chebyshev.hpp

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// Copyright (c) 2025 Simons Foundation
//
// This program 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.
//
// This program 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 may obtain a copy of the License at
//     https://www.gnu.org/licenses/gpl-3.0.txt
//
// Authors: Nils Wentzell

 
#pragma once
 
#include <nda/nda.hpp>
 
#include <cmath>
#include <numbers>
 
namespace triqs::utility {


  inline nda::vector<double> chebyshev_points(long N) {
    nda::vector<double> points(N);
    const double pi = std::numbers::pi;
    for (long i = 0; i < N; ++i) {
      // Store in ascending order (cos decreases as argument increases)
      points[N - 1 - i] = std::cos((2.0 * static_cast<double>(i) + 1.0) * pi / (2.0 * static_cast<double>(N)));
    }
    return points;
  }

  inline nda::vector<double> chebyshev_barycentric_weights(long N) {
    nda::vector<double> weights(N);
    const double pi = std::numbers::pi;
    for (long i = 0; i < N; ++i) {
      // Match point ordering (ascending)
      double sign        = (i % 2 == 0) ? 1.0 : -1.0;
      weights[N - 1 - i] = sign * std::sin((2.0 * static_cast<double>(i) + 1.0) * pi / (2.0 * static_cast<double>(N)));
    }
    return weights;
  }

  inline double to_standard_interval(double x, double a, double b) { return 2.0 * (x - 0.5 * (b + a)) / (b - a); }

  inline double from_standard_interval(double x, double a, double b) { return 0.5 * (b - a) * x + 0.5 * (b + a); }

 
} // namespace triqs::utility