jidt/demos/octave/CellularAutomata/plotLocalInfoMeasureForCA.m

385 lines
18 KiB
Matlab
Executable File

%%
%% Java Information Dynamics Toolkit (JIDT)
%% Copyright (C) 2012, Joseph T. Lizier
%%
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program 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 General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%
% function plotLocalInfoMeasureForCA(neighbourhood, base, rule, cells, timeSteps, measureId, measureParams, options)
%
% Plot one run of the given CA and compute and plot a local information dynamics profile for it
%
% Inputs:
% - neighbourhood - neighbourhood size for the rule (ECA has neighbourhood 3).
% For an even size neighbourhood (meaning a different number of neighbours on each side of the cell),
% we take an extra cell from the lower cell indices (i.e. from the left).
% - base - number of discrete states for each cell (for binary states this is 2)
% - rule - supplied as either:
% a. an integer rule number if <= 2^31 - 1 (Wolfram style; e.g. 110, 54 are the complex ECA rules)
% b. a HEX string, e.g. phi_par from Mitchell et al. is '0xfeedffdec1aaeec0eef000a0e1a020a0' (note: the leading 0x is not required)
% - cells - number of cells in the CA
% - timeSteps - number of rows to execute the CA for (including the random initial row)
% - measureId - which local info dynamics measure to plot - can be a string or an integer as follows:
% - 'active', 0 - active information storage (requires measureParams.k)
% - 'transfer', 1 - pairwise or apparent transfer entropy (requires measureParams.k and j)
% - 'transfercomplete', 2 - complete transfer entropy (requires measureParams.k and j), conditioning on all other sources
% - 'separable', 3 - separable information (requires measureParams.k)
% - 'entropy', 4 - excess entropy (requires no params)
% - 'entropyrate', 5 - excess entropy (requires measureParams.k)
% - 'excess', 6 - excess entropy (requires measureParams.k)
% - 'all', -1 - plot all measures
% - measureParams - a structure containing options as described for each measure above:
% - measureParams.k - history length for information dynamics measures
% (for excess entropy, predictive information formulation, this is the history length and future length)
% - measureParams.j - we measure information transfer across j cells to the right per time step
% - options - a stucture containing a range of other options, i.e.:
% - plotOptions - structure as defined for the plotLocalInfoValues function
% - plotOptions.figNum - figure number to plot the info value profile in
% - seed - state for the random number generator used to set the initial condition of the CA (use this
% for reproducibility of plots, or to produce profiles for several different measures of the same CA raw states).
% We set rand('state', options.seed) if options.seed is supplied, and restore the previous seed afterwards.
% - initialState - supply the initial state of the CA. If this option exists, no other random initial state is set.
% - plotRawCa - default true
% - saveImages - whether to save the plots or not (default false)
% - saveImagesFormat - 'eps' or 'pdf' (Default eps)
% - movingFrameSpeed - moving frame of reference's cells/time step, as in Lizier & Mahoney paper (default 0)
function [caStates, localValues] = plotLocalInfoMeasureForCA(neighbourhood, base, rule, cells, timeSteps, measureId, measureParams, options)
tic
if (nargin < 8)
options = {};
end
if not(isfield(options, 'plotOptions'))
options.plotOptions = {}; % Create it ready for plotRawCa etc
end
if not(isfield(options, 'saveImages'))
options.saveImages = false;
end
if not(isfield(options, 'saveImagesFormat'))
options.saveImagesFormat = 'eps';
end
if not(isfield(options, 'plotRawCa'))
options.plotRawCa = true;
end
% Add utilities to the path
addpath('..');
% Assumes the jar is two levels up - change this if this is not the case
% Octave is happy to have the path added multiple times; I'm unsure if this is true for matlab
javaaddpath('../../../infodynamics.jar');
% Simulate and plot the CA
if (isfield(options, 'initialState'))
% User has supplied an initial state for the CA
caStates = runCA(neighbourhood, base, rule, cells, timeSteps, false, options.initialState);
elseif (isfield(options, 'seed'))
previousSeed = rand('state');
caStates = runCA(neighbourhood, base, rule, cells, timeSteps, false, options.seed);
rand('state', previousSeed);
else
caStates = runCA(neighbourhood, base, rule, cells, timeSteps, false);
end
if (options.plotRawCa)
plotRawCa(caStates, rule, options.plotOptions, options.saveImages, options.saveImagesFormat);
end
if (ischar(rule))
ruleString = rule;
else
ruleString = sprintf('%d', rule);
end
if (strcmp(options.saveImagesFormat, 'eps'))
printDriver = 'epsc'; % to force colour
fontSize = 32;
else
printDriver = options.saveImagesFormat;
fontSize = 13;
end
if (not(isfield(options.plotOptions, 'figNum')))
figNum = 2;
else
figNum = options.plotOptions.figNum;
end
toc
% The offsets of the parents (see runCA for how this is computed, especially for even neighbourhood):
fullSetOfParents = ceil(-neighbourhood / 2) : ceil(-neighbourhood / 2) + (neighbourhood-1);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% The shift for each row of the CA is the negative of the movingFrameSpeed, since
% frame moving at 1 cell/time step is same as next row being shifted backwards by 1 cell:
caStates = accumulateShift(caStates, -options.movingFrameSpeed);
% Also account for the moved frame of reference in the offsets of parents to the destination:
fullSetOfParents = fullSetOfParents - options.movingFrameSpeed;
if (isfield(measureParams, 'j'))
% Also account for the moved frame of reference in the j parameter for transfer across j cells
measureParams.j = measureParams.j - options.movingFrameSpeed;
end
end
% convert the states to a format usable by java:
caStatesJInts = octaveToJavaIntMatrix(caStates);
toc
plottedOne = false;
% Make the local information dynamics measurement(s)
%============================
% Active information storage
if ((ischar(measureId) && (strcmpi('active', measureId) || strcmpi('all', measureId))) || ...
(not(ischar(measureId)) && ((measureId == 0) || (measureId == -1))))
% Compute active information storage
activeCalc = javaObject('infodynamics.measures.discrete.ActiveInformationCalculatorDiscrete', base, measureParams.k);
activeCalc.initialise();
activeCalc.addObservations(caStatesJInts);
avActive = activeCalc.computeAverageLocalOfObservations();
fprintf('Average active information storage = %.4f\n', avActive);
javaLocalValues = activeCalc.computeLocalFromPreviousObservations(caStatesJInts);
localValues = javaMatrixToOctave(javaLocalValues);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% Need to shift the computed info dynamics back (to compensate for earlier shift to CA states:
localValues = accumulateShift(localValues, options.movingFrameSpeed);
end
toc
figure(figNum)
figNum = figNum + 1;
plotLocalInfoValues(localValues, options.plotOptions);
if (options.saveImages)
set(gca, 'fontsize', fontSize);
colorbar('fontsize', fontSize);
print(sprintf('figures/%s-active-k%d.%s', ruleString, measureParams.k, options.saveImagesFormat), sprintf('-d%s', printDriver));
end
plottedOne = true;
end
%============================
% Apparent transfer entropy
if ((ischar(measureId) && (strcmpi('transfer', measureId) || strcmpi('all', measureId) || strcmpi('apparenttransfer', measureId))) || ...
(not(ischar(measureId)) && ((measureId == 1) || (measureId == -1))))
% Compute apparent transfer entropy
if (measureParams.j == 0)
error('Cannot compute transfer entropy from a cell to itself (setting measureParams.j == 0)');
end
transferCalc = javaObject('infodynamics.measures.discrete.TransferEntropyCalculatorDiscrete', base, measureParams.k);
transferCalc.initialise();
transferCalc.addObservations(caStatesJInts, measureParams.j);
avTransfer = transferCalc.computeAverageLocalOfObservations();
fprintf('Average apparent transfer entropy (j=%d) = %.4f\n', measureParams.j, avTransfer);
javaLocalValues = transferCalc.computeLocalFromPreviousObservations(caStatesJInts, measureParams.j);
localValues = javaMatrixToOctave(javaLocalValues);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% Need to shift the computed info dynamics back (to compensate for earlier shift to CA states:
localValues = accumulateShift(localValues, options.movingFrameSpeed);
end
toc
figure(figNum)
figNum = figNum + 1;
plotLocalInfoValues(localValues, options.plotOptions);
if (options.saveImages)
set(gca, 'fontsize', fontSize);
colorbar('fontsize', fontSize);
print(sprintf('figures/%s-transfer-k%d-j%d.%s', ruleString, measureParams.k, measureParams.j, options.saveImagesFormat), sprintf('-d%s', printDriver));
end
plottedOne = true;
end
%============================
% Complete transfer entropy, conditioning on all other sources
if ((ischar(measureId) && (strcmpi('transfercomplete', measureId) || strcmpi('completetransfer', measureId) || strcmpi('all', measureId))) || ...
(not(ischar(measureId)) && ((measureId == 2) || (measureId == -1))))
% Compute complete transfer entropy
if (measureParams.j == 0)
error('Cannot compute transfer entropy from a cell to itself (setting measureParams.j == 0)');
end
transferCalc = javaObject('infodynamics.measures.discrete.ConditionalTransferEntropyCalculatorDiscrete', ...
base, measureParams.k, neighbourhood - 2);
transferCalc.initialise();
% Offsets of all parents can be included here - even 0 and j, these will be eliminated internally:
transferCalc.addObservations(caStatesJInts, measureParams.j, octaveToJavaIntArray(fullSetOfParents));
avTransfer = transferCalc.computeAverageLocalOfObservations();
fprintf('Average complete transfer entropy (j=%d) = %.4f\n', measureParams.j, avTransfer);
javaLocalValues = transferCalc.computeLocalFromPreviousObservations(caStatesJInts, ...
measureParams.j, octaveToJavaIntArray(fullSetOfParents));
localValues = javaMatrixToOctave(javaLocalValues);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% Need to shift the computed info dynamics back (to compensate for earlier shift to CA states:
localValues = accumulateShift(localValues, options.movingFrameSpeed);
end
toc
figure(figNum)
figNum = figNum + 1;
plotLocalInfoValues(localValues, options.plotOptions);
if (options.saveImages)
set(gca, 'fontsize', fontSize);
colorbar('fontsize', fontSize);
print(sprintf('figures/%s-transferComp-k%d-j%d.%s', ruleString, measureParams.k, measureParams.j, options.saveImagesFormat), sprintf('-d%s', printDriver));
end
plottedOne = true;
end
%============================
% Separable information
if ((ischar(measureId) && (strcmpi('separable', measureId) || strcmpi('all', measureId))) || ...
(not(ischar(measureId)) && ((measureId == 3) || (measureId == -1))))
% Compute separable information
separableCalc = javaObject('infodynamics.measures.discrete.SeparableInfoCalculatorDiscrete', ...
base, measureParams.k, neighbourhood - 1);
separableCalc.initialise();
% Offsets of all parents can be included here - even 0 and j, these will be eliminated internally:
separableCalc.addObservations(caStatesJInts, octaveToJavaIntArray(fullSetOfParents));
avSeparable = separableCalc.computeAverageLocalOfObservations();
fprintf('Average separable information = %.4f\n', avSeparable);
javaLocalValues = separableCalc.computeLocalFromPreviousObservations(caStatesJInts, ...
octaveToJavaIntArray(fullSetOfParents));
localValues = javaMatrixToOctave(javaLocalValues);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% Need to shift the computed info dynamics back (to compensate for earlier shift to CA states:
localValues = accumulateShift(localValues, options.movingFrameSpeed);
end
toc
figure(figNum)
figNum = figNum + 1;
plotLocalInfoValues(localValues, options.plotOptions);
if (options.saveImages)
set(gca, 'fontsize', fontSize);
colorbar('fontsize', fontSize);
print(sprintf('figures/%s-separable-k%d.%s', ruleString, measureParams.k, options.saveImagesFormat), sprintf('-d%s', printDriver));
end
plottedOne = true;
end
%============================
% Entropy
if ((ischar(measureId) && (strcmpi('entropy', measureId) || strcmpi('all', measureId))) || ...
(not(ischar(measureId)) && ((measureId == 4) || (measureId == -1))))
% Compute entropy
entropyCalc = javaObject('infodynamics.measures.discrete.EntropyCalculatorDiscrete', ...
base);
entropyCalc.initialise();
entropyCalc.addObservations(caStatesJInts);
avEntropy = entropyCalc.computeAverageLocalOfObservations();
fprintf('Average entropy = %.4f\n', avEntropy);
javaLocalValues = entropyCalc.computeLocalFromPreviousObservations(caStatesJInts);
localValues = javaMatrixToOctave(javaLocalValues);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% Need to shift the computed info dynamics back (to compensate for earlier shift to CA states):
% (Note for entropy, the shifts to and back don't make any difference)
localValues = accumulateShift(localValues, options.movingFrameSpeed);
end
toc
figure(figNum)
figNum = figNum + 1;
plotLocalInfoValues(localValues, options.plotOptions);
if (options.saveImages)
set(gca, 'fontsize', fontSize);
colorbar('fontsize', fontSize);
print(sprintf('figures/%s-entropy.%s', ruleString, options.saveImagesFormat), sprintf('-d%s', printDriver));
end
plottedOne = true;
end
%============================
% Entropy rate
if ((ischar(measureId) && (strcmpi('entropyrate', measureId) || strcmpi('all', measureId))) || ...
(not(ischar(measureId)) && ((measureId == 5) || (measureId == -1))))
% Compute entropy rate
entRateCalc = javaObject('infodynamics.measures.discrete.EntropyRateCalculatorDiscrete', base, measureParams.k);
entRateCalc.initialise();
entRateCalc.addObservations(caStatesJInts);
avEntRate = entRateCalc.computeAverageLocalOfObservations();
fprintf('Average entropy rate = %.4f\n', avEntRate);
javaLocalValues = entRateCalc.computeLocalFromPreviousObservations(caStatesJInts);
localValues = javaMatrixToOctave(javaLocalValues);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% Need to shift the computed info dynamics back (to compensate for earlier shift to CA states:
localValues = accumulateShift(localValues, options.movingFrameSpeed);
end
toc
figure(figNum)
figNum = figNum + 1;
plotLocalInfoValues(localValues, options.plotOptions);
if (options.saveImages)
set(gca, 'fontsize', fontSize);
colorbar('fontsize', fontSize);
print(sprintf('figures/%s-entrate-k%d.%s', ruleString, measureParams.k, options.saveImagesFormat), sprintf('-d%s', printDriver));
end
plottedOne = true;
end
%============================
% Excess entropy
if ((ischar(measureId) && (strcmpi('excess', measureId) || strcmpi('all', measureId))) || ...
(not(ischar(measureId)) && ((measureId == 6) || (measureId == -1))))
% Compute excess entropy
excessEntropyCalc = javaObject('infodynamics.measures.discrete.PredictiveInformationCalculatorDiscrete', base, measureParams.k);
excessEntropyCalc.initialise();
excessEntropyCalc.addObservations(caStatesJInts);
avExcessEnt = excessEntropyCalc.computeAverageLocalOfObservations();
fprintf('Average excess entropy = %.4f\n', avExcessEnt);
javaLocalValues = excessEntropyCalc.computeLocalFromPreviousObservations(caStatesJInts);
localValues = javaMatrixToOctave(javaLocalValues);
if (isfield(options, 'movingFrameSpeed'))
% User has requested us to evaluate information dynamics with a moving frame of reference
% (see Lizier and Mahoney paper).
% Need to shift the computed info dynamics back (to compensate for earlier shift to CA states:
localValues = accumulateShift(localValues, options.movingFrameSpeed);
end
toc
figure(figNum)
figNum = figNum + 1;
plotLocalInfoValues(localValues, options.plotOptions);
if (options.saveImages)
set(gca, 'fontsize', fontSize);
colorbar('fontsize', fontSize);
print(sprintf('figures/%s-excessentropy-k%d.%s', ruleString, measureParams.k, options.saveImagesFormat), sprintf('-d%s', printDriver));
end
plottedOne = true;
end
if (not(plottedOne))
error(sprintf('Supplied measureId %s did not match any measurement types', measureId));
end
toc
end
% Perform a circular shift of each row of the matrix, shifting the first row by zero,
% the second by shiftPerRow, the third by 2*shiftPerRow, and so on
function shiftedMatrix = accumulateShift(matrix, shiftPerRow)
% Allocate required space up front (makes this much faster):
shiftedMatrix = zeros(size(matrix,1), size(matrix, 2));
shiftedMatrix(1,:) = matrix(1,:);
for r = 2 : size(matrix,1)
% circshift operates on shifting rows, so we transpose the input and output to it:
shiftedMatrix(r,:) = circshift(matrix(r,:)', shiftPerRow*(r-1))';
end
end