226 lines
7.8 KiB
C++
226 lines
7.8 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file GaussianBayesNet.h
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* @brief Chordal Bayes Net, the result of eliminating a factor graph
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* @brief GaussianBayesNet
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* @author Frank Dellaert
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*/
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// \callgraph
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#pragma once
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#include <gtsam/linear/GaussianConditional.h>
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#include <gtsam/inference/BayesNet.h>
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#include <gtsam/inference/FactorGraph.h>
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#include <gtsam/global_includes.h>
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namespace gtsam {
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/**
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* GaussianBayesNet is a Bayes net made from linear-Gaussian conditionals.
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* @addtogroup linear
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*/
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class GTSAM_EXPORT GaussianBayesNet: public BayesNet<GaussianConditional>
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{
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public:
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typedef BayesNet<GaussianConditional> Base;
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typedef GaussianBayesNet This;
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typedef GaussianConditional ConditionalType;
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typedef boost::shared_ptr<This> shared_ptr;
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typedef boost::shared_ptr<ConditionalType> sharedConditional;
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/// @name Standard Constructors
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/// @{
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/** Construct empty factor graph */
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GaussianBayesNet() {}
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/** Construct from iterator over conditionals */
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template <typename ITERATOR>
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GaussianBayesNet(ITERATOR firstConditional, ITERATOR lastConditional)
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: Base(firstConditional, lastConditional) {}
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/** Construct from container of factors (shared_ptr or plain objects) */
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template <class CONTAINER>
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explicit GaussianBayesNet(const CONTAINER& conditionals) {
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push_back(conditionals);
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}
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/** Implicit copy/downcast constructor to override explicit template
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* container constructor */
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template <class DERIVEDCONDITIONAL>
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explicit GaussianBayesNet(const FactorGraph<DERIVEDCONDITIONAL>& graph)
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: Base(graph) {}
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/// Destructor
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virtual ~GaussianBayesNet() {}
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/// @}
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/// @name Testable
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/// @{
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/** Check equality */
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bool equals(const This& bn, double tol = 1e-9) const;
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/// @}
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/// @name Standard Interface
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/// @{
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/// Solve the GaussianBayesNet, i.e. return \f$ x = R^{-1}*d \f$, by back-substitution
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VectorValues optimize() const;
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/// Version of optimize for incomplete BayesNet, needs solution for missing variables
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VectorValues optimize(const VectorValues& solutionForMissing) const;
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/**
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* Return ordering corresponding to a topological sort.
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* There are many topological sorts of a Bayes net. This one
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* corresponds to the one that makes 'matrix' below upper-triangular.
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* In case Bayes net is incomplete any non-frontal are added to the end.
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*/
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Ordering ordering() const;
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///@}
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///@name Linear Algebra
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///@{
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/**
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* Return (dense) upper-triangular matrix representation
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* Will return upper-triangular matrix only when using 'ordering' above.
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* In case Bayes net is incomplete zero columns are added to the end.
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*/
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std::pair<Matrix, Vector> matrix(const Ordering& ordering) const;
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/**
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* Return (dense) upper-triangular matrix representation
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* Will return upper-triangular matrix only when using 'ordering' above.
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* In case Bayes net is incomplete zero columns are added to the end.
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*/
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std::pair<Matrix, Vector> matrix() const;
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/**
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* Optimize along the gradient direction, with a closed-form computation to perform the line
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* search. The gradient is computed about \f$ \delta x=0 \f$.
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*
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* This function returns \f$ \delta x \f$ that minimizes a reparametrized problem. The error
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* function of a GaussianBayesNet is
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*
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* \f[ f(\delta x) = \frac{1}{2} |R \delta x - d|^2 = \frac{1}{2}d^T d - d^T R \delta x +
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* \frac{1}{2} \delta x^T R^T R \delta x \f]
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*
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* with gradient and Hessian
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*
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* \f[ g(\delta x) = R^T(R\delta x - d), \qquad G(\delta x) = R^T R. \f]
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*
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* This function performs the line search in the direction of the gradient evaluated at \f$ g =
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* g(\delta x = 0) \f$ with step size \f$ \alpha \f$ that minimizes \f$ f(\delta x = \alpha g)
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* \f$:
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*
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* \f[ f(\alpha) = \frac{1}{2} d^T d + g^T \delta x + \frac{1}{2} \alpha^2 g^T G g \f]
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*
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* Optimizing by setting the derivative to zero yields \f$ \hat \alpha = (-g^T g) / (g^T G g)
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* \f$. For efficiency, this function evaluates the denominator without computing the Hessian
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* \f$ G \f$, returning
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*
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* \f[ \delta x = \hat\alpha g = \frac{-g^T g}{(R g)^T(R g)} \f] */
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VectorValues optimizeGradientSearch() const;
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/** Compute the gradient of the energy function, \f$ \nabla_{x=x_0} \left\Vert \Sigma^{-1} R x -
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* d \right\Vert^2 \f$, centered around \f$ x = x_0 \f$. The gradient is \f$ R^T(Rx-d) \f$.
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*
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* @param x0 The center about which to compute the gradient
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* @return The gradient as a VectorValues */
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VectorValues gradient(const VectorValues& x0) const;
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/** Compute the gradient of the energy function, \f$ \nabla_{x=0} \left\Vert \Sigma^{-1} R x - d
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* \right\Vert^2 \f$, centered around zero. The gradient about zero is \f$ -R^T d \f$. See also
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* gradient(const GaussianBayesNet&, const VectorValues&).
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*
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* @param [output] g A VectorValues to store the gradient, which must be preallocated, see
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* allocateVectorValues */
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VectorValues gradientAtZero() const;
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/** 0.5 * sum of squared Mahalanobis distances. */
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double error(const VectorValues& x) const;
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/**
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* Computes the determinant of a GassianBayesNet. A GaussianBayesNet is an upper triangular
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* matrix and for an upper triangular matrix determinant is the product of the diagonal
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* elements. Instead of actually multiplying we add the logarithms of the diagonal elements and
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* take the exponent at the end because this is more numerically stable.
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* @param bayesNet The input GaussianBayesNet
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* @return The determinant */
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double determinant() const;
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/**
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* Computes the log of the determinant of a GassianBayesNet. A GaussianBayesNet is an upper
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* triangular matrix and for an upper triangular matrix determinant is the product of the
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* diagonal elements.
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* @param bayesNet The input GaussianBayesNet
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* @return The determinant */
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double logDeterminant() const;
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/**
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* Backsubstitute with a different RHS vector than the one stored in this BayesNet.
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* gy=inv(R*inv(Sigma))*gx
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*/
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VectorValues backSubstitute(const VectorValues& gx) const;
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/**
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* Transpose backsubstitute with a different RHS vector than the one stored in this BayesNet.
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* gy=inv(L)*gx by solving L*gy=gx.
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* gy=inv(R'*inv(Sigma))*gx
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* gz'*R'=gx', gy = gz.*sigmas
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*/
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VectorValues backSubstituteTranspose(const VectorValues& gx) const;
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/// print graph
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void print(
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const std::string& s = "",
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const KeyFormatter& formatter = DefaultKeyFormatter) const override {
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Base::print(s, formatter);
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}
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/**
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* @brief Save the GaussianBayesNet as an image. Requires `dot` to be
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* installed.
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*
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* @param s The name of the figure.
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* @param keyFormatter Formatter to use for styling keys in the graph.
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*/
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void saveGraph(const std::string& s, const KeyFormatter& keyFormatter =
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DefaultKeyFormatter) const;
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/// @}
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private:
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/** Serialization function */
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friend class boost::serialization::access;
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template<class ARCHIVE>
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void serialize(ARCHIVE & ar, const unsigned int /*version*/) {
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ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
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}
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};
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/// traits
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template<>
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struct traits<GaussianBayesNet> : public Testable<GaussianBayesNet> {
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};
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} //\ namespace gtsam
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