Markovian.m

classdef Markovian < ContinuousDistribution
    % An astract class for Markovian distributions
    %
    % Copyright (c) 2012-2026, Imperial College London
    % All rights reserved.
 
    methods (Hidden)
        function self = Markovian(name, numParam)
            % SELF = MARKOVIANDISTRIBUTION(NAME, NUMPARAM)
 
            % Abstract class constructor
            self@ContinuousDistribution(name, numParam, [0,Inf]);            
            nPhases = 0;
        end
    end
 
    properties (Hidden)
        process;
        nPhases;
    end
 
    methods
 
        % alpha,T process of a PH distribution
        % function alpha_vec = alpha(self)
        %     alpha_vec = self.getInitProb;
        % end
 
        % function T_mat = T(self)
        %     T_mat = self.getProcess{0};
        % end
 
        % D matrices process as in MAPs
        function Di = D(self, i, wantSparse)
            % Di = D(i)
            if nargin<3
                wantSparse = false;
            end
 
            % Return process matrix, e.g., D0=MAP.D(0)
            if wantSparse
                if nargin<2
                    Di=self.getProcess;
                else
                    Di=self.getProcess{i+1};
                end
            else
                if nargin<2
                    Di=self.getProcess;
                    for i=1:length(Di)
                        Di(i)=full(Di(i));
                    end
                else
                    Di=full(self.getProcess{i+1});
                end
            end
        end
 
        function X = sample(self, n)
            % X = SAMPLE(N)
 
            % Get n samples from the distribution
            if nargin<2 %~exist('n','var'),
                n = 1;
            end
            X = map_sample(self.getProcess,n);
        end
 
        function EXn = getMoments(self, n)
            % EXN = GETMOMENTS(N)
 
            if nargin<2 %~exist('n','var'),
                n = 3;
            end
            PH = self.getProcess;
            EXn = map_moment(PH,1:n);
        end
 
        function MEAN = getMean(self)
            % MEAN = GETMEAN()
            if ~isempty(self.mean)
                MEAN = self.mean;
            else
                if isnan(self.getProcess{1})
                    MEAN = NaN;
                else
                    MEAN = map_mean(self.getProcess);
                end
                self.mean = MEAN;
            end
            if isnan(self.immediate)
                self.immediate = MEAN < GlobalConstants.FineTol;
            end
        end
 
        function SCV = getSCV(self)
            % SCV = GETSCV()
            % Get the squared coefficient of variation of the distribution (SCV = variance / mean^2)
            if any(isnan(self.getProcess{1}))
                SCV = NaN;
            else
                SCV = map_scv(self.getProcess);
            end
        end
 
        function SKEW = getSkewness(self)
            % SKEW = GETSKEWNESS()
            if any(isnan(self.getProcess{1}))
                SKEW = NaN;
            else
                SKEW = map_skew(self.getProcess);
            end
        end
 
        function Ft = evalCDF(self,t)
            % FT = EVALCDF(SELF,T)
 
            % Evaluate the cumulative distribution function at t
            % AT T
 
            Ft = map_cdf(self.getProcess,t);
        end
 
        function alpha = getInitProb(self)
            % ALPHA = GETINITPROB()
            aph = self.getProcess;
            alpha = map_pie(aph);
        end
 
        function T = getSubgenerator(self)
            % T = GETSUBGENERATOR()
 
            % Get generator
            aph = self.getProcess;
            T = aph{1};
        end
 
        function mu = getMu(self)
            % MU = GETMU()
 
            % Return total outgoing rate from each state
            aph = self.getProcess;
            mu = - diag(aph{1});
        end
 
        function phi = getPhi(self)
            % PHI = GETPHI()
 
            % Return the probability that a transition out of a state is
            % absorbing
            aph = self.getProcess;
            if aph{1}(1,1)==0
                phi = 1;
            else
                phi = - aph{2}*ones(size(aph{1},1),1) ./ diag(aph{1});
            end
        end
 
    end
 
    methods
 
        % overload isImmediate for higher perofrmance
        function bool = isImmediate(self)
            % BOOL = ISIMMEDIATE()
            % Check if the distribution is equivalent to an Immediate
            % distribution
            if isnan(self.immediate)
                self.immediate = self.getMean < GlobalConstants.FineTol;
            end
            bool = self.immediate;
        end
 
        function setRate(self,RATE)
            % SETRATE(SELF,RATE)
 
            % Update rate
            self.setMean(1/RATE);
        end
 
        function self = setMean(self, MEAN)
            % SELF = UPDATEMEAN(MEAN)
 
            % Update distribution with given mean and variance
            md = self.fitMeanAndSCV(MEAN,self.getSCV);
            self.process = md.process;
            self.mean = MEAN;
            self.immediate = MEAN <  GlobalConstants.FineTol;
            self.params = md.params;
            self.support = md.support;
        end
 
        function phases = getNumberOfPhases(self)
            % PHASES = GETNUMBEROFPHASES()
 
            % Return number of phases in the distribution
            PH = self.getProcess;
            phases = length(PH{1});
        end
 
        function D = getProcess(self)
            % D = GETREPRESENTATION()
            D = self.process;
        end
 
        function setProcess(self, D)
            self.process = D;
        end
 
        function L = evalLST(self, s)
            % L = EVALLAPLACETRANSFORM(S)
 
            % Evaluate the Laplace transform of the distribution function at t
            % AT T
 
            PH = self.getProcess;
            pie = map_pie(PH);
            A = PH{1};
            e = ones(length(pie),1);
            L = pie*inv(s*eye(size(A))-A)*(-A)*e;
        end
 
        function plot(self)
            % PLOT()
 
            PH = self.getProcess;
            s = []; % source node
            t = []; % dest node
            w = []; % edge weight
            c = []; % edge color
            l = {}; % edge label
            for i=1:self.getNumberOfPhases
                for j=1:self.getNumberOfPhases
                    if i~=j
                        if PH{1}(i,j) > 0
                            s(end+1) = i;
                            t(end+1) = j;
                            w(end+1) = PH{1}(i,j);
                            c(end+1) = 0;
                            l{end+1} = num2str(w(end));
                        end
                    end
                    if PH{2}(i,j) > 0
                        s(end+1) = i;
                        t(end+1) = j;
                        w(end+1) = PH{2}(i,j);
                        c(end+1) = 1;
                        l{end+1} = num2str(w(end));
                    end
                end
            end
            G = digraph(s,t,w);
            p = plot(G,'EdgeColor','k','NodeColor','k','LineStyle','-','Marker','o','MarkerSize',4,'Layout','layered','EdgeLabel',l,'Direction','right');
            % highlight observable transitions in red
            highlight(p,s(c==1),t(c==1),'LineStyle','-','EdgeColor','r');
        end
    end
 
end