esei_Ellipsoid.h

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//********************************************************************************************************
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//                       ##  ##   ## ## ##  ###    ##     ######
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//
// name:           eshelbySoluEllipticIntegralsEllipsoid.h
// author(s):      Jan Novak
// language:       C, C++
// license:        This program is free software; you can redistribute it and/or modify
//                 it under the terms of the GNU Lesser General Public License as published by
//                 the Free Software Foundation; either version 2 of the License, or
//                 (at your option) any later version.
//
//                 This program is distributed in the hope that it will be useful,
//                 but WITHOUT ANY WARRANTY; without even the implied warranty of
//                 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//                 GNU Lesser General Public License for more details.
//
//                 You should have received a copy of the GNU Lesser General Public License
//                 along with this program; if not, write to the Free Software
//                 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
//********************************************************************************************************
#ifndef MUMECH_ESHELBY_SOLU_ELLIPTIC_INTEGRALS_ELLIPSOID_H
#define MUMECH_ESHELBY_SOLU_ELLIPTIC_INTEGRALS_ELLIPSOID_H

#include "types.h"
#include "esei.h"
#include <complex>


namespace mumech {

class eshelbySoluEllipticIntegralsEllipsoid : public eshelbySoluEllipticIntegrals
{
 public:
  eshelbySoluEllipticIntegralsEllipsoid (const InclusionRecord3D *i) : eshelbySoluEllipticIntegrals (i) { }
  virtual ~eshelbySoluEllipticIntegralsEllipsoid () {}
  
  void giveEllipticIntegrals (double J[13], double lambda, bool intpoint);
  
  void giveDerivativesOfEllipticIntegrals (Point *point, bool intpoint);
  
  
#ifndef DEBUG
 protected:
#endif
  
  //******************************************************************************************************
  // Function gives the first or seccond derivative of a component of elliptical integrals
  double giveEllipticIntegralDerivative (const double a[3], const double x[3], aLambda aLa,
                     ellipticIntegralComponent component,
                     derivativeDirection direction_1,
                     derivativeDirection direction_2 );
  
  //******************************************************************************************************
  //Function gives the solution of the integral I
  double eI( double a[3], double k, double Theta, double mult );
  //******************************************************************************************************
  //Function gives the solution of the integral I_1
  double I1(const double a[3], double k, double Theta, double mult );
  //******************************************************************************************************
  //Function gives the solution of the integral I_2
  double I2( double I1, double I3, double lambda, double mult, double Dla, bool intpoint);
  //******************************************************************************************************
  //Function gives the solution of the integral I_3
  double I3(const double a[3], double k, double Theta, double lambda, double mult, bool intpoint);
  //******************************************************************************************************
  //Function gives the solution of the integral I_11
  double I11(const double a[3], double I12, double I13, double lambda, double mult, double Dla, bool intpoint);
  //******************************************************************************************************
  //Function gives the solution of the integral I_12
  double I12(const double a[3], double I1, double I2 );
  //******************************************************************************************************
  //Function gives the solution of the integral I_13
  double I13(const double a[3], double I1, double I3 );
  //******************************************************************************************************
  //Function gives the solution of the integral I_22
  double I22(const double a[3], double I21, double I23, double lambda, double mult, double Dla, bool intpoint );
  //******************************************************************************************************
  //Function gives the solution of the integral I_23
  double I23(const double a[3], double I2, double I3 );
  //******************************************************************************************************
  //Function gives the solution of the integral I_33
  double I33(const double a[3], double I32, double I31, double lambda, double mult, double Dla, bool intpoint);
  
  
  //******************************************************************************************************
  //Function gives the values of all elliptic Ferers-Dysons integrals
  void give_Ii_and_Iij( double J[13], const double sort_a[3], double lambda );

  //******************************************************************************************************
  //Function gives the first derivative of the Elliptic integral
  double giveEllipticIntegralFirstDerivative(const double a[3], const double x[3], aLambda aLa,
                          ellipticIntegralComponent component,
                          derivativeDirection direction );
  
  //******************************************************************************************************
  //Function gives the seccond derivative of the Elliptic integral
  double giveEllipticIntegralSeccondDerivative(const double a[3], const double x[3], aLambda aLa,
                        ellipticIntegralComponent component,
                        derivativeDirection direction_1,
                        derivativeDirection direction_2 );
  
  //******************************************************************************************************
  //Function gives the first derivative I,p of Elliptic integral I according 'p' direction
  double give_Ip_Derivative(aLambda aLa, derivativeDirection p );
  
  //******************************************************************************************************
  //Function gives the first derivative I_i,p of Elliptic integral I_i according 'p' direction
  double give_Iip_Derivative(const double a[3], aLambda aLa,
                  ellipticIntegralComponent component, derivativeDirection p );
  //******************************************************************************************************
  //Function gives the first derivative I_ij,p of Elliptic integral I_ij according 'p' direction
  double give_Iijp_Derivative(const double a[3],  aLambda aLa,
                   ellipticIntegralComponent component, derivativeDirection p );
  //******************************************************************************************************
  //Function gives the seccond derivative of the  I_ij integral by 'p' and 'q' directions
  double give_Iijpq_Derivative(const double a[3], aLambda aLa, ellipticIntegralComponent component,
                derivativeDirection p, derivativeDirection q );
  //******************************************************************************************************
  //Function gives the seccond derivative of the  I_i integral by 'p' and 'q' directions
  double give_Iipq_Derivative(const double a[3], aLambda aLa, ellipticIntegralComponent component,
                derivativeDirection p, derivativeDirection q );
  //******************************************************************************************************
  //Function gives all first derivatives of Ferers-Dysons' integrals Ii
  void give_dIi( double dJi[9], const double sort_a[3], const double x[3], aLambda aLa );
  //******************************************************************************************************
  //Function gives all first derivatives of Ferers-Dysons' integrals Iij
  void give_dIij( double dJij[27], const double sort_a[3], const double x[3], aLambda aLa );
  //******************************************************************************************************
  //Function gives all second derivatives of Ferers-Dysons' integrals Ii
  void give_ddIi( double ddJi[27], const double sort_a[3], const double x[3], aLambda aLa );
  //******************************************************************************************************
  //Function gives all second derivatives of Ferers-Dysons' integrals Iij
  void give_ddIij( double ddJi[27], const double sort_a[3], const double x[3], aLambda aLa );
  //******************************************************************************************************

  //Complex numerical derivatives of Ferers-Dysons integrals:
  //---------------------------------------------------------

  //******************************************************************************************************
  //Function gives the first complex derivative of Ii_i in 'i' direction
  std::complex<double> cIi_i(const double a[3], std::complex<double> la, std::complex<double> Dla,
            std::complex<double> cdla_i, double mult, ellipticIntegralComponent component );
  //******************************************************************************************************
  //Function gives the first complex derivative of Iij_i in 'i' direction
  std::complex<double> cIij_i(const double a[3], std::complex<double> la, std::complex<double> Dla,
             std::complex<double> cdla_i, double mult, ellipticIntegralComponent component );
  //******************************************************************************************************

  //******************************************************************************************************

  //******************************************************************************************************
  //Function gives all first derivatives of Ferers-Dysons' integrals Ii by using the complex
  //differentiation
  //  void give_cdIi( double RedJi[9], double ImdJi[27], const double sort_a[3], const double x[3] );
  void give_cdIi( double RedJi[9], double ImdJi[27], const double sort_a[3], cLambda CLa );
  //******************************************************************************************************
  //Function gives all first derivatives of Ferers-Dysons' integrals Iij by using the complex
  //differentiation
  //  void give_cdIij( complex double dJij[27], const double sort_a[3], const double x[3] );
  void give_cdIij( double RedJij[27], double ImdJij[81], const double sort_a[3], cLambda CLa );
  //******************************************************************************************************
  //Function gives all second derivatives of Ferers-Dysons' integrals Ii by using
  //the complex differentiation
  void give_cddIi( double ddJi[27], double ImdJi[27] );
  //******************************************************************************************************
  //Function gives all second derivatives of Ferers-Dysons' integrals Iij by using
  //the complex differentiation
  void give_cddIij( double ddJij[81], double ImdJij[81] );
  //******************************************************************************************************
  //Function updates vectors cx according the derivative direction. Function is just a copy of the same
  //method from the "eshelbySoluEllipticIntegralsSphere" class
  //  void update_cx( complex double cx[3], derivativeDirection direction );
  //******************************************************************************************************

  //Numerical derivatives of Ferers-Dysons integrals:
  //---------------------------------------------------------

  //******************************************************************************************************
  //Function gives the first numerical derivative of Ii_i in 'i' direction
  double nIi_i(const double a[3], double la, double Dla, double dla_i, double mult,
        ellipticIntegralComponent component );
  //******************************************************************************************************
  //Function gives the first numerical derivative of Iij_i in 'i' direction
  double nIij_i(const double a[3], double la, double Dla, double dla_i, double mult,
         ellipticIntegralComponent component );
  //******************************************************************************************************
  //Function gives all first derivatives of Ferers-Dysons' integrals Ii by using
  //numerical differentiation
  void give_ndIi( double dJi[9], double ddJih[27], const double sort_a[3], nLambda nLa );
  //******************************************************************************************************

  //******************************************************************************************************

  //******************************************************************************************************

  double getLambda(const double a[3], double x1, double x2, double x3);
};

} // end of namespace mumech

#endif

/*end of file*/