Lemma/Modules/FDEM1D/include/hankeltransformhankel2.h

/* This file is part of Lemma, a geophysical modelling and inversion API */

/* 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     06/26/2009
  @version  $Id: hankeltransformhankel2.h 201 2015-01-03 00:07:47Z tirons $
 **/

#ifndef __HANKEL2_H
#define __HANKEL2_H

#include "hankeltransform.h"
#include "kernelem1dbase.h"
#include "KernelEM1DSpec.h"
#include "CubicSplineInterpolator.h"

namespace Lemma {

// ==========================================================================
//        Class:  Hankel2
/** \brief   Computes the Hankel transform of orders 0 and 1 using lagged
             and related convolutions.
    \details A rewrite of work by Anderson who wrote a FORTRAN program
             that he released while working at the USGS.
             The  transform evaluates an integral of the form:
             \f[ \int_0^\infty K(\lambda) J_I (\lambda r) ~ d \lambda
             \f]
             Where \f$ K(\lambda) \f$ is some kernel function. The value
             \f$ J_I \f$ is the Bessel function of order
             \f$I, I \in \{0,1\} \f$
             The kernel function is unique for each source and is computed
             in the class CalculateKernel. The value \f$r\f$ is the radial
             distance away from the centre of the grid \f$ r=\sqrt{x^2 + y^2} \f$
             The Hankel transform is useful as it allows a double fourier
             transform to be written as a single integral:
             \f[ \mathop {\int \!\!\! \int}_{\!\!\!\!\!-\infty}^{\,\,\infty}
             F(k_x^2 + k_y^2)
                 e^{\imath (k_x x + k_y y)} dk_x \, dk_y = 2 \pi
                 \int_0^\infty K(\lambda) J_I (\lambda r) ~ d \lambda
             \f]
             This can only be done where there is radial symmetry. Hence
             its application to 1D solutions here.
 */
// ==========================================================================

class Hankel2 : public HankelTransform {

    friend std::ostream &operator<<(std::ostream &stream, const Hankel2 &ob);

    public:

        // ====================  LIFECYCLE     ==============================
        /**
         *  Returns pointer to new Hankel2. Location is
         *  initialized to (0,0,0) type and polarization are
         *  initialized  to nonworking values that will throw
         *  exceptions if used.
         */
        static Hankel2 *New();

        /**
         * @copybrief LemmaObject::Delete()
         * @copydetails LemmaObject::Delete()
         */
        void Delete();

        // ====================  OPERATORS     ==============================

        // ====================  OPERATIONS    ==============================

        /// Sets the number of convolutions
        void SetNumConv(const int &i);

        /// Computes the hankel transform with arguments
        /// @param rho [input] rho is the hankel transform argument
        /// @param ntol [input] ntol is
        /// @param tol [input] tol is
        void Compute(const Real &rho, const int& ntol, const Real &tol);

        /// Computes the related
        void ComputeRelated(const Real &rho, KernelEm1DBase* Kernel);

        /// Computes the related
        void ComputeRelated(const Real &rho,  std::vector< KernelEm1DBase* > KernelVec);

        /// Computes the related
        void ComputeRelated(const Real &rho,  KernelEM1DManager* Manager);

        /// Computes the related and lagged convolutions
        void ComputeLaggedRelated(const Real &rho, const int& nlag,  KernelEM1DManager* Manager);

        // ====================  ACCESS        ==============================

        /// Returns the answer
        Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic>  GetAnswer();

        /// Returns the arguments for lagged convolutions
        VectorXr GetArg() {return Arg;};

        /// Returns the value of Abscissa stepping
        Real GetABSER( ) { return ABSER; };

        /// Sets the lagged kernel index so that the proper value is returned
        void SetLaggedArg(const Real& rho);


        // ====================  INQUIRY       ==============================

        /// Calculates Hankel Transform using filtering.
        /// 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
        Complex Zgauss(const int &ikk, const EMMODE &imode,
                        const int &itype, const Real &rho,
                        const Real &wavef, KernelEm1DBase *Kernel);

    protected:

        // ====================  LIFECYCLE     ==============================

        /** A rewrite of Anderson's Pseudo-subroutine. */
        inline void StoreRetreive(const int &idx, const int &lag,
                        Complex &Zsum, const int &irel, Complex &C, const Real& rho0) {

            int look = idx+lag;
    		int	iq = look/801;
    		int	ir = look%801;
    		int iroll = iq*800;

    		if(this->Key[ir] <= iroll) {
			    this->Key[ir] = iroll + ir;
 	    		++this->NumFun;
                Manager->ComputeReflectionCoeffs(this->Lambda, idx, rho0);
 			    for (unsigned int ir2=0; ir2<this->kernelVec.size(); ++ir2) {
 			        this->Zwork(ir, ir2) = this->kernelVec[ir2]->RelBesselArg(this->Lambda);
 			    }
		    }

		    C = this->Zwork(ir, irel) * this->FilterWeights(this->BesselOrder, idx);
		    Zsum += C;
		    return;
	    }

        /// Default protected constructor
        Hankel2(const std::string& name);

        /// Default protected destructor
        ~Hankel2();

        /**
         * @copybrief LemmaObject::Release()
         * @copydetails LemmaObject::Release()
         */
        void Release();

        // ====================  OPERATIONS    ==============================

        void DeleteSplines();

        // ====================  DATA MEMBERS  ==============================

        /// The hankel transform wavenumber embedded in the integral
        Real Lambda;

        /// Number of times a kernel was evaluated
        int NumFun;

        /// Number of lagged convolutions
        /// must be greater or equal to 1
        /// It is set automatically in the @see Compute function so
        /// that  \f$ \rho \exp\left( -.1*(\mathtt{NumConv} -1) \right) \f$
        /// does not underflow the exponent range
        int NumConv;

        /// Number of related kernels
        int NumRel;

        /** Bessel transform order to use */
        int BesselOrder;

        /** Lag argument */
        int iLag;

        /* Should results be cached? Useful for repeated calculations of few receiver points */
        // turned out to have only marginal benefits in best case, and awful consequences in many
        //bool cacheResults;

        /** Related Kernel Manager */
        KernelEM1DManager*          Manager;

        /// Used as base for filter abscissa generation
        static const Real ABSCISSA;

        /// Also used in abscissa generation \f$ ABSE = \exp{.1} \f$
        static const Real ABSE;

        /// Also used in abscissa generation \f$ ABSER = 1 / \exp{.1} \f$
        static const Real ABSER;

        /// Counter for calculated
        int icount;

        /// Kernel Calculator
        std::vector <KernelEm1DBase*> kernelVec;

        /// Spines for lagged convolutions (real part)
        std::vector <CubicSplineInterpolator*> splineVecReal;

        /// Spines for lagged convolutions (imaginary part)
        std::vector <CubicSplineInterpolator*> splineVecImag;

        /// Key used internally
        Eigen::Matrix<int, 801, 1> Key;
        //int  Key[801];
        //Eigen::Matrix<int, Eigen::Dynamic, 1> Key;

        /// Filter weight coefficients. Set for either \f$J_0\f$ or \f$J_1\f$
        /// internally by protected function SetFilterWeights.
        /// Fixed sized will yield better performance. (not necessarily)
        //Eigen::Matrix<Real, 801, 1> FilterWeights;
        static const Eigen::Matrix<Real, 2, 801> FilterWeights;
        //static const Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic> FilterWeights;

        /// Zwork from Anderson
        Eigen::Matrix<Complex, 801, Eigen::Dynamic> Zwork;
        //Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic> Zwork;

        /// Holds answer, dimensions are NumConv, and NumberRelated.
        Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic> Zans;

        /// Holds the arguments for lagged convolutions
        VectorXr Arg;

}; // -----  end of class  HankelTransform  -----

}

#endif // __HANKEL2_h