449 lines
18 KiB
C++
449 lines
18 KiB
C++
/**
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* @file numericalDerivative.h
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* @brief Some functions to compute numerical derivatives
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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 <boost/function.hpp>
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#include <boost/bind.hpp>
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#include <gtsam/base/Lie.h>
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#include <gtsam/base/LieVector.h>
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#include <gtsam/base/Matrix.h>
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//#define LINEARIZE_AT_IDENTITY
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namespace gtsam {
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/*
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* Note that all of these functions have two versions, a boost.function version and a
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* standard C++ function pointer version. This allows reformulating the arguments of
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* a function to fit the correct structure, which is useful for situations like
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* member functions and functions with arguments not involved in the derivative:
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*
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* Usage of the boost bind version to rearrange arguments:
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* for a function with one relevant param and an optional derivative:
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* Foo bar(const Obj& a, boost::optional<Matrix&> H1)
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* Use boost.bind to restructure:
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* boost::bind(bar, _1, boost::none)
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* This syntax will fix the optional argument to boost::none, while using the first argument provided
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*
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* For member functions, such as below, with an instantiated copy instanceOfSomeClass
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* Foo SomeClass::bar(const Obj& a)
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* Use boost bind as follows to create a function pointer that uses the member function:
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* boost::bind(&SomeClass::bar, ref(instanceOfSomeClass), _1)
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*
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* For additional details, see the documentation:
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* http://www.boost.org/doc/libs/1_43_0/libs/bind/bind.html
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*/
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/** global functions for converting to a LieVector for use with numericalDerivative */
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inline LieVector makeLieVector(const Vector& v) { return LieVector(v); }
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inline LieVector makeLieVectorD(double d) { return LieVector(Vector_(1, d)); }
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/**
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* Numerically compute gradient of scalar function
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* Class X is the input argument
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* The class X needs to have dim, expmap, logmap
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*/
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template<class X>
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Vector numericalGradient(boost::function<double(const X&)> h, const X& x, double delta=1e-5) {
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double factor = 1.0/(2.0*delta);
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const size_t n = x.dim();
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Vector d(n,0.0), g(n,0.0);
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for (size_t j=0;j<n;j++) {
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d(j) += delta; double hxplus = h(expmap(x,d));
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d(j) -= 2*delta; double hxmin = h(expmap(x,d));
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d(j) += delta; g(j) = (hxplus-hxmin)*factor;
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}
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return g;
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}
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template<class X>
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Vector numericalGradient(double (*h)(const X&), const X& x, double delta=1e-5) {
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return numericalGradient<X>(boost::bind(h, _1), x, delta);
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}
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/**
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* Compute numerical derivative in argument 1 of unary function
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* @param h unary function yielding m-vector
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* @param x n-dimensional value at which to evaluate h
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* @param delta increment for numerical derivative
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* Class Y is the output argument
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* Class X is the input argument
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* @return m*n Jacobian computed via central differencing
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* Both classes X,Y need dim, expmap, logmap
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*/
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template<class Y, class X>
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Matrix numericalDerivative11(boost::function<Y(const X&)> h, const X& x, double delta=1e-5) {
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Y hx = h(x);
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double factor = 1.0/(2.0*delta);
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const size_t m = hx.dim(), n = x.dim();
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Vector d(n,0.0);
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Matrix H = zeros(m,n);
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for (size_t j=0;j<n;j++) {
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d(j) += delta; Vector hxplus = hx.logmap(h(x.expmap(d)));
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d(j) -= 2*delta; Vector hxmin = hx.logmap(h(x.expmap(d)));
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d(j) += delta; Vector dh = (hxplus-hxmin)*factor;
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for (size_t i=0;i<m;i++) H(i,j) = dh(i);
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}
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return H;
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}
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/** use a raw C++ function pointer */
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template<class Y, class X>
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Matrix numericalDerivative11(Y (*h)(const X&), const X& x, double delta=1e-5) {
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return numericalDerivative11<Y,X>(boost::bind(h, _1), x, delta);
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}
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/** remapping for double valued functions */
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template<class X>
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Matrix numericalDerivative11(boost::function<double(const X&)> h, const X& x, double delta=1e-5) {
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return numericalDerivative11<LieVector, X>(boost::bind(makeLieVectorD, boost::bind(h, _1)), x, delta);
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}
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template<class X>
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Matrix numericalDerivative11(double (*h)(const X&), const X& x, double delta=1e-5) {
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return numericalDerivative11<LieVector, X>(boost::bind(makeLieVectorD, boost::bind(h, _1)), x, delta);
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}
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/** remapping for vector valued functions */
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template<class X>
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Matrix numericalDerivative11(boost::function<Vector(const X&)> h, const X& x, double delta=1e-5) {
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return numericalDerivative11<LieVector, X>(boost::bind(makeLieVector, boost::bind(h, _1)), x, delta);
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}
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template<class X>
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Matrix numericalDerivative11(Vector (*h)(const X&), const X& x, double delta=1e-5) {
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return numericalDerivative11<LieVector, X>(boost::bind(makeLieVector, boost::bind(h, _1)), x, delta);
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}
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/**
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* Compute numerical derivative in argument 1 of binary function
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* @param h binary function yielding m-vector
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* @param x1 n-dimensional first argument value
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* @param x2 second argument value
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* @param delta increment for numerical derivative
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* @return m*n Jacobian computed via central differencing
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* All classes Y,X1,X2 need dim, expmap, logmap
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*/
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template<class Y, class X1, class X2>
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Matrix numericalDerivative21(boost::function<Y(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta=1e-5) {
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Y hx = h(x1,x2);
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double factor = 1.0/(2.0*delta);
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const size_t m = hx.dim(), n = x1.dim();
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Vector d(n,0.0);
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Matrix H = zeros(m,n);
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for (size_t j=0;j<n;j++) {
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d(j) += delta; Vector hxplus = hx.logmap(h(x1.expmap(d),x2));
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d(j) -= 2*delta; Vector hxmin = hx.logmap(h(x1.expmap(d),x2));
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d(j) += delta; Vector dh = (hxplus-hxmin)*factor;
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for (size_t i=0;i<m;i++) H(i,j) = dh(i);
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}
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return H;
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}
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/** use a raw C++ function pointer */
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template<class Y, class X1, class X2>
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inline Matrix numericalDerivative21(Y (*h)(const X1&, const X2&),
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative21<Y,X1,X2>(boost::bind(h, _1, _2), x1, x2, delta);
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}
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/** pseudo-partial template specialization for double return values */
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template<class X1, class X2>
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Matrix numericalDerivative21(boost::function<double(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative21<LieVector,X1,X2>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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template<class X1, class X2>
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Matrix numericalDerivative21(double (*h)(const X1&, const X2&),
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative21<LieVector,X1,X2>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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/** pseudo-partial template specialization for vector return values */
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template<class X1, class X2>
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Matrix numericalDerivative21(boost::function<Vector(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative21<LieVector,X1,X2>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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template<class X1, class X2>
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inline Matrix numericalDerivative21(Vector (*h)(const X1&, const X2&),
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative21<LieVector,X1,X2>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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/**
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* Compute numerical derivative in argument 2 of binary function
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* @param h binary function yielding m-vector
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* @param x1 first argument value
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* @param x2 n-dimensional second argument value
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* @param delta increment for numerical derivative
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* @return m*n Jacobian computed via central differencing
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* All classes Y,X1,X2 need dim, expmap, logmap
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*/
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template<class Y, class X1, class X2>
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Matrix numericalDerivative22
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(boost::function<Y(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta=1e-5) {
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Y hx = h(x1,x2);
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double factor = 1.0/(2.0*delta);
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const size_t m = hx.dim(), n = x2.dim();
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Vector d(n,0.0);
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Matrix H = zeros(m,n);
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for (size_t j=0;j<n;j++) {
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d(j) += delta; Vector hxplus = hx.logmap(h(x1,x2.expmap(d)));
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d(j) -= 2*delta; Vector hxmin = hx.logmap(h(x1,x2.expmap(d)));
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d(j) += delta; Vector dh = (hxplus-hxmin)*factor;
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for (size_t i=0;i<m;i++) H(i,j) = dh(i);
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}
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return H;
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}
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/** use a raw C++ function pointer */
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template<class Y, class X1, class X2>
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inline Matrix numericalDerivative22
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(Y (*h)(const X1&, const X2&), const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative22<Y,X1,X2>(boost::bind(h, _1, _2), x1, x2, delta);
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}
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/** pseudo-partial template specialization for double return values */
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template<class X1, class X2>
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Matrix numericalDerivative22(boost::function<double(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative22<LieVector,X1,X2>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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template<class X1, class X2>
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inline Matrix numericalDerivative22(double (*h)(const X1&, const X2&),
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative22<LieVector,X1,X2>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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/** pseudo-partial template specialization for vector return values */
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template<class X1, class X2>
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Matrix numericalDerivative22(boost::function<Vector(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative22<LieVector,X1,X2>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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template<class X1, class X2>
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inline Matrix numericalDerivative22(Vector (*h)(const X1&, const X2&),
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const X1& x1, const X2& x2, double delta=1e-5) {
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return numericalDerivative22<LieVector,X1,X2>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2)), x1, x2, delta);
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}
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/**
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* Compute numerical derivative in argument 1 of ternary function
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* @param h ternary function yielding m-vector
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* @param x1 n-dimensional first argument value
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* @param x2 second argument value
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* @param x3 third argument value
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* @param delta increment for numerical derivative
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* @return m*n Jacobian computed via central differencing
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* All classes Y,X1,X2,X3 need dim, expmap, logmap
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*/
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template<class Y, class X1, class X2, class X3>
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Matrix numericalDerivative31
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(boost::function<Y(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5)
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{
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Y hx = h(x1,x2,x3);
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double factor = 1.0/(2.0*delta);
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const size_t m = hx.dim(), n = x1.dim();
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Vector d(n,0.0);
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Matrix H = zeros(m,n);
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for (size_t j=0;j<n;j++) {
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d(j) += delta; Vector hxplus = hx.logmap(h(x1.expmap(d),x2,x3));
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d(j) -= 2*delta; Vector hxmin = hx.logmap(h(x1.expmap(d),x2,x3));
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d(j) += delta; Vector dh = (hxplus-hxmin)*factor;
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for (size_t i=0;i<m;i++) H(i,j) = dh(i);
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}
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return H;
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}
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template<class Y, class X1, class X2, class X3>
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inline Matrix numericalDerivative31
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(Y (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative31<Y,X1,X2, X3>(boost::bind(h, _1, _2, _3), x1, x2, x3, delta);
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}
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/** pseudo-partial template specialization for double return values */
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template<class X1, class X2, class X3>
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Matrix numericalDerivative31(boost::function<double(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative31<LieVector,X1,X2,X3>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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template<class X1, class X2, class X3>
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inline Matrix numericalDerivative31(double (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative31<LieVector,X1,X2,X3>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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/** pseudo-partial template specialization for vector return values */
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template<class X1, class X2, class X3>
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Matrix numericalDerivative31(boost::function<Vector(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative31<LieVector,X1,X2,X3>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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template<class X1, class X2, class X3>
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inline Matrix numericalDerivative31(Vector (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative31<LieVector,X1,X2,X3>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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/**
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* Compute numerical derivative in argument 2 of ternary function
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* @param h ternary function yielding m-vector
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* @param x1 n-dimensional first argument value
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* @param x2 second argument value
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* @param x3 third argument value
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* @param delta increment for numerical derivative
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* @return m*n Jacobian computed via central differencing
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* All classes Y,X1,X2,X3 need dim, expmap, logmap
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*/
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template<class Y, class X1, class X2, class X3>
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Matrix numericalDerivative32
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(boost::function<Y(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5)
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{
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Y hx = h(x1,x2,x3);
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double factor = 1.0/(2.0*delta);
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const size_t m = hx.dim(), n = x2.dim();
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Vector d(n,0.0);
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Matrix H = zeros(m,n);
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for (size_t j=0;j<n;j++) {
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d(j) += delta; Vector hxplus = hx.logmap(h(x1, x2.expmap(d),x3));
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d(j) -= 2*delta; Vector hxmin = hx.logmap(h(x1, x2.expmap(d),x3));
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d(j) += delta; Vector dh = (hxplus-hxmin)*factor;
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for (size_t i=0;i<m;i++) H(i,j) = dh(i);
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}
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return H;
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}
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template<class Y, class X1, class X2, class X3>
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inline Matrix numericalDerivative32
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(Y (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative32<Y,X1,X2, X3>(boost::bind(h, _1, _2, _3), x1, x2, x3, delta);
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}
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/** pseudo-partial template specialization for double return values */
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template<class X1, class X2, class X3>
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Matrix numericalDerivative32(boost::function<double(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative32<LieVector,X1,X2,X3>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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template<class X1, class X2, class X3>
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inline Matrix numericalDerivative32(double (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative32<LieVector,X1,X2,X3>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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/** pseudo-partial template specialization for vector return values */
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template<class X1, class X2, class X3>
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Matrix numericalDerivative32(boost::function<Vector(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative32<LieVector,X1,X2,X3>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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template<class X1, class X2, class X3>
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inline Matrix numericalDerivative32(Vector (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative32<LieVector,X1,X2,X3>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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/**
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* Compute numerical derivative in argument 3 of ternary function
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* @param h ternary function yielding m-vector
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* @param x1 n-dimensional first argument value
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* @param x2 second argument value
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* @param x3 third argument value
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* @param delta increment for numerical derivative
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* @return m*n Jacobian computed via central differencing
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* All classes Y,X1,X2,X3 need dim, expmap, logmap
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*/
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template<class Y, class X1, class X2, class X3>
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Matrix numericalDerivative33
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(boost::function<Y(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5)
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{
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Y hx = h(x1,x2,x3);
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double factor = 1.0/(2.0*delta);
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const size_t m = hx.dim(), n = x3.dim();
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Vector d(n,0.0);
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Matrix H = zeros(m,n);
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for (size_t j=0;j<n;j++) {
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d(j) += delta; Vector hxplus = hx.logmap(h(x1, x2, x3.expmap(d)));
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d(j) -= 2*delta; Vector hxmin = hx.logmap(h(x1, x2, x3.expmap(d)));
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d(j) += delta; Vector dh = (hxplus-hxmin)*factor;
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for (size_t i=0;i<m;i++) H(i,j) = dh(i);
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}
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return H;
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}
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template<class Y, class X1, class X2, class X3>
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inline Matrix numericalDerivative33
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(Y (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative33<Y,X1,X2, X3>(boost::bind(h, _1, _2, _3), x1, x2, x3, delta);
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}
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/** pseudo-partial template specialization for double return values */
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template<class X1, class X2, class X3>
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Matrix numericalDerivative33(boost::function<double(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative33<LieVector,X1,X2,X3>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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template<class X1, class X2, class X3>
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inline Matrix numericalDerivative33(double (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative33<LieVector,X1,X2,X3>(
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boost::bind(makeLieVectorD, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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/** pseudo-partial template specialization for vector return values */
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template<class X1, class X2, class X3>
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Matrix numericalDerivative33(boost::function<Vector(const X1&, const X2&, const X3&)> h,
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative33<LieVector,X1,X2,X3>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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template<class X1, class X2, class X3>
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inline Matrix numericalDerivative33(Vector (*h)(const X1&, const X2&, const X3&),
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const X1& x1, const X2& x2, const X3& x3, double delta=1e-5) {
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return numericalDerivative33<LieVector,X1,X2,X3>(
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boost::bind(makeLieVector, boost::bind(h, _1, _2, _3)), x1, x2, x3, delta);
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}
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}
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