Function Set in OPEN CASCADE

/*
*    Copyright (c) 2016 Shing Liu All Rights Reserved.
*
*           File : main.cpp
*         Author : Shing Liu(eryar@163.com)
*           Date : 2016-01-12 21:00
*        Version : OpenCASCADE6.9.0
*
*    Description : test function set.
*/
#define WNT
#include <math_FunctionSetRoot.hxx>
#include <math_FunctionSetWithDerivatives.hxx>

#pragma comment(lib, "TKernel.lib")
#pragma comment(lib, "TKMath.lib")

/**
 * @brief test function for a circle and a curve:
 * 
 *  F1(x1,x2) = (x1)^2 + (x2)^2 -4
 *  F2(x1,x2) = e^(x1) + x2 - 1
 *
 * The derivatives of the function set are:
 *  Dx1f1(x1,x2) = 2.0 * x1
 *  Dx2f1(x1,x2) = 2.0 * x2
 *  Dx1f2(x1,x2) = e^(x1)
 *  Dx2f2(x1,x2) = 1.0
 */
class test_FunctionSet: public math_FunctionSetWithDerivatives
{
public:
    virtual Standard_Integer NbVariables() const
    {
        return 2;
    }

    virtual Standard_Integer NbEquations() const
    {
        return 2;
    }

    virtual Standard_Boolean Value(const math_Vector& X, math_Vector& F)
    {
        F(1) = X(1) * X(1) + X(2) * X(2) - 4.0;
        F(2) = exp(X(1)) + X(2) - 1.0;

        return Standard_True;
    }

    virtual Standard_Boolean Derivatives(const math_Vector& X, math_Matrix& D)
    {
        D(1,1) = 2.0 * X(1);
        D(1,2) = 2.0 * X(2);
        D(2,1) = exp(X(1));
        D(2,2) = 1.0;

        return Standard_True;
    }

    virtual Standard_Boolean Values(const math_Vector& X, math_Vector& F, math_Matrix& D)
    {
        Value(X, F);
        Derivatives(X, D);

        return Standard_True;
    }
};

void testFunctionSet(void)
{
    test_FunctionSet aTestFunctionSet;

    math_FunctionSetRoot aSolver(aTestFunctionSet);
    math_Vector aStartPoint(1, 2, 0.0);

    // initial guess point(-2.0, 0.0)
    aStartPoint(1) = -2.0;
    aStartPoint(2) = 0.0;
    aSolver.Perform(aTestFunctionSet, aStartPoint);
    std::cout << aSolver << std::endl;

    // initial guess point(0.0, -2.0)
    aStartPoint(1) = 0.0;
    aStartPoint(2) = -2.0;
    aSolver.Perform(aTestFunctionSet, aStartPoint);
    std::cout << aSolver << std::endl;
}

int main(int argc, char* argv[])
{
    testFunctionSet();
    return 0;
}

//! Functional for search of extremum of the distance between point P and
//! surface S, starting from approximate solution (u0, v0).
//!
//! The class inherits math_FunctionSetWithDerivatives and thus is intended
//! for use in math_FunctionSetRoot algorithm .
//!
//! Denoting derivatives of the surface S(u,v) by u and v, respectively, as
//! Su and Sv, the two functions to be nullified are:
//!
//! F1(u,v) = (S - P) * Su
//! F2(u,v) = (S - P) * Sv
//!
//! The derivatives of the functional are:
//!
//! Duf1(u,v) = Su^2    + (S-P) * Suu;
//! Dvf1(u,v) = Su * Sv + (S-P) * Suv
//! Duf2(u,v) = Sv * Su + (S-P) * Suv = Dvf1
//! Dvf2(u,v) = Sv^2    + (S-P) * Svv
//!
//! Here * denotes scalar product, and ^2 is square power.
class Extrema_FuncExtPS  : public math_FunctionSetWithDerivatives
{
public:

  DEFINE_STANDARD_ALLOC
  
  Standard_EXPORT Extrema_FuncExtPS();
  
  Standard_EXPORT Extrema_FuncExtPS(const gp_Pnt& P, const Adaptor3d_Surface& S);
  
  //! sets the field mysurf of the function.
  Standard_EXPORT void Initialize (const Adaptor3d_Surface& S);
  
  //! sets the field mysurf of the function.
  Standard_EXPORT void SetPoint (const gp_Pnt& P);
  
  Standard_EXPORT Standard_Integer NbVariables() const Standard_OVERRIDE;
  
  Standard_EXPORT Standard_Integer NbEquations() const Standard_OVERRIDE;
  
  //! Calculate Fi(U,V).
  Standard_EXPORT Standard_Boolean Value (const math_Vector& UV, math_Vector& F) Standard_OVERRIDE;
  
  //! Calculate Fi‘(U,V).
  Standard_EXPORT Standard_Boolean Derivatives (const math_Vector& UV, math_Matrix& DF) Standard_OVERRIDE;
  
  //! Calculate Fi(U,V) and Fi‘(U,V).
  Standard_EXPORT Standard_Boolean Values (const math_Vector& UV, math_Vector& F, math_Matrix& DF) Standard_OVERRIDE;
  
  //! Save the found extremum.
  Standard_EXPORT virtual Standard_Integer GetStateNumber() Standard_OVERRIDE;
  
  //! Return the number of found extrema.
  Standard_EXPORT Standard_Integer NbExt() const;
  
  //! Return the value of the Nth distance.
  Standard_EXPORT Standard_Real SquareDistance (const Standard_Integer N) const;
  
  //! Returns the Nth extremum.
  Standard_EXPORT const Extrema_POnSurf& Point (const Standard_Integer N) const;

protected:

private:
  gp_Pnt myP;
  Adaptor3d_SurfacePtr myS;
  Standard_Real myU;
  Standard_Real myV;
  gp_Pnt myPs;
  TColStd_SequenceOfReal mySqDist;
  Extrema_SequenceOfPOnSurf myPoint;
  Standard_Boolean myPinit;
  Standard_Boolean mySinit;
};