gram_savitzky_golay.hpp

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// Copyright (c) 2012-2019, CNRS-UM LIRMM, CNRS-AIST JRL
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// reference: https://github.com/arntanguy/gram_savitzky_golay
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// Modified in 2021 by Neuro-Electronics Research Flanders
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#pragma once
 
#include <cassert>
#include <cmath>
#include <vector>
 
namespace gram_sg {
 
inline double compute_gram_polynomial(const int i, const int m, const int k, const int s) {
    if (k > 0) {
        return (4. * k - 2.) / (k * (2. * m - k + 1.)) *
                   (i * compute_gram_polynomial(i, m, k - 1, s) +
                    s * compute_gram_polynomial(i, m, k - 1, s - 1)) -
               ((k - 1.) * (2. * m + k)) / (k * (2. * m - k + 1.)) *
                   compute_gram_polynomial(i, m, k - 2, s);
    }
 
    if (k == 0 && s == 0) {
        return 1.;
    } else {
        return 0.;
    }
};
 
inline double compute_generalized_factorial(const int a, const int b) {
    double gf = 1.;
 
    for (int j = (a - b) + 1; j <= a; j++) {
        gf *= j;
    }
    return gf;
};
 
inline double compute_weight(const int i, const int t, const int m, const int n, const int s) {
    double w = 0;
    for (int k = 0; k <= n; ++k) {
        w = w + (2 * k + 1) *
                    (compute_generalized_factorial(2 * m, k) /
                     compute_generalized_factorial(2 * m + k + 1, k + 1)) *
                    compute_gram_polynomial(i, m, k, 0) * compute_gram_polynomial(t, m, k, s);
    }
    return w;
};
 
inline std::vector<double> compute_weights(const int m, const int t, const int n, const int s) {
    std::vector<double> weights(2 * static_cast<size_t>(m) + 1);
 
    for (int i = 0; i < 2 * m + 1; ++i) {
        weights[static_cast<size_t>(i)] = compute_weight(i - m, t, m, n, s);
    }
    return weights;
};
}  // namespace gram_sg