MonotoneCubicInterpolation.h

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//* This file is part of the MOOSE framework
//* https://www.mooseframework.org
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include <vector>

#include "libmesh/libmesh_common.h"

using libMesh::Real;

class MonotoneCubicInterpolation
{
public:
  MonotoneCubicInterpolation();

  MonotoneCubicInterpolation(const std::vector<Real> & x, const std::vector<Real> & y);

  virtual ~MonotoneCubicInterpolation() = default;

  virtual void setData(const std::vector<Real> & x, const std::vector<Real> & y);

  virtual Real sample(const Real & x) const;

  virtual Real sampleDerivative(const Real & x) const;

  virtual Real sample2ndDerivative(const Real & x) const;

  virtual void dumpCSV(std::string filename, const std::vector<Real> & xnew);

  virtual unsigned int getSampleSize();

protected:
  // Error check routines run during initialization
  virtual void errorCheck();
  Real sign(const Real & x) const;

  // Building blocks of Hermite polynomials
  Real phi(const Real & t) const;
  Real psi(const Real & t) const;
  Real phiPrime(const Real & t) const;
  Real psiPrime(const Real & t) const;
  Real phiDoublePrime(const Real & t) const;
  Real psiDoublePrime(const Real & t) const;

  // Cubic Hermite polynomials
  Real h1(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h2(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h3(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h4(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h1Prime(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h2Prime(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h3Prime(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h4Prime(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h1DoublePrime(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h2DoublePrime(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h3DoublePrime(const Real & xhi, const Real & xlo, const Real & x) const;
  Real h4DoublePrime(const Real & xhi, const Real & xlo, const Real & x) const;

  // Interpolating cubic polynomial and derivatives
  virtual Real p(const Real & xhi,
                 const Real & xlo,
                 const Real & fhi,
                 const Real & flo,
                 const Real & dhi,
                 const Real & dlo,
                 const Real & x) const;
  virtual Real pPrime(const Real & xhi,
                      const Real & xlo,
                      const Real & fhi,
                      const Real & flo,
                      const Real & dhi,
                      const Real & dlo,
                      const Real & x) const;
  virtual Real pDoublePrime(const Real & xhi,
                            const Real & xlo,
                            const Real & fhi,
                            const Real & flo,
                            const Real & dhi,
                            const Real & dlo,
                            const Real & x) const;

  // Algorithm routines
  virtual void initialize_derivs();
  virtual void modify_derivs(
      const Real & alpha, const Real & beta, const Real & delta, Real & yp_lo, Real & yp_hi);
  virtual void solve();
  virtual void findInterval(const Real & x, unsigned int & klo, unsigned int & khi) const;

  std::vector<Real> _x;
  std::vector<Real> _y;
  std::vector<Real> _h;
  std::vector<Real> _yp;
  std::vector<Real> _delta;
  std::vector<Real> _alpha;
  std::vector<Real> _beta;

  unsigned int _n_knots;
  unsigned int _n_intervals;
  unsigned int _internal_knots;
};