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Add NumericDiffFirstOrderFunction
This has been a long requested feature so that users can minimize functions using numeric differentiation. As part of this, I have also redone rosenbrock.cc, which now has three variants. rosenbrock.cc now uses automatic differentiation. rosenbrock_numeric_diff.cc uses numeric differentiation. rosenbrock_analytic_diff.cc uses analytic derivatives. This is analogus to how the helloworld example code is structured. The tutorial for GradientProblemSolver has also been updated to reflect this. https://github.com/ceres-solver/ceres-solver/issues/691 Change-Id: Ib0fb9e35127fe4c8299d4793bea3558722c70dd7
This commit is contained in:
Sameer Agarwal
@@ -8,46 +8,46 @@
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General Unconstrained Minimization
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==================================
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While much of Ceres Solver is devoted to solving non-linear least
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squares problems, internally it contains a solver that can solve
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general unconstrained optimization problems using just their objective
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function value and gradients. The ``GradientProblem`` and
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``GradientProblemSolver`` objects give the user access to this solver.
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So without much further ado, let us look at how one goes about using
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them.
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Ceres Solver besides being able to solve non-linear least squares
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problem can also solve general unconstrained problems using just their
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objective function value and gradients. In this chapter we will see
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how to do this.
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Rosenbrock's Function
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=====================
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We consider the minimization of the famous `Rosenbrock's function
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Consider minimizing the famous `Rosenbrock's function
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<http://en.wikipedia.org/wiki/Rosenbrock_function>`_ [#f1]_.
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We begin by defining an instance of the ``FirstOrderFunction``
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interface. This is the object that is responsible for computing the
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objective function value and the gradient (if required). This is the
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analog of the :class:`CostFunction` when defining non-linear least
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squares problems in Ceres.
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The simplest way to minimize is to define a templated functor to
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evaluate the objective value of this function and then use Ceres
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Solver's automatic differentiation to compute its derivatives.
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We begin by defining a templated functor and then using
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``AutoDiffFirstOrderFunction`` to construct an instance of the
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``FirstOrderFunction`` interface. This is the object that is
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responsible for computing the objective function value and the
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gradient (if required). This is the analog of the
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:class:`CostFunction` when defining non-linear least squares problems
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in Ceres.
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.. code::
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class Rosenbrock : public ceres::FirstOrderFunction {
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public:
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virtual bool Evaluate(const double* parameters,
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double* cost,
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double* gradient) const {
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const double x = parameters[0];
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const double y = parameters[1];
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// f(x,y) = (1-x)^2 + 100(y - x^2)^2;
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struct Rosenbrock {
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template <typename T>
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bool operator()(const T* parameters, T* cost) const {
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const T x = parameters[0];
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const T y = parameters[1];
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cost[0] = (1.0 - x) * (1.0 - x) + 100.0 * (y - x * x) * (y - x * x);
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if (gradient != nullptr) {
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gradient[0] = -2.0 * (1.0 - x) - 200.0 * (y - x * x) * 2.0 * x;
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gradient[1] = 200.0 * (y - x * x);
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}
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return true;
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}
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virtual int NumParameters() const { return 2; }
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static ceres::FirstOrderFunction* Create() {
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constexpr int kNumParameters = 2;
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return new ceres::AutoDiffFirstOrderFunction<Rosenbrock, kNumParameters>(
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new Rosenbrock);
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}
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};
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@@ -58,7 +58,7 @@ Minimizing it then is a straightforward matter of constructing a
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double parameters[2] = {-1.2, 1.0};
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ceres::GradientProblem problem(new Rosenbrock());
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ceres::GradientProblem problem(Rosenbrock::Create());
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ceres::GradientProblemSolver::Options options;
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options.minimizer_progress_to_stdout = true;
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@@ -74,43 +74,43 @@ algorithm.
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.. code-block:: bash
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0: f: 2.420000e+01 d: 0.00e+00 g: 2.16e+02 h: 0.00e+00 s: 0.00e+00 e: 0 it: 2.00e-05 tt: 2.00e-05
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1: f: 4.280493e+00 d: 1.99e+01 g: 1.52e+01 h: 2.01e-01 s: 8.62e-04 e: 2 it: 7.32e-05 tt: 2.19e-04
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2: f: 3.571154e+00 d: 7.09e-01 g: 1.35e+01 h: 3.78e-01 s: 1.34e-01 e: 3 it: 2.50e-05 tt: 2.68e-04
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3: f: 3.440869e+00 d: 1.30e-01 g: 1.73e+01 h: 1.36e-01 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 2.92e-04
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4: f: 3.213597e+00 d: 2.27e-01 g: 1.55e+01 h: 1.06e-01 s: 4.59e-01 e: 1 it: 2.86e-06 tt: 3.14e-04
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5: f: 2.839723e+00 d: 3.74e-01 g: 1.05e+01 h: 1.34e-01 s: 5.24e-01 e: 1 it: 2.86e-06 tt: 3.36e-04
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6: f: 2.448490e+00 d: 3.91e-01 g: 1.29e+01 h: 3.04e-01 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 3.58e-04
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7: f: 1.943019e+00 d: 5.05e-01 g: 4.00e+00 h: 8.81e-02 s: 7.43e-01 e: 1 it: 4.05e-06 tt: 3.79e-04
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8: f: 1.731469e+00 d: 2.12e-01 g: 7.36e+00 h: 1.71e-01 s: 4.60e-01 e: 2 it: 9.06e-06 tt: 4.06e-04
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9: f: 1.503267e+00 d: 2.28e-01 g: 6.47e+00 h: 8.66e-02 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 4.33e-04
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10: f: 1.228331e+00 d: 2.75e-01 g: 2.00e+00 h: 7.70e-02 s: 7.90e-01 e: 1 it: 3.81e-06 tt: 4.54e-04
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11: f: 1.016523e+00 d: 2.12e-01 g: 5.15e+00 h: 1.39e-01 s: 3.76e-01 e: 2 it: 1.00e-05 tt: 4.82e-04
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12: f: 9.145773e-01 d: 1.02e-01 g: 6.74e+00 h: 7.98e-02 s: 1.00e+00 e: 1 it: 3.10e-06 tt: 5.03e-04
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13: f: 7.508302e-01 d: 1.64e-01 g: 3.88e+00 h: 5.76e-02 s: 4.93e-01 e: 1 it: 2.86e-06 tt: 5.25e-04
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14: f: 5.832378e-01 d: 1.68e-01 g: 5.56e+00 h: 1.42e-01 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 5.47e-04
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15: f: 3.969581e-01 d: 1.86e-01 g: 1.64e+00 h: 1.17e-01 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 5.68e-04
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16: f: 3.171557e-01 d: 7.98e-02 g: 3.84e+00 h: 1.18e-01 s: 3.97e-01 e: 2 it: 9.06e-06 tt: 5.94e-04
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17: f: 2.641257e-01 d: 5.30e-02 g: 3.27e+00 h: 6.14e-02 s: 1.00e+00 e: 1 it: 3.10e-06 tt: 6.16e-04
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18: f: 1.909730e-01 d: 7.32e-02 g: 5.29e-01 h: 8.55e-02 s: 6.82e-01 e: 1 it: 4.05e-06 tt: 6.42e-04
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19: f: 1.472012e-01 d: 4.38e-02 g: 3.11e+00 h: 1.20e-01 s: 3.47e-01 e: 2 it: 1.00e-05 tt: 6.69e-04
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20: f: 1.093558e-01 d: 3.78e-02 g: 2.97e+00 h: 8.43e-02 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 6.91e-04
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21: f: 6.710346e-02 d: 4.23e-02 g: 1.42e+00 h: 9.64e-02 s: 8.85e-01 e: 1 it: 3.81e-06 tt: 7.12e-04
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22: f: 3.993377e-02 d: 2.72e-02 g: 2.30e+00 h: 1.29e-01 s: 4.63e-01 e: 2 it: 9.06e-06 tt: 7.39e-04
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23: f: 2.911794e-02 d: 1.08e-02 g: 2.55e+00 h: 6.55e-02 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 7.62e-04
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24: f: 1.457683e-02 d: 1.45e-02 g: 2.77e-01 h: 6.37e-02 s: 6.14e-01 e: 1 it: 3.81e-06 tt: 7.84e-04
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25: f: 8.577515e-03 d: 6.00e-03 g: 2.86e+00 h: 1.40e-01 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 8.05e-04
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26: f: 3.486574e-03 d: 5.09e-03 g: 1.76e-01 h: 1.23e-02 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 8.27e-04
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27: f: 1.257570e-03 d: 2.23e-03 g: 1.39e-01 h: 5.08e-02 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 8.48e-04
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28: f: 2.783568e-04 d: 9.79e-04 g: 6.20e-01 h: 6.47e-02 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 8.69e-04
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29: f: 2.533399e-05 d: 2.53e-04 g: 1.68e-02 h: 1.98e-03 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 8.91e-04
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30: f: 7.591572e-07 d: 2.46e-05 g: 5.40e-03 h: 9.27e-03 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 9.12e-04
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31: f: 1.902460e-09 d: 7.57e-07 g: 1.62e-03 h: 1.89e-03 s: 1.00e+00 e: 1 it: 2.86e-06 tt: 9.33e-04
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32: f: 1.003030e-12 d: 1.90e-09 g: 3.50e-05 h: 3.52e-05 s: 1.00e+00 e: 1 it: 3.10e-06 tt: 9.54e-04
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33: f: 4.835994e-17 d: 1.00e-12 g: 1.05e-07 h: 1.13e-06 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 9.81e-04
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34: f: 1.885250e-22 d: 4.84e-17 g: 2.69e-10 h: 1.45e-08 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 1.00e-03
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0: f: 2.420000e+01 d: 0.00e+00 g: 2.16e+02 h: 0.00e+00 s: 0.00e+00 e: 0 it: 2.29e-05 tt: 2.29e-05
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1: f: 4.280493e+00 d: 1.99e+01 g: 1.52e+01 h: 2.01e-01 s: 8.62e-04 e: 2 it: 8.39e-05 tt: 1.62e-04
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2: f: 3.571154e+00 d: 7.09e-01 g: 1.35e+01 h: 3.78e-01 s: 1.34e-01 e: 3 it: 2.22e-05 tt: 1.91e-04
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3: f: 3.440869e+00 d: 1.30e-01 g: 1.73e+01 h: 1.36e-01 s: 1.00e+00 e: 1 it: 5.01e-06 tt: 2.01e-04
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4: f: 3.213597e+00 d: 2.27e-01 g: 1.55e+01 h: 1.06e-01 s: 4.59e-01 e: 1 it: 3.81e-06 tt: 2.10e-04
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5: f: 2.839723e+00 d: 3.74e-01 g: 1.05e+01 h: 1.34e-01 s: 5.24e-01 e: 1 it: 4.05e-06 tt: 2.19e-04
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6: f: 2.448490e+00 d: 3.91e-01 g: 1.29e+01 h: 3.04e-01 s: 1.00e+00 e: 1 it: 5.01e-06 tt: 2.28e-04
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7: f: 1.943019e+00 d: 5.05e-01 g: 4.00e+00 h: 8.81e-02 s: 7.43e-01 e: 1 it: 4.05e-06 tt: 2.36e-04
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8: f: 1.731469e+00 d: 2.12e-01 g: 7.36e+00 h: 1.71e-01 s: 4.60e-01 e: 2 it: 1.22e-05 tt: 2.52e-04
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9: f: 1.503267e+00 d: 2.28e-01 g: 6.47e+00 h: 8.66e-02 s: 1.00e+00 e: 1 it: 5.96e-06 tt: 2.66e-04
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10: f: 1.228331e+00 d: 2.75e-01 g: 2.00e+00 h: 7.70e-02 s: 7.90e-01 e: 1 it: 4.05e-06 tt: 2.75e-04
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11: f: 1.016523e+00 d: 2.12e-01 g: 5.15e+00 h: 1.39e-01 s: 3.76e-01 e: 2 it: 9.06e-06 tt: 2.88e-04
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12: f: 9.145773e-01 d: 1.02e-01 g: 6.74e+00 h: 7.98e-02 s: 1.00e+00 e: 1 it: 5.01e-06 tt: 2.97e-04
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13: f: 7.508302e-01 d: 1.64e-01 g: 3.88e+00 h: 5.76e-02 s: 4.93e-01 e: 1 it: 5.01e-06 tt: 3.05e-04
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14: f: 5.832378e-01 d: 1.68e-01 g: 5.56e+00 h: 1.42e-01 s: 1.00e+00 e: 1 it: 4.77e-06 tt: 3.13e-04
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15: f: 3.969581e-01 d: 1.86e-01 g: 1.64e+00 h: 1.17e-01 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 3.20e-04
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16: f: 3.171557e-01 d: 7.98e-02 g: 3.84e+00 h: 1.18e-01 s: 3.97e-01 e: 2 it: 8.82e-06 tt: 3.33e-04
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17: f: 2.641257e-01 d: 5.30e-02 g: 3.27e+00 h: 6.14e-02 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 3.42e-04
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18: f: 1.909730e-01 d: 7.32e-02 g: 5.29e-01 h: 8.55e-02 s: 6.82e-01 e: 1 it: 1.00e-05 tt: 4.64e-04
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19: f: 1.472012e-01 d: 4.38e-02 g: 3.11e+00 h: 1.20e-01 s: 3.47e-01 e: 2 it: 1.29e-05 tt: 4.87e-04
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20: f: 1.093558e-01 d: 3.78e-02 g: 2.97e+00 h: 8.43e-02 s: 1.00e+00 e: 1 it: 5.01e-06 tt: 4.97e-04
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21: f: 6.710346e-02 d: 4.23e-02 g: 1.42e+00 h: 9.64e-02 s: 8.85e-01 e: 1 it: 4.05e-06 tt: 5.06e-04
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22: f: 3.993377e-02 d: 2.72e-02 g: 2.30e+00 h: 1.29e-01 s: 4.63e-01 e: 2 it: 1.00e-05 tt: 5.25e-04
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23: f: 2.911794e-02 d: 1.08e-02 g: 2.55e+00 h: 6.55e-02 s: 1.00e+00 e: 1 it: 5.01e-06 tt: 5.34e-04
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24: f: 1.457683e-02 d: 1.45e-02 g: 2.77e-01 h: 6.37e-02 s: 6.14e-01 e: 1 it: 4.05e-06 tt: 5.42e-04
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25: f: 8.577515e-03 d: 6.00e-03 g: 2.86e+00 h: 1.40e-01 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 5.49e-04
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26: f: 3.486574e-03 d: 5.09e-03 g: 1.76e-01 h: 1.23e-02 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 5.57e-04
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27: f: 1.257570e-03 d: 2.23e-03 g: 1.39e-01 h: 5.08e-02 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 5.65e-04
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28: f: 2.783568e-04 d: 9.79e-04 g: 6.20e-01 h: 6.47e-02 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 5.73e-04
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29: f: 2.533399e-05 d: 2.53e-04 g: 1.68e-02 h: 1.98e-03 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 5.81e-04
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30: f: 7.591572e-07 d: 2.46e-05 g: 5.40e-03 h: 9.27e-03 s: 1.00e+00 e: 1 it: 5.96e-06 tt: 6.30e-04
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31: f: 1.902460e-09 d: 7.57e-07 g: 1.62e-03 h: 1.89e-03 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 6.39e-04
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32: f: 1.003030e-12 d: 1.90e-09 g: 3.50e-05 h: 3.52e-05 s: 1.00e+00 e: 1 it: 3.81e-06 tt: 6.47e-04
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33: f: 4.835994e-17 d: 1.00e-12 g: 1.05e-07 h: 1.13e-06 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 6.59e-04
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34: f: 1.885250e-22 d: 4.84e-17 g: 2.69e-10 h: 1.45e-08 s: 1.00e+00 e: 1 it: 4.05e-06 tt: 6.67e-04
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Solver Summary (v 1.12.0-lapack-suitesparse-cxsparse-no_openmp)
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Solver Summary (v 2.0.0-eigen-(3.3.9)-lapack-suitesparse-(5.8.1)-cxsparse-(3.2.0)-acceleratesparse-eigensparse-no_openmp-no_custom_blas)
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Parameters 2
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Line search direction LBFGS (20)
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@@ -119,20 +119,86 @@ algorithm.
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Cost:
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Initial 2.420000e+01
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Final 1.885250e-22
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Final 1.955192e-27
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Change 2.420000e+01
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Minimizer iterations 35
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Minimizer iterations 36
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Time (in seconds):
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Cost evaluation 0.000
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Gradient evaluation 0.000
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Total 0.003
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Cost evaluation 0.000000 (0)
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Gradient & cost evaluation 0.000008 (44)
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Polynomial minimization 0.000067
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Total 0.000721
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Termination: CONVERGENCE (Gradient tolerance reached. Gradient max norm: 9.032775e-13 <= 1.000000e-10)
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Termination: CONVERGENCE (Parameter tolerance reached. Relative step_norm: 1.890726e-11 <= 1.000000e-08.)
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Initial x: -1.2 y: 1
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Final x: 1 y: 1
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If you are unable to use automatic differentiation for some reason
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(say beacause you need to call an external library), then you can
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use numeric differentiation. In that case the functor is defined as
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follows [#f2]_.
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.. code::
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// f(x,y) = (1-x)^2 + 100(y - x^2)^2;
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struct Rosenbrock {
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bool operator()(const double* parameters, double* cost) const {
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const double x = parameters[0];
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const double y = parameters[1];
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cost[0] = (1.0 - x) * (1.0 - x) + 100.0 * (y - x * x) * (y - x * x);
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return true;
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}
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static ceres::FirstOrderFunction* Create() {
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constexpr int kNumParameters = 2;
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return new ceres::NumericDiffFirstOrderFunction<Rosenbrock,
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ceres::CENTRAL,
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kNumParameters>(
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new Rosenbrock);
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}
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};
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And finally, if you would rather compute the derivatives by hand (say
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because the size of the parameter vector is too large to be
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automatically differentiated). Then you should define an instance of
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``FirstOrderFunction``, which is the analog of :class:`CostFunction`
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for non-linear least squares problems [#f3]_.
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.. code::
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// f(x,y) = (1-x)^2 + 100(y - x^2)^2;
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class Rosenbrock final : public ceres::FirstOrderFunction {
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public:
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~Rosenbrock() override {}
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bool Evaluate(const double* parameters,
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double* cost,
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double* gradient) const override {
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const double x = parameters[0];
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const double y = parameters[1];
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cost[0] = (1.0 - x) * (1.0 - x) + 100.0 * (y - x * x) * (y - x * x);
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if (gradient) {
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gradient[0] = -2.0 * (1.0 - x) - 200.0 * (y - x * x) * 2.0 * x;
|
||||
gradient[1] = 200.0 * (y - x * x);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
int NumParameters() const override { return 2; }
|
||||
};
|
||||
|
||||
.. rubric:: Footnotes
|
||||
|
||||
.. [#f1] `examples/rosenbrock.cc
|
||||
<https://ceres-solver.googlesource.com/ceres-solver/+/master/examples/rosenbrock.cc>`_
|
||||
|
||||
.. [#f2] `examples/rosenbrock_numeric_diff.cc
|
||||
<https://ceres-solver.googlesource.com/ceres-solver/+/master/examples/rosenbrock_numeric_diff.cc>`_
|
||||
|
||||
.. [#f3] `examples/rosenbrock_analytic_diff.cc
|
||||
<https://ceres-solver.googlesource.com/ceres-solver/+/master/examples/rosenbrock_analytic_diff.cc>`_
|
||||
|
||||
@@ -50,6 +50,12 @@ target_link_libraries(curve_fitting Ceres::ceres)
|
||||
add_executable(rosenbrock rosenbrock.cc)
|
||||
target_link_libraries(rosenbrock Ceres::ceres)
|
||||
|
||||
add_executable(rosenbrock_analytic_diff rosenbrock_analytic_diff.cc)
|
||||
target_link_libraries(rosenbrock_analytic_diff Ceres::ceres)
|
||||
|
||||
add_executable(rosenbrock_numeric_diff rosenbrock_numeric_diff.cc)
|
||||
target_link_libraries(rosenbrock_numeric_diff Ceres::ceres)
|
||||
|
||||
add_executable(curve_fitting_c curve_fitting.c)
|
||||
target_link_libraries(curve_fitting_c Ceres::ceres)
|
||||
# Force CMake to link curve_fitting_c using the C linker.
|
||||
|
||||
+12
-17
@@ -1,5 +1,5 @@
|
||||
// Ceres Solver - A fast non-linear least squares minimizer
|
||||
// Copyright 2015 Google Inc. All rights reserved.
|
||||
// Copyright 2021 Google Inc. All rights reserved.
|
||||
// http://ceres-solver.org/
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
@@ -32,25 +32,20 @@
|
||||
#include "glog/logging.h"
|
||||
|
||||
// f(x,y) = (1-x)^2 + 100(y - x^2)^2;
|
||||
class Rosenbrock : public ceres::FirstOrderFunction {
|
||||
public:
|
||||
virtual ~Rosenbrock() {}
|
||||
|
||||
virtual bool Evaluate(const double* parameters,
|
||||
double* cost,
|
||||
double* gradient) const {
|
||||
const double x = parameters[0];
|
||||
const double y = parameters[1];
|
||||
|
||||
struct Rosenbrock {
|
||||
template <typename T>
|
||||
bool operator()(const T* parameters, T* cost) const {
|
||||
const T x = parameters[0];
|
||||
const T y = parameters[1];
|
||||
cost[0] = (1.0 - x) * (1.0 - x) + 100.0 * (y - x * x) * (y - x * x);
|
||||
if (gradient != NULL) {
|
||||
gradient[0] = -2.0 * (1.0 - x) - 200.0 * (y - x * x) * 2.0 * x;
|
||||
gradient[1] = 200.0 * (y - x * x);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
virtual int NumParameters() const { return 2; }
|
||||
static ceres::FirstOrderFunction* Create() {
|
||||
constexpr int kNumParameters = 2;
|
||||
return new ceres::AutoDiffFirstOrderFunction<Rosenbrock, kNumParameters>(
|
||||
new Rosenbrock);
|
||||
}
|
||||
};
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
@@ -62,7 +57,7 @@ int main(int argc, char** argv) {
|
||||
options.minimizer_progress_to_stdout = true;
|
||||
|
||||
ceres::GradientProblemSolver::Summary summary;
|
||||
ceres::GradientProblem problem(new Rosenbrock());
|
||||
ceres::GradientProblem problem(Rosenbrock::Create());
|
||||
ceres::Solve(options, problem, parameters, &summary);
|
||||
|
||||
std::cout << summary.FullReport() << "\n";
|
||||
|
||||
@@ -0,0 +1,75 @@
|
||||
// Ceres Solver - A fast non-linear least squares minimizer
|
||||
// Copyright 2021 Google Inc. All rights reserved.
|
||||
// http://ceres-solver.org/
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright notice,
|
||||
// this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above copyright notice,
|
||||
// this list of conditions and the following disclaimer in the documentation
|
||||
// and/or other materials provided with the distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its contributors may be
|
||||
// used to endorse or promote products derived from this software without
|
||||
// specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
||||
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
// POSSIBILITY OF SUCH DAMAGE.
|
||||
//
|
||||
// Author: sameeragarwal@google.com (Sameer Agarwal)
|
||||
|
||||
#include "ceres/ceres.h"
|
||||
#include "glog/logging.h"
|
||||
|
||||
// f(x,y) = (1-x)^2 + 100(y - x^2)^2;
|
||||
class Rosenbrock final : public ceres::FirstOrderFunction {
|
||||
public:
|
||||
~Rosenbrock() override {}
|
||||
|
||||
bool Evaluate(const double* parameters,
|
||||
double* cost,
|
||||
double* gradient) const override {
|
||||
const double x = parameters[0];
|
||||
const double y = parameters[1];
|
||||
|
||||
cost[0] = (1.0 - x) * (1.0 - x) + 100.0 * (y - x * x) * (y - x * x);
|
||||
|
||||
if (gradient) {
|
||||
gradient[0] = -2.0 * (1.0 - x) - 200.0 * (y - x * x) * 2.0 * x;
|
||||
gradient[1] = 200.0 * (y - x * x);
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
int NumParameters() const override { return 2; }
|
||||
};
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
google::InitGoogleLogging(argv[0]);
|
||||
|
||||
double parameters[2] = {-1.2, 1.0};
|
||||
|
||||
ceres::GradientProblemSolver::Options options;
|
||||
options.minimizer_progress_to_stdout = true;
|
||||
|
||||
ceres::GradientProblemSolver::Summary summary;
|
||||
ceres::GradientProblem problem(new Rosenbrock());
|
||||
ceres::Solve(options, problem, parameters, &summary);
|
||||
|
||||
std::cout << summary.FullReport() << "\n";
|
||||
std::cout << "Initial x: " << -1.2 << " y: " << 1.0 << "\n";
|
||||
std::cout << "Final x: " << parameters[0] << " y: " << parameters[1]
|
||||
<< "\n";
|
||||
return 0;
|
||||
}
|
||||
@@ -0,0 +1,69 @@
|
||||
// Ceres Solver - A fast non-linear least squares minimizer
|
||||
// Copyright 2021 Google Inc. All rights reserved.
|
||||
// http://ceres-solver.org/
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright notice,
|
||||
// this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above copyright notice,
|
||||
// this list of conditions and the following disclaimer in the documentation
|
||||
// and/or other materials provided with the distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its contributors may be
|
||||
// used to endorse or promote products derived from this software without
|
||||
// specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
||||
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
// POSSIBILITY OF SUCH DAMAGE.
|
||||
//
|
||||
// Author: sameeragarwal@google.com (Sameer Agarwal)
|
||||
|
||||
#include "ceres/ceres.h"
|
||||
#include "glog/logging.h"
|
||||
|
||||
// f(x,y) = (1-x)^2 + 100(y - x^2)^2;
|
||||
struct Rosenbrock {
|
||||
bool operator()(const double* parameters, double* cost) const {
|
||||
const double x = parameters[0];
|
||||
const double y = parameters[1];
|
||||
cost[0] = (1.0 - x) * (1.0 - x) + 100.0 * (y - x * x) * (y - x * x);
|
||||
return true;
|
||||
}
|
||||
|
||||
static ceres::FirstOrderFunction* Create() {
|
||||
constexpr int kNumParameters = 2;
|
||||
return new ceres::NumericDiffFirstOrderFunction<Rosenbrock,
|
||||
ceres::CENTRAL,
|
||||
kNumParameters>(
|
||||
new Rosenbrock);
|
||||
}
|
||||
};
|
||||
|
||||
int main(int argc, char** argv) {
|
||||
google::InitGoogleLogging(argv[0]);
|
||||
|
||||
double parameters[2] = {-1.2, 1.0};
|
||||
|
||||
ceres::GradientProblemSolver::Options options;
|
||||
options.minimizer_progress_to_stdout = true;
|
||||
|
||||
ceres::GradientProblemSolver::Summary summary;
|
||||
ceres::GradientProblem problem(Rosenbrock::Create());
|
||||
ceres::Solve(options, problem, parameters, &summary);
|
||||
|
||||
std::cout << summary.FullReport() << "\n";
|
||||
std::cout << "Initial x: " << -1.2 << " y: " << 1.0 << "\n";
|
||||
std::cout << "Final x: " << parameters[0] << " y: " << parameters[1]
|
||||
<< "\n";
|
||||
return 0;
|
||||
}
|
||||
@@ -35,6 +35,7 @@
|
||||
#define CERES_PUBLIC_CERES_H_
|
||||
|
||||
#include "ceres/autodiff_cost_function.h"
|
||||
#include "ceres/autodiff_first_order_function.h"
|
||||
#include "ceres/autodiff_local_parameterization.h"
|
||||
#include "ceres/conditioned_cost_function.h"
|
||||
#include "ceres/context.h"
|
||||
@@ -47,6 +48,7 @@
|
||||
#include "ceres/dynamic_cost_function_to_functor.h"
|
||||
#include "ceres/dynamic_numeric_diff_cost_function.h"
|
||||
#include "ceres/evaluation_callback.h"
|
||||
#include "ceres/first_order_function.h"
|
||||
#include "ceres/gradient_checker.h"
|
||||
#include "ceres/gradient_problem.h"
|
||||
#include "ceres/gradient_problem_solver.h"
|
||||
@@ -55,6 +57,7 @@
|
||||
#include "ceres/local_parameterization.h"
|
||||
#include "ceres/loss_function.h"
|
||||
#include "ceres/numeric_diff_cost_function.h"
|
||||
#include "ceres/numeric_diff_first_order_function.h"
|
||||
#include "ceres/numeric_diff_options.h"
|
||||
#include "ceres/ordered_groups.h"
|
||||
#include "ceres/problem.h"
|
||||
|
||||
@@ -0,0 +1,162 @@
|
||||
// Ceres Solver - A fast non-linear least squares minimizer
|
||||
// Copyright 2019 Google Inc. All rights reserved.
|
||||
// http://ceres-solver.org/
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright notice,
|
||||
// this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above copyright notice,
|
||||
// this list of conditions and the following disclaimer in the documentation
|
||||
// and/or other materials provided with the distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its contributors may be
|
||||
// used to endorse or promote products derived from this software without
|
||||
// specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
||||
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
// POSSIBILITY OF SUCH DAMAGE.
|
||||
//
|
||||
// Author: sameeragarwal@google.com (Sameer Agarwal)
|
||||
|
||||
#ifndef CERES_PUBLIC_NUMERIC_DIFF_FIRST_ORDER_FUNCTION_H_
|
||||
#define CERES_PUBLIC_NUMERIC_DIFF_FIRST_ORDER_FUNCTION_H_
|
||||
|
||||
#include <algorithm>
|
||||
#include <memory>
|
||||
|
||||
#include "ceres/first_order_function.h"
|
||||
#include "ceres/internal/eigen.h"
|
||||
#include "ceres/internal/fixed_array.h"
|
||||
#include "ceres/internal/numeric_diff.h"
|
||||
#include "ceres/internal/parameter_dims.h"
|
||||
#include "ceres/internal/variadic_evaluate.h"
|
||||
#include "ceres/numeric_diff_options.h"
|
||||
#include "ceres/types.h"
|
||||
|
||||
|
||||
namespace ceres {
|
||||
|
||||
// Creates FirstOrderFunctions as needed by the GradientProblem
|
||||
// framework, with gradients computed via numeric differentiation. For
|
||||
// more information on numeric differentiation, see the wikipedia
|
||||
// article at https://en.wikipedia.org/wiki/Numerical_differentiation
|
||||
//
|
||||
// To get an numerically differentiated cost function, you must define
|
||||
// a class with an operator() (a functor) that computes the cost.
|
||||
//
|
||||
// The function must write the computed value in the last argument
|
||||
// (the only non-const one) and return true to indicate success.
|
||||
//
|
||||
// For example, consider a scalar error e = x'y - a, where both x and y are
|
||||
// two-dimensional column vector parameters, the prime sign indicates
|
||||
// transposition, and a is a constant.
|
||||
//
|
||||
// To write an numerically-differentiable cost function for the above model,
|
||||
// first define the object
|
||||
//
|
||||
// class QuadraticCostFunctor {
|
||||
// public:
|
||||
// explicit QuadraticCostFunctor(double a) : a_(a) {}
|
||||
// bool operator()(const double* const xy, double* cost) const {
|
||||
// constexpr int kInputVectorLength = 2;
|
||||
// const double* const x = xy;
|
||||
// const double* const y = xy + kInputVectorLength;
|
||||
// *cost = x[0] * y[0] + x[1] * y[1] - a_;
|
||||
// return true;
|
||||
// }
|
||||
//
|
||||
// private:
|
||||
// double a_;
|
||||
// };
|
||||
//
|
||||
//
|
||||
// Note that in the declaration of operator() the input parameters xy
|
||||
// come first, and are passed as const pointers to array of
|
||||
// doubles. The output cost is the last parameter.
|
||||
//
|
||||
// Then given this class definition, the numerically differentiated
|
||||
// first order function with central differences used for computing the
|
||||
// derivative can be constructed as follows.
|
||||
//
|
||||
// FirstOrderFunction* function
|
||||
// = new NumericDiffFirstOrderFunction<MyScalarCostFunctor, CENTRAL, 4>(
|
||||
// new QuadraticCostFunctor(1.0)); ^ ^ ^
|
||||
// | | |
|
||||
// Finite Differencing Scheme -+ | |
|
||||
// Dimension of xy ------------------------+
|
||||
//
|
||||
//
|
||||
// In the instantiation above, the template parameters following
|
||||
// "QuadraticCostFunctor", "CENTRAL, 4", describe the finite
|
||||
// differencing scheme as "central differencing" and the functor as
|
||||
// computing its cost from a 4 dimensional input.
|
||||
template <typename FirstOrderFunctor,
|
||||
NumericDiffMethodType method,
|
||||
int kNumParameters>
|
||||
class NumericDiffFirstOrderFunction : public FirstOrderFunction {
|
||||
public:
|
||||
NumericDiffFirstOrderFunction(
|
||||
FirstOrderFunctor* functor,
|
||||
Ownership ownership = TAKE_OWNERSHIP,
|
||||
const NumericDiffOptions& options = NumericDiffOptions())
|
||||
: functor_(functor), ownership_(ownership), options_(options) {
|
||||
static_assert(kNumParameters > 0, "kNumParameters must be positive");
|
||||
}
|
||||
|
||||
~NumericDiffFirstOrderFunction() override {
|
||||
if (ownership_ != TAKE_OWNERSHIP) {
|
||||
functor_.release();
|
||||
}
|
||||
}
|
||||
|
||||
bool Evaluate(const double* const parameters,
|
||||
double* cost,
|
||||
double* gradient) const override {
|
||||
using ParameterDims = internal::StaticParameterDims<kNumParameters>;
|
||||
constexpr int kNumResiduals = 1;
|
||||
|
||||
// Get the function value (cost) at the the point to evaluate.
|
||||
if (!internal::VariadicEvaluate<ParameterDims>(
|
||||
*functor_, ¶meters, cost)) {
|
||||
return false;
|
||||
}
|
||||
|
||||
if (gradient == nullptr) {
|
||||
return true;
|
||||
}
|
||||
|
||||
// Create a copy of the parameters which will get mutated.
|
||||
internal::FixedArray<double, 32> parameters_copy(kNumParameters);
|
||||
std::copy_n(parameters, kNumParameters, parameters_copy.data());
|
||||
double* parameters_ptr = parameters_copy.data();
|
||||
internal::EvaluateJacobianForParameterBlocks<
|
||||
ParameterDims>::template Apply<method, kNumResiduals>(functor_.get(),
|
||||
cost,
|
||||
options_,
|
||||
kNumResiduals,
|
||||
¶meters_ptr,
|
||||
&gradient);
|
||||
return true;
|
||||
}
|
||||
|
||||
int NumParameters() const override { return kNumParameters; }
|
||||
|
||||
private:
|
||||
std::unique_ptr<FirstOrderFunctor> functor_;
|
||||
Ownership ownership_;
|
||||
NumericDiffOptions options_;
|
||||
};
|
||||
|
||||
} // namespace ceres
|
||||
|
||||
#endif // CERES_PUBLIC_NUMERIC_DIFF_FIRST_ORDER_FUNCTION_H_
|
||||
@@ -486,6 +486,7 @@ if (BUILD_TESTING AND GFLAGS)
|
||||
ceres_test(minimizer)
|
||||
ceres_test(normal_prior)
|
||||
ceres_test(numeric_diff_cost_function)
|
||||
ceres_test(numeric_diff_first_order_function)
|
||||
ceres_test(ordered_groups)
|
||||
ceres_test(parallel_for)
|
||||
ceres_test(parallel_utils)
|
||||
@@ -549,4 +550,3 @@ if (BUILD_BENCHMARKS)
|
||||
|
||||
add_subdirectory(autodiff_benchmarks)
|
||||
endif (BUILD_BENCHMARKS)
|
||||
|
||||
|
||||
@@ -44,7 +44,7 @@ class QuadraticCostFunctor {
|
||||
explicit QuadraticCostFunctor(double a) : a_(a) {}
|
||||
template <typename T>
|
||||
bool operator()(const T* const x, T* cost) const {
|
||||
cost[0] = x[0] * x[1] + x[2] * x[3] - T(a_);
|
||||
cost[0] = x[0] * x[1] + x[2] * x[3] - a_;
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
@@ -0,0 +1,79 @@
|
||||
// Ceres Solver - A fast non-linear least squares minimizer
|
||||
// Copyright 2021 Google Inc. All rights reserved.
|
||||
// http://ceres-solver.org/
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright notice,
|
||||
// this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above copyright notice,
|
||||
// this list of conditions and the following disclaimer in the documentation
|
||||
// and/or other materials provided with the distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its contributors may be
|
||||
// used to endorse or promote products derived from this software without
|
||||
// specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
||||
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
// POSSIBILITY OF SUCH DAMAGE.
|
||||
//
|
||||
// Author: sameeragarwal@google.com (Sameer Agarwal)
|
||||
|
||||
#include "ceres/numeric_diff_first_order_function.h"
|
||||
|
||||
#include <memory>
|
||||
|
||||
#include "ceres/array_utils.h"
|
||||
#include "ceres/first_order_function.h"
|
||||
#include "gtest/gtest.h"
|
||||
|
||||
namespace ceres {
|
||||
namespace internal {
|
||||
|
||||
class QuadraticCostFunctor {
|
||||
public:
|
||||
explicit QuadraticCostFunctor(double a) : a_(a) {}
|
||||
bool operator()(const double* const x, double* cost) const {
|
||||
cost[0] = x[0] * x[1] + x[2] * x[3] - a_;
|
||||
return true;
|
||||
}
|
||||
|
||||
private:
|
||||
double a_;
|
||||
};
|
||||
|
||||
TEST(NumericDiffFirstOrderFunction, BilinearDifferentiationTest) {
|
||||
std::unique_ptr<FirstOrderFunction> function(
|
||||
new NumericDiffFirstOrderFunction<QuadraticCostFunctor, CENTRAL, 4>(
|
||||
new QuadraticCostFunctor(1.0)));
|
||||
|
||||
double parameters[4] = {1.0, 2.0, 3.0, 4.0};
|
||||
double gradient[4];
|
||||
double cost;
|
||||
|
||||
function->Evaluate(parameters, &cost, nullptr);
|
||||
EXPECT_EQ(cost, 13.0);
|
||||
|
||||
cost = -1.0;
|
||||
function->Evaluate(parameters, &cost, gradient);
|
||||
|
||||
EXPECT_EQ(cost, 13.0);
|
||||
|
||||
const double kTolerance = 1e-9;
|
||||
EXPECT_NEAR(gradient[0], parameters[1], kTolerance);
|
||||
EXPECT_NEAR(gradient[1], parameters[0], kTolerance);
|
||||
EXPECT_NEAR(gradient[2], parameters[3], kTolerance);
|
||||
EXPECT_NEAR(gradient[3], parameters[2], kTolerance);
|
||||
}
|
||||
|
||||
} // namespace internal
|
||||
} // namespace ceres
|
||||
Reference in New Issue
Block a user