fixed_topology_xor_network.hpp

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#pragma once
 
#include <array>
#include <cmath>
#include <stdexcept>
#include <vector>
 
namespace pulsatrix {
 
inline constexpr size_t kFixedTopologyXORNumParams = 9;
 
namespace detail {
inline double Sigmoid(double x) { return 1.0 / (1.0 + std::exp(-x)); }
}  // namespace detail
 
inline double FixedTopologyXORForward(const std::vector<double>& theta, const std::array<double, 2>& inputs) {
    if (theta.size() != kFixedTopologyXORNumParams) {
        throw std::invalid_argument("FixedTopologyXORForward: theta must have exactly kFixedTopologyXORNumParams entries");
    }
    double h0 = detail::Sigmoid(theta[0] * inputs[0] + theta[1] * inputs[1] + theta[2]);
    double h1 = detail::Sigmoid(theta[3] * inputs[0] + theta[4] * inputs[1] + theta[5]);
    return detail::Sigmoid(theta[6] * h0 + theta[7] * h1 + theta[8]);
}
 
inline double FixedTopologyXORFitness(const std::vector<double>& theta) {
    static const std::array<std::array<double, 2>, 4> kInputs{
        {{0.0, 0.0}, {0.0, 1.0}, {1.0, 0.0}, {1.0, 1.0}}};
    static const std::array<double, 4> kExpected{0.0, 1.0, 1.0, 0.0};
 
    double sum_squared_error = 0.0;
    for (size_t i = 0; i < kInputs.size(); ++i) {
        double actual = FixedTopologyXORForward(theta, kInputs[i]);
        double error = kExpected[i] - actual;
        sum_squared_error += error * error;
    }
    return 4.0 - sum_squared_error;
}
 
}  // namespace pulsatrix