251 lines
7.5 KiB
C++
251 lines
7.5 KiB
C++
/**
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* @file GaussianFactorGraph.h
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* @brief Linear Factor Graph where all factors are Gaussians
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* @author Kai Ni
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* @author Christian Potthast
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* @author Alireza Fathi
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*/
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// $Id: GaussianFactorGraph.h,v 1.24 2009/08/14 20:48:51 acunning Exp $
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// \callgraph
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#pragma once
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#include <boost/shared_ptr.hpp>
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#include "FactorGraph.h"
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#include "Errors.h"
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#include "GaussianFactor.h"
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#include "GaussianBayesNet.h" // needed for MATLAB toolbox !!
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namespace gtsam {
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class Ordering;
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/**
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* A Linear Factor Graph is a factor graph where all factors are Gaussian, i.e.
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* Factor == GaussianFactor
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* VectorConfig = A configuration of vectors
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* Most of the time, linear factor graphs arise by linearizing a non-linear factor graph.
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*/
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class GaussianFactorGraph : public FactorGraph<GaussianFactor> {
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public:
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/**
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* Default constructor
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*/
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GaussianFactorGraph() {}
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/**
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* Constructor that receives a Chordal Bayes Net and returns a GaussianFactorGraph
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*/
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GaussianFactorGraph(const GaussianBayesNet& CBN);
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/** Add a null factor */
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inline void add(const Vector& b) {
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push_back(sharedFactor(new GaussianFactor(b)));
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}
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/** Add a unary factor */
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inline void add(const Symbol& key1, const Matrix& A1,
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const Vector& b, double sigma) {
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push_back(sharedFactor(new GaussianFactor(key1,A1,b,sigma)));
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}
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/** Add a binary factor */
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inline void add(const Symbol& key1, const Matrix& A1,
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const Symbol& key2, const Matrix& A2,
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const Vector& b, double sigma) {
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push_back(sharedFactor(new GaussianFactor(key1,A1,key2,A2,b,sigma)));
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}
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/** Add a ternary factor */
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inline void add(const Symbol& key1, const Matrix& A1,
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const Symbol& key2, const Matrix& A2,
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const Symbol& key3, const Matrix& A3,
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const Vector& b, double sigma) {
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push_back(sharedFactor(new GaussianFactor(key1,A1,key2,A2,key3,A3,b,sigma)));
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}
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/** Add an n-ary factor */
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inline void add(const std::vector<std::pair<Symbol, Matrix> > &terms,
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const Vector &b, double sigma) {
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push_back(sharedFactor(new GaussianFactor(terms,b,sigma)));
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}
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/** return A*x-b */
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Errors errors(const VectorConfig& x) const;
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/** unnormalized error */
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double error(const VectorConfig& x) const;
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/** return A*x */
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Errors operator*(const VectorConfig& x) const;
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/** return A^x */
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VectorConfig operator^(const Errors& e) const;
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/**
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* Calculate Gradient of A^(A*x-b) for a given config
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* @param x: VectorConfig specifying where to calculate gradient
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* @return gradient, as a VectorConfig as well
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*/
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VectorConfig gradient(const VectorConfig& x) const;
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/** Unnormalized probability. O(n) */
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double probPrime(const VectorConfig& c) const {
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return exp(-0.5 * error(c));
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}
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/**
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* find the separator, i.e. all the nodes that have at least one
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* common factor with the given node. FD: not used AFAIK.
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*/
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std::set<Symbol> find_separator(const Symbol& key) const;
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/**
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* Eliminate a single node yielding a conditional Gaussian
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* Eliminates the factors from the factor graph through findAndRemoveFactors
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* and adds a new factor on the separator to the factor graph
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*/
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GaussianConditional::shared_ptr eliminateOne(const Symbol& key);
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/**
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* eliminate factor graph in place(!) in the given order, yielding
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* a chordal Bayes net. Allows for passing an incomplete ordering
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* that does not completely eliminate the graph
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*/
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GaussianBayesNet eliminate(const Ordering& ordering);
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/**
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* optimize a linear factor graph
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* @param ordering fg in order
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*/
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VectorConfig optimize(const Ordering& ordering);
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/**
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* shared pointer versions for MATLAB
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*/
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boost::shared_ptr<GaussianBayesNet> eliminate_(const Ordering&);
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boost::shared_ptr<VectorConfig> optimize_(const Ordering&);
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/**
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* static function that combines two factor graphs
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* @param const &lfg1 Linear factor graph
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* @param const &lfg2 Linear factor graph
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* @return a new combined factor graph
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*/
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static GaussianFactorGraph combine2(const GaussianFactorGraph& lfg1,
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const GaussianFactorGraph& lfg2);
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/**
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* combine two factor graphs
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* @param *lfg Linear factor graph
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*/
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void combine(const GaussianFactorGraph &lfg);
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/**
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* Find all variables and their dimensions
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* @return The set of all variable/dimension pairs
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*/
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Dimensions dimensions() const;
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/**
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* Add zero-mean i.i.d. Gaussian prior terms to each variable
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* @param sigma Standard deviation of Gaussian
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*/
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GaussianFactorGraph add_priors(double sigma) const;
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/**
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* Return RHS (b./sigmas) as Errors class
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*/
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Errors rhs() const;
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/**
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* Return (dense) matrix associated with factor graph
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* @param ordering of variables needed for matrix column order
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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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* get the starting column indices for all variables
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* @param ordering of variables needed for matrix column order
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* @return The set of all variable/index pairs
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*/
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Dimensions columnIndices(const Ordering& ordering) const;
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/**
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* Return 3*nzmax matrix where the rows correspond to the vectors i, j, and s
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* to generate an m-by-n sparse matrix, which can be given to MATLAB's sparse function.
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* The standard deviations are baked into A and b
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* @param ordering of variables needed for matrix column order
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*/
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Matrix sparse(const Ordering& ordering) const;
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/**
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* Take an optimal step in direction d by calculating optimal step-size
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* @param x: starting point for search
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* @param d: search direction
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*/
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VectorConfig optimalUpdate(const VectorConfig& x0, const VectorConfig& d) const;
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/**
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* Find solution using gradient descent
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* @param x0: VectorConfig specifying initial estimate
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* @return solution
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*/
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VectorConfig steepestDescent(const VectorConfig& x0, bool verbose = false,
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double epsilon = 1e-3, size_t maxIterations = 0) const;
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/**
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* shared pointer versions for MATLAB
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*/
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boost::shared_ptr<VectorConfig>
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steepestDescent_(const VectorConfig& x0, bool verbose = false,
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double epsilon = 1e-3, size_t maxIterations = 0) const;
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/**
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* Find solution using conjugate gradient descent
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* @param x0: VectorConfig specifying initial estimate
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* @return solution
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*/
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VectorConfig conjugateGradientDescent(const VectorConfig& x0, bool verbose =
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false, double epsilon = 1e-3, size_t maxIterations = 0) const;
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/**
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* shared pointer versions for MATLAB
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*/
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boost::shared_ptr<VectorConfig> conjugateGradientDescent_(
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const VectorConfig& x0, bool verbose = false, double epsilon = 1e-3,
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size_t maxIterations = 0) const;
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};
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/**
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* A linear system solver using factorization
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*/
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template <class NonlinearGraph, class Config>
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class Factorization {
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public:
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Factorization() {}
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Factorization(const NonlinearGraph& g, const Config& config) {}
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/**
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* solve for the optimal displacement in the tangent space, and then solve
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* the resulted linear system
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*/
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VectorConfig optimize(GaussianFactorGraph& fg, const Ordering& ordering) const {
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return fg.optimize(ordering);
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}
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/**
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* linearize the non-linear graph around the current config,
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*/
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VectorConfig linearizeAndOptimize(const NonlinearGraph& g, const Config& config,
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const Ordering& ordering) const {
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GaussianFactorGraph linear = g.linearize(config);
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return optimize(linear, ordering);
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}
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};
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}
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