Examples of PCCA

stallone.mc.pcca.PCCA
A java implementation of the Inner Simplex Algorithm (ISA) from Marcus Weber. For details refer to:
Marcus Weber: Improved Perron Cluster Analysis, ZIB-Report 03-04.
Marcus Weber and Tobias Galliat: Charakterization of Transition States in Conformational Dynamics using Fuzzy States, ZIB-Report 02-12.
See www.zib.de/bib/pub/index.en.html.
A typical application is the computation of meta stable sets of a Markov chain represented by a given reversible transition matrix. This requires the following steps:
1) Compute a reversible transition matrix, say P.
2) Determine the number of meta stable sets, for instance via the size of the Perron Cluster, say k.
3) Compute the k eigenvectors belonging to the k eigenvalues closest to 1.
4) Use the eigenvectors as input data to the cluster algorithm.
5) With {@link #getClusters} you get an array containing the allocation of each indices to a cluster, which is anumber between 0,...,k-1.
6) Use {@link #getPermutationArray} to obtain a permutation array. With this array you can permute the state space ofP, such that states belonging to the same cluster are neighbours.
@author meerbach@math.fu-berlin.de

Examples of stallone.mc.pcca.PCCA

        return( deltaG );
    }


    public PCCA createPCCA(IDoubleArray M, int nstates)
    {
        PCCA pcca = new PCCA();


        IDoubleArray evec = M;


        if (MarkovModel.util.isTransitionMatrix(M))
        {
            IEigenvalueDecomposition evd = Algebra.util.evd(M,nstates);
            evec = evd.getRightEigenvectorMatrix();
            evec = evec.viewBlock(0,0,M.rows(),nstates);
        }
        else
        {
            if (evec.columns() < nstates)
                throw(new IllegalArgumentException("Attempting to create PCCA decomposition into "+nstates+" states."+
                                                    "but only "+evec.columns()+" eigenvectors were provided"));
        }


        pcca.setEigenvectors(evec);
        pcca.perform();


        return(pcca);
    }

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Examples of stallone.mc.pcca.PCCA

     * @param nstates
     * @return
     */
    public IIntArray metastableStates(IDoubleArray M, int nstates)
    {
        PCCA pcca = MarkovModel.create.createPCCA(M, nstates);
        return(pcca.getClusters());
    }

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Examples of stallone.mc.pcca.PCCA

     * @param nstates
     * @return
     */
    public IDoubleArray metastableMemberships(IDoubleArray M, int nstates)
    {
        PCCA pcca = MarkovModel.create.createPCCA(M, nstates);
        return(pcca.getFuzzy());
    }

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Examples of stallone.mc.pcca.PCCA

        IDoubleArray Lambda = evd.getDiagonalMatrix();
        System.out.println("old timescales: "+ts1);
        System.out.println("Lambda = \n"+Lambda+"\n");


        int nhidden = 2;
        PCCA pcca = msmNew.createPCCA(T, nhidden);
        IDoubleArray R = evd.getRightEigenvectorMatrix().viewReal();
        IDoubleArray Rsub = R.viewBlock(0, 0, T.rows(), nhidden);
        pcca.setEigenvectors(Rsub);
        pcca.perform();
        IDoubleArray M = pcca.getFuzzy();
        
        System.out.println("M\n"+M);


        IDoubleArray pi = msm.stationaryDistribution(T);
        IDoubleArray Pi = doublesNew.diag(pi);

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