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// File: BinarySubstitutionModel.h
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// Created by: Laurent Gueguen
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Copyright or � or Copr. CNRS, (November 16, 2004)
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This software is a computer program whose purpose is to provide classes
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for phylogenetic data analysis.
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This software is governed by the CeCILL license under French law and
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abiding by the rules of distribution of free software. You can use,
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modify and/ or redistribute the software under the terms of the CeCILL
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license as circulated by CEA, CNRS and INRIA at the following URL
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"http://www.cecill.info".
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As a counterpart to the access to the source code and rights to copy,
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modify and redistribute granted by the license, users are provided only
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with a limited warranty and the software's author, the holder of the
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economic rights, and the successive licensors have only limited
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In this respect, the user's attention is drawn to the risks associated
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with loading, using, modifying and/or developing or reproducing the
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software by the user in light of its specific status of free software,
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that may mean that it is complicated to manipulate, and that also
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therefore means that it is reserved for developers and experienced
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professionals having in-depth computer knowledge. Users are therefore
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encouraged to load and test the software's suitability as regards their
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requirements in conditions enabling the security of their systems and/or
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data to be ensured and, more generally, to use and operate it in the
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same conditions as regards security.
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The fact that you are presently reading this means that you have had
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knowledge of the CeCILL license and that you accept its terms.
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#ifndef _BINARYSUBSTITUTIONMODEL_H_
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#define _BINARYSUBSTITUTIONMODEL_H_
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#include "AbstractSubstitutionModel.h"
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#include <Bpp/Seq/Alphabet/BinaryAlphabet.h>
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* @brief The Model on two states
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* Q = r.\begin{pmatrix}
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* \pi = diag\left(\frac{1}{\kappa+1}, \frac{\kappa}{\kappa+1}\right)
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* Normalization: \f$r\f$ is set so that \f$\sum_i Q_{i,i}\pi_i = -1\f$:
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* -\frac{\kappa + 1}2 & \frac{\kappa + 1}2 \\
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* \frac{\kappa+1}{2\kappa} & -\frac{\kappa+1}{2\kappa}\\
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* The eigen values are \f$\left(0, - \frac{(\kappa+1)^2}{2\kappa}\right)\f$,
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* and IF \f$\kappa \neq 1\f$, the left eigen vectors are, by row:
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* \frac{1}{1+\kappa} & \frac{\kappa}{1+\kappa} \\
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* \frac{\kappa-1}{\kappa+1} & -\frac{\kappa-1}{\kappa+1} \\
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* and the right eigen vectors are by column:
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* U^{-1} = \begin{pmatrix}
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* 1 & \frac \kappa{\kappa-1} \\
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* 1 & - \frac 1{\kappa-1} \\
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* The probabilities of changes are computed analytically using the formulas, with \f$\lambda= \frac{(\kappa+1)^2}{2\kappa}\f$ :
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* P_{i,j}(t) = \begin{pmatrix}
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* \frac{1}{\kappa+1} + \frac{\kappa}{\kappa+1}e^{-\lambda t} & \frac{\kappa}{\kappa+1} - \frac{\kappa}{\kappa+1}e^{-\lambda t} \\
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* \frac{1}{\kappa+1} - \frac{1}{\kappa+1}e^{-\lambda t} & \frac{\kappa}{\kappa+1} + \frac{1}{\kappa+1}e^{-\lambda t} \\
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* \frac{\partial P_{i,j}(t)}{\partial t} = \begin{pmatrix}
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* -\frac {\kappa+1} 2 e^{-\lambda t} & \frac {\kappa+1} 2 e^{-\lambda t} \\
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* \frac {\kappa+1} {2\kappa} e^{-\lambda t} & - \frac {\kappa+1} {2\kappa} e^{-\lambda t} \ \
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* \frac{\partial^2 P_{i,j}(t)}{\partial t^2} = \\
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* \frac {\lambda (\kappa+1)} 2 e^{-\lambda t} & -\ frac {\lambda (\kappa+1)} 2 e^{-\lambda t} \\
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* \frac {\lambda (\kappa+1)} {2\kappa} e^{-\lambda t} & - \frac {\lambda (\kappa+1)} {2\kappa} e^{-\lambda t} \ \
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* The parameter is named \c "kappa"
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* and its value may be retrieve with the command
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* getParameterValue("kappa")
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class BinarySubstitutionModel :
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public AbstractSubstitutionModel
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mutable double _lambda, _exp;
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mutable RowMatrix<double> _p;
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BinarySubstitutionModel(const BinaryAlphabet* alpha, double kappa = 1.);
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virtual ~BinarySubstitutionModel() {}
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BinarySubstitutionModel* clone() const { return new BinarySubstitutionModel(*this); }
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double Pij_t (unsigned int i, unsigned int j, double d) const;
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double dPij_dt (unsigned int i, unsigned int j, double d) const;
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double d2Pij_dt2(unsigned int i, unsigned int j, double d) const;
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const Matrix<double>& getPij_t (double d) const;
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const Matrix<double>& getdPij_dt (double d) const;
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const Matrix<double>& getd2Pij_dt2(double d) const;
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std::string getName() const { return "Binary"; }
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void setFreq(std::map<int, double>& freqs);
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unsigned int getNumberOfStates() const { return 2; }
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void updateMatrices();
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} // end of namespace bpp.
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#endif // _BINARYSUBSTITUTIONMODEL_H_
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src/Bpp/Phyl/Model/BinarySubstitutionModel.h
