linear_interpolation.hpp

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/*
 * Copyright (C) 2010-2026 The ESPResSo project
 *
 * This file is part of ESPResSo.
 *
 * ESPResSo is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * ESPResSo is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#pragma once
 
#include <cassert>
#include <cstddef>
 
namespace Utils {
/** Linear interpolation between two data points.
 *  @param[in] table   Tabulated values, equally-spaced along the x-axis
 *  @param[in] hi      Inverse distance on the x-axis between tabulated values
 *  @param[in] offset  Position on the x-axis of the first tabulated value
 *  @param[in] x       Position on the x-axis at which to interpolate the value
 *  @return Interpolated value on the y-axis at @p x.
 */
template <typename T, typename Container>
T linear_interpolation(Container const &table, T hi, T offset, T x) {
  auto const dind = (x - offset) * hi;
  auto const ind = static_cast<int>(dind);
  assert(ind <= dind);
  assert((ind >= 0) and (static_cast<std::size_t>(ind) < table.size()));
  auto const dx = dind - static_cast<T>(ind);
  auto const uind = static_cast<unsigned int>(ind);
 
  /* linear interpolation between data points; the upper point may be the last
   * tabulated value (e.g. a single-point/constant table), in which case dx is
   * zero and the second term must not perform an out-of-bounds read */
  auto const upper = (uind + 1u < table.size()) ? table[uind + 1] : table[uind];
  return table[uind] * (T{1} - dx) + upper * dx;
}
} // namespace Utils