coco
113 lines
4.9 KiB
C++
113 lines
4.9 KiB
C++
// Copyright (C) 2010 Davis E. King (davis@dlib.net)
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// License: Boost Software License See LICENSE.txt for the full license.
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#undef DLIB_OPTIMIZATIOn_LEAST_SQUARES_ABSTRACT_
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#ifdef DLIB_OPTIMIZATIOn_LEAST_SQUARES_ABSTRACT_
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#include "../matrix/matrix_abstract.h"
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#include "optimization_trust_region_abstract.h"
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namespace dlib
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{
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// ----------------------------------------------------------------------------------------
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template <
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typename stop_strategy_type,
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typename funct_type,
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typename funct_der_type,
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typename vector_type,
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typename T
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>
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double solve_least_squares (
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stop_strategy_type stop_strategy,
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const funct_type& f,
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const funct_der_type& der,
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const vector_type& list,
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T& x,
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double radius = 1
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);
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/*!
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requires
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- stop_strategy == an object that defines a stop strategy such as one of
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the objects from dlib/optimization/optimization_stop_strategies_abstract.h
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- list == a matrix or something convertible to a matrix via mat()
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such as a std::vector.
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- is_vector(list) == true
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- list.size() > 0
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- is_col_vector(x) == true
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- radius > 0
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- for all valid i:
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- f(list(i),x) must be a valid expression that evaluates to a floating point value.
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- der(list(i),x) must be a valid expression that evaluates to the derivative of f(list(i),x)
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with respect to x. This derivative must take the form of a column vector.
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ensures
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- This function performs an unconstrained minimization of the least squares
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function g(x) defined by:
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- g(x) = sum over all i: 0.5*pow( f(list(i),x), 2 )
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- This method combines the Levenberg-Marquardt method with a quasi-newton method
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for approximating the second order terms of the hessian and is appropriate for
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large residual problems (i.e. problems where the f() function isn't driven to 0).
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In particular, it uses the method of Dennis, Gay, and Welsch as described in
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Numerical Optimization by Nocedal and Wright (second edition).
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- Since this is a trust region algorithm, the radius parameter defines the initial
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size of the trust region.
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- The function is optimized until stop_strategy decides that an acceptable
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point has been found or the trust region subproblem fails to make progress.
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- #x == the value of x that was found to minimize g()
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- returns g(#x).
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!*/
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// ----------------------------------------------------------------------------------------
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template <
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typename stop_strategy_type,
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typename funct_type,
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typename funct_der_type,
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typename vector_type,
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typename T
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>
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double solve_least_squares_lm (
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stop_strategy_type stop_strategy,
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const funct_type& f,
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const funct_der_type& der,
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const vector_type& list,
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T& x,
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double radius = 1
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);
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/*!
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requires
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- stop_strategy == an object that defines a stop strategy such as one of
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the objects from dlib/optimization/optimization_stop_strategies_abstract.h
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- list == a matrix or something convertible to a matrix via mat()
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such as a std::vector.
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- is_vector(list) == true
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- list.size() > 0
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- is_col_vector(x) == true
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- radius > 0
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- for all valid i:
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- f(list(i),x) must be a valid expression that evaluates to a floating point value.
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- der(list(i),x) must be a valid expression that evaluates to the derivative of f(list(i),x)
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with respect to x. This derivative must take the form of a column vector.
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ensures
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- This function performs an unconstrained minimization of the least squares
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function g(x) defined by:
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- g(x) = sum over all i: 0.5*pow( f(list(i),x), 2 )
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- This method implements a plain Levenberg-Marquardt approach for approximating
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the hessian of g(). Therefore, it is most appropriate for small residual problems
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(i.e. problems where f() goes to 0 at the solution).
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- Since this is a trust region algorithm, the radius parameter defines the initial
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size of the trust region.
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- The function is optimized until stop_strategy decides that an acceptable
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point has been found or the trust region subproblem fails to make progress.
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- #x == the value of x that was found to minimize g()
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- returns g(#x).
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!*/
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// ----------------------------------------------------------------------------------------
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}
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#endif // DLIB_OPTIMIZATIOn_LEAST_SQUARES_ABSTRACT_
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