583 lines
17 KiB
C++
583 lines
17 KiB
C++
/* ----------------------------------------------------------------------------
|
|
|
|
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
|
|
* Atlanta, Georgia 30332-0415
|
|
* All Rights Reserved
|
|
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
|
|
|
|
* See LICENSE for the license information
|
|
|
|
* -------------------------------------------------------------------------- */
|
|
|
|
/**
|
|
* @file Expression-inl.h
|
|
* @date September 18, 2014
|
|
* @author Frank Dellaert
|
|
* @author Paul Furgale
|
|
* @brief Internals for Expression.h, not for general consumption
|
|
*/
|
|
|
|
#pragma once
|
|
|
|
#include <gtsam/nonlinear/Values.h>
|
|
#include <gtsam/base/Matrix.h>
|
|
#include <boost/foreach.hpp>
|
|
|
|
namespace gtsam {
|
|
|
|
template<typename T>
|
|
class Expression;
|
|
|
|
typedef std::map<Key, Matrix> JacobianMap;
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/**
|
|
* Value and Jacobians
|
|
*/
|
|
template<class T>
|
|
class Augmented {
|
|
|
|
private:
|
|
|
|
T value_;
|
|
JacobianMap jacobians_;
|
|
|
|
typedef std::pair<Key, Matrix> Pair;
|
|
|
|
/// Insert terms into jacobians_, adding if already exists
|
|
void add(const JacobianMap& terms) {
|
|
BOOST_FOREACH(const Pair& term, terms) {
|
|
JacobianMap::iterator it = jacobians_.find(term.first);
|
|
if (it != jacobians_.end())
|
|
it->second += term.second;
|
|
else
|
|
jacobians_[term.first] = term.second;
|
|
}
|
|
}
|
|
|
|
/// Insert terms into jacobians_, premultiplying by H, adding if already exists
|
|
void add(const Matrix& H, const JacobianMap& terms) {
|
|
BOOST_FOREACH(const Pair& term, terms) {
|
|
JacobianMap::iterator it = jacobians_.find(term.first);
|
|
if (it != jacobians_.end())
|
|
it->second += H * term.second;
|
|
else
|
|
jacobians_[term.first] = H * term.second;
|
|
}
|
|
}
|
|
|
|
public:
|
|
|
|
/// Construct value that does not depend on anything
|
|
Augmented(const T& t) :
|
|
value_(t) {
|
|
}
|
|
|
|
/// Construct value dependent on a single key
|
|
Augmented(const T& t, Key key) :
|
|
value_(t) {
|
|
size_t n = t.dim();
|
|
jacobians_[key] = Eigen::MatrixXd::Identity(n, n);
|
|
}
|
|
|
|
/// Construct value, pre-multiply jacobians by dTdA
|
|
Augmented(const T& t, const Matrix& dTdA, const JacobianMap& jacobians) :
|
|
value_(t) {
|
|
add(dTdA, jacobians);
|
|
}
|
|
|
|
/// Construct value, pre-multiply jacobians
|
|
Augmented(const T& t, const Matrix& dTdA1, const JacobianMap& jacobians1,
|
|
const Matrix& dTdA2, const JacobianMap& jacobians2) :
|
|
value_(t) {
|
|
add(dTdA1, jacobians1);
|
|
add(dTdA2, jacobians2);
|
|
}
|
|
|
|
/// Construct value, pre-multiply jacobians
|
|
Augmented(const T& t, const Matrix& dTdA1, const JacobianMap& jacobians1,
|
|
const Matrix& dTdA2, const JacobianMap& jacobians2, const Matrix& dTdA3,
|
|
const JacobianMap& jacobians3) :
|
|
value_(t) {
|
|
add(dTdA1, jacobians1);
|
|
add(dTdA2, jacobians2);
|
|
add(dTdA3, jacobians3);
|
|
}
|
|
|
|
/// Return value
|
|
const T& value() const {
|
|
return value_;
|
|
}
|
|
|
|
/// Return jacobians
|
|
const JacobianMap& jacobians() const {
|
|
return jacobians_;
|
|
}
|
|
|
|
/// Return jacobians
|
|
JacobianMap& jacobians() {
|
|
return jacobians_;
|
|
}
|
|
|
|
/// Not dependent on any key
|
|
bool constant() const {
|
|
return jacobians_.empty();
|
|
}
|
|
|
|
/// debugging
|
|
void print(const KeyFormatter& keyFormatter = DefaultKeyFormatter) {
|
|
BOOST_FOREACH(const Pair& term, jacobians_)
|
|
std::cout << "(" << keyFormatter(term.first) << ", " << term.second.rows()
|
|
<< "x" << term.second.cols() << ") ";
|
|
std::cout << std::endl;
|
|
}
|
|
};
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<class T>
|
|
struct JacobianTrace {
|
|
T t;
|
|
T value() const {
|
|
return t;
|
|
}
|
|
virtual void reverseAD(JacobianMap& jacobians) const = 0;
|
|
virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const = 0;
|
|
};
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/**
|
|
* Expression node. The superclass for objects that do the heavy lifting
|
|
* An Expression<T> has a pointer to an ExpressionNode<T> underneath
|
|
* allowing Expressions to have polymorphic behaviour even though they
|
|
* are passed by value. This is the same way boost::function works.
|
|
* http://loki-lib.sourceforge.net/html/a00652.html
|
|
*/
|
|
template<class T>
|
|
class ExpressionNode {
|
|
|
|
protected:
|
|
ExpressionNode() {
|
|
}
|
|
|
|
public:
|
|
|
|
/// Destructor
|
|
virtual ~ExpressionNode() {
|
|
}
|
|
|
|
/// Return keys that play in this expression as a set
|
|
virtual std::set<Key> keys() const = 0;
|
|
|
|
/// Return value
|
|
virtual T value(const Values& values) const = 0;
|
|
|
|
/// Return value and derivatives
|
|
virtual Augmented<T> forward(const Values& values) const = 0;
|
|
|
|
/// Construct an execution trace for reverse AD
|
|
virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
|
|
const Values& values) const = 0;
|
|
};
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// Constant Expression
|
|
template<class T>
|
|
class ConstantExpression: public ExpressionNode<T> {
|
|
|
|
/// The constant value
|
|
T constant_;
|
|
|
|
/// Constructor with a value, yielding a constant
|
|
ConstantExpression(const T& value) :
|
|
constant_(value) {
|
|
}
|
|
|
|
friend class Expression<T> ;
|
|
|
|
public:
|
|
|
|
/// Destructor
|
|
virtual ~ConstantExpression() {
|
|
}
|
|
|
|
/// Return keys that play in this expression, i.e., the empty set
|
|
virtual std::set<Key> keys() const {
|
|
std::set<Key> keys;
|
|
return keys;
|
|
}
|
|
|
|
/// Return value
|
|
virtual T value(const Values& values) const {
|
|
return constant_;
|
|
}
|
|
|
|
/// Return value and derivatives
|
|
virtual Augmented<T> forward(const Values& values) const {
|
|
return Augmented<T>(constant_);
|
|
}
|
|
|
|
/// Trace structure for reverse AD
|
|
struct Trace: public JacobianTrace<T> {
|
|
/// If the expression is just a constant, we do nothing
|
|
virtual void reverseAD(JacobianMap& jacobians) const {
|
|
}
|
|
/// Base case: we simply ignore the given df/dT
|
|
virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
|
|
}
|
|
};
|
|
|
|
/// Construct an execution trace for reverse AD
|
|
virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
|
|
const Values& values) const {
|
|
boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
|
|
trace->t = constant_;
|
|
return trace;
|
|
}
|
|
};
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// Leaf Expression
|
|
template<class T>
|
|
class LeafExpression: public ExpressionNode<T> {
|
|
|
|
/// The key into values
|
|
Key key_;
|
|
|
|
/// Constructor with a single key
|
|
LeafExpression(Key key) :
|
|
key_(key) {
|
|
}
|
|
|
|
friend class Expression<T> ;
|
|
|
|
public:
|
|
|
|
/// Destructor
|
|
virtual ~LeafExpression() {
|
|
}
|
|
|
|
/// Return keys that play in this expression
|
|
virtual std::set<Key> keys() const {
|
|
std::set<Key> keys;
|
|
keys.insert(key_);
|
|
return keys;
|
|
}
|
|
|
|
/// Return value
|
|
virtual T value(const Values& values) const {
|
|
return values.at<T>(key_);
|
|
}
|
|
|
|
/// Return value and derivatives
|
|
virtual Augmented<T> forward(const Values& values) const {
|
|
T t = value(values);
|
|
return Augmented<T>(t, key_);
|
|
}
|
|
|
|
/// Trace structure for reverse AD
|
|
struct Trace: public JacobianTrace<T> {
|
|
Key key;
|
|
/// If the expression is just a leaf, we just insert an identity matrix
|
|
virtual void reverseAD(JacobianMap& jacobians) const {
|
|
size_t n = T::Dim();
|
|
jacobians[key] = Eigen::MatrixXd::Identity(n, n);
|
|
}
|
|
/// Base case: given df/dT, add it jacobians with correct key and we are done
|
|
virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
|
|
JacobianMap::iterator it = jacobians.find(key);
|
|
if (it != jacobians.end())
|
|
it->second += dFdT;
|
|
else
|
|
jacobians[key] = dFdT;
|
|
}
|
|
};
|
|
|
|
/// Construct an execution trace for reverse AD
|
|
virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
|
|
const Values& values) const {
|
|
boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
|
|
trace->t = value(values);
|
|
trace->key = key_;
|
|
return trace;
|
|
}
|
|
|
|
};
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// Unary Function Expression
|
|
template<class T, class A>
|
|
class UnaryExpression: public ExpressionNode<T> {
|
|
|
|
public:
|
|
|
|
typedef Eigen::Matrix<double, T::dimension, A::dimension> JacobianTA;
|
|
typedef boost::function<T(const A&, boost::optional<JacobianTA&>)> Function;
|
|
|
|
private:
|
|
|
|
Function function_;
|
|
boost::shared_ptr<ExpressionNode<A> > expressionA_;
|
|
|
|
/// Constructor with a unary function f, and input argument e
|
|
UnaryExpression(Function f, const Expression<A>& e) :
|
|
function_(f), expressionA_(e.root()) {
|
|
}
|
|
|
|
friend class Expression<T> ;
|
|
|
|
public:
|
|
|
|
/// Destructor
|
|
virtual ~UnaryExpression() {
|
|
}
|
|
|
|
/// Return keys that play in this expression
|
|
virtual std::set<Key> keys() const {
|
|
return expressionA_->keys();
|
|
}
|
|
|
|
/// Return value
|
|
virtual T value(const Values& values) const {
|
|
return function_(this->expressionA_->value(values), boost::none);
|
|
}
|
|
|
|
/// Return value and derivatives
|
|
virtual Augmented<T> forward(const Values& values) const {
|
|
using boost::none;
|
|
Augmented<A> argument = this->expressionA_->forward(values);
|
|
JacobianTA dTdA;
|
|
T t = function_(argument.value(),
|
|
argument.constant() ? none : boost::optional<JacobianTA&>(dTdA));
|
|
return Augmented<T>(t, dTdA, argument.jacobians());
|
|
}
|
|
|
|
/// Trace structure for reverse AD
|
|
struct Trace: public JacobianTrace<T> {
|
|
boost::shared_ptr<JacobianTrace<A> > trace1;
|
|
JacobianTA dTdA;
|
|
/// Start the reverse AD process
|
|
virtual void reverseAD(JacobianMap& jacobians) const {
|
|
trace1->reverseAD(dTdA, jacobians);
|
|
}
|
|
/// Given df/dT, multiply in dT/dA and continue reverse AD process
|
|
virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
|
|
trace1->reverseAD(dFdT * dTdA, jacobians);
|
|
}
|
|
};
|
|
|
|
/// Construct an execution trace for reverse AD
|
|
virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
|
|
const Values& values) const {
|
|
boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
|
|
trace->trace1 = this->expressionA_->traceExecution(values);
|
|
trace->t = function_(trace->trace1->value(), trace->dTdA);
|
|
return trace;
|
|
}
|
|
};
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// Binary Expression
|
|
|
|
template<class T, class A1, class A2>
|
|
class BinaryExpression: public ExpressionNode<T> {
|
|
|
|
public:
|
|
|
|
typedef Eigen::Matrix<double, T::dimension, A1::dimension> JacobianTA1;
|
|
typedef Eigen::Matrix<double, T::dimension, A2::dimension> JacobianTA2;
|
|
typedef boost::function<
|
|
T(const A1&, const A2&, boost::optional<JacobianTA1&>,
|
|
boost::optional<JacobianTA2&>)> Function;
|
|
|
|
private:
|
|
|
|
Function function_;
|
|
boost::shared_ptr<ExpressionNode<A1> > expressionA1_;
|
|
boost::shared_ptr<ExpressionNode<A2> > expressionA2_;
|
|
|
|
/// Constructor with a binary function f, and two input arguments
|
|
BinaryExpression(Function f, //
|
|
const Expression<A1>& e1, const Expression<A2>& e2) :
|
|
function_(f), expressionA1_(e1.root()), expressionA2_(e2.root()) {
|
|
}
|
|
|
|
friend class Expression<T> ;
|
|
|
|
public:
|
|
|
|
/// Destructor
|
|
virtual ~BinaryExpression() {
|
|
}
|
|
|
|
/// Return keys that play in this expression
|
|
virtual std::set<Key> keys() const {
|
|
std::set<Key> keys1 = expressionA1_->keys();
|
|
std::set<Key> keys2 = expressionA2_->keys();
|
|
keys1.insert(keys2.begin(), keys2.end());
|
|
return keys1;
|
|
}
|
|
|
|
/// Return value
|
|
virtual T value(const Values& values) const {
|
|
using boost::none;
|
|
return function_(this->expressionA1_->value(values),
|
|
this->expressionA2_->value(values), none, none);
|
|
}
|
|
|
|
/// Return value and derivatives
|
|
virtual Augmented<T> forward(const Values& values) const {
|
|
using boost::none;
|
|
Augmented<A1> a1 = this->expressionA1_->forward(values);
|
|
Augmented<A2> a2 = this->expressionA2_->forward(values);
|
|
JacobianTA1 dTdA1;
|
|
JacobianTA2 dTdA2;
|
|
T t = function_(a1.value(), a2.value(),
|
|
a1.constant() ? none : boost::optional<JacobianTA1&>(dTdA1),
|
|
a2.constant() ? none : boost::optional<JacobianTA2&>(dTdA2));
|
|
return Augmented<T>(t, dTdA1, a1.jacobians(), dTdA2, a2.jacobians());
|
|
}
|
|
|
|
/// Trace structure for reverse AD
|
|
struct Trace: public JacobianTrace<T> {
|
|
boost::shared_ptr<JacobianTrace<A1> > trace1;
|
|
boost::shared_ptr<JacobianTrace<A2> > trace2;
|
|
JacobianTA1 dTdA1;
|
|
JacobianTA2 dTdA2;
|
|
/// Start the reverse AD process
|
|
virtual void reverseAD(JacobianMap& jacobians) const {
|
|
trace1->reverseAD(dTdA1, jacobians);
|
|
trace2->reverseAD(dTdA2, jacobians);
|
|
}
|
|
/// Given df/dT, multiply in dT/dA and continue reverse AD process
|
|
virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
|
|
trace1->reverseAD(dFdT * dTdA1, jacobians);
|
|
trace2->reverseAD(dFdT * dTdA2, jacobians);
|
|
}
|
|
};
|
|
|
|
/// Construct an execution trace for reverse AD
|
|
virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
|
|
const Values& values) const {
|
|
boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
|
|
trace->trace1 = this->expressionA1_->traceExecution(values);
|
|
trace->trace2 = this->expressionA2_->traceExecution(values);
|
|
trace->t = function_(trace->trace1->value(), trace->trace2->value(),
|
|
trace->dTdA1, trace->dTdA2);
|
|
return trace;
|
|
}
|
|
|
|
};
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// Ternary Expression
|
|
|
|
template<class T, class A1, class A2, class A3>
|
|
class TernaryExpression: public ExpressionNode<T> {
|
|
|
|
public:
|
|
|
|
typedef Eigen::Matrix<double, T::dimension, A1::dimension> JacobianTA1;
|
|
typedef Eigen::Matrix<double, T::dimension, A2::dimension> JacobianTA2;
|
|
typedef Eigen::Matrix<double, T::dimension, A3::dimension> JacobianTA3;
|
|
typedef boost::function<
|
|
T(const A1&, const A2&, const A3&, boost::optional<JacobianTA1&>,
|
|
boost::optional<JacobianTA2&>, boost::optional<JacobianTA3&>)> Function;
|
|
|
|
private:
|
|
|
|
Function function_;
|
|
boost::shared_ptr<ExpressionNode<A1> > expressionA1_;
|
|
boost::shared_ptr<ExpressionNode<A2> > expressionA2_;
|
|
boost::shared_ptr<ExpressionNode<A3> > expressionA3_;
|
|
|
|
/// Constructor with a ternary function f, and three input arguments
|
|
TernaryExpression(
|
|
Function f, //
|
|
const Expression<A1>& e1, const Expression<A2>& e2,
|
|
const Expression<A3>& e3) :
|
|
function_(f), expressionA1_(e1.root()), expressionA2_(e2.root()), expressionA3_(
|
|
e3.root()) {
|
|
}
|
|
|
|
friend class Expression<T> ;
|
|
|
|
public:
|
|
|
|
/// Destructor
|
|
virtual ~TernaryExpression() {
|
|
}
|
|
|
|
/// Return keys that play in this expression
|
|
virtual std::set<Key> keys() const {
|
|
std::set<Key> keys1 = expressionA1_->keys();
|
|
std::set<Key> keys2 = expressionA2_->keys();
|
|
std::set<Key> keys3 = expressionA3_->keys();
|
|
keys2.insert(keys3.begin(), keys3.end());
|
|
keys1.insert(keys2.begin(), keys2.end());
|
|
return keys1;
|
|
}
|
|
|
|
/// Return value
|
|
virtual T value(const Values& values) const {
|
|
using boost::none;
|
|
return function_(this->expressionA1_->value(values),
|
|
this->expressionA2_->value(values), this->expressionA3_->value(values),
|
|
none, none, none);
|
|
}
|
|
|
|
/// Return value and derivatives
|
|
virtual Augmented<T> forward(const Values& values) const {
|
|
using boost::none;
|
|
Augmented<A1> a1 = this->expressionA1_->forward(values);
|
|
Augmented<A2> a2 = this->expressionA2_->forward(values);
|
|
Augmented<A3> a3 = this->expressionA3_->forward(values);
|
|
JacobianTA1 dTdA1;
|
|
JacobianTA2 dTdA2;
|
|
JacobianTA3 dTdA3;
|
|
T t = function_(a1.value(), a2.value(), a3.value(),
|
|
a1.constant() ? none : boost::optional<JacobianTA1&>(dTdA1),
|
|
a2.constant() ? none : boost::optional<JacobianTA2&>(dTdA2),
|
|
a3.constant() ? none : boost::optional<JacobianTA3&>(dTdA3));
|
|
return Augmented<T>(t, dTdA1, a1.jacobians(), dTdA2, a2.jacobians(), dTdA3,
|
|
a3.jacobians());
|
|
}
|
|
|
|
/// Trace structure for reverse AD
|
|
struct Trace: public JacobianTrace<T> {
|
|
boost::shared_ptr<JacobianTrace<A1> > trace1;
|
|
boost::shared_ptr<JacobianTrace<A2> > trace2;
|
|
boost::shared_ptr<JacobianTrace<A3> > trace3;
|
|
JacobianTA1 dTdA1;
|
|
JacobianTA2 dTdA2;
|
|
JacobianTA3 dTdA3;
|
|
/// Start the reverse AD process
|
|
virtual void reverseAD(JacobianMap& jacobians) const {
|
|
trace1->reverseAD(dTdA1, jacobians);
|
|
trace2->reverseAD(dTdA2, jacobians);
|
|
trace3->reverseAD(dTdA3, jacobians);
|
|
}
|
|
/// Given df/dT, multiply in dT/dA and continue reverse AD process
|
|
virtual void reverseAD(const Matrix& dFdT, JacobianMap& jacobians) const {
|
|
trace1->reverseAD(dFdT * dTdA1, jacobians);
|
|
trace2->reverseAD(dFdT * dTdA2, jacobians);
|
|
trace3->reverseAD(dFdT * dTdA3, jacobians);
|
|
}
|
|
};
|
|
|
|
/// Construct an execution trace for reverse AD
|
|
virtual boost::shared_ptr<JacobianTrace<T> > traceExecution(
|
|
const Values& values) const {
|
|
boost::shared_ptr<Trace> trace = boost::make_shared<Trace>();
|
|
trace->trace1 = this->expressionA1_->traceExecution(values);
|
|
trace->trace2 = this->expressionA2_->traceExecution(values);
|
|
trace->trace3 = this->expressionA3_->traceExecution(values);
|
|
trace->t = function_(trace->trace1->value(), trace->trace2->value(),
|
|
trace->trace3->value(), trace->dTdA1, trace->dTdA2, trace->dTdA3);
|
|
return trace;
|
|
}
|
|
|
|
};
|
|
//-----------------------------------------------------------------------------
|
|
}
|
|
|