAGINARY PARTS RETURNED BY BESTRN /// iorder ORDER OF THE BESSEL FUNCTIONC NG NUMBER OF GAUSS /// POINTS TO USE IN THE QUADRATURE ROUTINE. /// NG=1 THROUGH 7 SELECTS 3,7,15,31,63,126,AND 255 TERMS. /// R ARGUMENT OF THE BESSEL FUNCTION /// RERR,AERR SPECIFIED RELATIVE AND ABSOLUTE ERROR FOR THE /// CALCULATION. THE INTEGRATION /// TERMINATES WHEN AN ADDITIONAL TERM DOES NOT CHANGE THE /// RESULT BY MORE THAN RERR*RESULT+AERR /// NPCS NUMBER OF PIECES INTO WHICH EACH PARTIAL I /// NTEGRAND IS DIVIDED, /// ORDINARILY SET TO ONE. FOR VERY SMALL VALUES OF RANGE /// WHERE THE KERNEL FUNCTION IS APPRECIABLE ONLY OVER THE /// FIRST FEW LOOPS OF THE BESSEL FUNCTION, NPCS MAY BE /// INCREASED TO ACHIEVE REASONABLE ACCURACY. NOTE THAT /// NPCS AFFECTS ONLY THE PADE /// SUM PORTION OF THE INTEGRATION, OVER X(NSUM) TO INFINITY. /// XSUM VECTOR OF VALUES OF THE KERNEL ARGUMENT OF FUNCT FOR WHICH /// EXPLICIT CALCULATION OF THE INTEGRAL IS DESIRED, SO THAT THE /// INTEGRAL OVER 0 TO XSUM(NSUM) IS ADDED TO THE INTEGRAL OVER /// XSUM(NSUM) TO INFINITY WITH THE PADE METHOD INVOKED ONLY FOR /// THE LATTER. THIS ALLOWS THE PADE SUMMATION METHOD TO BE /// OVERRIDDEN AND SOME TYPES OF SINGULARITIES TO BE HANDLED. /// NSUM NUMBER OF VALUES IN XSUM, MAY BE ZERO. /// NEW DETERMINES METHOD OF KERNEL CALCULATION /// NEW=0 MEANS CALCULATE BUT DO NOT SAVE INTEGRANDS /// NEW=1 MEANS CALCULATE KERNEL BY CALLING FUNCT-SAVE KERNEL /// TIMES BESSEL FUNCTION /// NEW=2 MEANS USE SAVED KERNELS TIMES BESSEL FUNCTIONS IN /// COMMON /BESINT/. NOTE THAT ORDER,R,NPCS,XSUM, AND /// NSUM MAY NOT BE CHANGED WHEN SETTING NEW=2. /// IERR ERROR PARAMETER /// 0 NORMAL RETURN-INTEGRAL CONVERGED /// 1 MEANS NO CONVERGENCE AFTER NSTOP TERMS IN THE PADE SUM /// /// SUBROUTINES REQUIRED: /// BESQUD,PADECF,CF,ZEROJ,DOT,JBESS /// A.CHAVE IGPP/UCSD /// NTERM IS MAXIMUM NUMBER OF BESSEL FUNCTION LOOPS STORED IF /// NEW.NE.0 /// NSTOP IS MAXIMUM Number of Pade terms //template <EMMODE T> void Bestrn( Real &BESR, Real &BESI, const int &iorder, const int &NG, const Real &R, const Real &RERR, const Real &AERR, const int &npcs, VectorXi &XSUM, int &NSUM, int &NEW, int &IERR, int &NCNTRL, const Real &AORB, KernelEm1DBase *Kernel); /// CALCULATES THE INTEGRAL OF F(X)*J-SUB-N(X*R) OVER THE /// INTERVAL A TO B AT A SPECIFIED GAUSS ORDER THE RESULT IS /// OBTAINED USING A SEQUENCE OF 1, 3, 7, 15, 31, 63, 127, AND 255 /// POINT INTERLACING GAUSS FORMULAE SO THAT NO INTEGRAND /// EVALUATIONS ARE WASTED. THE KERNEL FUNCTIONS MAY BE /// SAVED SO THAT BESSEL TRANSFORMS OF SIMILAR KERNELS ARE COMPUTED /// WITHOUT NEW EVALUATION OF THE KERNEL. DETAILS ON THE FORMULAE /// ARE GIVEN IN 'THE OPTIMUM ADDITION OF POINTS TO QUADRATURE /// FORMULAE' BY T.N.L. PATTERSON, MATHS.COMP. 22,847-856 (1968). /// GAUSS WEIGHTS TAKEN FROM COMM. A.C.M. 16,694-699 (1973) /// ARGUMENT LIST: /// A LOWER LIMIT OF INTEGRATION /// B UPPER LIMIT OF INTEGRATION /// BESR,BESI RETURNED INTEGRAL VALUE REAL AND IMAGINARY PARTS /// NG NUMBER OF POINTS IN THE GAUSS FORMULA. NG=1,...7 /// SELECTS 3,7,15,31,63,127,AND 255 POINT QUADRATURE. /// NEW SELECTS METHOD OF KERNEL EVALUATION /// NEW=0 CALCULATES KERNELS BY CALLING F - NOTHING SAVED /// NEW=1 CALCULATES KERNELS BY CALLING F AND SAVES KERNEL TIMES /// BESSEL FUNCTION IN COMMON /BESINT/ /// NEW=2 USES SAVED KERNEL TIMES BESSEL FUNCTIONS IN /// COMMON /BESINT/ /// iorder ORDER OF THE BESSEL FUNCTION /// R ARGUMENT OF THE BESSEL FUNCTION /// F F(X) IS THE EXTERNAL INTEGRAND SUBROUTINE /// A.CHAVE IGPP/UCSDC /// MAXIMUM NUMBER OF BESSEL FUNCTION LOOPS THAT CAN BE SAVED //template <EMMODE T> void Besqud(const Real &A, const Real &B, Real &BESR, Real &BESI, const int &NG, const int &NEW, const int &iorder, const Real &R, KernelEm1DBase *Kernel); /// COMPUTES SUM(S(I)),I=1,...N BY COMPUTATION OF PADE APPROXIMANT /// USING CONTINUED FRACTION EXPANSION. FUNCTION IS DESIGNED TO BE /// CALLED SEQUENTIALLY AS N IS INCREMENTED FROM 1 TO ITS FINAL /// VALUE. THE NTH CONTINUED FRACTION COEFFICIENT IS CALCULATED AND /// STORED AND THE NTH CONVERGENT RETURNED. IT IS UP TO THE USER TO /// STOP THE CALCULATION WHEN THE DESIRED ACCURACY IS ACHIEVED. /// ALGORITHM FROM HANGGI ET AL., Z.NATURFORSCH. 33A,402-417 (1977) /// IN THEIR NOTATION, VECTORS CFCOR,CFCOI ARE LOWER CASE D, /// VECTORS DR, DI ARE UPPER CASE D, VECTORS XR,XI ARE X, AND /// VECTORS SR,SI ARE S /// A.CHAVE IGPP/UCSD void Padecf(Real &SUMR, Real &SUMI, const int &N); /// EVALUATES A COMPLEX CONTINUED FRACTION BY RECURSIVE DIVISION /// STARTING AT THE BOTTOM, AS USED BY PADECF /// RESR,RESI ARE REAL AND IMAGINARY PARTS RETURNED /// CFCOR,CFCOI ARE REAL AND IMAGINARY VECTORS OF CONTINUED FRACTION /// COEFFICIENTS void CF( Real& RESR, Real &RESI, Eigen::Matrix<Real, 100, 1> &CFCOR, Eigen::Matrix<Real, 100, 1> &CFCOI, const int &N); /// COMPUTES ZERO OF BESSEL FUNCTION OF THE FIRST KIND FROM /// MCMAHON'S ASYMPTOTIC EXPANSION /// NZERO-NUMBER OF THE ZERO /// iorder-ORDER OF THE BESSEL FUNCTION (0 OR 1) Real ZeroJ(const int &ZERO, const int &IORDER); /// COMPUTES BESSEL FUNCTION OF ORDER "ORDER" AND ARGUMENT X BY /// CALLING NBS ROUTINES J0X AND J1X (REAL*8 BUT APPROXIMATELY /// REAL*4 ACCURACY). /// FOR MORE ACCURACY JBESS COULD BE CHANGED TO CALL, FOR EXAMPLE, /// THE IMSL ROUTINES MMBSJ0,MMBSJ1 << SEE C// BELOW >> Real Jbess(const Real &X, const int &IORDER); /// COMPUTES DOT PRODUCT OF TWO D.P. VECTORS WITH NONUNIT /// INCREMENTING ALLOWED. REPLACEMENT FOR BLAS SUBROUTINE SDOT. /// Currently does no checking, kind of stupid. /// The fortran version will wrap around if (inc*N) > X1.size() /// but not in a nice way. Real _dot(const int&N, const Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic> &X1, const int &INC1, const Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic> &X2, const int &INC2); // ==================== DATA MEMBERS ============================ static const Real PI2; static const Real X01P; static const Real XMAX; static const Real XSMALL; static const Real J0_X01; static const Real J0_X02; static const Real J0_X11; static const Real J0_X12; static const Real FUDGE; static const Real FUDGEX; static const Real TWOPI1; static const Real TWOPI2; static const Real RTPI2; static const Real XMIN; static const Real J1_X01; static const Real J1_X02; static const Real J1_X11; static const Real J1_X12; /// Highest gauss order used, Was NG int HighestGaussOrder; /// Total number of partial integrals on last call, was NI int NumberPartialIntegrals; /// Total number of function calls, was NF int NumberFunctionEvals; int np; int nps; ///////////////////////////////////////////////////////////// // Eigen members // Shared constant values static const VectorXr WT; static const VectorXr WA; Eigen::Matrix<int, 100, 1> Nk; //Eigen::Matrix<Real, 255, 100> karg; //Eigen::Matrix<Real, 510, 100> kern; Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic> karg; Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic> kern; // Was Besval COMMON block Eigen::Matrix<Real, 100, 1> Xr; Eigen::Matrix<Real, 100, 1> Xi; Eigen::Matrix<Real, 100, 1> Dr; Eigen::Matrix<Real, 100, 1> Di; Eigen::Matrix<Real, 100, 1> Sr; Eigen::Matrix<Real, 100, 1> Si; Eigen::Matrix<Real, 100, 1> Cfcor; Eigen::Matrix<Real, 100, 1> Cfcoi; private: }; // ----- end of class HankelTransformGaussianQuadrature ----- ////////////////////////////////////////////////////////////// // Exception Classes /** If the lower integration limit is greater than the upper limit, throw this * error. */ class LowerGaussLimitGreaterThanUpperGaussLimit : public std::runtime_error { /** Thrown when the LowerGaussLimit is greater than the upper limit. */ public: LowerGaussLimitGreaterThanUpperGaussLimit(); }; } // ----- end of Lemma name ----- #endif // ----- #ifndef _HANKELTRANSFORMGAUSSIANQUADRATURE_h_INC -----