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//                                               -*- C++ -*-
/**
 *  @file  UniVariatePolynomialImplementation.hxx
 *  @brief This is a 1D polynomial
 *
 *  (C) Copyright 2005-2011 EDF-EADS-Phimeca
 *
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public
 *  License as published by the Free Software Foundation; either
 *  version 2.1 of the License.
 *
 *  This library is distributed in the hope that it will be useful
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *  Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public
 *  License along with this library; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
 *
 *  @author: $LastChangedBy: dutka $
 *  @date:   $LastChangedDate: 2008-05-21 17:44:02 +0200 (Wed, 21 May 2008) $
 *  Id:      $Id: Object.hxx 818 2008-05-21 15:44:02Z dutka $
 */
#ifndef OPENTURNS_UNIVARIATEPOLYNOMIALIMPLEMENTATION_HXX
#define OPENTURNS_UNIVARIATEPOLYNOMIALIMPLEMENTATION_HXX

#include "OTprivate.hxx"
#include "NumericalPoint.hxx"
#include "Graph.hxx"
#include "Matrix.hxx"
#include "Pointer.hxx"
#include "PersistentObject.hxx"

namespace OpenTURNS
{

  namespace Base
  {

    namespace Func
    {

      /**
       * @class UniVariatePolynomialImplementation
       *
       * This is a 1D polynomial
       */

      class UniVariatePolynomialImplementation
        : public Common::PersistentObject
      {
        CLASSNAME;
      public:

        typedef Pointer<UniVariatePolynomialImplementation> Implementation;
        typedef Common::StorageManager                                    StorageManager;
        typedef Type::NumericalPoint                                      NumericalPoint;
        typedef Type::Matrix                                              Matrix;
        typedef Matrix::NumericalComplexCollection                        NumericalComplexCollection;
        typedef NumericalPoint                                            Coefficients;
        typedef Graph::Graph                                              Graph;

        /** Default constructor */
        UniVariatePolynomialImplementation();

        /** Constructor from coefficients */
        UniVariatePolynomialImplementation(const Coefficients & coefficients);

        /** Virtual constructor */
        virtual UniVariatePolynomialImplementation * clone() const;

        /** String converter */
        virtual String __repr__() const;
        virtual String __str__(const String & offset = "",
                               const String & variableName = "X") const;

        /** UniVariatePolynomialImplementation are evaluated as functors */
        NumericalScalar operator() (const NumericalScalar x) const;
        NumericalComplex operator() (const NumericalComplex z) const;

        /** UniVariatePolynomialImplementation derivative */
        NumericalScalar derivative(const NumericalScalar x) const;

        /** Compute the derivative of the polynomial */
        UniVariatePolynomialImplementation derivate() const;

        /** Multiply the polynomial P by a NumericalScalar */
        UniVariatePolynomialImplementation operator * (const NumericalScalar scalar) const;

        /** Multiply the polynomial P by a polynomial Q */
        UniVariatePolynomialImplementation operator * (const UniVariatePolynomialImplementation & uniVariatePolynomial) const;

        /** Multiply the polynomial by (x to the power degree) */
        UniVariatePolynomialImplementation incrementDegree (const UnsignedLong degree = 1) const;

        /** Sum of two polynomials of any degree */
        UniVariatePolynomialImplementation operator + (const UniVariatePolynomialImplementation & uniVariatePolynomial) const;

        /** Substraction of two polynomials of any degree */
        UniVariatePolynomialImplementation operator - (const UniVariatePolynomialImplementation & uniVariatePolynomial) const;

        /** Coefficients accessor */
        void setCoefficients(const Coefficients & coefficients);
        Coefficients getCoefficients() const;

        /** Get the degree of the polynomial */
        UnsignedLong getDegree() const;

        /** Root of the polynomial of degree n as the eigenvalues of the associated matrix */
        NumericalComplexCollection getRoots() const;

        /** Method to draw the graph of the polynomial between given bounds */
        Graph draw(const NumericalScalar xMin,
                   const NumericalScalar xMax,
                   const UnsignedLong pointNumber) const;

        /** Method save() stores the object through the StorageManager */
        void save(StorageManager::Advocate & adv) const;

        /** Method load() reloads the object from the StorageManager */
        void load(StorageManager::Advocate & adv);

      protected:

        /** Remove null leading coefficients */
        void compactCoefficients();

        /** The table of polynomial coefficients in ascending order: P(X) = C0 + C1 * X + ... + Cn * X^n */
        Coefficients coefficients_;

      private:

      } ; /* Class UniVariatePolynomialImplementation */

    } /* namespace Func */
  } /* namespace Base */
} /* namespace OpenTURNS */

#endif /* OPENTURNS_UNIVARIATEPOLYNOMIALIMPLEMENTATION_HXX */