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+/*M///////////////////////////////////////////////////////////////////////////////////////
+//
+//  IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+//
+//  By downloading, copying, installing or using the software you agree to this license.
+//  If you do not agree to this license, do not download, install,
+//  copy or use the software.
+//
+//
+//                           License Agreement
+//                For Open Source Computer Vision Library
+//
+// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
+// Third party copyrights are property of their respective owners.
+//
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+// are permitted provided that the following conditions are met:
+//
+//   * Redistribution's of source code must retain the above copyright notice,
+//     this list of conditions and the following disclaimer.
+//
+//   * Redistribution's in binary form must reproduce the above copyright notice,
+//     this list of conditions and the following disclaimer in the documentation
+//     and/or other materials provided with the distribution.
+//
+//   * The name of the copyright holders may not be used to endorse or promote products
+//     derived from this software without specific prior written permission.
+//
+// This software is provided by the copyright holders and contributors "as is" and
+// any express or implied warranties, including, but not limited to, the implied
+// warranties of merchantability and fitness for a particular purpose are disclaimed.
+// In no event shall the OpenCV Foundation or contributors be liable for any direct,
+// indirect, incidental, special, exemplary, or consequential damages
+// (including, but not limited to, procurement of substitute goods or services;
+// loss of use, data, or profits; or business interruption) however caused
+// and on any theory of liability, whether in contract, strict liability,
+// or tort (including negligence or otherwise) arising in any way out of
+// the use of this software, even if advised of the possibility of such damage.
+//
+//M*/
+
+#ifndef OPENCV_OPTIM_HPP
+#define OPENCV_OPTIM_HPP
+
+#include "opencv2/core.hpp"
+
+namespace cv
+{
+
+/** @addtogroup core_optim
+The algorithms in this section minimize or maximize function value within specified constraints or
+without any constraints.
+@{
+*/
+
+/** @brief Basic interface for all solvers
+ */
+class CV_EXPORTS MinProblemSolver : public Algorithm
+{
+public:
+    /** @brief Represents function being optimized
+     */
+    class CV_EXPORTS Function
+    {
+    public:
+        virtual ~Function() {}
+        virtual int getDims() const = 0;
+        virtual double getGradientEps() const;
+        virtual double calc(const double* x) const = 0;
+        virtual void getGradient(const double* x,double* grad);
+    };
+
+    /** @brief Getter for the optimized function.
+
+    The optimized function is represented by Function interface, which requires derivatives to
+    implement the sole method calc(double*) to evaluate the function.
+
+    @return Smart-pointer to an object that implements Function interface - it represents the
+    function that is being optimized. It can be empty, if no function was given so far.
+     */
+    virtual Ptr<Function> getFunction() const = 0;
+
+    /** @brief Setter for the optimized function.
+
+    *It should be called at least once before the call to* minimize(), as default value is not usable.
+
+    @param f The new function to optimize.
+     */
+    virtual void setFunction(const Ptr<Function>& f) = 0;
+
+    /** @brief Getter for the previously set terminal criteria for this algorithm.
+
+    @return Deep copy of the terminal criteria used at the moment.
+     */
+    virtual TermCriteria getTermCriteria() const = 0;
+
+    /** @brief Set terminal criteria for solver.
+
+    This method *is not necessary* to be called before the first call to minimize(), as the default
+    value is sensible.
+
+    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.
+    @param termcrit Terminal criteria to be used, represented as cv::TermCriteria structure.
+     */
+    virtual void setTermCriteria(const TermCriteria& termcrit) = 0;
+
+    /** @brief actually runs the algorithm and performs the minimization.
+
+    The sole input parameter determines the centroid of the starting simplex (roughly, it tells
+    where to start), all the others (terminal criteria, initial step, function to be minimized) are
+    supposed to be set via the setters before the call to this method or the default values (not
+    always sensible) will be used.
+
+    @param x The initial point, that will become a centroid of an initial simplex. After the algorithm
+    will terminate, it will be setted to the point where the algorithm stops, the point of possible
+    minimum.
+    @return The value of a function at the point found.
+     */
+    virtual double minimize(InputOutputArray x) = 0;
+};
+
+/** @brief 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.
+
+@note 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.
+
+@note term criteria should meet following condition:
+@code
+    termcrit.type == (TermCriteria::MAX_ITER + TermCriteria::EPS) && termcrit.epsilon > 0 && termcrit.maxCount > 0
+@endcode
+ */
+class CV_EXPORTS DownhillSolver : public MinProblemSolver
+{
+public:
+    /** @brief Returns the initial step that will be used in downhill simplex algorithm.
+
+    @param 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 DownhillSolver::setInitStep
+     */
+    virtual void getInitStep(OutputArray step) const=0;
+
+    /** @brief 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 \f$s,x_0\in\mathbb{R}^n\f$ are
+    the initial step and initial point respectively, the vertices of a simplex will be:
+    \f$v_0:=x_0-\frac{1}{2} s\f$ and \f$v_i:=x_0+s_i\f$ for \f$i=1,2,\dots,n\f$ where \f$s_i\f$ denotes
+    projections of the initial step of *n*-th coordinate (the result of projection is treated to be
+    vector given by \f$s_i:=e_i\cdot\left<e_i\cdot s\right>\f$, where \f$e_i\f$ form canonical basis)
+
+    @param step Initial step that will be used in algorithm. Roughly said, it determines the spread
+    (size in each dimension) of an initial simplex.
+     */
+    virtual void setInitStep(InputArray step)=0;
+
+    /** @brief 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).
+    @param f Pointer to the function that will be minimized, similarly to the one you submit via
+    MinProblemSolver::setFunction.
+    @param initStep Initial step, that will be used to construct the initial simplex, similarly to the one
+    you submit via MinProblemSolver::setInitStep.
+    @param termcrit Terminal criteria to the algorithm, similarly to the one you submit via
+    MinProblemSolver::setTermCriteria.
+     */
+    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));
+};
+
+/** @brief This class is used to perform the non-linear non-constrained minimization of a function
+with known gradient,
+
+defined on an *n*-dimensional Euclidean space, using the **Nonlinear Conjugate Gradient method**.
+The implementation was done based on the beautifully clear explanatory article [An Introduction to
+the Conjugate Gradient Method Without the Agonizing
+Pain](http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf) by Jonathan Richard
+Shewchuk. The method can be seen as an adaptation of a standard Conjugate Gradient method (see, for
+example <http://en.wikipedia.org/wiki/Conjugate_gradient_method>) for numerically solving the
+systems of linear equations.
+
+It should be noted, that this method, although deterministic, is rather a heuristic method and
+therefore may converge to a local minima, not necessary a global one. What is even more disastrous,
+most of its behaviour is ruled by gradient, therefore it essentially cannot distinguish between
+local minima and maxima. Therefore, if it starts sufficiently near to the local maximum, it may
+converge to it. Another obvious restriction is that it should be possible to compute the gradient of
+a function at any point, thus it is preferable to have analytic expression for gradient and
+computational burden should be born by the user.
+
+The latter responsibility is accompilished via the getGradient method of a
+MinProblemSolver::Function interface (which represents function being optimized). This method takes
+point a point in *n*-dimensional space (first argument represents the array of coordinates of that
+point) and comput its gradient (it should be stored in the second argument as an array).
+
+@note class ConjGradSolver thus does not add any new methods to the basic MinProblemSolver interface.
+
+@note term criteria should meet following condition:
+@code
+    termcrit.type == (TermCriteria::MAX_ITER + TermCriteria::EPS) && termcrit.epsilon > 0 && termcrit.maxCount > 0
+    // or
+    termcrit.type == TermCriteria::MAX_ITER) && termcrit.maxCount > 0
+@endcode
+ */
+class CV_EXPORTS ConjGradSolver : public MinProblemSolver
+{
+public:
+    /** @brief This function returns the reference to the ready-to-use ConjGradSolver 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() should be called upon the obtained
+    object, if the function was not given to create(). Otherwise, the two ways (submit it to
+    create() or miss it out and call the MinProblemSolver::setFunction()) are absolutely equivalent
+    (and will drop the same errors in the same way, should invalid input be detected).
+    @param f Pointer to the function that will be minimized, similarly to the one you submit via
+    MinProblemSolver::setFunction.
+    @param termcrit Terminal criteria to the algorithm, similarly to the one you submit via
+    MinProblemSolver::setTermCriteria.
+    */
+    static Ptr<ConjGradSolver> create(const Ptr<MinProblemSolver::Function>& f=Ptr<ConjGradSolver::Function>(),
+                                      TermCriteria termcrit=TermCriteria(TermCriteria::MAX_ITER+TermCriteria::EPS,5000,0.000001));
+};
+
+//! return codes for cv::solveLP() function
+enum SolveLPResult
+{
+    SOLVELP_UNBOUNDED    = -2, //!< problem is unbounded (target function can achieve arbitrary high values)
+    SOLVELP_UNFEASIBLE    = -1, //!< problem is unfeasible (there are no points that satisfy all the constraints imposed)
+    SOLVELP_SINGLE    = 0, //!< there is only one maximum for target function
+    SOLVELP_MULTI    = 1 //!< there are multiple maxima for target function - the arbitrary one is returned
+};
+
+/** @brief Solve given (non-integer) linear programming problem using the Simplex Algorithm (Simplex Method).
+
+What we mean here by "linear programming problem" (or LP problem, for short) can be formulated as:
+
+\f[\mbox{Maximize } c\cdot x\\
+ \mbox{Subject to:}\\
+ Ax\leq b\\
+ x\geq 0\f]
+
+Where \f$c\f$ is fixed `1`-by-`n` row-vector, \f$A\f$ is fixed `m`-by-`n` matrix, \f$b\f$ is fixed `m`-by-`1`
+column vector and \f$x\f$ is an arbitrary `n`-by-`1` column vector, which satisfies the constraints.
+
+Simplex algorithm is one of many algorithms that are designed to handle this sort of problems
+efficiently. Although it is not optimal in theoretical sense (there exist algorithms that can solve
+any problem written as above in polynomial time, while simplex method degenerates to exponential
+time for some special cases), it is well-studied, easy to implement and is shown to work well for
+real-life purposes.
+
+The particular implementation is taken almost verbatim from **Introduction to Algorithms, third
+edition** by T. H. Cormen, C. E. Leiserson, R. L. Rivest and Clifford Stein. In particular, the
+Bland's rule <http://en.wikipedia.org/wiki/Bland%27s_rule> is used to prevent cycling.
+
+@param Func This row-vector corresponds to \f$c\f$ in the LP problem formulation (see above). It should
+contain 32- or 64-bit floating point numbers. As a convenience, column-vector may be also submitted,
+in the latter case it is understood to correspond to \f$c^T\f$.
+@param Constr `m`-by-`n+1` matrix, whose rightmost column corresponds to \f$b\f$ in formulation above
+and the remaining to \f$A\f$. It should containt 32- or 64-bit floating point numbers.
+@param z The solution will be returned here as a column-vector - it corresponds to \f$c\f$ in the
+formulation above. It will contain 64-bit floating point numbers.
+@return One of cv::SolveLPResult
+ */
+CV_EXPORTS_W int solveLP(const Mat& Func, const Mat& Constr, Mat& z);
+
+//! @}
+
+}// cv
+
+#endif