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:
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. |