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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_h__
#define __math_gradient_descent_h__
#include <limits>
namespace MR
{
namespace Math
{
//! \addtogroup Optimisation
// @{
namespace {
class LinearUpdate { 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) {
bool changed = false;
for (ssize_t n = 0; n < x.size(); ++n) {
newx[n] = x[n] - step_size * g[n];
if (newx[n] != x[n])
changed = true;
}
return changed;
}
};
}
//! Computes the minimum of a function using a gradient descent approach.
template <class Function, class UpdateFunctor=LinearUpdate>
class GradientDescent
{ MEMALIGN(GradientDescent<Function,UpdateFunctor>)
public:
using value_type = typename Function::value_type;
GradientDescent (Function& function, UpdateFunctor update_functor = LinearUpdate(), value_type step_size_upfactor = 3.0, value_type step_size_downfactor = 0.1, bool verbose = false) :
func (function),
update_func (update_functor),
step_up (step_size_upfactor),
step_down (step_size_downfactor),
verbose (verbose),
delim (","),
niter (0),
x (func.size()),
x2 (func.size()),
g (func.size()),
g2 (func.size()) { }
value_type value () const throw () { return f; }
const Eigen::Matrix<value_type, Eigen::Dynamic, 1>& state () const throw () { return x; }
const Eigen::Matrix<value_type, Eigen::Dynamic, 1>& gradient () const throw () { return g; }
value_type step_size () const { return dt; }
value_type gradient_norm () const throw () { return normg; }
int function_evaluations () const throw () { 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 < x.size() ; a++ )
log_os << delim + "x_" + str(a+1) ;
for ( ssize_t a = 0 ; a < x.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(x.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 (x);
nfeval = 0;
f = evaluate_func (x, g, verbose);
compute_normg_and_step_unscaled ();
normg = g.norm();
assert(std::isfinite(normg));
assert(!std::isnan(normg));
dt /= normg;
if (verbose) {
CONSOLE ("initialise: f = " + str (f) + ", |g| = " + str (normg) + ":");
CONSOLE (" x = [ " + str(x.transpose()) + "]");
}
if (normg == 0.0)
return;
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< x.size(); ++i){ log_os << delim << str(x(i)); }
for (ssize_t i=0; i< x.size(); ++i){ log_os << delim << str(g(i)); }
log_os << std::endl;
}
}
bool iterate () {
std::ostream dummy (nullptr);
return iterate (dummy);
}
bool iterate (std::ostream& log_os) {
// assert (normg != 0.0);
assert (std::isfinite (normg));
while (normg != 0.0) {
if (!update_func (x2, x, g, dt))
return false;
value_type f2 = evaluate_func (x2, g2, verbose);
// quadratic minimum:
value_type step_length = step_unscaled*dt;
value_type denom = 2.0 * (normg*step_length + f2 - f);
value_type quadratic_minimum = denom > 0.0 ? normg * step_length / denom : step_up;
if (quadratic_minimum < step_down) quadratic_minimum = step_down;
if (quadratic_minimum > step_up) quadratic_minimum = step_up;
if (f2 < f) {
++niter;
dt *= quadratic_minimum;
f = f2;
x.swap (x2);
g.swap (g2);
if (log_os) {
log_os << niter << delim << nfeval << delim << str(f) << delim << str(dt);
for (ssize_t i=0; i< x.size(); ++i){ log_os << delim << str(x(i)); }
for (ssize_t i=0; i< x.size(); ++i){ log_os << delim << str(g(i)); }
log_os << std::endl;
}
compute_normg_and_step_unscaled ();
return true;
}
if (quadratic_minimum >= 1.0)
quadratic_minimum = 0.5;
dt *= quadratic_minimum;
if (dt <= 0.0)
return false;
}
return false;
}
protected:
Function& func;
UpdateFunctor update_func;
const value_type step_up, step_down;
bool verbose;
std::string delim;
size_t niter;
Eigen::Matrix<value_type, Eigen::Dynamic, 1> x, x2, g, g2, preconditioner_weights;
value_type f, dt, normg, step_unscaled;
size_t nfeval;
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) + " >>");
return cost;
}
void compute_normg_and_step_unscaled () {
normg = step_unscaled = g.norm();
assert(std::isfinite(normg));
if (normg > 0.0){
if (preconditioner_weights.size()) {
value_type g_projected = 0.0;
for (ssize_t n = 0; n < g.size(); ++n) {
g_projected += preconditioner_weights[n] * Math::pow2(g[n]);
}
g.array() *= preconditioner_weights.array();
normg = g_projected / normg;
assert(std::isfinite(normg));
}
}
}
};
//! @}
}
}
#endif
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