LegendrePolynomial.hpp

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 * [1] Drisko et al., J. Open Source Softw. 9, 7004 (2024).
 *
 * Good starting points for code and simulation methodology are:
 *
 * [2] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
 * [3] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
 * [4] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
 * [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 * [6] Kuang & Gezelter, Mol. Phys., 110, 691-701 (2012).
 * [7] Lamichhane, Gezelter & Newman, J. Chem. Phys. 141, 134109 (2014).
 * [8] Bhattarai, Newman & Gezelter, Phys. Rev. B 99, 094106 (2019).
 * [9] Drisko & Gezelter, J. Chem. Theory Comput. 20, 4986-4997 (2024).
 */
 
/**
 * @file LegendrePolynomial.hpp
 * @author    teng lin
 * @date  11/16/2004
 * @version 1.0
 */
 
#ifndef MATH_LEGENDREPOLYNOMIALS_HPP
#define MATH_LEGENDREPOLYNOMIALS_HPP
 
#include <cassert>
#include <vector>
 
#include "math/Polynomial.hpp"
 
namespace OpenMD {
 
  /**
   * @class LegendrePolynomial
   * A collection of Legendre Polynomials.
   * @todo document
   */
  class LegendrePolynomial {
  public:
    LegendrePolynomial(int maxPower);
    virtual ~LegendrePolynomial() {}
    /**
     * Calculates the value of the nth Legendre Polynomial evaluated at the
     * given x value.
     * @return The value of the nth Legendre Polynomial evaluates at the given x
     * value
     * @param n
     * @param x the value of the independent variable for the nth Legendre
     * Polynomial  function
     */
 
    RealType evaluate(int n, RealType x) {
      assert(n <= maxPower_ && n >= 0);
      return polyList_[n].evaluate(x);
    }
 
    /**
     * Returns the first derivative of the nth Legendre Polynomial.
     * @return the first derivative of the nth Legendre Polynomial
     * @param n
     * @param x the value of the independent variable for the nth Legendre
     * Polynomial  function
     */
    RealType evaluateDerivative(int n, RealType x) {
      assert(n <= maxPower_ && n >= 0);
      return polyList_[n].evaluateDerivative(x);
    }
 
    /**
     * Returns the nth Legendre Polynomial
     * @return the nth Legendre Polynomial
     * @param n
     */
    const DoublePolynomial& getLegendrePolynomial(int n) const {
      assert(n <= maxPower_ && n >= 0);
      return polyList_[n];
    }
 
  protected:
    std::vector<DoublePolynomial> polyList_;
 
  private:
    void GeneratePolynomials(int maxPower);
    virtual void GenerateFirstTwoTerms();
 
    int maxPower_;
  };
}  // namespace OpenMD
 
#endif