Chebyshev2.h

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/* ----------------------------------------------------------------------------
 
 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
 
 * See LICENSE for the license information
 
 * -------------------------------------------------------------------------- */

 
#pragma once
 
#include <gtsam/base/Manifold.h>
#include <gtsam/basis/Basis.h>
 
namespace gtsam {

class GTSAM_EXPORT Chebyshev2 : public Basis<Chebyshev2> {
 public:
  using Base = Basis<Chebyshev2>;
  using Parameters = Eigen::Matrix<double, /*Nx1*/ -1, 1>;
  using DiffMatrix = Eigen::Matrix<double, /*NxN*/ -1, -1>;

  static double Point(size_t N, int j);

  static double Point(size_t N, int j, double a, double b);

  static Vector Points(size_t N);

  static Vector Points(size_t N, double a, double b);

  static Weights CalculateWeights(size_t N, double x, double a = -1, double b = 1);

  static Weights DerivativeWeights(size_t N, double x, double a = -1, double b = 1);

  static DiffMatrix DifferentiationMatrix(size_t N);

  static DiffMatrix DifferentiationMatrix(size_t N, double a, double b);

  static Matrix IntegrationMatrix(size_t N);

  static Matrix IntegrationMatrix(size_t N, double a, double b);

  static Weights IntegrationWeights(size_t N);

  static Weights IntegrationWeights(size_t N, double a, double b);

  static Weights DoubleIntegrationWeights(size_t N);

  static Weights DoubleIntegrationWeights(size_t N, double a, double b);

  static Vector vector(std::function<double(double)> f,
    size_t N, double a = -1, double b = 1);

  template <size_t M>
  static Matrix matrix(std::function<Eigen::Matrix<double, M, 1>(double)> f,
    size_t N, double a = -1, double b = 1) {
    Matrix Xmat(M, N);
    const Vector points = Points(N, a, b);
    for (size_t j = 0; j < N; j++) Xmat.col(j) = f(points(j));
    return Xmat;
  }
};  // \ Chebyshev2
 
}  // namespace gtsam