contrib/test/NumericalDiff.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
// SPDX-License-Identifier: MPL-2.0

#include <stdio.h>

#include "main.h"
#include <contrib/Eigen/NumericalDiff>

// Generic functor
template <typename Scalar_, int NX = Dynamic, int NY = Dynamic>
struct Functor {
  typedef Scalar_ Scalar;
  enum { InputsAtCompileTime = NX, ValuesAtCompileTime = NY };
  typedef Matrix<Scalar, InputsAtCompileTime, 1> InputType;
  typedef Matrix<Scalar, ValuesAtCompileTime, 1> ValueType;
  typedef Matrix<Scalar, ValuesAtCompileTime, InputsAtCompileTime> JacobianType;

  int m_inputs, m_values;

  Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
  Functor(int inputs_, int values_) : m_inputs(inputs_), m_values(values_) {}

  int inputs() const { return m_inputs; }
  int values() const { return m_values; }
};

struct my_functor : Functor<double> {
  my_functor(void) : Functor<double>(3, 15) {}
  int operator()(const VectorXd &x, VectorXd &fvec) const {
    double tmp1, tmp2, tmp3;
    double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1, 3.9e-1,
                    3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34,   2.1,    4.39};

    for (int i = 0; i < values(); i++) {
      tmp1 = i + 1;
      tmp2 = 16 - i - 1;
      tmp3 = (i >= 8) ? tmp2 : tmp1;
      fvec[i] = y[i] - (x[0] + tmp1 / (x[1] * tmp2 + x[2] * tmp3));
    }
    return 0;
  }

  int actual_df(const VectorXd &x, MatrixXd &fjac) const {
    double tmp1, tmp2, tmp3, tmp4;
    for (int i = 0; i < values(); i++) {
      tmp1 = i + 1;
      tmp2 = 16 - i - 1;
      tmp3 = (i >= 8) ? tmp2 : tmp1;
      tmp4 = (x[1] * tmp2 + x[2] * tmp3);
      tmp4 = tmp4 * tmp4;
      fjac(i, 0) = -1;
      fjac(i, 1) = tmp1 * tmp2 / tmp4;
      fjac(i, 2) = tmp1 * tmp3 / tmp4;
    }
    return 0;
  }
};

// Scaling by a power of two is exact, so the difference quotients of this map equal the scales
// iff each divisor is the representable step actually applied to x.
struct pow2_scaling_functor : Functor<double> {
  pow2_scaling_functor() : Functor<double>(7, 7), scale(7) { scale << 0.25, 1.0, 8.0, -2.0, 0.5, 4.0, -0.125; }
  int operator()(const VectorXd &x, VectorXd &fvec) const {
    fvec = scale.cwiseProduct(x);
    return 0;
  }
  VectorXd scale;
};

void test_forward() {
  VectorXd x(3);
  MatrixXd jac(15, 3);
  MatrixXd actual_jac(15, 3);
  my_functor functor;

  x << 0.082, 1.13, 2.35;

  // real one
  functor.actual_df(x, actual_jac);
  //    std::cout << actual_jac << std::endl << std::endl;

  // using NumericalDiff
  NumericalDiff<my_functor> numDiff(functor);
  numDiff.df(x, jac);
  //    std::cout << jac << std::endl;

  VERIFY_IS_APPROX(jac, actual_jac);
}

void test_central() {
  VectorXd x(3);
  MatrixXd jac(15, 3);
  MatrixXd actual_jac(15, 3);
  my_functor functor;

  x << 0.082, 1.13, 2.35;

  // real one
  functor.actual_df(x, actual_jac);

  // using NumericalDiff
  NumericalDiff<my_functor, Central> numDiff(functor);
  numDiff.df(x, jac);

  VERIFY_IS_APPROX(jac, actual_jac);
}

void test_small() {
  VectorXd x(3);
  MatrixXd jac(15, 3);
  MatrixXd actual_jac(15, 3);
  my_functor functor;

  x << 0.082, 1.13, 1e-8;

  // real one
  functor.actual_df(x, actual_jac);

  // using NumericalDiff
  NumericalDiff<my_functor, Central> numDiff(functor);
  numDiff.df(x, jac);

  VERIFY_IS_APPROX(jac, actual_jac);
}

template <NumericalDiffMode Mode>
void test_step_alignment(double epsfcn) {
  pow2_scaling_functor functor;
  NumericalDiff<pow2_scaling_functor, Mode> numDiff(functor, epsfcn);

  // Non-dyadic coordinates, so that x + h rounds; the first two take the absolute step eps, and the
  // last two are negative with |x| at or just above a power of two, where x - h is a rounding tie.
  VectorXd x(7);
  x << 0.0, 0.082, 1.13, -2350.7, 7.7e8 + 0.3, -1.0 - std::ldexp(1.0, -27), -1.0;
  MatrixXd jac(7, 7);
  numDiff.df(x, jac);

  MatrixXd expected = functor.scale.asDiagonal();
  VERIFY_IS_EQUAL(jac, expected);
}

EIGEN_DECLARE_TEST(NumericalDiff) {
  CALL_SUBTEST(test_forward());
  CALL_SUBTEST(test_central());
  CALL_SUBTEST(test_small());
  CALL_SUBTEST(test_step_alignment<Forward>(0.0));
  CALL_SUBTEST(test_step_alignment<Central>(0.0));
  // A non-dyadic eps also misaligns the absolute step taken for |x| < 1.
  CALL_SUBTEST(test_step_alignment<Forward>(1e-10));
  CALL_SUBTEST(test_step_alignment<Central>(1e-10));
}