85 lines
2.3 KiB
C++
85 lines
2.3 KiB
C++
/*
|
|
* iterative-inl.h
|
|
* @brief Iterative methods, template implementation
|
|
* @author Frank Dellaert
|
|
* Created on: Dec 28, 2009
|
|
*/
|
|
|
|
#pragma once
|
|
|
|
#include "GaussianFactorGraph.h"
|
|
#include "iterative.h"
|
|
|
|
using namespace std;
|
|
|
|
namespace gtsam {
|
|
|
|
/* ************************************************************************* */
|
|
/**
|
|
* conjugate gradient method.
|
|
* S: linear system, V: step vector, E: errors
|
|
*/
|
|
template<class S, class V, class E>
|
|
V conjugateGradients(const S& Ab, V x, bool verbose, double epsilon, double epsilon_abs,
|
|
size_t maxIterations, bool steepest = false) {
|
|
if (maxIterations == 0) maxIterations = dim(x) * (steepest ? 10 : 1);
|
|
size_t reset = (size_t)(sqrt(dim(x))+0.5); // when to reset
|
|
|
|
// Start with g0 = A'*(A*x0-b), d0 = - g0
|
|
// i.e., first step is in direction of negative gradient
|
|
V g = Ab.gradient(x);
|
|
V d = g; // instead of negating gradient, alpha will be negated
|
|
double gamma0 = dot(g, g), gamma_old = gamma0;
|
|
if (gamma0 < epsilon_abs) return x;
|
|
double threshold = epsilon * epsilon * gamma0;
|
|
|
|
if (verbose) cout << "CG: epsilon = " << epsilon << ", maxIterations = "
|
|
<< maxIterations << ", ||g0||^2 = " << gamma0 << ", threshold = "
|
|
<< threshold << endl;
|
|
|
|
// Allocate and calculate A*d for first iteration
|
|
E Ad = Ab * d;
|
|
|
|
// loop maxIterations times
|
|
for (size_t k = 1;; k++) {
|
|
|
|
// calculate optimal step-size
|
|
double alpha = - dot(d, g) / dot(Ad, Ad);
|
|
|
|
// do step in new search direction
|
|
axpy(alpha, d, x); // x += alpha*d
|
|
if (k==maxIterations) break;
|
|
|
|
// update gradient (or re-calculate at reset time)
|
|
if (k%reset==0)
|
|
g = Ab.gradient(x);
|
|
else
|
|
axpy(alpha, Ab ^ Ad, g); // g += alpha*(Ab^Ad)
|
|
|
|
// check for convergence
|
|
double gamma = dot(g, g);
|
|
if (verbose) cout << "iteration " << k << ": alpha = " << alpha
|
|
<< ", dotg = " << gamma << endl;
|
|
if (gamma < threshold) break;
|
|
|
|
// calculate new search direction
|
|
if (steepest)
|
|
d = g;
|
|
else {
|
|
double beta = gamma / gamma_old;
|
|
gamma_old = gamma;
|
|
// d = g + d*beta;
|
|
scal(beta,d);
|
|
axpy(1.0, g, d);
|
|
}
|
|
|
|
// In-place recalculation Ad <- A*d to avoid re-allocating Ad
|
|
Ab.multiplyInPlace(d,Ad);
|
|
}
|
|
return x;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
|
|
} // namespace gtsam
|