176 lines
6.2 KiB
C++
176 lines
6.2 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/GaussianConditionalUnordered.h>
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#include <gtsam/inference/FactorGraphUnordered.h>
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#include <gtsam/global_includes.h>
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namespace gtsam {
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/** A Bayes net made from linear-Gaussian densities */
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class GTSAM_EXPORT GaussianBayesNetUnordered: public FactorGraphUnordered<GaussianConditionalUnordered>
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{
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public:
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typedef FactorGraphUnordered<GaussianConditionalUnordered> Base;
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typedef GaussianBayesNetUnordered This;
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typedef GaussianConditionalUnordered 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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GaussianBayesNetUnordered() {}
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/** Construct from iterator over conditionals */
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template<typename ITERATOR>
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GaussianBayesNetUnordered(ITERATOR firstConditional, ITERATOR lastConditional) : 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 GaussianBayesNetUnordered(const CONTAINER& conditionals) : Base(conditionals) {}
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/** Implicit copy/downcast constructor to override explicit template container constructor */
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template<class DERIVEDCONDITIONAL>
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GaussianBayesNetUnordered(const FactorGraphUnordered<DERIVEDCONDITIONAL>& graph) : Base(graph) {}
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/**
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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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/**
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* Solve the GaussianBayesNet, i.e. return \f$ x = R^{-1}*d \f$, computed by
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* back-substitution.
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*/
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VectorValuesUnordered optimize() const;
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/**
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* Optimize along the gradient direction, with a closed-form computation to
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* perform the line search. The gradient is computed about \f$ \delta x=0 \f$.
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*
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* This function returns \f$ \delta x \f$ that minimizes a reparametrized
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* problem. The error 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 + \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
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* gradient evaluated at \f$ g = g(\delta x = 0) \f$ with step size
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* \f$ \alpha \f$ that minimizes \f$ f(\delta x = \alpha g) \f$:
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*
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* \f[ f(\alpha) = \frac{1}{2} d^T d + g^T \delta x + \frac{1}{2} \alpha^2 g^T G g \f]
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*
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* Optimizing by setting the derivative to zero yields
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* \f$ \hat \alpha = (-g^T g) / (g^T G g) \f$. For efficiency, this function
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* evaluates the denominator without computing the Hessian \f$ G \f$, returning
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*
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* \f[ \delta x = \hat\alpha g = \frac{-g^T g}{(R g)^T(R g)} \f]
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*
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* @param bn The GaussianBayesNet on which to perform this computation
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* @return The resulting \f$ \delta x \f$ as described above
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*/
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//VectorValuesUnordered optimizeGradientSearch() 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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*/
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std::pair<Matrix, Vector> matrix() const;
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/**
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* Compute the gradient of the energy function,
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* \f$ \nabla_{x=x_0} \left\Vert \Sigma^{-1} R x - d \right\Vert^2 \f$,
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* centered around \f$ x = x_0 \f$.
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* The gradient is \f$ R^T(Rx-d) \f$.
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* @param bayesNet The Gaussian Bayes net $(R,d)$
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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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*/
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//VectorValuesUnordered gradient(const VectorValuesUnordered& x0) const;
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/**
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* Compute the gradient of the energy function,
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* \f$ \nabla_{x=0} \left\Vert \Sigma^{-1} R x - d \right\Vert^2 \f$,
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* centered around zero.
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* The gradient about zero is \f$ -R^T d \f$. See also gradient(const GaussianBayesNet&, const VectorValues&).
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* @param bayesNet The Gaussian Bayes net $(R,d)$
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* @param [output] g A VectorValues to store the gradient, which must be preallocated, see allocateVectorValues
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* @return The gradient as a VectorValues
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*/
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//VectorValuesUnordered gradientAtZero() 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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VectorValuesUnordered backSubstitute(const VectorValuesUnordered& 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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VectorValuesUnordered backSubstituteTranspose(const VectorValuesUnordered& gx) const;
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/// @}
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};
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} /// namespace gtsam
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