class cv::DownhillSolver

Overview

This class is used to perform the non-linear non-constrained minimization of a function,. More…

#include <optim.hpp>

class DownhillSolver: public cv::MinProblemSolver
{
public:
    // methods

    virtual
    void
    getInitStep(OutputArray step) const = 0;

    virtual
    void
    setInitStep(InputArray step) = 0;

    static
    Ptr<DownhillSolver>
    create(
        const Ptr<MinProblemSolver::Function>& f = Ptr<MinProblemSolver::Function>(),
        InputArray initStep = Mat_<double>(1, 1, 0.0),
        TermCriteria termcrit = TermCriteria(TermCriteria::MAX_ITER+TermCriteria::EPS, 5000, 0.000001)
        );
};

Inherited Members

public:
    // classes

    class Function;

    // methods

    virtual
    void
    clear();

    virtual
    bool
    empty() const;

    virtual
    String
    getDefaultName() const;

    virtual
    void
    read(const FileNode& fn);

    virtual
    void
    save(const String& filename) const;

    virtual
    void
    write(FileStorage& fs) const;

    template <typename _Tp>
    static
    Ptr<_Tp>
    load(
        const String& filename,
        const String& objname = String()
        );

    template <typename _Tp>
    static
    Ptr<_Tp>
    loadFromString(
        const String& strModel,
        const String& objname = String()
        );

    template <typename _Tp>
    static
    Ptr<_Tp>
    read(const FileNode& fn);

    virtual
    Ptr<Function>
    getFunction() const = 0;

    virtual
    TermCriteria
    getTermCriteria() const = 0;

    virtual
    double
    minimize(InputOutputArray x) = 0;

    virtual
    void
    setFunction(const Ptr<Function>& f) = 0;

    virtual
    void
    setTermCriteria(const TermCriteria& termcrit) = 0;

protected:
    // methods

    void
    writeFormat(FileStorage& fs) const;

Detailed Documentation

This class is used to perform the non-linear non-constrained minimization of a function,.

defined on an n -dimensional Euclidean space, using the Nelder-Mead method, also known as downhill simplex method**. The basic idea about the method can be obtained from http://en.wikipedia.org/wiki/Nelder-Mead_method.

It should be noted, that this method, although deterministic, is rather a heuristic and therefore may converge to a local minima, not necessary a global one. It is iterative optimization technique, which at each step uses an information about the values of a function evaluated only at n+1 points, arranged as a simplex in n -dimensional space (hence the second name of the method). At each step new point is chosen to evaluate function at, obtained value is compared with previous ones and based on this information simplex changes it’s shape , slowly moving to the local minimum. Thus this method is using only function values to make decision, on contrary to, say, Nonlinear Conjugate Gradient method (which is also implemented in optim).

Algorithm stops when the number of function evaluations done exceeds termcrit.maxCount, when the function values at the vertices of simplex are within termcrit.epsilon range or simplex becomes so small that it can enclosed in a box with termcrit.epsilon sides, whatever comes first, for some defined by user positive integer termcrit.maxCount and positive non-integer termcrit.epsilon.

DownhillSolver is a derivative of the abstract interface cv::MinProblemSolver, which in turn is derived from the Algorithm interface and is used to encapsulate the functionality, common to all non-linear optimization algorithms in the optim module.

term criteria should meet following condition:

termcrit.type == (TermCriteria::MAX_ITER + TermCriteria::EPS) && termcrit.epsilon > 0 && termcrit.maxCount > 0

Methods

virtual
void
getInitStep(OutputArray step) const = 0

Returns the initial step that will be used in downhill simplex algorithm.

Parameters:

step Initial step that will be used in algorithm. Note, that although corresponding setter accepts column-vectors as well as row-vectors, this method will return a row-vector.

See also:

DownhillSolver::setInitStep

virtual
void
setInitStep(InputArray step) = 0

Sets the initial step that will be used in downhill simplex algorithm.

Step, together with initial point (givin in DownhillSolver::minimize) are two n -dimensional vectors that are used to determine the shape of initial simplex. Roughly said, initial point determines the position of a simplex (it will become simplex’s centroid), while step determines the spread (size in each dimension) of a simplex. To be more precise, if \(s,x_0\in\mathbb{R}^n\) are the initial step and initial point respectively, the vertices of a simplex will be: \(v_0:=x_0-\frac{1}{2} s\) and \(v_i:=x_0+s_i\) for \(i=1,2,\dots,n\) where \(s_i\) denotes projections of the initial step of n -th coordinate (the result of projection is treated to be vector given by \(s_i:=e_i\cdot\left<e_i\cdot s\right>\), where \(e_i\) form canonical basis)

Parameters:

step Initial step that will be used in algorithm. Roughly said, it determines the spread (size in each dimension) of an initial simplex.
static
Ptr<DownhillSolver>
create(
    const Ptr<MinProblemSolver::Function>& f = Ptr<MinProblemSolver::Function>(),
    InputArray initStep = Mat_<double>(1, 1, 0.0),
    TermCriteria termcrit = TermCriteria(TermCriteria::MAX_ITER+TermCriteria::EPS, 5000, 0.000001)
    )

This function returns the reference to the ready-to-use DownhillSolver object.

All the parameters are optional, so this procedure can be called even without parameters at all. In this case, the default values will be used. As default value for terminal criteria are the only sensible ones, MinProblemSolver::setFunction() and DownhillSolver::setInitStep() should be called upon the obtained object, if the respective parameters were not given to create(). Otherwise, the two ways (give parameters to createDownhillSolver() or miss them out and call the MinProblemSolver::setFunction() and DownhillSolver::setInitStep()) are absolutely equivalent (and will drop the same errors in the same way, should invalid input be detected).

Parameters:

f Pointer to the function that will be minimized, similarly to the one you submit via MinProblemSolver::setFunction.
initStep Initial step, that will be used to construct the initial simplex, similarly to the one you submit via MinProblemSolver::setInitStep.
termcrit Terminal criteria to the algorithm, similarly to the one you submit via MinProblemSolver::setTermCriteria.