spline.h

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#pragma once
 
#include <cmath>
#include <iostream>
 
#include "../config.h"
#include "../util/linalg.h"
 
namespace alfi::util::spline {
    template <typename Number = DefaultNumber, template <typename, typename...> class Container = DefaultContainer>
        Container<Number> simple_spline(const Container<Number>& X, const Container<Number>& Y, SizeT degree) {
        if (X.size() != Y.size()) {
            std::cerr << "Error in function " << __FUNCTION__
                      << ": Vectors X (of size " << X.size()
                      << ") and Y (of size " << Y.size()
                      << ") are not the same size. Returning an empty array..." << std::endl;
            return {};
        }
 
        const auto n = X.size();
        const auto m = degree + 1;
 
        if (n > m) {
            std::cerr << "Error in function " << __FUNCTION__
                      << ": Number of points (" << n
                      << ") is bigger than degree + 1 (" << m
                      << "). The spline is not simple. Returning an empty array..." << std::endl;
            return {};
        }
 
        if (n == 0) {
            return {};
        }
 
        if (n == 1) {
            Container<Number> coeffs(m, 0);
            coeffs[m-1] = Y[0];
            return coeffs;
        }
 
        if (n == 2) {
            Container<Number> coeffs(m, 0);
            coeffs[m-2] = (Y[1] - Y[0]) / (X[1] - X[0]);
            coeffs[m-1] = Y[0];
            return coeffs;
        }
 
        if (n == 3) {
            const auto h1 = X[1] - X[0], h2 = X[2] - X[1];
            const auto d1 = (Y[1] - Y[0]) / h1, d2 = (Y[2] - Y[1]) / h2;
 
            Container<Number> coeffs(2*m, 0);
 
            coeffs[m-3] = (d2 - d1) / (h1 + h2);
            coeffs[m-2] = d1 - h1 * coeffs[m-3];
            coeffs[m-1] = Y[0];
            coeffs[2*m-3] = coeffs[m-3];
            coeffs[2*m-2] = d1 + h1 * coeffs[m-3];
            coeffs[2*m-1] = Y[1];
 
            return coeffs;
        }
 
        if (n == 4) {
            const auto h1 = X[1]-X[0], h2 = X[2]-X[1];
            const auto h12 = X[2]-X[0], h13 = X[3]-X[0];
            const auto d1 = Y[1]-Y[0], d12 = Y[2]-Y[0], d13 = Y[3]-Y[0];
 
            const auto abc = linalg::lup_solve<Number,Container>(
                {{std::pow(h1, 3), std::pow(h1, 2), h1},
                    {std::pow(h12, 3), std::pow(h12, 2), h12},
                    {std::pow(h13, 3), std::pow(h13, 2), h13}},
                {d1, d12, d13});
            if (abc.empty()) {
                std::cerr << "Error in function " << __FUNCTION__ << ": Could not compute. Returning an empty array..." << std::endl;
                return {};
            }
 
            const auto a = abc[0], b = abc[1], c = abc[2];
 
            Container<Number> coeffs(3*m, 0);
 
            coeffs[m-4] = a;
            coeffs[m-3] = b;
            coeffs[m-2] = c;
            coeffs[m-1] = Y[0];
            coeffs[2*m-4] = a;
            coeffs[2*m-3] = 3 * a * h1 + b;
            coeffs[2*m-2] = 3 * a * std::pow(h1, 2) + 2 * b * h1 + c;
            coeffs[2*m-1] = Y[1];
            coeffs[3*m-4] = a;
            coeffs[3*m-3] = 3 * a * h2 + coeffs[2*m-3];
            coeffs[3*m-2] = 3 * a * std::pow(h2, 2) + 2 * coeffs[2*m-3] * h2 + coeffs[2*m-2];
            coeffs[3*m-1] = Y[2];
 
            return coeffs;
        }
 
        std::cerr << "Error in function " << __FUNCTION__
                  << ": Number of points (" << n
                  << ") is too big (bigger than 4). Returning an empty array..." << std::endl;
        return {};
    }
}