interpolation.h

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/*
 *
 *    Copyright (c) 2014-2020
 *      SMASH Team
 *
 *    GNU General Public License (GPLv3 or later)
 *
 */
 
#ifndef SRC_INCLUDE_SMASH_INTERPOLATION_H_
#define SRC_INCLUDE_SMASH_INTERPOLATION_H_
 
#include <gsl/gsl_errno.h>
#include <gsl/gsl_spline.h>
 
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <numeric>
#include <sstream>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>
 
namespace smash {
 
template <typename T>
class InterpolateLinear {
 public:
  T slope_;
  T yintercept_;
  InterpolateLinear(T x0, T y0, T x1, T y1);
 
  T operator()(T x) const;
};
 
template <typename T>
class InterpolateDataLinear {
 public:
  InterpolateDataLinear(const std::vector<T>& x, const std::vector<T>& y);
  T operator()(T x) const;
 
 private:
  std::vector<T> x_;
  std::vector<InterpolateLinear<T>> f_;
};
 
template <typename T>
InterpolateLinear<T>::InterpolateLinear(T x0, T y0, T x1, T y1) {
  assert(x0 != x1);
  slope_ = (y1 - y0) / (x1 - x0);
  yintercept_ = y0 - slope_ * x0;
}
 
template <typename T>
T InterpolateLinear<T>::operator()(T x) const {
  return slope_ * x + yintercept_;
}
 
template <typename T>
T interpolate_trilinear(T ax, T ay, T az, T f1, T f2, T f3, T f4, T f5, T f6,
                        T f7, T f8) {
  T res = az * (ax * (ay * f8 + (1.0 - ay) * f6) +
                (1.0 - ax) * (ay * f7 + (1.0 - ay) * f5)) +
          (1 - az) * (ax * (ay * f4 + (1.0 - ay) * f2) +
                      (1.0 - ax) * (ay * f3 + (1.0 - ay) * f1));
  return res;
}
 
using Permutation = std::vector<size_t>;
 
template <typename T, typename Cmp>
Permutation generate_sort_permutation(std::vector<T> const& v, Cmp compare) {
  Permutation p(v.size());
  std::iota(p.begin(), p.end(), 0);
  std::sort(p.begin(), p.end(),
            [&](size_t i, size_t j) { return compare(v[i], v[j]); });
  return p;
}
 
template <typename T>
std::vector<T> apply_permutation(const std::vector<T>& v,
                                 const Permutation& p) {
  std::vector<T> copied_v = v;
  std::transform(p.begin(), p.end(), copied_v.begin(),
                 [&](size_t i) { return v[i]; });
  return copied_v;
}
 
template <typename T>
void check_duplicates(const std::vector<T>& x,
                      const std::string& error_position) {
  auto it = std::adjacent_find(x.begin(), x.end());
  if (it != x.end()) {
    std::stringstream error_msg;
    error_msg << error_position << ": Each x value must be unique. \"" << *it
              << "\" was found twice.";
    throw std::runtime_error(error_msg.str());
  }
}
 
template <typename T>
InterpolateDataLinear<T>::InterpolateDataLinear(const std::vector<T>& x,
                                                const std::vector<T>& y) {
  assert(x.size() == y.size());
  const size_t n = x.size();
  const auto p = generate_sort_permutation(
      x, [&](T const& a, T const& b) { return a < b; });
  x_ = apply_permutation(x, p);
  check_duplicates(x_, "InterpolateDataLinear");
  std::vector<T> y_sorted = std::move(apply_permutation(y, p));
  f_.reserve(n - 1);
  for (size_t i = 0; i < n - 1; i++) {
    f_.emplace_back(
        InterpolateLinear<T>(x_[i], y_sorted[i], x_[i + 1], y_sorted[i + 1]));
  }
}
 
template <typename T>
size_t find_index(const std::vector<T>& v, T x) {
  const auto it = std::lower_bound(v.begin(), v.end(), x);
  if (it == v.begin()) {
    return 0;
  } else {
    return it - 1 - v.begin();
  }
}
 
template <typename T>
T InterpolateDataLinear<T>::operator()(T x0) const {
  // Find the piecewise linear interpolation corresponding to x0.
  size_t i = find_index(x_, x0);
  if (i >= f_.size()) {
    // We don't have a linear interpolation beyond the last point in x_.
    // Use the last linear interpolation instead.
    i = f_.size() - 1;
  }
  return f_[i](x0);
}
 
class InterpolateDataSpline {
 public:
  InterpolateDataSpline(const std::vector<double>& x,
                        const std::vector<double>& y);
 
  ~InterpolateDataSpline();
 
  double operator()(double x) const;
 
 private:
  double first_x_;
  double last_x_;
  double first_y_;
  double last_y_;
  gsl_interp_accel* acc_;
  gsl_spline* spline_;
};
 
}  // namespace smash
 
#endif  // SRC_INCLUDE_SMASH_INTERPOLATION_H_