LinearInterpolation.C

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
//* 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

#include "LinearInterpolation.h"
#include "MooseUtils.h"

#include "ChainedReal.h"

#include <cassert>
#include <fstream>
#include <stdexcept>

LinearInterpolation::LinearInterpolation(const std::vector<Real> & x,
                                         const std::vector<Real> & y,
                                         const bool extrap)
  : _x(x), _y(y), _extrap(extrap)
{
  errorCheck();
}

void
LinearInterpolation::errorCheck()
{
  if (_x.size() != _y.size())
    throw std::domain_error("Vectors are not the same length");

  for (unsigned int i = 0; i + 1 < _x.size(); ++i)
    if (_x[i] >= _x[i + 1])
    {
      std::ostringstream oss;
      oss << "x-values are not strictly increasing: x[" << i << "]: " << _x[i] << " x[" << i + 1
          << "]: " << _x[i + 1];
      throw std::domain_error(oss.str());
    }
}

template <typename T>
T
LinearInterpolation::sample(const T & x) const
{
  // this is a hard error
  if (_x.empty())
    mooseError("Trying to evaluate an empty LinearInterpolation");

  // special case for single function nodes
  if (_x.size() == 1)
    return _y[0];

  // endpoint cases
  if (_extrap)
  {
    if (x < _x[0])
      return _y[0] + (x - _x[0]) / (_x[1] - _x[0]) * (_y[1] - _y[0]);
    if (x >= _x.back())
      return _y.back() +
             (x - _x.back()) / (_x[_x.size() - 2] - _x.back()) * (_y[_y.size() - 2] - _y.back());
  }
  else
  {
    if (x < _x[0])
      return _y[0];
    if (x >= _x.back())
      return _y.back();
  }

  auto upper = std::upper_bound(_x.begin(), _x.end(), x);
  const auto i = cast_int<std::size_t>(std::distance(_x.begin(), upper) - 1);
  if (i == cast_int<std::size_t>(_x.size() - 1))
    // std::upper_bound returns the end() iterator if there are no elements that are
    // an upper bound to the value. Since x >= _x.back() has already returned above,
    // this means x is a NaN, so we return a NaN here.
    return std::nan("");
  else
    return _y[i] + (_y[i + 1] - _y[i]) * (x - _x[i]) / (_x[i + 1] - _x[i]);
}

template Real LinearInterpolation::sample<Real>(const Real &) const;
template ADReal LinearInterpolation::sample<ADReal>(const ADReal &) const;
template ChainedReal LinearInterpolation::sample<ChainedReal>(const ChainedReal &) const;

template <typename T>
T
LinearInterpolation::sampleDerivative(const T & x) const
{
  // endpoint cases
  if (_extrap)
  {
    if (x <= _x[0])
      return (_y[1] - _y[0]) / (_x[1] - _x[0]);
    if (x >= _x.back())
      return (_y[_y.size() - 2] - _y.back()) / (_x[_x.size() - 2] - _x.back());
  }
  else
  {
    if (x < _x[0])
      return 0.0;
    if (x >= _x.back())
      return 0.0;
  }

  auto upper = std::upper_bound(_x.begin(), _x.end(), x);
  const auto i = cast_int<std::size_t>(std::distance(_x.begin(), upper) - 1);
  if (i == cast_int<std::size_t>(_x.size() - 1))
    // std::upper_bound returns the end() iterator if there are no elements that are
    // an upper bound to the value. Since x >= _x.back() has already returned above,
    // this means x is a NaN, so we return a NaN here.
    return std::nan("");
  else
    return (_y[i + 1] - _y[i]) / (_x[i + 1] - _x[i]);
}

template Real LinearInterpolation::sampleDerivative<Real>(const Real &) const;
template ADReal LinearInterpolation::sampleDerivative<ADReal>(const ADReal &) const;
template ChainedReal LinearInterpolation::sampleDerivative<ChainedReal>(const ChainedReal &) const;

Real
LinearInterpolation::integrate()
{
  Real answer = 0;
  for (unsigned int i = 1; i < _x.size(); ++i)
    answer += 0.5 * (_y[i] + _y[i - 1]) * (_x[i] - _x[i - 1]);

  return answer;
}

Real
LinearInterpolation::integratePartial(Real xA, Real xB) const
{
  // integral computation below will assume that x2 > x1; if this is not the
  // case, compute as if it is and then use identity to convert
  Real x1, x2;
  bool switch_bounds;
  if (MooseUtils::absoluteFuzzyEqual(xA, xB))
    return 0.0;
  else if (xB > xA)
  {
    x1 = xA;
    x2 = xB;
    switch_bounds = false;
  }
  else
  {
    x1 = xB;
    x2 = xA;
    switch_bounds = true;
  }

  // compute integral with knowledge that x2 > x1
  Real integral = 0.0;
  // find minimum i : x[i] > x; if x > x[n-1], i = n
  auto n = _x.size();
  const unsigned int i1 =
      x1 <= _x[n - 1] ? std::distance(_x.begin(), std::upper_bound(_x.begin(), _x.end(), x1)) : n;
  const unsigned int i2 =
      x2 <= _x[n - 1] ? std::distance(_x.begin(), std::upper_bound(_x.begin(), _x.end(), x2)) : n;
  unsigned int i = i1;
  while (i <= i2)
  {
    if (i == 0)
    {
      // note i1 = i
      Real integral1, integral2;
      if (_extrap)
      {
        const Real dydx = (_y[1] - _y[0]) / (_x[1] - _x[0]);
        const Real y1 = _y[0] + dydx * (x1 - _x[0]);
        integral1 = 0.5 * (y1 + _y[0]) * (_x[0] - x1);
        if (i2 == i)
        {
          const Real y2 = _y[0] + dydx * (x2 - _x[0]);
          integral2 = 0.5 * (y2 + _y[0]) * (_x[0] - x2);
        }
        else
          integral2 = 0.0;
      }
      else
      {
        integral1 = _y[0] * (_x[0] - x1);
        if (i2 == i)
          integral2 = _y[0] * (_x[0] - x2);
        else
          integral2 = 0.0;
      }

      integral += integral1 - integral2;
    }
    else if (i == n)
    {
      // note i2 = i
      Real integral1, integral2;
      if (_extrap)
      {
        const Real dydx = (_y[n - 1] - _y[n - 2]) / (_x[n - 1] - _x[n - 2]);
        const Real y2 = _y[n - 1] + dydx * (x2 - _x[n - 1]);
        integral2 = 0.5 * (y2 + _y[n - 1]) * (x2 - _x[n - 1]);
        if (i1 == n)
        {
          const Real y1 = _y[n - 1] + dydx * (x1 - _x[n - 1]);
          integral1 = 0.5 * (y1 + _y[n - 1]) * (x1 - _x[n - 1]);
        }
        else
          integral1 = 0.0;
      }
      else
      {
        integral2 = _y[n - 1] * (x2 - _x[n - 1]);
        if (i1 == n)
          integral1 = _y[n - 1] * (x1 - _x[n - 1]);
        else
          integral1 = 0.0;
      }

      integral += integral2 - integral1;
    }
    else
    {
      Real integral1;
      if (i == i1)
      {
        const Real dydx = (_y[i] - _y[i - 1]) / (_x[i] - _x[i - 1]);
        const Real y1 = _y[i - 1] + dydx * (x1 - _x[i - 1]);
        integral1 = 0.5 * (y1 + _y[i - 1]) * (x1 - _x[i - 1]);
      }
      else
        integral1 = 0.0;

      Real integral2;
      if (i == i2)
      {
        const Real dydx = (_y[i] - _y[i - 1]) / (_x[i] - _x[i - 1]);
        const Real y2 = _y[i - 1] + dydx * (x2 - _x[i - 1]);
        integral2 = 0.5 * (y2 + _y[i - 1]) * (x2 - _x[i - 1]);
      }
      else
        integral2 = 0.5 * (_y[i] + _y[i - 1]) * (_x[i] - _x[i - 1]);

      integral += integral2 - integral1;
    }

    i++;
  }

  // apply identity if bounds were switched
  if (switch_bounds)
    return -1.0 * integral;
  else
    return integral;
}

Real
LinearInterpolation::domain(int i) const
{
  return _x[i];
}

Real
LinearInterpolation::range(int i) const
{
  return _y[i];
}

unsigned int
LinearInterpolation::getSampleSize() const
{
  return _x.size();
}