104 lines
2.9 KiB
C++
104 lines
2.9 KiB
C++
/*
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* iterative.h
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* @brief Iterative methods, implementation
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* @author Frank Dellaert
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* Created on: Dec 28, 2009
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*/
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#include "Matrix.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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/** gradient of objective function 0.5*|Ax-b_|^2 at x = A_'*(Ax-b_) */
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Vector gradient(const Vector& x) const {
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return A_ ^ (A_ * x - b_);
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}
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/** Apply operator A_ */
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inline Vector operator*(const Vector& x) const {
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return A_ * x;
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}
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/** Apply operator A_^T */
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inline 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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/**
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* Method of steepest gradients, System version
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*/
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Vector steepestDescent(const System& Ab, const Vector& x, bool verbose =
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false, double epsilon = 1e-3, size_t maxIterations = 0);
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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(const System& Ab, const Vector& x,
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bool verbose = false, double epsilon = 1e-3, size_t maxIterations = 0);
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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(const Matrix& A, const Vector& b, const Vector& x,
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bool verbose = false, double epsilon = 1e-3, size_t maxIterations = 0);
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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(const Matrix& A, const Vector& b,
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const Vector& x, bool verbose = false, double epsilon = 1e-3,
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size_t maxIterations = 0);
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class GaussianFactorGraph;
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class VectorConfig;
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/**
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* Method of steepest gradients, Gaussian Factor Graph version
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* */
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VectorConfig steepestDescent(const GaussianFactorGraph& fg,
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const VectorConfig& x, bool verbose = false, double epsilon = 1e-3,
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size_t maxIterations = 0);
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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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VectorConfig conjugateGradientDescent(const GaussianFactorGraph& fg,
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const VectorConfig& x, bool verbose = false, double epsilon = 1e-3,
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size_t maxIterations = 0);
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} // namespace gtsam
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