BicubicInterpolation.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 "MooseTypes.h"
#include "BidimensionalInterpolation.h"

class BicubicInterpolation : public BidimensionalInterpolation
{
public:
  BicubicInterpolation(const std::vector<Real> & x1,
                       const std::vector<Real> & x2,
                       const std::vector<std::vector<Real>> & y);

  virtual ~BicubicInterpolation() = default;

  void errorCheck();

  Real sample(const Real x1, const Real x2) const override;
  ADReal sample(const ADReal & x1, const ADReal & x2) const override;
  ChainedReal sample(const ChainedReal & x1, const ChainedReal & x2) const override;

  using BidimensionalInterpolation::sampleValueAndDerivatives;
  virtual void
  sampleValueAndDerivatives(Real x1, Real x2, Real & y, Real & dy1, Real & dy2) const override;
  virtual void sampleValueAndDerivatives(
      const ADReal & x1, const ADReal & x2, ADReal & y, ADReal & dy1, ADReal & dy2) const override;
  virtual void sampleValueAndDerivatives(const ChainedReal & x1,
                                         const ChainedReal & x2,
                                         ChainedReal & y,
                                         ChainedReal & dy1,
                                         ChainedReal & dy2) const override;

  using BidimensionalInterpolation::sampleDerivative;
  Real sampleDerivative(Real x1, Real x2, unsigned int deriv_var) const override;

  Real sample2ndDerivative(Real x1, Real x2, unsigned int deriv_var) const override;

  void precomputeCoefficients();

protected:
  template <typename T>
  void findInterval(const std::vector<Real> & x,
                    const T & xi,
                    unsigned int & klo,
                    unsigned int & khi,
                    T & xs) const;

  template <typename T>
  T sampleInternal(const T & x1, const T & x2) const;

  template <typename T>
  void sampleValueAndDerivativesInternal(T x1, T x2, T & y, T & dy1, T & dy2) const;

  void tableDerivatives(std::vector<std::vector<Real>> & dy_dx1,
                        std::vector<std::vector<Real>> & dy_dx2,
                        std::vector<std::vector<Real>> & d2y_dx1x2);

  std::vector<std::vector<Real>> _y;

  std::vector<std::vector<std::vector<std::vector<Real>>>> _bicubic_coeffs;

  const std::vector<std::vector<int>> _wt{
      {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
      {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
      {-3, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0},
      {2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0},
      {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
      {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
      {0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, -1},
      {0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 1},
      {-3, 3, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
      {0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, -2, -1, 0, 0},
      {9, -9, 9, -9, 6, 3, -3, -6, 6, -6, -3, 3, 4, 2, 1, 2},
      {-6, 6, -6, 6, -4, -2, 2, 4, -3, 3, 3, -3, -2, -1, -1, -2},
      {2, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
      {0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 1, 1, 0, 0},
      {-6, 6, -6, 6, -3, -3, 3, 3, -4, 4, 2, -2, -2, -2, -1, -1},
      {4, -4, 4, -4, 2, 2, -2, -2, 2, -2, -2, 2, 1, 1, 1, 1}};
};