154 lines
3.9 KiB
C++
154 lines
3.9 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 iterative.h
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* @brief Iterative methods, implementation
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* @author Frank Dellaert
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* @date Dec 28, 2009
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*/
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#pragma once
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#include <gtsam/base/Matrix.h>
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#include <gtsam/linear/VectorValues.h>
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#include <gtsam/linear/ConjugateGradientSolver.h>
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namespace gtsam {
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/**
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* Method of conjugate gradients (CG) template
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* "System" class S needs gradient(S,v), e=S*v, v=S^e
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* "Vector" class V needs dot(v,v), -v, v+v, s*v
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* "Vector" class E needs dot(v,v)
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* @param Ab, the "system" that needs to be solved, examples below
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* @param x is the initial estimate
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* @param epsilon determines the convergence criterion: norm(g)<epsilon*norm(g0)
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* @param maxIterations, if 0 will be set to |x|
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* @param steepest flag, if true does steepest descent, not CG
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* */
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template<class S, class V, class E>
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V conjugateGradients(const S& Ab, V x, bool verbose, double epsilon,
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size_t maxIterations, bool steepest = false);
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/**
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* Helper class encapsulating the combined system |Ax-b_|^2
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* Needed to run Conjugate Gradients on matrices
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* */
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class System {
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private:
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const Matrix& A_;
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const Vector& b_;
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public:
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System(const Matrix& A, const Vector& b) :
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A_(A), b_(b) {
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}
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/** Access A matrix */
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const Matrix& A() const { return A_; }
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/** Access b vector */
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const Vector& b() const { return b_; }
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/** Apply operator A'*e */
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Vector operator^(const Vector& e) const {
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return A_ ^ e;
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}
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/**
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* Print with optional string
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*/
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void print (const std::string& s = "System") const;
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};
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/** gradient of objective function 0.5*|Ax-b_|^2 at x = A_'*(Ax-b_) */
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inline Vector gradient(const System& system, const Vector& x) {
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return system.A() ^ (system.A() * x - system.b());
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}
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/** Apply operator A */
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inline Vector operator*(const System& system, const Vector& x) {
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return system.A() * x;
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}
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/** Apply operator A in place */
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inline void multiplyInPlace(const System& system, const Vector& x, Vector& e) {
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e = system.A() * x;
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}
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/** x += alpha* A'*e */
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inline void transposeMultiplyAdd(const System& system, double alpha, const Vector& e, Vector& x) {
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transposeMultiplyAdd(alpha,system.A(),e,x);
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}
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/**
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* Method of steepest gradients, System version
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*/
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Vector steepestDescent(
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const System& Ab,
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const Vector& x,
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const IterativeOptimizationParameters & parameters);
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/**
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* Method of conjugate gradients (CG), System version
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*/
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Vector conjugateGradientDescent(
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const System& Ab,
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const Vector& x,
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const ConjugateGradientParameters & parameters);
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/** convenience calls using matrices, will create System class internally: */
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/**
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* Method of steepest gradients, Matrix version
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*/
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Vector steepestDescent(
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const Matrix& A,
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const Vector& b,
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const Vector& x,
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const ConjugateGradientParameters & parameters);
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/**
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* Method of conjugate gradients (CG), Matrix version
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*/
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Vector conjugateGradientDescent(
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const Matrix& A,
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const Vector& b,
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const Vector& x,
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const ConjugateGradientParameters & parameters);
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class GaussianFactorGraph;
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/**
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* Method of steepest gradients, Gaussian Factor Graph version
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* */
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VectorValues steepestDescent(
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const GaussianFactorGraph& fg,
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const VectorValues& x,
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const ConjugateGradientParameters & parameters);
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/**
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* Method of conjugate gradients (CG), Gaussian Factor Graph version
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* */
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VectorValues conjugateGradientDescent(
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const GaussianFactorGraph& fg,
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const VectorValues& x,
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const ConjugateGradientParameters & parameters);
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} // namespace gtsam
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#include <gtsam_unstable/linear/iterative-inl.h>
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