576 lines
17 KiB
C++
576 lines
17 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 Expression-inl.h
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* @date September 18, 2014
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* @author Frank Dellaert
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* @author Paul Furgale
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* @brief Internals for Expression.h, not for general consumption
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*/
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#pragma once
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#include <gtsam/nonlinear/Values.h>
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#include <gtsam/base/Matrix.h>
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#include <boost/foreach.hpp>
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namespace gtsam {
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template<typename T>
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class Expression;
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typedef std::map<Key, Matrix> JacobianMap;
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//-----------------------------------------------------------------------------
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/**
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* Value and Jacobians
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*/
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template<class T>
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class Augmented {
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private:
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T value_;
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JacobianMap jacobians_;
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typedef std::pair<Key, Matrix> Pair;
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/// Insert terms into jacobians_, adding if already exists
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void add(const JacobianMap& terms) {
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BOOST_FOREACH(const Pair& term, terms) {
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JacobianMap::iterator it = jacobians_.find(term.first);
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if (it != jacobians_.end())
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it->second += term.second;
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else
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jacobians_[term.first] = term.second;
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}
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}
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/// Insert terms into jacobians_, premultiplying by H, adding if already exists
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void add(const Matrix& H, const JacobianMap& terms) {
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BOOST_FOREACH(const Pair& term, terms) {
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JacobianMap::iterator it = jacobians_.find(term.first);
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if (it != jacobians_.end())
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it->second += H * term.second;
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else
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jacobians_[term.first] = H * term.second;
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}
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}
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public:
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/// Construct value that does not depend on anything
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Augmented(const T& t) :
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value_(t) {
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}
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/// Construct value dependent on a single key
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Augmented(const T& t, Key key) :
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value_(t) {
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size_t n = t.dim();
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jacobians_[key] = Eigen::MatrixXd::Identity(n, n);
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}
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/// Construct value, pre-multiply jacobians by dTdA
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Augmented(const T& t, const Matrix& dTdA, const JacobianMap& jacobians) :
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value_(t) {
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add(dTdA, jacobians);
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}
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/// Construct value, pre-multiply jacobians
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Augmented(const T& t, const Matrix& dTdA1, const JacobianMap& jacobians1,
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const Matrix& dTdA2, const JacobianMap& jacobians2) :
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value_(t) {
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add(dTdA1, jacobians1);
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add(dTdA2, jacobians2);
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}
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/// Construct value, pre-multiply jacobians
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Augmented(const T& t, const Matrix& dTdA1, const JacobianMap& jacobians1,
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const Matrix& dTdA2, const JacobianMap& jacobians2, const Matrix& dTdA3,
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const JacobianMap& jacobians3) :
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value_(t) {
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add(dTdA1, jacobians1);
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add(dTdA2, jacobians2);
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add(dTdA3, jacobians3);
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}
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/// Return value
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const T& value() const {
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return value_;
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}
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/// Return jacobians
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const JacobianMap& jacobians() const {
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return jacobians_;
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}
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/// Return jacobians
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JacobianMap& jacobians() {
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return jacobians_;
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}
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/// Not dependent on any key
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bool constant() const {
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return jacobians_.empty();
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}
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/// debugging
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void print(const KeyFormatter& keyFormatter = DefaultKeyFormatter) {
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BOOST_FOREACH(const Pair& term, jacobians_)
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std::cout << "(" << keyFormatter(term.first) << ", " << term.second.rows()
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<< "x" << term.second.cols() << ") ";
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std::cout << std::endl;
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}
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};
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//-----------------------------------------------------------------------------
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template<class T>
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struct JacobianTrace {
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T t;
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T value() const {
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return t;
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}
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virtual void reverseAD(JacobianMap& jacobians) const = 0;
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virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const = 0;
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};
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//-----------------------------------------------------------------------------
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/**
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* Expression node. The superclass for objects that do the heavy lifting
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* An Expression<T> has a pointer to an ExpressionNode<T> underneath
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* allowing Expressions to have polymorphic behaviour even though they
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* are passed by value. This is the same way boost::function works.
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* http://loki-lib.sourceforge.net/html/a00652.html
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*/
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template<class T>
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class ExpressionNode {
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protected:
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ExpressionNode() {
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}
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public:
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/// Destructor
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virtual ~ExpressionNode() {
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}
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/// Return keys that play in this expression as a set
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virtual std::set<Key> keys() const = 0;
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/// Return value
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virtual T value(const Values& values) const = 0;
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/// Return value and derivatives
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virtual Augmented<T> forward(const Values& values) const = 0;
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/// Construct an execution trace for reverse AD
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virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
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const Values& values) const = 0;
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};
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//-----------------------------------------------------------------------------
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/// Constant Expression
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template<class T>
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class ConstantExpression: public ExpressionNode<T> {
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/// The constant value
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T constant_;
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/// Constructor with a value, yielding a constant
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ConstantExpression(const T& value) :
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constant_(value) {
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}
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friend class Expression<T> ;
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public:
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/// Destructor
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virtual ~ConstantExpression() {
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}
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/// Return keys that play in this expression, i.e., the empty set
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virtual std::set<Key> keys() const {
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std::set<Key> keys;
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return keys;
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}
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/// Return value
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virtual T value(const Values& values) const {
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return constant_;
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}
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/// Return value and derivatives
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virtual Augmented<T> forward(const Values& values) const {
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return Augmented<T>(constant_);
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}
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/// Trace structure for reverse AD
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struct Trace: public JacobianTrace<T> {
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/// If the expression is just a constant, we do nothing
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virtual void reverseAD(JacobianMap& jacobians) const {
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}
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/// Base case: we simply ignore the given df/dT
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virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
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}
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};
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/// Construct an execution trace for reverse AD
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virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
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const Values& values) const {
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boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
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trace->t = constant_;
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return trace;
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}
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};
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//-----------------------------------------------------------------------------
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/// Leaf Expression
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template<class T>
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class LeafExpression: public ExpressionNode<T> {
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/// The key into values
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Key key_;
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/// Constructor with a single key
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LeafExpression(Key key) :
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key_(key) {
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}
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friend class Expression<T> ;
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public:
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/// Destructor
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virtual ~LeafExpression() {
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}
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/// Return keys that play in this expression
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virtual std::set<Key> keys() const {
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std::set<Key> keys;
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keys.insert(key_);
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return keys;
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}
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/// Return value
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virtual T value(const Values& values) const {
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return values.at<T>(key_);
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}
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/// Return value and derivatives
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virtual Augmented<T> forward(const Values& values) const {
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T t = value(values);
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return Augmented<T>(t, key_);
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}
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/// Trace structure for reverse AD
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struct Trace: public JacobianTrace<T> {
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Key key;
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/// If the expression is just a leaf, we just insert an identity matrix
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virtual void reverseAD(JacobianMap& jacobians) const {
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size_t n = T::Dim();
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jacobians[key] = Eigen::MatrixXd::Identity(n, n);
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}
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/// Base case: given df/dT, add it jacobians with correct key and we are done
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virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
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JacobianMap::iterator it = jacobians.find(key);
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if (it != jacobians.end())
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it->second += dFdT;
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else
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jacobians[key] = dFdT;
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}
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};
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/// Construct an execution trace for reverse AD
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virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
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const Values& values) const {
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boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
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trace->t = value(values);
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trace->key = key_;
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return trace;
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}
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};
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//-----------------------------------------------------------------------------
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/// Unary Function Expression
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template<class T, class A>
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class UnaryExpression: public ExpressionNode<T> {
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public:
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typedef Eigen::Matrix<double,T::dimension,A::dimension> JacobianTA;
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typedef boost::function<T(const A&, boost::optional<JacobianTA&>)> Function;
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private:
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Function function_;
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boost::shared_ptr<ExpressionNode<A> > expressionA_;
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/// Constructor with a unary function f, and input argument e
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UnaryExpression(Function f, const Expression<A>& e) :
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function_(f), expressionA_(e.root()) {
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}
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friend class Expression<T> ;
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public:
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/// Destructor
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virtual ~UnaryExpression() {
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}
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/// Return keys that play in this expression
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virtual std::set<Key> keys() const {
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return expressionA_->keys();
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}
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/// Return value
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virtual T value(const Values& values) const {
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return function_(this->expressionA_->value(values), boost::none);
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}
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/// Return value and derivatives
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virtual Augmented<T> forward(const Values& values) const {
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using boost::none;
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Augmented<A> argument = this->expressionA_->forward(values);
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JacobianTA dTdA;
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T t = function_(argument.value(),
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argument.constant() ? none : boost::optional<JacobianTA&>(dTdA));
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return Augmented<T>(t, dTdA, argument.jacobians());
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}
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/// Trace structure for reverse AD
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struct Trace: public JacobianTrace<T> {
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boost::shared_ptr<JacobianTrace<A> > trace1;
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JacobianTA dTdA;
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/// Start the reverse AD process
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virtual void reverseAD(JacobianMap& jacobians) const {
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trace1->reverseAD(dTdA, jacobians);
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}
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/// Given df/dT, multiply in dT/dA and continue reverse AD process
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virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
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trace1->reverseAD(dFdT * dTdA, jacobians);
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}
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};
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/// Construct an execution trace for reverse AD
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virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
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const Values& values) const {
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boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
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trace->trace1 = this->expressionA_->traceExecution(values);
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trace->t = function_(trace->trace1->value(), trace->dTdA);
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return trace;
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}
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};
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//-----------------------------------------------------------------------------
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/// Binary Expression
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template<class T, class A1, class A2>
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class BinaryExpression: public ExpressionNode<T> {
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public:
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typedef Eigen::Matrix<double,T::dimension,A1::dimension> JacobianTA1;
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typedef Eigen::Matrix<double,T::dimension,A2::dimension> JacobianTA2;
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typedef boost::function<
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T(const A1&, const A2&, boost::optional<JacobianTA1&>,
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boost::optional<JacobianTA2&>)> Function;
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private:
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Function function_;
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boost::shared_ptr<ExpressionNode<A1> > expressionA1_;
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boost::shared_ptr<ExpressionNode<A2> > expressionA2_;
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/// Constructor with a binary function f, and two input arguments
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BinaryExpression(Function f, //
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const Expression<A1>& e1, const Expression<A2>& e2) :
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function_(f), expressionA1_(e1.root()), expressionA2_(e2.root()) {
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}
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friend class Expression<T> ;
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public:
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/// Destructor
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virtual ~BinaryExpression() {
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}
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/// Return keys that play in this expression
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virtual std::set<Key> keys() const {
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std::set<Key> keys1 = expressionA1_->keys();
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std::set<Key> keys2 = expressionA2_->keys();
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keys1.insert(keys2.begin(), keys2.end());
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return keys1;
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}
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/// Return value
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virtual T value(const Values& values) const {
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using boost::none;
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return function_(this->expressionA1_->value(values),
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this->expressionA2_->value(values), none, none);
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}
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/// Return value and derivatives
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virtual Augmented<T> forward(const Values& values) const {
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using boost::none;
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Augmented<A1> a1 = this->expressionA1_->forward(values);
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Augmented<A2> a2 = this->expressionA2_->forward(values);
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JacobianTA1 dTdA1;
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JacobianTA2 dTdA2;
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T t = function_(a1.value(), a2.value(),
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a1.constant() ? none : boost::optional<JacobianTA1&>(dTdA1),
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a2.constant() ? none : boost::optional<JacobianTA2&>(dTdA2));
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return Augmented<T>(t, dTdA1, a1.jacobians(), dTdA2, a2.jacobians());
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}
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/// Trace structure for reverse AD
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struct Trace: public JacobianTrace<T> {
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boost::shared_ptr<JacobianTrace<A1> > trace1;
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boost::shared_ptr<JacobianTrace<A2> > trace2;
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JacobianTA1 dTdA1;
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JacobianTA2 dTdA2;
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/// Start the reverse AD process
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virtual void reverseAD(JacobianMap& jacobians) const {
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trace1->reverseAD(dTdA1, jacobians);
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trace2->reverseAD(dTdA2, jacobians);
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}
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/// Given df/dT, multiply in dT/dA and continue reverse AD process
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virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
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trace1->reverseAD(dFdT * dTdA1, jacobians);
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trace2->reverseAD(dFdT * dTdA2, jacobians);
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}
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};
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/// Construct an execution trace for reverse AD
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virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
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const Values& values) const {
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boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
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trace->trace1 = this->expressionA1_->traceExecution(values);
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trace->trace2 = this->expressionA2_->traceExecution(values);
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trace->t = function_(trace->trace1->value(), trace->trace2->value(),
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trace->dTdA1, trace->dTdA2);
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return trace;
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}
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};
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//-----------------------------------------------------------------------------
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/// Ternary Expression
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template<class T, class A1, class A2, class A3>
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class TernaryExpression: public ExpressionNode<T> {
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public:
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typedef boost::function<
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T(const A1&, const A2&, const A3&, boost::optional<Matrix&>,
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boost::optional<Matrix&>, boost::optional<Matrix&>)> Function;
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private:
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Function function_;
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boost::shared_ptr<ExpressionNode<A1> > expressionA1_;
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boost::shared_ptr<ExpressionNode<A2> > expressionA2_;
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boost::shared_ptr<ExpressionNode<A3> > expressionA3_;
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/// Constructor with a ternary function f, and three input arguments
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TernaryExpression(
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Function f, //
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const Expression<A1>& e1, const Expression<A2>& e2,
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const Expression<A3>& e3) :
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function_(f), expressionA1_(e1.root()), expressionA2_(e2.root()), expressionA3_(
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e3.root()) {
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}
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friend class Expression<T> ;
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public:
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/// Destructor
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virtual ~TernaryExpression() {
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}
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/// Return keys that play in this expression
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virtual std::set<Key> keys() const {
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std::set<Key> keys1 = expressionA1_->keys();
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std::set<Key> keys2 = expressionA2_->keys();
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std::set<Key> keys3 = expressionA3_->keys();
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keys2.insert(keys3.begin(), keys3.end());
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keys1.insert(keys2.begin(), keys2.end());
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return keys1;
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}
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/// Return value
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virtual T value(const Values& values) const {
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using boost::none;
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return function_(this->expressionA1_->value(values),
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this->expressionA2_->value(values), this->expressionA3_->value(values),
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none, none, none);
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}
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/// Return value and derivatives
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virtual Augmented<T> forward(const Values& values) const {
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using boost::none;
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Augmented<A1> a1 = this->expressionA1_->forward(values);
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Augmented<A2> a2 = this->expressionA2_->forward(values);
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Augmented<A3> a3 = this->expressionA3_->forward(values);
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Matrix dTdA1, dTdA2, dTdA3;
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T t = function_(a1.value(), a2.value(), a3.value(),
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a1.constant() ? none : boost::optional<Matrix&>(dTdA1),
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a2.constant() ? none : boost::optional<Matrix&>(dTdA2),
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a3.constant() ? none : boost::optional<Matrix&>(dTdA3));
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return Augmented<T>(t, dTdA1, a1.jacobians(), dTdA2, a2.jacobians(), dTdA3,
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a3.jacobians());
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}
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/// Trace structure for reverse AD
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struct Trace: public JacobianTrace<T> {
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boost::shared_ptr<JacobianTrace<A1> > trace1;
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boost::shared_ptr<JacobianTrace<A2> > trace2;
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boost::shared_ptr<JacobianTrace<A3> > trace3;
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Matrix dTdA1, dTdA2, dTdA3;
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/// Start the reverse AD process
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virtual void reverseAD(JacobianMap& jacobians) const {
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trace1->reverseAD(dTdA1, jacobians);
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trace2->reverseAD(dTdA2, jacobians);
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trace3->reverseAD(dTdA3, jacobians);
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}
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/// Given df/dT, multiply in dT/dA and continue reverse AD process
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virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
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trace1->reverseAD(dFdT * dTdA1, jacobians);
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trace2->reverseAD(dFdT * dTdA2, jacobians);
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trace3->reverseAD(dFdT * dTdA3, jacobians);
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}
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};
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/// Construct an execution trace for reverse AD
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virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
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const Values& values) const {
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boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
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trace->trace1 = this->expressionA1_->traceExecution(values);
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trace->trace2 = this->expressionA2_->traceExecution(values);
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trace->trace3 = this->expressionA3_->traceExecution(values);
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trace->t = function_(trace->trace1->value(), trace->trace2->value(),
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trace->trace3->value(), trace->dTdA1, trace->dTdA2, trace->dTdA3);
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return trace;
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}
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};
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//-----------------------------------------------------------------------------
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}
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