vnl_real_npolynomial.h

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#ifndef vnl_real_npolynomial_h_
#define vnl_real_npolynomial_h_

// This is vxl/vnl/vnl_real_npolynomial.h

//:
//  \file
//  \brief contains class for polynomials with N variables
//  \authur Marc Pollefeys, ESAT-VISICS, K.U.Leuven, 12-08-97
//  Implements a polynomial with N variables
//

//
//  \verbatim
//  Modifications
//  Peter Vanroose 10 Oct 1999 - added simplify();
//                               determine nterms_ nvar_ ideg_ automatically
//  Peter Vanroose 20 Oct 1999 - Added operator+(), - * and ostream <<
//  dac (Manchester) 15/03/2001: Tidied up the documentation + added binary_io
//  \endverbatim


//-----------------------------------------------------------------------------

#include <vnl/vnl_vector.h>
#include <vnl/vnl_matrix.h>

//: real polynomial in N variables.
//  \verbatim
//    vnl_real_npolynomial represents a polynomial in multiple variables.
//    Used by vnl_rnpoly_solve which solves systems of polynomial equations.
//    Representation:  an N-omial (N terms) is represented by (1) a vector
//    with the N coefficients (vnl_vector<double>), and (2) a matrix with
//    N rows, the i-th row representing the exponents of term i, as follows:
//    (vnl_matrix<int>) column k contains the (integer) exponent of variable
//    k.  Example: the polynomial A*X^3 + B*X*Y + C*Y^2 + D*X*Y^2 is
//    represented by the coefficients vector [A B C D] and the exponents
//    matrix
//    [3 0]
//    [1 1]
//    [0 2]
//    [1 2].
//  \endverbatim 
//

class vnl_real_npolynomial {
  friend class vnl_rnpoly_solve;

public:
  
  // Constructor-----------------------------------------------------------------
  vnl_real_npolynomial() { } // don't use this. only here for the STL vector class.
  vnl_real_npolynomial(const vnl_vector<double>& c, const vnl_matrix<int>& p);

  // Computations--------------------------------------------------------------

  double eval(const vnl_vector<double>& x);
  int degree();
  vnl_real_npolynomial operator-() const; // unary minus
  vnl_real_npolynomial operator+(vnl_real_npolynomial const& ) const;
  vnl_real_npolynomial operator-(vnl_real_npolynomial const& ) const;
  vnl_real_npolynomial operator*(vnl_real_npolynomial const& ) const;
  vnl_real_npolynomial operator+(double ) const;
  vnl_real_npolynomial operator-(double P) const { return operator+(-P); }
  vnl_real_npolynomial operator*(double ) const;
  vnl_real_npolynomial& operator*=(double P) { coeffs_ *= P; return *this; }
  vnl_real_npolynomial operator/(double P) const { return operator*(1.0/P); }
  vnl_real_npolynomial& operator/=(double P) { return operator*=(1.0/P); }
  friend vcl_ostream& operator<<(vcl_ostream& , vnl_real_npolynomial const& );


  // nb also added functions to access the coeffs_ member variable

  // Data Access---------------------------------------------------------------

  //: Return the degree (highest power of x) of the polynomial.
  int degree() const { return coeffs_.size() - 1; }

  //: Access to the polynomial coefficients
  double& operator [] (int i)       { return coeffs_[i]; }
  //: Access to the polynomial coefficients
  double  operator [] (int i) const { return coeffs_[i]; }

  //: Return the vector of coefficients
  const vnl_vector<double>& coefficients() const { return coeffs_; }
  //: Return the vector of coefficients
  vnl_vector<double>& coefficients()       { return coeffs_; }

  //: Set vector of coefficients of each product
  void set(const vnl_vector<double> & c, const vnl_matrix<int> & p);
  
  //: Return the polynomial matrix 
  // (ie specifying the variables in each product)
  const vnl_matrix<int>& polyn() const { return polyn_; }

  //: Return the vector of coefficients
  vnl_matrix<int>& polyn()       { return polyn_; }


private:
  void simplify();
  double eval(const vnl_matrix<double>& xn);

  // Data Members--------------------------------------------------------------
  //: coefficients
  vnl_vector<double> coeffs_; 
  //: degrees of every term for every variable
  vnl_matrix<int>    polyn_;  
  //: number of variables = # columns of polyn_
  int                nvar_;
  //: number of terms of polynomial
  int                nterms_; 
  //: max. degree of polynomial
  int                ideg_;   
};


#endif // vnl_real_npolynomial_h_

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