arts-docs-master/doxygen/tmatrix_8cc_source.html

/* Copyright (C) 2013 Oliver Lemke

 *

 * This program is free software: you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation, either version 3 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 General Public License for more details.

 *

 * You should have received a copy of the GNU General Public License

 * along with this program.  If not, see <http://www.gnu.org/licenses/>.

 *

 */


#include "tmatrix.h"

#include <cmath>

#include <cstring>

#include <stdexcept>

#include "matpack_complex.h"

#include "math_funcs.h"

#include "matpackI.h"

#include "messages.h"

#include "optproperties.h"


void calc_phamat(Matrix& z,

                 const Index& nmax,

                 const Numeric& lam,

                 const Numeric& thet0,

                 const Numeric& thet,

                 const Numeric& phi0,

                 const Numeric& phi,

                 const Numeric& beta,

                 const Numeric& alpha);


void ampmat_to_phamat(Matrix& z,

                      const Complex& s11,

                      const Complex& s12,

                      const Complex& s21,

                      const Complex& s22);


void integrate_phamat_alpha10(Matrix& phamat,

                              const Index& nmax,

                              const Numeric& lam,

                              const Numeric& thet0,

                              const Numeric& thet,

                              const Numeric& phi0,

                              const Numeric& phi,

                              const Numeric& beta,

                              const Numeric& alpha_1,

                              const Numeric& alpha_2);


void integrate_phamat_alpha6(Matrix& phamat,

                             const Index& nmax,

                             const Numeric& lam,

                             const Numeric& thet0,

                             const Numeric& thet,

                             const Numeric& phi0,

                             const Numeric& phi,

                             const Numeric& beta,

                             const Numeric& alpha_1,

                             const Numeric& alpha_2);


void integrate_phamat_theta0_phi10(Matrix& phamat,

                                   const Index& nmax,

                                   const Numeric& lam,

                                   const Numeric& thet0_1,

                                   const Numeric& thet0_2,

                                   const Numeric& thet,

                                   const Numeric& phi0,

                                   const Numeric& phi_1,

                                   const Numeric& phi_2,

                                   const Numeric& beta,

                                   const Numeric& alpha);


void integrate_phamat_theta0_phi_alpha6(Matrix& phamat,

                                        const Index& nmax,

                                        const Numeric& lam,

                                        const Numeric& thet0_1,

                                        const Numeric& thet0_2,

                                        const Numeric& thet,

                                        const Numeric& phi0,

                                        const Numeric& phi_1,

                                        const Numeric& phi_2,

                                        const Numeric& beta,

                                        const Numeric& alpha_1,

                                        const Numeric& alpha_2);


#ifdef ENABLE_TMATRIX

extern "C" {

#endif

void tmd_(const Numeric& rat,

          const Index& ndistr,

          const Numeric& axmax,

          const Index& npnax,

          const Numeric& b,

          const Numeric& gam,

          const Index& nkmax,

          const Numeric& eps,

          const Index& np,

          const Numeric& lam,

          const Numeric& mrr,

          const Numeric& mri,

          const Numeric& ddelt,

          const Index& npna,

          const Index& ndgs,

          const Numeric& r1rat,

          const Numeric& r2rat,

          const Index& quiet,

          Numeric& reff,   // OUT

          Numeric& veff,   // OUT

          Numeric& cext,   // OUT

          Numeric& csca,   // OUT

          Numeric& walb,   // OUT

          Numeric& asymm,  // OUT

          Numeric* f11,    // Array npna

          Numeric* f22,    // Array npna

          Numeric* f33,    // Array npna

          Numeric* f44,    // Array npna

          Numeric* f12,    // Array npna

          Numeric* f34,    // Array npna

          char* errmsg);


void tmatrix_(const Numeric& rat,

              const Numeric& axi,

              const Index& np,

              const Numeric& lam,

              const Numeric& eps,

              const Numeric& mrr,

              const Numeric& mri,

              const Numeric& ddelt,

              const Index& quiet,

              Index& nmax,

              Numeric& csca,

              Numeric& cext,

              char* errmsg);


void ampl_(const Index& nmax,

           const Numeric& lam,

           const Numeric& thet0,

           const Numeric& thet,

           const Numeric& phi0,

           const Numeric& phi,

           const Numeric& alpha,

           const Numeric& beta,

           Complex& s11,

           Complex& s12,

           Complex& s21,

           Complex& s22);


void avgtmatrix_(const Index& nmax);

#ifdef ENABLE_TMATRIX

}

#endif


// Define dummy functions that throw runtime errors if ARTS is

// compiled without T-Matrix support.

#ifndef ENABLE_TMATRIX


// T-matrix code for randomly oriented nonspherical particles.

void tmd_(const Numeric&,

          const Index&,

          const Numeric&,

          const Index&,

          const Numeric&,

          const Numeric&,

          const Index&,

          const Numeric&,

          const Index&,

          const Numeric&,

          const Numeric&,

          const Numeric&,

          const Numeric&,

          const Index&,

          const Index&,

          const Numeric&,

          const Numeric&,

          const Index&,

          Numeric&,

          Numeric&,

          Numeric&,

          Numeric&,

          Numeric&,

          Numeric&,

          Numeric*,

          Numeric*,

          Numeric*,

          Numeric*,

          Numeric*,

          Numeric*,

          char*) {

  throw std::runtime_error(

      "This version of ARTS was compiled without T-Matrix support.");

}


// T-matrix code for nonspherical particles in a fixed orientation

void tmatrix_(const Numeric&,

              const Numeric&,

              const Index&,

              const Numeric&,

              const Numeric&,

              const Numeric&,

              const Numeric&,

              const Numeric&,

              const Index&,

              Index&,

              Numeric&,

              Numeric&,

              char*) {

  throw std::runtime_error(

      "This version of ARTS was compiled without T-Matrix support.");

}


// T-matrix code for nonspherical particles in a fixed orientation

void ampl_(const Index&,

           const Numeric&,

           const Numeric&,

           const Numeric&,

           const Numeric&,

           const Numeric&,

           const Numeric&,

           const Numeric&,

           Complex&,

           Complex&,

           Complex&,

           Complex&) {

  throw std::runtime_error(

      "This version of ARTS was compiled without T-Matrix support.");

}


void avgtmatrix_(const Index&) {

  throw std::runtime_error(

      "This version of ARTS was compiled without T-Matrix support.");

}


#endif


void calc_phamat(Matrix& z,

                 const Index& nmax,

                 const Numeric& lam,

                 const Numeric& thet0,

                 const Numeric& thet,

                 const Numeric& phi0,

                 const Numeric& phi,

                 const Numeric& beta,

                 const Numeric& alpha) {

  Complex s11;

  Complex s12;

  Complex s21;

  Complex s22;

  ampl_(nmax, lam, thet0, thet, phi0, phi, alpha, beta, s11, s12, s21, s22);


  ampmat_to_phamat(z, s11, s12, s21, s22);

}


void ampmat_to_phamat(Matrix& z,

                      const Complex& s11,

                      const Complex& s12,

                      const Complex& s21,

                      const Complex& s22) {

  z.resize(4, 4);

  z(0, 0) = 0.5 * (s11 * conj(s11) + s12 * conj(s12) + s21 * conj(s21) +

                   s22 * conj(s22))

                      .real();

  z(0, 1) = 0.5 * (s11 * conj(s11) - s12 * conj(s12) + s21 * conj(s21) -

                   s22 * conj(s22))

                      .real();

  z(0, 2) = (-s11 * conj(s12) - s22 * conj(s21)).real();

  z(0, 3) = (Complex(0., 1.) * (s11 * conj(s12) - s22 * conj(s21))).real();


  z(1, 0) = 0.5 * (s11 * conj(s11) + s12 * conj(s12) - s21 * conj(s21) -

                   s22 * conj(s22))

                      .real();

  z(1, 1) = 0.5 * (s11 * conj(s11) - s12 * conj(s12) - s21 * conj(s21) +

                   s22 * conj(s22))

                      .real();

  z(1, 2) = (-s11 * conj(s12) + s22 * conj(s21)).real();

  z(1, 3) = (Complex(0., 1.) * (s11 * conj(s12) + s22 * conj(s21))).real();


  z(2, 0) = (-s11 * conj(s21) - s22 * conj(s12)).real();

  z(2, 1) = (-s11 * conj(s21) + s22 * conj(s12)).real();

  z(2, 2) = (s11 * conj(s22) + s12 * conj(s21)).real();

  z(2, 3) = (Complex(0., -1.) * (s11 * conj(s22) + s21 * conj(s12))).real();


  z(3, 0) = (Complex(0., 1.) * (s21 * conj(s11) + s22 * conj(s12))).real();

  z(3, 1) = (Complex(0., 1.) * (s21 * conj(s11) - s22 * conj(s12))).real();

  z(3, 2) = (Complex(0., -1.) * (s22 * conj(s11) - s12 * conj(s21))).real();

  z(3, 3) = (s22 * conj(s11) - s12 * conj(s21)).real();

}


static const Numeric GaussLeg6[][3] = {{0.23861918, 0.66120939, 0.93246951},

                                       {0.46791393, 0.36076157, 0.17132449}};


static const Numeric GaussLeg10[][5] = {

    {0.14887434, 0.43339539, 0.67940957, 0.86506337, 0.97390653},

    {0.29552422, 0.26926672, 0.21908636, 0.14945135, 0.06667134}};


void integrate_phamat_alpha10(Matrix& phamat,

                              const Index& nmax,

                              const Numeric& lam,

                              const Numeric& thet0,

                              const Numeric& thet,

                              const Numeric& phi0,

                              const Numeric& phi,

                              const Numeric& beta,

                              const Numeric& alpha_1,

                              const Numeric& alpha_2) {

  const Numeric c = 0.5 * (alpha_2 + alpha_1);

  const Numeric m = 0.5 * (alpha_2 - alpha_1);


  phamat.resize(4, 4);

  phamat = 0.;

  Matrix z;


  for (Index i = 0; i < 5; ++i) {

    const Numeric abscissa = GaussLeg10[0][i];

    const Numeric weight = GaussLeg10[1][i];


    calc_phamat(z, nmax, lam, thet0, thet, phi0, phi, beta, c + m * abscissa);

    z *= weight;

    phamat += z;


    calc_phamat(z, nmax, lam, thet0, thet, phi0, phi, beta, c - m * abscissa);

    z *= weight;

    phamat += z;

  }

  phamat *= m;

}


void integrate_phamat_alpha6(Matrix& phamat,

                             const Index& nmax,

                             const Numeric& lam,

                             const Numeric& thet0,

                             const Numeric& thet,

                             const Numeric& phi0,

                             const Numeric& phi,

                             const Numeric& beta,

                             const Numeric& alpha_1,

                             const Numeric& alpha_2) {

  const Numeric c = 0.5 * (alpha_2 + alpha_1);

  const Numeric m = 0.5 * (alpha_2 - alpha_1);


  phamat.resize(4, 4);

  phamat = 0.;

  Matrix z;


  for (Index i = 0; i < 3; ++i) {

    const Numeric abscissa = GaussLeg6[0][i];

    const Numeric weight = GaussLeg6[1][i];


    calc_phamat(z, nmax, lam, thet0, thet, phi0, phi, beta, c + m * abscissa);

    z *= weight;

    phamat += z;


    calc_phamat(z, nmax, lam, thet0, thet, phi0, phi, beta, c - m * abscissa);

    z *= weight;

    phamat += z;

  }

  phamat *= m;

}


void integrate_phamat_theta0_phi10(Matrix& phamat,

                                   const Index& nmax,

                                   const Numeric& lam,

                                   const Numeric& thet0_1,

                                   const Numeric& thet0_2,

                                   const Numeric& thet,

                                   const Numeric& phi0,

                                   const Numeric& phi_1,

                                   const Numeric& phi_2,

                                   const Numeric& beta,

                                   const Numeric& alpha) {

  extern const Numeric PI;


  phamat.resize(4, 4);

  phamat = 0.;

  Matrix z;


  const Numeric c_thet0 = 0.5 * (thet0_2 + thet0_1);

  const Numeric m_thet0 = 0.5 * (thet0_2 - thet0_1);

  const Numeric c_phi = 0.5 * (phi_2 + phi_1);

  const Numeric m_phi = 0.5 * (phi_2 - phi_1);


  for (Index t = 0; t < 5; ++t) {

    const Numeric abscissa_thet0 = GaussLeg10[0][t];

    const Numeric weight_thet0 = GaussLeg10[1][t];


    Matrix phamat_phi(4, 4, 0.);


    for (Index p = 0; p < 5; ++p) {

      const Numeric abscissa_phi = GaussLeg10[0][p];

      const Numeric weight_phi = GaussLeg10[1][p];


      Numeric this_thet0 = c_thet0 + m_thet0 * abscissa_thet0;

      calc_phamat(z,

                  nmax,

                  lam,

                  this_thet0,

                  thet,

                  phi0,

                  c_phi + m_phi * abscissa_phi,

                  beta,

                  alpha);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;


      calc_phamat(z,

                  nmax,

                  lam,

                  this_thet0,

                  thet,

                  phi0,

                  c_phi - m_phi * abscissa_phi,

                  beta,

                  alpha);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;


      this_thet0 = c_thet0 - m_thet0 * abscissa_thet0;

      calc_phamat(z,

                  nmax,

                  lam,

                  this_thet0,

                  thet,

                  phi0,

                  c_phi + m_phi * abscissa_phi,

                  beta,

                  alpha);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;


      calc_phamat(z,

                  nmax,

                  lam,

                  this_thet0,

                  thet,

                  phi0,

                  c_phi - m_phi * abscissa_phi,

                  beta,

                  alpha);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;

    }

    phamat_phi *= m_phi * weight_thet0;

    phamat += phamat_phi;

  }


  phamat *= m_thet0;

}


void integrate_phamat_theta0_phi_alpha6(Matrix& phamat,

                                        const Index& nmax,

                                        const Numeric& lam,

                                        const Numeric& thet0_1,

                                        const Numeric& thet0_2,

                                        const Numeric& thet,

                                        const Numeric& phi0,

                                        const Numeric& phi_1,

                                        const Numeric& phi_2,

                                        const Numeric& beta,

                                        const Numeric& alpha_1,

                                        const Numeric& alpha_2) {

  extern const Numeric PI;


  Matrix z;

  Matrix phamat_phi(4, 4);


  const Numeric c_thet0 = 0.5 * (thet0_2 + thet0_1);

  const Numeric m_thet0 = 0.5 * (thet0_2 - thet0_1);

  const Numeric c_phi = 0.5 * (phi_2 + phi_1);

  const Numeric m_phi = 0.5 * (phi_2 - phi_1);


  phamat.resize(4, 4);

  phamat = 0.;


  for (Index t = 0; t < 3; ++t) {

    const Numeric abscissa_thet0 = GaussLeg6[0][t];

    const Numeric weight_thet0 = GaussLeg6[1][t];


    phamat_phi = 0.;


    for (Index p = 0; p < 3; ++p) {

      const Numeric abscissa_phi = GaussLeg6[0][p];

      const Numeric weight_phi = GaussLeg6[1][p];


      Numeric this_thet0 = c_thet0 + m_thet0 * abscissa_thet0;

      integrate_phamat_alpha6(z,

                              nmax,

                              lam,

                              this_thet0,

                              thet,

                              phi0,

                              c_phi + m_phi * abscissa_phi,

                              beta,

                              alpha_1,

                              alpha_2);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;


      integrate_phamat_alpha6(z,

                              nmax,

                              lam,

                              this_thet0,

                              thet,

                              phi0,

                              c_phi - m_phi * abscissa_phi,

                              beta,

                              alpha_1,

                              alpha_2);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;


      this_thet0 = c_thet0 - m_thet0 * abscissa_thet0;

      integrate_phamat_alpha6(z,

                              nmax,

                              lam,

                              this_thet0,

                              thet,

                              phi0,

                              c_phi + m_phi * abscissa_phi,

                              beta,

                              alpha_1,

                              alpha_2);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;


      integrate_phamat_alpha6(z,

                              nmax,

                              lam,

                              this_thet0,

                              thet,

                              phi0,

                              c_phi - m_phi * abscissa_phi,

                              beta,

                              alpha_1,

                              alpha_2);

      z *= weight_phi * sin(this_thet0 * PI / 180.);

      phamat_phi += z;

    }

    phamat_phi *= m_phi * weight_thet0;

    phamat += phamat_phi;

  }


  phamat *= m_thet0;

}


void tmatrix_random_orientation(Numeric& cext,

                                Numeric& csca,

                                Vector& f11,

                                Vector& f22,

                                Vector& f33,

                                Vector& f44,

                                Vector& f12,

                                Vector& f34,

                                const Numeric equiv_radius,

                                const Numeric aspect_ratio,

                                const Index np,

                                const Numeric lam,

                                const Numeric ref_index_real,

                                const Numeric ref_index_imag,

                                const Numeric precision,

                                const Index nza,

                                const Index ndgs,

                                const Index quiet = 1) {

  Numeric reff;

  Numeric veff;

  Numeric walb;

  Numeric asymm;


  char errmsg[1024] = "";


  f11.resize(nza);

  f11 = NAN;

  f22.resize(nza);

  f22 = NAN;

  f33.resize(nza);

  f33 = NAN;

  f44.resize(nza);

  f44 = NAN;

  f12.resize(nza);

  f12 = NAN;

  f34.resize(nza);

  f34 = NAN;


  // It is necessary to make sure that the Fortran code is not

  // called from different threads at the same time. The common

  // blocks are not threadsafe.

#pragma omp critical(tmatrix_code)

  tmd_(1.0,

       4,

       equiv_radius,

       1,

       0.1,

       1.0,

       -1,

       aspect_ratio,

       np,

       lam,

       ref_index_real,

       ref_index_imag,

       precision,

       nza,

       ndgs,

       0.9999999,

       1.0000001,

       quiet,

       reff,

       veff,

       cext,

       csca,

       walb,

       asymm,

       f11.get_c_array(),

       f22.get_c_array(),

       f33.get_c_array(),

       f44.get_c_array(),

       f12.get_c_array(),

       f34.get_c_array(),

       errmsg);


  if (strlen(errmsg)) {

    std::ostringstream os;

    os << "T-Matrix code failed: " << errmsg;

    throw std::runtime_error(os.str());

  }

}


void tmatrix_fixed_orientation(Numeric& cext,

                               Numeric& csca,

                               Index& nmax,

                               const Numeric equiv_radius,

                               const Numeric aspect_ratio,

                               const Index np,

                               const Numeric lam,

                               const Numeric ref_index_real,

                               const Numeric ref_index_imag,

                               const Numeric precision,

                               const Index quiet = 1) {

  char errmsg[1024] = "";


  // It is necessary to make sure that the Fortran code is not

  // called from different threads at the same time. The common

  // blocks are not threadsafe.

#pragma omp critical(tmatrix_code)

  tmatrix_(1.,

           equiv_radius,

           np,

           lam,

           aspect_ratio,

           ref_index_real,

           ref_index_imag,

           precision,

           quiet,

           nmax,

           csca,

           cext,

           errmsg);


  if (strlen(errmsg)) {

    std::ostringstream os;

    os << "T-Matrix code failed: " << errmsg;

    throw std::runtime_error(os.str());

  }

}


void calcSingleScatteringDataProperties(SingleScatteringData& ssd,

                                        ConstMatrixView ref_index_real,

                                        ConstMatrixView ref_index_imag,

                                        const Numeric equiv_radius,

                                        const Index np,

                                        const Numeric aspect_ratio,

                                        const Numeric precision,

                                        const Index ndgs,

                                        const Index robust,

                                        const Index quiet) {

  const Index nf = ssd.f_grid.nelem();

  const Index nT = ssd.T_grid.nelem();


  extern const Numeric PI;

  extern const Numeric SPEED_OF_LIGHT;


  if (ref_index_real.nrows() != nf)

    throw std::runtime_error(

        "Number of rows of refractive index real part must match ssd.f_grid.");

  if (ref_index_real.ncols() != nT)

    throw std::runtime_error(

        "Number of cols of refractive index real part must match ssd.T_grid.");

  if (ref_index_imag.nrows() != nf)

    throw std::runtime_error(

        "Number of rows of refractive index imaginary part must match ssd.f_grid.");

  if (ref_index_imag.ncols() != nT)

    throw std::runtime_error(

        "Number of cols of refractive index imaginary part must match ssd.T_grid.");


  // The T-Matrix code needs wavelength

  Vector lam(nf, SPEED_OF_LIGHT);

  lam /= ssd.f_grid;


  switch (ssd.ptype) {

    case PTYPE_TOTAL_RND: {

      const Index nza = ssd.za_grid.nelem();


      ssd.pha_mat_data.resize(nf, nT, nza, 1, 1, 1, 6);

      ssd.ext_mat_data.resize(nf, nT, 1, 1, 1);

      ssd.abs_vec_data.resize(nf, nT, 1, 1, 1);


      ssd.pha_mat_data = NAN;

      ssd.ext_mat_data = NAN;

      ssd.abs_vec_data = NAN;


      // Output variables

      Numeric cext = NAN;

      Numeric csca = NAN;

      Vector f11;

      Vector f22;

      Vector f33;

      Vector f44;

      Vector f12;

      Vector f34;

      Matrix mono_pha_mat_data(nza, 6, NAN);


      ostringstream os;

      os << "Calculation of SingleScatteringData properties failed for\n\n";

      bool anyfailed = false;

#pragma omp critical(tmatrix_ssp)

      for (Index f_index = 0; f_index < nf; ++f_index)

        for (Index T_index = 0; T_index < nT; ++T_index) {

          bool thisfailed = false;

          try {

            tmatrix_random_orientation(cext,

                                       csca,

                                       f11,

                                       f22,

                                       f33,

                                       f44,

                                       f12,

                                       f34,

                                       equiv_radius,

                                       aspect_ratio,

                                       np,

                                       lam[f_index],

                                       ref_index_real(f_index, T_index),

                                       ref_index_imag(f_index, T_index),

                                       precision,

                                       nza,

                                       ndgs,

                                       quiet);

          } catch (const std::runtime_error& e) {

            //ostringstream os;

            //os << "Calculation of SingleScatteringData properties failed for\n"

            os << "f_grid[" << f_index << "] = " << ssd.f_grid[f_index] << "\n"

               << "T_grid[" << T_index << "] = " << ssd.T_grid[T_index]

               << "\n\n";

            //<< e.what();

            //throw std::runtime_error(os.str());

            thisfailed = true;

            anyfailed = true;

            cout << "\n\n";

          }


          if (!thisfailed) {

            mono_pha_mat_data(joker, 0) = f11;

            mono_pha_mat_data(joker, 1) = f12;

            mono_pha_mat_data(joker, 2) = f22;

            mono_pha_mat_data(joker, 3) = f33;

            mono_pha_mat_data(joker, 4) = f34;

            mono_pha_mat_data(joker, 5) = f44;


            mono_pha_mat_data *= csca / 4. / PI;

            ssd.pha_mat_data(f_index, T_index, joker, 0, 0, 0, joker) =

                mono_pha_mat_data;


            ssd.ext_mat_data(f_index, T_index, 0, 0, 0) = cext;

            ssd.abs_vec_data(f_index, T_index, 0, 0, 0) = cext - csca;

          }

        }

      if (anyfailed)

        if (robust)

          cout << os.str();

        else

          throw std::runtime_error(os.str());

      else {

        os << "None\n";

      }


      break;

    }

    case PTYPE_AZIMUTH_RND: {

      const Index nza = ssd.za_grid.nelem();

      const Index naa = ssd.aa_grid.nelem();


      ssd.pha_mat_data.resize(nf, nT, nza, naa, nza, 1, 16);

      ssd.ext_mat_data.resize(nf, nT, nza, 1, 3);

      ssd.abs_vec_data.resize(nf, nT, nza, 1, 2);


      ssd.ext_mat_data = NAN;

      ssd.pha_mat_data = NAN;

      ssd.abs_vec_data = NAN;


      // Output variables

      Numeric cext = NAN;

      Numeric csca = NAN;

      Index nmax = -1;


      Tensor5 csca_data(nf, nT, nza, 1, 2);


#pragma omp critical(tmatrix_ssp)

      for (Index f_index = 0; f_index < nf; ++f_index) {

        const Numeric lam_f = lam[f_index];


        for (Index T_index = 0; T_index < nT; ++T_index) {

          try {

            tmatrix_fixed_orientation(cext,

                                      csca,

                                      nmax,

                                      equiv_radius,

                                      aspect_ratio,

                                      np,

                                      lam_f,

                                      ref_index_real(f_index, T_index),

                                      ref_index_imag(f_index, T_index),

                                      precision);

          } catch (const std::runtime_error& e) {

            ostringstream os;

            os << "Calculation of SingleScatteringData properties failed for\n"

               << "f_grid[" << f_index << "] = " << ssd.f_grid[f_index] << "\n"

               << "T_grid[" << T_index << "] = " << ssd.T_grid[T_index] << "\n"

               << e.what();

            throw std::runtime_error(os.str());

          }


          Matrix phamat;

          for (Index za_scat_index = 0; za_scat_index < nza; ++za_scat_index)

            for (Index aa_index = 0; aa_index < naa; ++aa_index)

              for (Index za_inc_index = 0; za_inc_index < nza; ++za_inc_index) {

                if (aspect_ratio < 1.0) {

                  // Phase matrix for prolate particles

                  integrate_phamat_alpha10(phamat,

                                           nmax,

                                           lam_f,

                                           ssd.za_grid[za_inc_index],

                                           ssd.za_grid[za_scat_index],

                                           0.0,

                                           ssd.aa_grid[aa_index],

                                           90.0,

                                           0.0,

                                           180.0);

                  phamat /= 180.;

                } else {

                  // Phase matrix for oblate particles

                  calc_phamat(phamat,

                              nmax,

                              lam_f,

                              ssd.za_grid[za_inc_index],

                              ssd.za_grid[za_scat_index],

                              0.0,

                              ssd.aa_grid[aa_index],

                              0.0,

                              0.0);

                }


                ssd.pha_mat_data(f_index,

                                 T_index,

                                 za_scat_index,

                                 aa_index,

                                 za_inc_index,

                                 0,

                                 Range(0, 4)) = phamat(0, joker);

                ssd.pha_mat_data(f_index,

                                 T_index,

                                 za_scat_index,

                                 aa_index,

                                 za_inc_index,

                                 0,

                                 Range(4, 4)) = phamat(1, joker);

                ssd.pha_mat_data(f_index,

                                 T_index,

                                 za_scat_index,

                                 aa_index,

                                 za_inc_index,

                                 0,

                                 Range(8, 4)) = phamat(2, joker);

                ssd.pha_mat_data(f_index,

                                 T_index,

                                 za_scat_index,

                                 aa_index,

                                 za_inc_index,

                                 0,

                                 Range(12, 4)) = phamat(3, joker);

              }


          // Csca integral

          for (Index za_scat_index = 0; za_scat_index < nza; ++za_scat_index) {

            Matrix csca_integral;

            if (aspect_ratio < 1.0) {

              // Csca for prolate particles

              integrate_phamat_theta0_phi_alpha6(csca_integral,

                                                 nmax,

                                                 lam_f,

                                                 0,

                                                 180,

                                                 ssd.za_grid[za_scat_index],

                                                 0.,

                                                 0.,

                                                 180.,

                                                 90.,

                                                 0.,

                                                 180.);

              csca_integral /= 180.;

            } else {

              // Csca for oblate particles

              integrate_phamat_theta0_phi10(csca_integral,

                                            nmax,

                                            lam_f,

                                            0,

                                            180,

                                            ssd.za_grid[za_scat_index],

                                            0.,

                                            0.,

                                            180,

                                            0.,

                                            0.);

            }

            csca_data(f_index, T_index, za_scat_index, 0, joker) =

                csca_integral(Range(0, 2), 0);

          }


          // Extinction matrix

          if (aspect_ratio < 1.0) {

            // Average T-Matrix for prolate particles

            avgtmatrix_(nmax);

          }


          for (Index za_inc_index = 0; za_inc_index < nza; ++za_inc_index) {

            Complex s11;

            Complex s12;

            Complex s21;

            Complex s22;

            VectorView K =

                ssd.ext_mat_data(f_index, T_index, za_inc_index, 0, joker);


            const Numeric beta = 0.;

            const Numeric alpha = 0.;

            ampl_(nmax,

                  lam_f,

                  ssd.za_grid[za_inc_index],

                  ssd.za_grid[za_inc_index],

                  0.,

                  0.,

                  alpha,

                  beta,

                  s11,

                  s12,

                  s21,

                  s22);


            K[0] = (Complex(0., -1.) * (s11 + s22)).real();

            K[1] = (Complex(0., 1.) * (s22 - s11)).real();

            K[2] = (s22 - s11).real();


            K *= lam_f;

          }

        }

      }


      csca_data *= 2. * PI * PI / 32400.;

      ssd.abs_vec_data =

          ssd.ext_mat_data(joker, joker, joker, joker, Range(0, 2));

      ssd.abs_vec_data -= csca_data;


      break;

    }

    default: {

      std::ostringstream os;

      os << "Only particle types totally_random and azimuthally_random\n"

         << "are currently supported: " << ssd.ptype;

      throw std::runtime_error(os.str());

      break;

    }

  }

}


// Documentation in header file.

void tmatrix_ampld_test(const Verbosity& verbosity) {

  CREATE_OUT0;


  out0 << "======================================================\n";

  out0 << "Test for nonspherical particles in a fixed orientation\n";

  out0 << "Output should match 3rdparty/tmatrix/tmatrix_ampld.ref\n";

  out0 << "======================================================\n";


  // Same inputs as in example included in original ampld.lp.f

  Numeric rat = 1.;

  Numeric axi = 10.;  //[um]

  Index np = -1;

  Numeric lam = acos(-1.) * 2.;  //[um]

  Numeric eps = 0.5;

  Numeric mrr = 1.5;

  Numeric mri = 0.02;

  Numeric ddelt = 0.001;


  Index quiet = 1;


  // Output variables

  Index nmax;

  Numeric csca;

  Numeric cext;

  char errmsg[1024] = "";


  tmatrix_(

      rat, axi, np, lam, eps, mrr, mri, ddelt, quiet, nmax, csca, cext, errmsg);


  out0 << "nmax: " << nmax << "\n";

  out0 << "csca: " << csca << " um2\n";

  out0 << "cext: " << cext << " um2\n";


  out0 << "Error message: " << (strlen(errmsg) ? errmsg : "None") << "\n";


  // Same inputs as in example included in original ampld.lp.f

  Numeric alpha = 145.;

  Numeric beta = 52.;

  Numeric thet0 = 56.;

  Numeric thet = 65.;

  Numeric phi0 = 114.;

  Numeric phi = 128.;


  // Output variables

  Complex s11;

  Complex s12;

  Complex s21;

  Complex s22;

  ampl_(nmax, lam, thet0, thet, phi0, phi, alpha, beta, s11, s12, s21, s22);


  out0 << "AMPLITUDE MATRIX (all in [um]): \n";

  out0 << "s11: " << s11 << "\n";

  out0 << "s12: " << s12 << "\n";

  out0 << "s21: " << s21 << "\n";

  out0 << "s22: " << s22 << "\n";


  Matrix z;

  ampmat_to_phamat(z, s11, s12, s21, s22);

  //z *= 1e12; // meter^2 to micron^2 for comparison with original results


  out0 << "PHASE MATRIX (all un [um2]): \n" << z << "\n";

}


// Documentation in header file.

void tmatrix_tmd_test(const Verbosity& verbosity) {

  CREATE_OUT0;


  out0 << "======================================================\n";

  out0 << "Test for randomly oriented nonspherical particles\n";

  out0 << "Output should match 3rdparty/tmatrix/tmatrix_tmd.ref\n";

  out0 << "======================================================\n";


  // Same inputs as in example included in original tmd.lp.f

  Numeric rat = 0.5;

  Index ndistr = 3;

  Numeric axmax = 1.;  //[um]

  Index npnax = 2;

  Numeric b = 0.1;

  Numeric gam = 0.5;

  Index nkmax = 5;

  Numeric eps = 2;

  Index np = -1;

  Numeric lam = 0.5;  //[um]

  Numeric mrr = 1.53;

  Numeric mri = 0.008;

  Numeric ddelt = 0.001;

  Index npna = 19;

  Index ndgs = 2;

  Numeric r1rat = 0.89031;

  Numeric r2rat = 1.56538;


  Index quiet = 1;


  // Output variables

  Numeric reff;

  Numeric veff;

  Numeric cext;

  Numeric csca;

  Numeric walb;

  Numeric asymm;

  Vector f11(npna, 0.);

  Vector f22(npna, 0.);

  Vector f33(npna, 0.);

  Vector f44(npna, 0.);

  Vector f12(npna, 0.);

  Vector f34(npna, 0.);

  char errmsg[1024] = "";


  tmd_(rat,

       ndistr,

       axmax,

       npnax,

       b,

       gam,

       nkmax,

       eps,

       np,

       lam,

       mrr,

       mri,

       ddelt,

       npna,

       ndgs,

       r1rat,

       r2rat,

       quiet,

       reff,

       veff,

       cext,

       csca,

       walb,

       asymm,

       f11.get_c_array(),

       f22.get_c_array(),

       f33.get_c_array(),

       f44.get_c_array(),

       f12.get_c_array(),

       f34.get_c_array(),

       errmsg);


  out0 << "reff: " << reff << " um\n";

  out0 << "veff: " << veff << "\n";

  out0 << "cext: " << cext << " um2\n";

  out0 << "csca: " << csca << " um2\n";

  out0 << "walb: " << walb << "\n";

  out0 << "asymm: " << asymm << "\n";

  out0 << "f11: " << f11 << "\n";

  out0 << "f22: " << f22 << "\n";

  out0 << "f33: " << f33 << "\n";

  out0 << "f44: " << f44 << "\n";

  out0 << "f12: " << f12 << "\n";

  out0 << "f34: " << f34 << "\n";


  out0 << "Error message: " << (strlen(errmsg) ? errmsg : "None") << "\n";

}


// Documentation in header file.

void calc_ssp_random_test(const Verbosity& verbosity) {

  CREATE_OUT0;

  out0 << "======================================================\n";

  out0 << "Test calculation of single scattering data\n";

  out0 << "for randomly oriented, oblate particles\n";

  out0 << "======================================================\n";


  SingleScatteringData ssd;


  ssd.ptype = PTYPE_TOTAL_RND;

  ssd.f_grid = {230e9, 240e9};

  ssd.T_grid = {220, 250};

  nlinspace(ssd.za_grid, 0, 180, 19);

  nlinspace(ssd.aa_grid, 0, 180, 19);


  // Refractive index real and imagenary parts

  // Dimensions: [nf, nT];

  Matrix mrr(ssd.f_grid.nelem(), ssd.T_grid.nelem(), 1.78031135);

  Matrix mri(ssd.f_grid.nelem(), ssd.T_grid.nelem(), 0.00278706);


  mrr(0, 0) = 1.78031135;

  mrr(0, 1) = 1.78150475;

  mrr(1, 0) = 1.78037238;

  mrr(1, 1) = 1.78147686;


  mri(0, 0) = 0.00278706;

  mri(0, 1) = 0.00507565;

  mri(1, 0) = 0.00287245;

  mri(1, 1) = 0.00523012;


  calcSingleScatteringDataProperties(ssd, mrr, mri, 200.e-6, -1, 1.5);


  out0 << "ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker):\n"

       << ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker) << "\n\n";


  out0 << "ssd.ext_mat_data:\n" << ssd.ext_mat_data << "\n\n";

  out0 << "ssd.abs_vec_data:\n" << ssd.abs_vec_data << "\n\n";


  out0 << "======================================================\n";

  out0 << "Test calculation of single scattering data\n";

  out0 << "for randomly oriented, prolate particles\n";

  out0 << "======================================================\n";


  calcSingleScatteringDataProperties(ssd, mrr, mri, 200.e-6, -1, 0.7);


  out0 << "ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker):\n"

       << ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker) << "\n\n";


  out0 << "ssd.ext_mat_data:\n" << ssd.ext_mat_data << "\n\n";

  out0 << "ssd.abs_vec_data:\n" << ssd.abs_vec_data << "\n\n";

}


// Documentation in header file.

void calc_ssp_fixed_test(const Verbosity& verbosity) {

  CREATE_OUT0;

  out0 << "======================================================\n";

  out0 << "Test calculation of single scattering data\n";

  out0 << "for oblate particles with fixed orientation\n";

  out0 << "======================================================\n";


  SingleScatteringData ssd;


  ssd.ptype = PTYPE_AZIMUTH_RND;

  ssd.f_grid = {230e9, 240e9};

  ssd.T_grid = {220, 250};

  nlinspace(ssd.za_grid, 0, 180, 19);

  nlinspace(ssd.aa_grid, 0, 180, 19);


  // Refractive index real and imagenary parts

  // Dimensions: [nf, nT];

  Matrix mrr(ssd.f_grid.nelem(), ssd.T_grid.nelem(), 1.78031135);

  Matrix mri(ssd.f_grid.nelem(), ssd.T_grid.nelem(), 0.00278706);


  mrr(0, 0) = 1.78031135;

  mrr(0, 1) = 1.78150475;

  mrr(1, 0) = 1.78037238;

  mrr(1, 1) = 1.78147686;


  mri(0, 0) = 0.00278706;

  mri(0, 1) = 0.00507565;

  mri(1, 0) = 0.00287245;

  mri(1, 1) = 0.00523012;


  calcSingleScatteringDataProperties(ssd, mrr, mri, 200.e-6, -1, 1.5);


  out0 << "ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker):\n"

       << ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker) << "\n\n";


  out0 << "ssd.ext_mat_data(0, 0, joker, joker, joker):\n"

       << ssd.ext_mat_data(0, 0, joker, joker, joker) << "\n\n";


  out0 << "abs_vec_data:\n" << ssd.abs_vec_data << "\n\n";


  out0 << "======================================================\n";

  out0 << "Test calculation of single scattering data\n";

  out0 << "for prolate particles with fixed orientation\n";

  out0 << "======================================================\n";

  calcSingleScatteringDataProperties(ssd, mrr, mri, 200.e-6, -1, 0.7);


  out0 << "ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker):\n"

       << ssd.pha_mat_data(0, 0, joker, 0, 0, joker, joker) << "\n\n";


  out0 << "ssd.ext_mat_data(0, 0, joker, joker, joker):\n"

       << ssd.ext_mat_data(0, 0, joker, joker, joker) << "\n\n";


  out0 << "abs_vec_data:\n" << ssd.abs_vec_data << "\n\n";

}

SPEED_OF_LIGHT
const Numeric SPEED_OF_LIGHT

ConstMatrixView
A constant view of a Matrix.
Definition: matpackI.h:1014

ConstMatrixView::nrows
Index nrows() const ARTS_NOEXCEPT
Returns the number of rows.
Definition: matpackI.cc:433

ConstMatrixView::ncols
Index ncols() const ARTS_NOEXCEPT
Returns the number of columns.
Definition: matpackI.cc:436

ConstVectorView::nelem
Index nelem() const ARTS_NOEXCEPT
Returns the number of elements.
Definition: matpackI.cc:48

Matrix
The Matrix class.
Definition: matpackI.h:1225

Matrix::resize
void resize(Index r, Index c)
Resize function.
Definition: matpackI.cc:1056

Range
The range class.
Definition: matpackI.h:165

Tensor5
The Tensor5 class.
Definition: matpackV.h:506

Tensor5::resize
void resize(Index s, Index b, Index p, Index r, Index c)
Resize function.
Definition: matpackV.cc:1741

Tensor7::resize
void resize(Index l, Index v, Index s, Index b, Index p, Index r, Index c)
Resize function.
Definition: matpackVII.cc:5482

VectorView
The VectorView class.
Definition: matpackI.h:626

VectorView::get_c_array
const Numeric * get_c_array() const ARTS_NOEXCEPT
Conversion to plain C-array, const-version.
Definition: matpackI.cc:271

Vector
The Vector class.
Definition: matpackI.h:876

Vector::resize
void resize(Index n)
Resize function.
Definition: matpackI.cc:408

Verbosity
Definition: messages.h:49

PI
const Numeric PI
Global constant, pi.

beta
#define beta
Definition: legacy_continua.cc:21376

precision
#define precision
Definition: logic.cc:43

nlinspace
void nlinspace(Vector &x, const Numeric start, const Numeric stop, const Index n)
nlinspace
Definition: math_funcs.cc:225

math_funcs.h

matpackI.h
Implementation of Matrix, Vector, and such stuff.

Index
INDEX Index
The type to use for all integer numbers and indices.
Definition: matpack.h:39

Numeric
NUMERIC Numeric
The type to use for all floating point numbers.
Definition: matpack.h:33

matpack_complex.h

joker
const Joker joker

conj
constexpr Complex conj(Complex c) noexcept
the conjugate of c
Definition: matpack_complex.h:80

Complex
std::complex< Numeric > Complex
Definition: matpack_complex.h:35

real
constexpr Numeric real(Complex c) noexcept
real
Definition: matpack_complex.h:83

messages.h
Declarations having to do with the four output streams.

CREATE_OUT0
#define CREATE_OUT0
Definition: messages.h:204

optproperties.h
Scattering database structure and functions.

PTYPE_AZIMUTH_RND
@ PTYPE_AZIMUTH_RND
Definition: optproperties.h:54

PTYPE_TOTAL_RND
@ PTYPE_TOTAL_RND
Definition: optproperties.h:55

c
#define c

b
#define b

SingleScatteringData
Definition: optproperties.h:79

SingleScatteringData::pha_mat_data
Tensor7 pha_mat_data
Definition: optproperties.h:86

SingleScatteringData::ptype
PType ptype
Definition: optproperties.h:80

SingleScatteringData::ext_mat_data
Tensor5 ext_mat_data
Definition: optproperties.h:87

SingleScatteringData::f_grid
Vector f_grid
Definition: optproperties.h:82

SingleScatteringData::za_grid
Vector za_grid
Definition: optproperties.h:84

SingleScatteringData::aa_grid
Vector aa_grid
Definition: optproperties.h:85

SingleScatteringData::abs_vec_data
Tensor5 abs_vec_data
Definition: optproperties.h:88

SingleScatteringData::T_grid
Vector T_grid
Definition: optproperties.h:83

calc_ssp_fixed_test
void calc_ssp_fixed_test(const Verbosity &verbosity)
Single scattering properties calculation for particles with fixed orientation.
Definition: tmatrix.cc:1507

calcSingleScatteringDataProperties
void calcSingleScatteringDataProperties(SingleScatteringData &ssd, ConstMatrixView ref_index_real, ConstMatrixView ref_index_imag, const Numeric equiv_radius, const Index np, const Numeric aspect_ratio, const Numeric precision, const Index ndgs, const Index robust, const Index quiet)
Calculate SingleScatteringData properties.
Definition: tmatrix.cc:979

integrate_phamat_alpha6
void integrate_phamat_alpha6(Matrix &phamat, const Index &nmax, const Numeric &lam, const Numeric &thet0, const Numeric &thet, const Numeric &phi0, const Numeric &phi, const Numeric &beta, const Numeric &alpha_1, const Numeric &alpha_2)
Integrate phase matrix over particle orientation angle.
Definition: tmatrix.cc:560

tmatrix_fixed_orientation
void tmatrix_fixed_orientation(Numeric &cext, Numeric &csca, Index &nmax, const Numeric equiv_radius, const Numeric aspect_ratio, const Index np, const Numeric lam, const Numeric ref_index_real, const Numeric ref_index_imag, const Numeric precision, const Index quiet=1)
Calculate properties for particles in a fixed orientation.
Definition: tmatrix.cc:941

calc_phamat
void calc_phamat(Matrix &z, const Index &nmax, const Numeric &lam, const Numeric &thet0, const Numeric &thet, const Numeric &phi0, const Numeric &phi, const Numeric &beta, const Numeric &alpha)
Definition: tmatrix.cc:419

tmatrix_random_orientation
void tmatrix_random_orientation(Numeric &cext, Numeric &csca, Vector &f11, Vector &f22, Vector &f33, Vector &f44, Vector &f12, Vector &f34, const Numeric equiv_radius, const Numeric aspect_ratio, const Index np, const Numeric lam, const Numeric ref_index_real, const Numeric ref_index_imag, const Numeric precision, const Index nza, const Index ndgs, const Index quiet=1)
Calculate properties for randomly oriented particles.
Definition: tmatrix.cc:843

tmatrix_tmd_test
void tmatrix_tmd_test(const Verbosity &verbosity)
T-Matrix validation test.
Definition: tmatrix.cc:1361

tmatrix_
void tmatrix_(const Numeric &rat, const Numeric &axi, const Index &np, const Numeric &lam, const Numeric &eps, const Numeric &mrr, const Numeric &mri, const Numeric &ddelt, const Index &quiet, Index &nmax, Numeric &csca, Numeric &cext, char *errmsg)
T-matrix code for nonspherical particles in a fixed orientation.
Definition: tmatrix.cc:378

calc_ssp_random_test
void calc_ssp_random_test(const Verbosity &verbosity)
Single scattering properties calculation for randomly oriented particles.
Definition: tmatrix.cc:1454

avgtmatrix_
void avgtmatrix_(const Index &nmax)
Perform orientation averaging.
Definition: tmatrix.cc:412

tmatrix_ampld_test
void tmatrix_ampld_test(const Verbosity &verbosity)
T-Matrix validation test.
Definition: tmatrix.cc:1297

ampl_
void ampl_(const Index &nmax, const Numeric &lam, const Numeric &thet0, const Numeric &thet, const Numeric &phi0, const Numeric &phi, const Numeric &alpha, const Numeric &beta, Complex &s11, Complex &s12, Complex &s21, Complex &s22)
T-matrix code for nonspherical particles in a fixed orientation.
Definition: tmatrix.cc:396

tmd_
void tmd_(const Numeric &rat, const Index &ndistr, const Numeric &axmax, const Index &npnax, const Numeric &b, const Numeric &gam, const Index &nkmax, const Numeric &eps, const Index &np, const Numeric &lam, const Numeric &mrr, const Numeric &mri, const Numeric &ddelt, const Index &npna, const Index &ndgs, const Numeric &r1rat, const Numeric &r2rat, const Index &quiet, Numeric &reff, Numeric &veff, Numeric &cext, Numeric &csca, Numeric &walb, Numeric &asymm, Numeric *f11, Numeric *f22, Numeric *f33, Numeric *f44, Numeric *f12, Numeric *f34, char *errmsg)
T-matrix code for randomly oriented nonspherical particles.
Definition: tmatrix.cc:342

integrate_phamat_alpha10
void integrate_phamat_alpha10(Matrix &phamat, const Index &nmax, const Numeric &lam, const Numeric &thet0, const Numeric &thet, const Numeric &phi0, const Numeric &phi, const Numeric &beta, const Numeric &alpha_1, const Numeric &alpha_2)
Integrate phase matrix over particle orientation angle.
Definition: tmatrix.cc:510

ampmat_to_phamat
void ampmat_to_phamat(Matrix &z, const Complex &s11, const Complex &s12, const Complex &s21, const Complex &s22)
Calculate phase matrix from amplitude matrix.
Definition: tmatrix.cc:450

integrate_phamat_theta0_phi10
void integrate_phamat_theta0_phi10(Matrix &phamat, const Index &nmax, const Numeric &lam, const Numeric &thet0_1, const Numeric &thet0_2, const Numeric &thet, const Numeric &phi0, const Numeric &phi_1, const Numeric &phi_2, const Numeric &beta, const Numeric &alpha)
Integrate phase matrix over angles thet0 and phi.
Definition: tmatrix.cc:612

integrate_phamat_theta0_phi_alpha6
void integrate_phamat_theta0_phi_alpha6(Matrix &phamat, const Index &nmax, const Numeric &lam, const Numeric &thet0_1, const Numeric &thet0_2, const Numeric &thet, const Numeric &phi0, const Numeric &phi_1, const Numeric &phi_2, const Numeric &beta, const Numeric &alpha_1, const Numeric &alpha_2)
Integrate phase matrix over angles thet0, phi and alpha.
Definition: tmatrix.cc:723

tmatrix.h
Declarations for the T-Matrix interface.