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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_quadratic_line_search_h__
#define __math_quadratic_line_search_h__
#include "progressbar.h"
namespace MR
{
namespace Math
{
/** \addtogroup Optimisation
@{ */
//! Computes the minimum of a 1D function using a quadratic line search.
/*! This functor operates on a cost function class that must define a
* operator() const method. The method must take a single ValueType
* argument x and return the cost of the function at x.
*
* This line search is fast for functions that are smooth and convex.
* Functions that do not obey these criteria may not converge.
*
* The min_bound and max_bound arguments define values that are used to
* initialise the search. If these bounds do not bracket the minimum,
* then the search will return NaN. Furthermore, if the relevant function
* is not sufficiently smooth, and the search begins to diverge before
* finding a local minimum to within the specified tolerance, then the
* search will also return NaN.
*
* This effect can be cancelled by calling:
* \code
* set_exit_if_outside_bounds (false);
* \endcode
* That way, if the estimated minimum is outside the current
* bracketed area, the search area will be widened accordingly, and the
* process repeated until a local minimum is found to within the specified
* tolerance. Beware however; there is no guarantee that the search will
* converge in all cases, so be conscious of the nature of your data.
*
*
* Typical usage:
* \code
* CostFunction cost_function();
* QuadraticLineSearch<double> line_search (-1.0, 1.0);
* line_search.set_tolerance (0.01);
* line_search.set_message ("optimising");
* const double optimal_value = line_search (cost_function);
*
* \endcode
*/
template <typename ValueType>
class QuadraticLineSearch
{ MEMALIGN(QuadraticLineSearch<ValueType>)
public:
// TODO Return error code if converging toward a maxima instead of a minima
// TODO Separate return codes for above & below domain
enum return_t {SUCCESS, EXECUTING, OUTSIDE_BOUNDS, NONCONVEX, NONCONVERGING};
QuadraticLineSearch (const ValueType lower_bound, const ValueType upper_bound) :
init_lower (lower_bound),
init_mid (0.5 * (lower_bound + upper_bound)),
init_upper (upper_bound),
value_tolerance (0.001 * (upper_bound - lower_bound)),
function_tolerance (0.0),
exit_outside_bounds (true),
max_iters (50),
status (SUCCESS) { }
void set_lower_bound (const ValueType i) { init_lower = i; }
void set_init_estimate (const ValueType i) { init_mid = i; }
void set_upper_bound (const ValueType i) { init_upper = i; }
void set_value_tolerance (const ValueType i) { value_tolerance = i; }
void set_function_tolerance (const ValueType i) { function_tolerance = i; }
void set_exit_if_outside_bounds (const bool i) { exit_outside_bounds = i; }
void set_max_iterations (const size_t i) { max_iters = i; }
void set_message (const std::string& i) { message = i; }
return_t get_status() const { return status; }
template <class Functor>
ValueType operator() (Functor& functor) const
{
status = EXECUTING;
std::unique_ptr<ProgressBar> progress (message.size() ? new ProgressBar (message) : nullptr);
ValueType l = init_lower, m = init_mid, u = init_upper;
ValueType fl = functor (l), fm = functor (m), fu = functor (u);
// TODO Need to test if these bounds are producing a NaN CF
size_t iters = 0;
while (iters++ < max_iters) {
// TODO When testing for nonconvexity, the problem may also arise due to quantisation
// in the cost function
// Would like to have a fractional threshold on the cost function i.e. if it's really flat,
// return successfully
// Difficult to do this without knowledge of the cost function
if (fm > (fl + ((fu-fl)*(m-l)/(u-l)))) {
if ((std::min(m-l, u-m) < value_tolerance) || (abs((fu-fl)/(0.5*(fu+fl))) < function_tolerance)) {
status = SUCCESS;
return m;
}
status = NONCONVEX;
return NaN;
}
const ValueType sl = (fm-fl) / (m-l);
const ValueType su = (fu-fm) / (u-m);
const ValueType n = (0.5*(l+m)) - ((sl*(u-l)) / (2.0*(su-sl)));
const ValueType fn = functor (n);
if (!std::isfinite(fn))
return m;
if (n < l) {
if (exit_outside_bounds) {
status = OUTSIDE_BOUNDS;
return NaN;
}
u = m; fu = fm;
m = l; fm = fl;
l = n; fl = fn;
} else if (n < m) {
if (fn > fm) {
l = n; fl = fn;
} else {
u = m; fu = fm;
m = n; fm = fn;
}
} else if (n == m) {
return n;
} else if (n < u) {
if (fn > fm) {
u = n; fu = fn;
} else {
l = m; fl = fm;
m = n; fm = fn;
}
} else {
if (exit_outside_bounds) {
status = OUTSIDE_BOUNDS;
return NaN;
}
l = m; fl = fm;
m = u; fm = fu;
u = n; fu = fn;
}
if (progress)
++(*progress);
if ((u-l) < value_tolerance) {
status = SUCCESS;
return m;
}
}
status = NONCONVERGING;
return NaN;
}
template <class Functor>
ValueType verbose (Functor& functor) const
{
status = EXECUTING;
ValueType l = init_lower, m = init_mid, u = init_upper;
ValueType fl = functor (l), fm = functor (m), fu = functor (u);
std::cerr << "Initialising quadratic line search\n";
std::cerr << " Lower Mid Upper\n";
std::cerr << "Pos " << str (l) << " " << str(m) << " " << str(u) << "\n";
std::cerr << "Value " << str (fl) << " " << str(fm) << " " << str(fu) << "\n";
size_t iters = 0;
while (iters++ < max_iters) {
if (fm > (fl + ((fu-fl)*(m-l)/(u-l)))) {
if (std::min(m-l, u-m) < value_tolerance) {
std::cerr << "Returning due to nonconvexity, through successfully\n";
status = SUCCESS;
return m;
}
status = NONCONVEX;
std::cerr << "Returning due to nonconvexity, unsuccessfully\n";
return NaN;
}
const ValueType sl = (fm-fl) / (m-l);
const ValueType su = (fu-fm) / (u-m);
const ValueType n = (0.5*(l+m)) - ((sl*(u-l)) / (2.0*(su-sl)));
const ValueType fn = functor (n);
std::cerr << " New point " << str(n) << ", value " << str(fn) << "\n";
if (n < l) {
if (exit_outside_bounds) {
status = OUTSIDE_BOUNDS;
return NaN;
}
u = m; fu = fm;
m = l; fm = fl;
l = n; fl = fn;
} else if (n < m) {
if (fn > fm) {
l = n; fl = fn;
} else {
u = m; fu = fm;
m = n; fm = fn;
}
} else if (n == m) {
return n;
} else if (n < u) {
if (fn > fm) {
u = n; fu = fn;
} else {
l = m; fl = fm;
m = n; fm = fn;
}
} else {
if (exit_outside_bounds) {
status = OUTSIDE_BOUNDS;
return NaN;
}
l = m; fl = fm;
m = u; fm = fu;
u = n; fu = fn;
}
std::cerr << "\n";
std::cerr << "Pos " << str (l) << " " << str(m) << " " << str(u) << "\n";
std::cerr << "Value " << str (fl) << " " << str(fm) << " " << str(fu) << "\n";
if ((u-l) < value_tolerance) {
status = SUCCESS;
std::cerr << "Returning successfully\n";
return m;
}
}
status = NONCONVERGING;
std::cerr << "Returning due to too many iterations\n";
return NaN;
}
private:
ValueType init_lower, init_mid, init_upper, value_tolerance, function_tolerance;
bool exit_outside_bounds;
size_t max_iters;
std::string message;
mutable return_t status;
};
}
}
#endif
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