132 lines
3.5 KiB
C++
132 lines
3.5 KiB
C++
/*
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* iterative-inl.h
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* @brief Iterative methods, template 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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#pragma once
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#include "GaussianFactorGraph.h"
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#include "iterative.h"
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using namespace std;
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namespace gtsam {
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/* ************************************************************************* */
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// state for CG method
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template<class S, class V, class E>
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struct CGState {
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bool steepest, verbose;
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double gamma, threshold;
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size_t k, maxIterations, reset;
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V g, d;
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E Ad;
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/** constructor */
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CGState(const S& Ab, const V& x, bool verb, double epsilon,
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double epsilon_abs, size_t maxIt, bool steep) {
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k = 0;
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verbose = verb;
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steepest = steep;
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maxIterations = (maxIt > 0) ? maxIt : dim(x) * (steepest ? 10 : 1);
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reset = (size_t) (sqrt(dim(x)) + 0.5); // when to reset
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// Start with g0 = A'*(A*x0-b), d0 = - g0
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// i.e., first step is in direction of negative gradient
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g = Ab.gradient(x);
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d = g; // instead of negating gradient, alpha will be negated
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// init gamma and calculate threshold
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gamma = dot(g, g);
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threshold = ::max(epsilon_abs, epsilon * epsilon * gamma);
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// Allocate and calculate A*d for first iteration
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if (gamma > epsilon) Ad = Ab * d;
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}
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/** print */
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void print(const V& x) {
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cout << "iteration = " << k << endl;
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gtsam::print(x,"x");
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gtsam::print(g, "g");
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cout << "dotg = " << gamma << endl;
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gtsam::print(d, "d");
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gtsam::print(Ad, "Ad");
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}
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/** step the solution */
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double takeOptimalStep(V& x) {
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// TODO: can we use gamma instead of dot(d,g) ????? Answer not trivial
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double alpha = -dot(d, g) / dot(Ad, Ad); // calculate optimal step-size
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axpy(alpha, d, x); // // do step in new search direction, x += alpha*d
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return alpha;
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}
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/** take a step, return true if converged */
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bool step(const S& Ab, V& x) {
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k += 1; // increase iteration number
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double alpha = takeOptimalStep(x);
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if (k >= maxIterations) return true; //---------------------------------->
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// update gradient (or re-calculate at reset time)
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if (k % reset == 0)
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g = Ab.gradient(x);
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else
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// axpy(alpha, Ab ^ Ad, g); // g += alpha*(Ab^Ad)
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Ab.transposeMultiplyAdd(alpha, Ad, g);
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// check for convergence
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double new_gamma = dot(g, g);
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if (verbose) cout << "iteration " << k << ": alpha = " << alpha
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<< ", dotg = " << new_gamma << endl;
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if (new_gamma < threshold) return true; //---------------------------------->
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// calculate new search direction
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if (steepest)
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d = g;
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else {
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double beta = new_gamma / gamma;
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// d = g + d*beta;
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scal(beta, d);
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axpy(1.0, g, d);
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}
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gamma = new_gamma;
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// In-place recalculation Ad <- A*d to avoid re-allocating Ad
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Ab.multiplyInPlace(d, Ad);
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return false;
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}
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};
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/**
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* conjugate gradient method.
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* S: linear system, V: step vector, E: errors
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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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double epsilon_abs, size_t maxIterations, bool steepest = false) {
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CGState<S, V, E> state(Ab, x, verbose, epsilon, epsilon_abs, maxIterations,
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steepest);
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if (state.gamma < state.threshold) return x;
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if (verbose) cout << "CG: epsilon = " << epsilon << ", maxIterations = "
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<< state.maxIterations << ", ||g0||^2 = " << state.gamma
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<< ", threshold = " << state.threshold << endl;
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// loop maxIterations times
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while (!state.step(Ab, x))
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;
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return x;
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}
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/* ************************************************************************* */
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} // namespace gtsam
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