allwpilib/wpimath/src/test/native/cpp/system/RungeKuttaTimeVaryingTest.cpp

// Copyright (c) FIRST and other WPILib contributors.
// Open Source Software; you can modify and/or share it under the terms of
// the WPILib BSD license file in the root directory of this project.

#include <gtest/gtest.h>

#include <cmath>

#include "frc/system/RungeKuttaTimeVarying.h"

namespace {
Eigen::Vector<double, 1> RungeKuttaTimeVaryingSolution(double t) {
  return Eigen::Vector<double, 1>{12.0 * std::exp(t) /
                                  (std::pow(std::exp(t) + 1.0, 2.0))};
}
}  // namespace

// Tests RK4 with a time varying solution. From
// http://www2.hawaii.edu/~jmcfatri/math407/RungeKuttaTest.html:
//   x' = x (2 / (e^t + 1) - 1)
//
// The true (analytical) solution is:
//
// x(t) = 12 * e^t / ((e^t + 1)^2)
TEST(RungeKuttaTimeVaryingTest, RungeKuttaTimeVarying) {
  Eigen::Vector<double, 1> y0 = RungeKuttaTimeVaryingSolution(5.0);

  Eigen::Vector<double, 1> y1 = frc::RungeKuttaTimeVarying(
      [](units::second_t t, const Eigen::Vector<double, 1>& x) {
        return Eigen::Vector<double, 1>{
            x(0) * (2.0 / (std::exp(t.to<double>()) + 1.0) - 1.0)};
      },
      5_s, y0, 1_s);
  EXPECT_NEAR(y1(0), RungeKuttaTimeVaryingSolution(6.0)(0), 1e-3);
}