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<title>Automatic Derivatives — Ceres Solver</title>
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Ceres Solver
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1.13
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Why?
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Installation
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Tutorial
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On Derivatives
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Spivak Notation
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Analytic Derivatives
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Numeric derivatives
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Automatic Derivatives
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Dual Numbers & Jets
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Implementing Jets
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Pitfalls
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Interfacing with Automatic Differentiation
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Modeling Non-linear Least Squares
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Solving Non-linear Least Squares
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Covariance Estimation
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General Unconstrained Minimization
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FAQS, Tips & Tricks
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Users
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Contributing
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Version History
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Bibliography
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License
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Ceres Solver
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Docs »
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On Derivatives »
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Automatic Derivatives
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Automatic DerivativesΒΆ
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We will now consider automatic differentiation. It is a technique that
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can compute exact derivatives, fast, while requiring about the same
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effort from the user as is needed to use numerical differentiation.
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Don’t believe me? Well here goes. The following code fragment
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implements an automatically differentiated CostFunction for Rat43.
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struct Rat43CostFunctor {
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Rat43CostFunctor(const double x, const double y) : x_(x), y_(y) {}
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template <typename T>
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bool operator()(const T* parameters, T* residuals) const {
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const T b1 = parameters[0];
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const T b2 = parameters[1];
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const T b3 = parameters[2];
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const T b4 = parameters[3];
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residuals[0] = b1 * pow(1.0 + exp(b2 - b3 * x_), -1.0 / b4) - y_;
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return true;
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}
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private:
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const double x_;
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const double y_;
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};
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CostFunction* cost_function =
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new AutoDiffCostFunction<Rat43CostFunctor, 1, 4>(
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new Rat43CostFunctor(x, y));
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