sphericalHarmonicUtils.h

Go to the documentation of this file.

// ---------------------------------------------------------------------
//
// Copyright (c) 2017-2025 The Regents of the University of Michigan and DFT-FE
// authors.
//
// This file is part of the DFT-FE code.
//
// The DFT-FE code is free software; you can use it, 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 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the DFT-FE distribution.
//
// ---------------------------------------------------------------------
//
// @author  Vishal Subramanian, Kartick Ramakrishnan, Sambit Das
//
#ifndef DFTFE_SPHERICALHARMONICUTILS_H
#define DFTFE_SPHERICALHARMONICUTILS_H
#include <interpolation.h>
namespace dftfe
{
  namespace sphericalHarmonicUtils
  {
    inline void
    getRadialFunctionVal(const double                       radialCoordinate,
                         double &                           splineVal,
                         const alglib::spline1dinterpolant *spline)
    {
      splineVal = alglib::spline1dcalc(*spline, radialCoordinate);
      return;
    }
 
    inline void
    getSphericalHarmonicVal(const double theta,
                            const double phi,
                            const int    l,
                            const int    m,
                            double &     sphericalHarmonicVal)
    {
      if (m < 0)
        sphericalHarmonicVal =
          std::sqrt(2.0) * boost::math::spherical_harmonic_i(l, -m, theta, phi);
 
      else if (m == 0)
        sphericalHarmonicVal =
          boost::math::spherical_harmonic_r(l, m, theta, phi);
 
      else if (m > 0)
        sphericalHarmonicVal =
          std::sqrt(2.0) * boost::math::spherical_harmonic_r(l, m, theta, phi);
 
      return;
    }
 
    inline void
    convertCartesianToSpherical(double *x,
                                double &r,
                                double &theta,
                                double &phi)
    {
      double tolerance = 1e-12;
      r                = std::sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
 
      if (std::fabs(r - 0.0) <= tolerance)
        {
          theta = 0.0;
          phi   = 0.0;
        }
      else
        {
          theta = std::acos(x[2] / r);
          //
          // check if theta = 0 or PI (i.e, whether the point is on the Z-axis)
          // If yes, assign phi = 0.0.
          // NOTE: In case theta = 0 or PI, phi is undetermined. The actual
          // value of phi doesn't matter in computing the enriched function
          // value or its gradient. We assign phi = 0.0 here just as a dummy
          // value
          //
          if (fabs(theta - 0.0) >= tolerance && fabs(theta - M_PI) >= tolerance)
            phi = std::atan2(x[1], x[0]);
          else
            phi = 0.0;
        }
    }
  } // end of namespace sphericalHarmonicUtils
} // end of namespace dftfe
#endif // DFTFE_SPHERICALHARMONICUTILS_H