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/* Copyright (c) 2008-2022 the MRtrix3 contributors.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Covered Software is provided under this License on an "as is"
* basis, without warranty of any kind, either expressed, implied, or
* statutory, including, without limitation, warranties that the
* Covered Software is free of defects, merchantable, fit for a
* particular purpose or non-infringing.
* See the Mozilla Public License v. 2.0 for more details.
*
* For more details, see http://www.mrtrix.org/.
*/
#ifndef __math_gradient_descent_bb_h__
#define __math_gradient_descent_bb_h__
#include <limits>
#include <iostream>
#include <fstream>
#include <deque>
#include <limits>
#include <fstream>
#include "math/check_gradient.h"
namespace MR
{
namespace Math
{
//! \addtogroup Optimisation
// @{
class LinearUpdateBB { NOMEMALIGN
public:
template <typename ValueType>
inline bool operator() (Eigen::Matrix<ValueType, Eigen::Dynamic, 1>& newx, const Eigen::Matrix<ValueType, Eigen::Dynamic, 1>& x,
const Eigen::Matrix<ValueType, Eigen::Dynamic, 1>& g, ValueType step_size) {
assert (newx.size() == x.size());
assert (g.size() == x.size());
newx = x - step_size * g;
return !newx.isApprox(x);
}
};
//! Computes the minimum of a function using a Barzilai Borwein gradient descent approach. ENH: implement stabilised version https://arxiv.org/abs/1907.06409
template <class Function, class UpdateFunctor=LinearUpdateBB>
class GradientDescentBB
{ MEMALIGN(GradientDescentBB<Function,UpdateFunctor>)
public:
using value_type = typename Function::value_type;
GradientDescentBB (Function& function, UpdateFunctor update_functor = LinearUpdateBB(), bool verbose = false) :
func (function),
update_func (update_functor),
x1 (func.size()),
x2 (func.size()),
x3 (func.size()),
g1 (func.size()),
g2 (func.size()),
g3 (func.size()),
nfeval (0),
niter (0),
verbose (verbose),
delim (",") { }
value_type value () const { return f; }
const Eigen::Matrix<value_type, Eigen::Dynamic, 1>& state () const { return x2; }
const Eigen::Matrix<value_type, Eigen::Dynamic, 1>& gradient () const { return g2; }
value_type step_size () const { return dt; }
value_type gradient_norm () const { return normg; }
int function_evaluations () const { return nfeval; }
void be_verbose (bool v) { verbose = v; }
void precondition (const Eigen::Matrix<value_type, Eigen::Dynamic, 1>& weights) {
preconditioner_weights = weights;
}
void run (const size_t max_iterations = 1000,
const value_type grad_tolerance = 1e-6,
std::streambuf* log_stream = nullptr)
{
std::ostream log_os(log_stream? log_stream : nullptr);
if (log_os){
log_os << "#iteration" << delim << "feval" << delim << "cost" << delim << "stepsize";
for ( ssize_t a = 0 ; a < x1.size() ; a++ )
log_os << delim + "x_" + str(a+1) ;
for ( ssize_t a = 0 ; a < x1.size() ; a++ )
log_os << delim + "g_" + str(a+1) ;
log_os << "\n" << std::flush;
}
init (log_os);
const value_type gradient_tolerance (grad_tolerance * normg);
DEBUG ("Gradient descent iteration: init; cost: " + str(f));
while (niter < max_iterations) {
bool retval = iterate (log_os);
DEBUG ("Gradient descent iteration: " + str(niter) + "; cost: " + str(f));
if (verbose){
CONSOLE ("iteration " + str (niter) + ": f = " + str (f) + ", |g| = " + str (normg) + ":");
CONSOLE (" x = [ " + str(x2.transpose()) + "]");
}
if (normg < gradient_tolerance) {
if (verbose)
CONSOLE ("normg (" + str(normg) + ") < gradient tolerance (" + str(gradient_tolerance) + ")");
return;
}
if (!retval){
if (verbose)
CONSOLE ("unchanged parameters");
return;
}
}
}
void init () {
std::ostream dummy (nullptr);
init (dummy);
}
void init (std::ostream& log_os) {
dt = func.init (x1);
f = evaluate_func (x1, g1, verbose);
normg = g1.norm();
if (normg == 0.0) {
x2 = x1;
g2 = g1;
return;
}
assert(std::isfinite(normg)); assert(!std::isnan(normg));
dt /= normg;
if (verbose) {
CONSOLE ("initialise: f = " + str (f) + ", |g| = " + str (normg) + ", step = " + str(dt) + ":");
CONSOLE (" x = [ " + str(x1.transpose()) + "]");
}
if (log_os) {
log_os << niter << delim << nfeval << delim << str(f) << delim << str(dt);
for (ssize_t i=0; i< x2.size(); ++i){ log_os << delim << str(x1(i)); }
for (ssize_t i=0; i< x2.size(); ++i){ log_os << delim << str(g1(i)); }
log_os << std::endl;
}
assert (std::isfinite(f)); assert (!std::isnan(f));
assert (std::isfinite (normg)); assert (!std::isnan(normg));
if (update_func (x2, x1, g1, dt)){
f = evaluate_func (x2, g2, verbose);
} else {
dt = 0.0;
return;
}
compute_normg_and_step ();
assert (std::isfinite (f)); assert (!std::isnan(f));
assert (std::isfinite(normg)); assert (!std::isnan(normg));
if (log_os) {
log_os << niter << delim << nfeval << delim << str(f) << delim << str(dt);
for (ssize_t i=0; i< x2.size(); ++i){ log_os << delim << str(x2(i)); }
for (ssize_t i=0; i< x2.size(); ++i){ log_os << delim << str(g2(i)); }
log_os << std::endl;
}
if (verbose) {
CONSOLE (" f = " + str (f) + ", |g| = " + str (normg) + ", step = " + str(dt) + ":");
CONSOLE (" x = [ " + str(x2.transpose()) + "]");
}
}
bool iterate () {
std::ostream dummy (nullptr);
return iterate (dummy);
}
bool iterate (std::ostream& log_os) {
assert (std::isfinite (normg));
if ((normg == 0.0) or !update_func (x3, x2, g2, dt))
return false;
f = evaluate_func (x3, g3, verbose);
x2.swap(x3);
x1.swap(x3);
g2.swap(g3);
g1.swap(g3);
++niter;
if (log_os) {
log_os << niter << delim << nfeval << delim << str(f) << delim << str(dt);
for (ssize_t i=0; i< x2.size(); ++i){ log_os << delim << str(x2(i)); }
for (ssize_t i=0; i< x2.size(); ++i){ log_os << delim << str(g2(i)); }
log_os << std::endl;
}
compute_normg_and_step ();
return true;
}
protected:
Function& func;
UpdateFunctor update_func;
Eigen::Matrix<value_type, Eigen::Dynamic, 1> x1, x2, x3, g1, g2, g3, preconditioner_weights;
value_type f, dt, normg;
size_t nfeval;
size_t niter;
bool verbose;
std::string delim;
value_type evaluate_func (const Eigen::Matrix<value_type, Eigen::Dynamic, 1>& newx, Eigen::Matrix<value_type, Eigen::Dynamic, 1>& newg, bool verbose = false) {
++nfeval;
value_type cost = func (newx, newg);
if (!std::isfinite (cost))
throw Exception ("cost function is NaN or Inf!");
if (verbose){
CONSOLE (" << eval " + str(nfeval) + ", f = " + str (cost) + " >>");
CONSOLE (" << newx = [ " + str(newx.transpose()) + "]");
CONSOLE (" << newg = [ " + str(newg.transpose()) + "]");
}
return cost;
}
void compute_normg_and_step () {
if (preconditioner_weights.size()) {
g2.array() *= preconditioner_weights.array();
}
normg = g2.norm();
assert((g2-g1).norm()>0.0);
dt = (x2-x1).norm()/(g2-g1).norm();
}
};
//! @}
}
}
#endif
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