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// Created by: Julien Dutheil
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// Created on: Thu Jan 22 16:17:39 2004
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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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#include "NucleotideSubstitutionModel.h"
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#include "AbstractSubstitutionModel.h"
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#include <Bpp/Numeric/Constraints.h>
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#include <Bpp/Seq/Alphabet/NucleicAlphabet.h>
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* @brief The Hasegawa M, Kishino H and Yano T (1985) substitution model for nucleotides.
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* This model is similar to K80 model,
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* but allows distinct equilibrium frequencies between A, C, G and T.
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* \cdots & r & \kappa r & r \\
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* r & \cdots & r & \kappa r \\
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* \kappa r & r & \cdots & r \\
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* r & \kappa r & r & \cdots \\
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* \pi = \left(\pi_A, \pi_C, \pi_G, \pi_T\right)
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* This models hence includes five parameters, the transition / transversion
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* relative rate \f$\kappa\f$ and four frequencies \f$\pi_A, \pi_C, \pi_G, \pi_T\f$.
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* These four frequencies are not independent parameters, since they have the constraint to
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* We use instead a different parametrization to remove this constraint:
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* \theta = \pi_C + \pi_G\\
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* \theta_1 = \frac{\pi_A}{1 - \theta} = \frac{\pi_A}{\pi_A + \pi_T}\\
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* \theta_2 = \frac{\pi_G}{\theta} = \frac{\pi_G}{\pi_C + \pi_G}\\
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* \pi_A = \theta_1 (1 - \theta)\\
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* \pi_C = (1 - \theta_2) \theta\\
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* \pi_G = \theta_2 \theta\\
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* \pi_T = (1 - \theta_1)(1 - \theta).
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* These parameters can also be measured from the data and not optimized.
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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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* S = \frac{1}{P}\begin{pmatrix}
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* \frac{-\pi_T-\kappa\pi_G-\pi_C}{\pi_A} & 1 & \kappa & 1 \\
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* 1 & \frac{-\kappa\pi_T-\pi_G-\pi_A}{\pi_C} & 1 & \kappa \\
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* \kappa & 1 & \frac{-\pi_T-\pi_C-\kappa\pi_A}{\pi_G} & 1 \\
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* 1 & \kappa & 1 & \frac{-\pi_G-\kappa\pi_C-\pi_A}{\pi_T} \\
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* with \f$P=2\left(\pi_A \pi_C + \pi_C \pi_G + \pi_A \pi_T + \pi_G \pi_T + \kappa \left(\pi_C \pi_T + \pi_A \pi_G\right)\right)\f$.
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* The normalized generator is obtained by taking the dot product of \f$S\f$ and \f$\pi\f$:
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* Q = S . \pi = \frac{1}{P}\begin{pmatrix}
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* -\pi_T-\kappa\pi_G-\pi_C & \pi_C & \kappa\pi_G & \pi_T \\
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* \pi_A & -\kappa\pi_T-\pi_G-\pi_A & \pi_G & \kappa\pi_T \\
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* \kappa\pi_A & \pi_C & -\pi_T-\pi_C-\kappa\pi_A & \pi_T \\
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* \pi_A & \kappa\pi_C & \pi_G & -\pi_G-\kappa\pi_C-\pi_A \\
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* The eigen values are \f$\left(0, -\frac{\pi_R + \kappa\pi_Y}{P}, -\frac{\pi_Y + \kappa\pi_R}{P}, -\frac{1}{P}\right)\f$,
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* with \f$\pi_R=\pi_A+\pi_G\f$ and \f$\pi_Y=\pi_C+\pi_T\f$.
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* The left eigen vectors are, by row:
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* U = \begin{pmatrix}
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* \pi_A & \pi_C & \pi_G & \pi_T \\
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* 0 & \frac{\pi_T}{\pi_Y} & 0 & -\frac{\pi_T}{\pi_Y} \\
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* \frac{\pi_G}{\pi_R} & 0 & -\frac{\pi_G}{\pi_R} & 0 \\
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* \frac{\pi_A\pi_Y}{\pi_R} & -\pi_C & \frac{\pi_G\pi_Y}{\pi_R} & -\pi_T \\
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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 & 1 & 0 & -\frac{\pi_R}{\pi_Y} \\
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* 1 & 0 & \frac{\pi_A}{\pi_G} & 1 \\
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* 1 & -\frac{\pi_C}{\pi_T} & 0 & -\frac{\pi_R}{\pi_Y} \\
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* In addition, a rate_ factor defines the mean rate of the model.
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* The probabilities of changes are computed analytically using the formulas:
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* \frac{\pi_G}{\pi_R}A + \frac{\pi_A\pi_Y}{\pi_R}B + \pi_A & \pi_C - \pi_CB & -\frac{\pi_G}{\pi_R}A + \frac{\pi_G\pi_Y}{\pi_R}B + \pi_G & \pi_T - \pi_TB \\
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* \pi_A - \pi_AB & \frac{\pi_T}{\pi_Y}A + \frac{\pi_C\pi_R}{\pi_Y}B + \pi_C & \pi_G - \pi_GB & -\frac{\pi_T}{\pi_Y}A + \frac{\pi_T\pi_R}{\pi_Y}B + \pi_T \\
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* -\frac{\pi_A}{\pi_R}A + \frac{\pi_A\pi_Y}{\pi_R}B + \pi_A & \pi_C - \pi_CB & \frac{\pi_A}{\pi_R}A + \frac{\pi_G\pi_Y}{\pi_R}B + \pi_G & \pi_T - \pi_TB \\
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* \pi_A - \pi_AB & -\frac{\pi_C}{\pi_Y}A + \frac{\pi_C\pi_R}{\pi_Y}B + \pi_C & \pi_G - \pi_GB & \frac{\pi_C}{\pi_Y}A + \frac{\pi_R\pi_T}{\pi_Y}B + \pi_T \\
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* with \f$A=e^{-\frac{rate\_*(\pi_Y+\kappa\pi_R)t}{P}}\f$ and \f$B = e^{-\frac{rate\_*t}{P}}\f$.
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* First and second order derivatives are also computed analytically using the formulas:
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* \frac{\partial P_{i,j}(t)}{\partial t} = rate\_ * \\
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* -\frac{\pi_G(\pi_Y+\kappa\pi_R)}{\pi_R}A - \frac{\pi_A\pi_Y}{\pi_R}B & \pi_CB & \frac{\pi_G(\pi_Y+\kappa\pi_R)}{\pi_R}A - \frac{\pi_G\pi_Y}{\pi_R}B & \pi_TB \\
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* \pi_AB & -\frac{\pi_T(\pi_R+\kappa\pi_Y)}{\pi_Y}A - \frac{\pi_C\pi_R}{\pi_Y}B & \pi_GB & \frac{\pi_T(\pi_R+\kappa\pi_Y)}{\pi_Y}A - \frac{\pi_T\pi_R}{\pi_Y}B \\
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* \frac{\pi_A(\pi_Y+\kappa\pi_R)}{\pi_R}A - \frac{\pi_A\pi_Y}{\pi_R}B & \pi_CB & -\frac{\pi_A(\pi_Y+\kappa\pi_R)}{\pi_R}A - \frac{\pi_G\pi_Y}{\pi_R}B & \pi_TB \\
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* \pi_AB & \frac{\pi_C(\pi_R+\kappa\pi_Y)}{\pi_Y}A - \frac{\pi_C\pi_R}{\pi_Y}B & \pi_GB & -\frac{\pi_C(\pi_R+\kappa\pi_Y)}{\pi_Y}A - \frac{\pi_R\pi_T}{\pi_Y}B \\
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* \frac{\partial^2 P_{i,j}(t)}{\partial t^2} = rate\_^2 * \\
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* \frac{\pi_G{(\pi_Y+\kappa\pi_R)}^2}{\pi_R}A + \frac{\pi_A\pi_Y}{\pi_R}B & -\pi_CB & -\frac{\pi_G{(\pi_Y+\kappa\pi_R)}^2}{\pi_R}A + \frac{\pi_G\pi_Y}{\pi_R}B & -\pi_TB \\
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* -\pi_AB & \frac{\pi_T{(\pi_R+\kappa\pi_Y)}^2}{\pi_Y}A + \frac{\pi_C\pi_R}{\pi_Y}B & -\pi_GB & -\frac{\pi_T{(\pi_R+\kappa\pi_Y)}^2}{\pi_Y}A + \frac{\pi_T\pi_R}{\pi_Y}B \\
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* -\frac{\pi_A{(\pi_Y+\kappa\pi_R)}^2}{\pi_R}A + \frac{\pi_A\pi_Y}{\pi_R}B & -\pi_CB & \frac{\pi_A{(\pi_Y+\kappa\pi_R)}^2}{\pi_R}A + \frac{\pi_G\pi_Y}{\pi_R}B & -\pi_TB \\
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* -\pi_AB & -\frac{\pi_C{(\pi_R+\kappa\pi_Y)}^2}{\pi_Y}A + \frac{\pi_C\pi_R}{\pi_Y}B & -\pi_GB & \frac{\pi_C{(\pi_R+\kappa\pi_Y)}^2}{\pi_Y}A + \frac{\pi_R\pi_T}{\pi_Y}B \\
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* The parameters are named \c "kappa", \c "theta", \c "theta1", and \c "theta2"
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* and their values may be retrieve with the command
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* getParameterValue("kappa")
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* - Hasegawa M, Kishino H and Yano T (1985), Molecular_ Biology And Evolution_ 22(2) 160-74.
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public virtual NucleotideSubstitutionModel,
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public AbstractReversibleSubstitutionModel
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double kappa_, k1_, k2_, r_, piA_, piC_, piG_, piT_, piY_, piR_, theta_, theta1_, theta2_;
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mutable double exp1_, exp21_, exp22_, l_;
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mutable RowMatrix<double> p_;
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const NucleicAlphabet * alpha,
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#ifndef NO_VIRTUAL_COV
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clone() const { return new HKY85(*this); }
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double Pij_t (int i, int j, double d) const;
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double dPij_dt (int i, int j, double d) const;
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double d2Pij_dt2(int i, 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 "HKY85"; }
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* @brief This method is redefined to actualize the corresponding parameters piA, piT, piG and piC too.
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void setFreq(std::map<int, double>& freqs);
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void updateMatrices();
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} //end of namespace bpp.
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removed
src/Bpp/Phyl/Model/HKY85.h
