LegendrePolynomial.cpp

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 * work.  Good starting points are:
 *
 * [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
 * [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
 * [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
 * [4] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 * [5] Kuang & Gezelter, Mol. Phys., 110, 691-701 (2012).
 * [6] Lamichhane, Gezelter & Newman, J. Chem. Phys. 141, 134109 (2014).
 * [7] Lamichhane, Newman & Gezelter, J. Chem. Phys. 141, 134110 (2014).
 * [8] Bhattarai, Newman & Gezelter, Phys. Rev. B 99, 094106 (2019).
 */
 
#include "math/LegendrePolynomial.hpp"
 
namespace OpenMD {
  LegendrePolynomial::LegendrePolynomial(int maxPower) : maxPower_(maxPower) {
    assert(maxPower >= 0);
    GeneratePolynomials(maxPower_);
  }
 
  void LegendrePolynomial::GeneratePolynomials(int maxPower) {
    GenerateFirstTwoTerms();
 
    DoublePolynomial x;
    x.setCoefficient(1, 1.0);
 
    // recursive generate the high order term of Legendre Polynomials
    // P_{l+1}= \frac{(2l+1)(x)P_l-l P_{l-1}{l+1}
    for (int i = 2; i <= maxPower; ++i) {
      DoublePolynomial pn;
      RealType tmp1 = (2.0 * i - 1.0) / i;
      RealType tmp2 = (i - 1.0) / i;
      pn            = polyList_[i - 1] * x * tmp1 - polyList_[i - 2] * tmp2;
      polyList_.push_back(pn);
    }
  }
 
  void LegendrePolynomial::GenerateFirstTwoTerms() {
    DoublePolynomial p0;
    p0.setCoefficient(0, 1.0);
    polyList_.push_back(p0);
 
    DoublePolynomial p1;
    p1.setCoefficient(1, 1.0);
    polyList_.push_back(p1);
  }
 
}  // namespace OpenMD