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/*
* 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/>.
*/
package infodynamics.measures.discrete;
import infodynamics.utils.AnalyticMeasurementDistribution;
import infodynamics.utils.AnalyticNullDistributionComputer;
import infodynamics.utils.ChiSquareMeasurementDistribution;
import infodynamics.utils.MathsUtils;
import infodynamics.utils.MatrixUtils;
import infodynamics.utils.EmpiricalMeasurementDistribution;
import infodynamics.utils.RandomGenerator;
/**
* <p>Implements <b>transfer entropy</b>
* for univariate discrete time-series data.
* That is, it is applied to <code>int[]</code> data, indexed
* by time.
* See Schreiber below for the definition of transfer entropy,
* and Lizier et al. for the definition of local transfer entropy.
* Specifically, this class implements the pairwise or <i>apparent</i>
* transfer entropy; i.e. we compute the transfer that appears to
* come from a single source variable, without examining any other
* potential sources
* (see Lizier et al, PRE, 2008).</p>
*
* <p>
* Usage of the child classes implementing this interface is intended to follow this paradigm:
* </p>
* <ol>
* <li>Construct the calculator via {@link #TransferEntropyCalculatorDiscrete(int, int)}
* or {@link #TransferEntropyCalculatorDiscrete(int, int, int)}
* or {@link #TransferEntropyCalculatorDiscrete(int, int, int, int, int, int)};</li>
* <li>Initialise the calculator using
* {@link #initialise()};</li>
* <li>Provide the observations/samples for the calculator
* to set up the PDFs, using one or more calls to
* the set of {@link #addObservations(int[], int[])} methods, then</li>
* <li>Compute the required quantities, being one or more of:
* <ul>
* <li>the average TE: {@link #computeAverageLocalOfObservations()};</li>
* <li>the local TE values for these samples: {@link #computeLocalOfPreviousObservations()}</li>
* <li>local TE values for a specific set of samples: e.g.
* {@link #computeLocalFromPreviousObservations(int[], int[])} etc.</li>
* <li>the distribution of TE values under the null hypothesis
* of no relationship between source and
* destination values: {@link #computeSignificance(int)} or
* {@link #computeSignificance(int[][])}.</li>
* </ul>
* </li>
* <li>As an alternative to steps 3 and 4, the user may undertake
* standalone computation from a single set of observations, via
* e.g.: {@link #computeLocal(int[], int[])} or
* {@link #computeAverageLocal(int[][], int)}.</li>
* <li>
* Return to step 2 to re-use the calculator on a new data set.
* </li>
* </ol>
*
* <p><b>References:</b><br/>
* <ul>
* <li>T. Schreiber, <a href="http://dx.doi.org/10.1103/PhysRevLett.85.461">
* "Measuring information transfer"</a>,
* Physical Review Letters 85 (2) pp.461-464, 2000.</li>
* <li>J. T. Lizier, M. Prokopenko and A. Zomaya,
* <a href="http://dx.doi.org/10.1103/PhysRevE.77.026110">
* "Local information transfer as a spatiotemporal filter for complex systems"</a>
* Physical Review E 77, 026110, 2008.</li>
* </ul>
*
* @author Joseph Lizier, <a href="joseph.lizier at gmail.com">email</a>,
* <a href="http://lizier.me/joseph/">www</a>
*/
public class TransferEntropyCalculatorDiscrete extends ContextOfPastMeasureCalculatorDiscrete
implements ChannelCalculatorDiscrete, AnalyticNullDistributionComputer {
/**
* Counts of (source,dest_next,dest_embedded_past) tuples
*/
protected int[][][] sourceNextPastCount = null; // count for (source[n],dest[n+1],dest[n]^k) tuples
/**
* Counts of (source,dest_embedded_past) tuples
*/
protected int[][] sourcePastCount = null; // count for (source[n],dest[n]^k) tuples
/**
* Whether to assume periodic boundary conditions for channels across
* the boundary of the multidimensional
* calls supplying observations, e.g.
* {@link #addObservations(int[][], int)} calls
*/
protected boolean periodicBoundaryConditions = true;
/**
* Embedding delay for the destination variable,
* i.e. time lag between each sample in the past
*/
protected int destEmbeddingDelay = 1;
/**
* Embedding length of the source variable.
* This is "l" in Schreiber's notation.
*/
protected int sourceHistoryEmbedLength = 1;
/**
* Embedding delay for the source variable,
* i.e. time lag between each sample in the past
*/
protected int sourceEmbeddingDelay = 1;
/**
* Source-destination delay to consider the information transfer across
*/
protected int delay = 1;
/**
* A cached value of base^sourceHistoryEmbedLength
*/
protected int base_power_l = 1;
/**
* A cached value of each discrete value left shifted (in "base" counting) by (sourceHistoryEmbedLength-1).
*/
protected int[] maxShiftedSourceValue = null; // states * (base^(sourceHistoryEmbedLength-1))
/**
* First time step at which we can take an observation
* (needs to account for an embedding in the previous steps)
*/
protected int startObservationTime = 1;
/**
* Tracks whether the measure has been computed since the last initialisation
*/
protected boolean estimateComputed = false;
/**
* User was formerly forced to create new instances through this factory method.
* Retained for backwards compatibility.
*
* @param base
* @param destHistoryEmbedLength
*
* @return a new TransferEntropyCalculator object
* @deprecated
*/
public static TransferEntropyCalculatorDiscrete newInstance(int base, int destHistoryEmbedLength) {
return new TransferEntropyCalculatorDiscrete(base, destHistoryEmbedLength);
// Old code for an attempted optimisation:
/*
if (isPowerOf2(base)) {
return new ApparentTransferEntropyCalculatorBase2(base, history);
} else {
return new ApparentTransferEntropyCalculator(base, history);
}
*/
}
/**
* Create a new TE calculator with all parameters as default
* (base 2 and all embedding/delay parameters 1)
*
*/
public TransferEntropyCalculatorDiscrete() {
this(2, 1, 1, 1, 1, 1);
}
/**
* Create a new TE calculator for the given base and destination history embedding length
* (leave the other embedding parameters as default)
*
* @param base number of symbols for each variable.
* E.g. binary variables are in base-2.
* @param destHistoryEmbedLength embedded history length of the destination to condition on -
* this is k in Schreiber's notation.
*/
public TransferEntropyCalculatorDiscrete(int base, int destHistoryEmbedLength) {
this(base, destHistoryEmbedLength, 1, 1, 1, 1);
}
/**
* Create a new TE calculator for the given base, destination and source history embedding lengths.
*
* @param base number of quantisation levels for each variable.
* E.g. binary variables are in base-2.
* @param destHistoryEmbedLength embedded history length of the destination to condition on -
* this is k in Schreiber's notation.
* @param sourceHistoryEmbeddingLength embedded history length of the source to include -
* this is l in Schreiber's notation.
*/
public TransferEntropyCalculatorDiscrete(int base, int destHistoryEmbedLength, int sourceHistoryEmbeddingLength) {
this(base, destHistoryEmbedLength, 1, sourceHistoryEmbeddingLength, 1, 1);
}
/**
* Create a new TE calculator for the given base, destination and source history embedding lengths
* and delays.
*
* @param base number of quantisation levels for each variable.
* E.g. binary variables are in base-2.
* @param destHistoryEmbedLength embedded history length of the destination to condition on -
* this is k in Schreiber's notation.
* @param destEmbeddingDelay embedding delay of the destination for conditioning on -
* this is the delay between each of the k samples from the past history
* @param sourceHistoryEmbeddingLength embedded history length of the source to include -
* this is l in Schreiber's notation.
* @param sourceEmbeddingDelay embedding delay of the source -
* this is the delay between each of the l samples from the past history
* @param delay source-destination delay to consider the information transfer across
* (should be >= 0, default is 1)
*/
public TransferEntropyCalculatorDiscrete(int base, int destHistoryEmbedLength, int destEmbeddingDelay,
int sourceHistoryEmbeddingLength, int sourceEmbeddingDelay, int delay) {
super(base, destHistoryEmbedLength);
updateParameters(base, destHistoryEmbedLength, destEmbeddingDelay,
sourceHistoryEmbeddingLength, sourceEmbeddingDelay, delay);
}
/**
* Private method to update the estimators parameters,
* save for parts only concerning base and destHistoryEmbedLength
* which are to be handled before this by the super
*
* @param base
* @param destHistoryEmbedLength
* @param destEmbeddingDelay
* @param sourceHistoryEmbeddingLength
* @param sourceEmbeddingDelay
* @param delay
*/
private void updateParameters(int base, int destHistoryEmbedLength, int destEmbeddingDelay,
int sourceHistoryEmbeddingLength, int sourceEmbeddingDelay, int delay) {
this.destEmbeddingDelay = destEmbeddingDelay;
if (sourceHistoryEmbeddingLength <= 0) {
throw new RuntimeException("Cannot have source embedding length of zero or less");
}
this.sourceHistoryEmbedLength = sourceHistoryEmbeddingLength;
this.sourceEmbeddingDelay = sourceEmbeddingDelay;
this.delay = delay;
base_power_l = MathsUtils.power(base, sourceHistoryEmbedLength);
// Check that we can convert the history value into an integer ok:
if (sourceHistoryEmbedLength > Math.log(Integer.MAX_VALUE) / log_base) {
throw new RuntimeException("Base and source history combination too large");
}
// Create constants for tracking sourceValues
maxShiftedSourceValue = new int[base];
for (int v = 0; v < base; v++) {
maxShiftedSourceValue[v] = v * MathsUtils.power(base, sourceHistoryEmbedLength-1);
}
// Which time step do we start taking observations from?
// These two integers represent the earliest next time step, in the cases where the destination
// embedding itself determines where we can start taking observations, or
// the case where the source embedding plus delay is longer and so determines
// where we can start taking observations.
int startTimeBasedOnDestPast = (k-1)*destEmbeddingDelay + 1;
int startTimeBasedOnSourcePast = (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay + delay;
startObservationTime = Math.max(startTimeBasedOnDestPast, startTimeBasedOnSourcePast);
}
/**
* Initialise with (potentially) new parameters
*
* @param base
* @param destHistoryEmbedLength
* @param destEmbeddingDelay
* @param sourceHistoryEmbeddingLength
* @param sourceEmbeddingDelay
* @param delay
*/
public void initialise(int base, int destHistoryEmbedLength, int destEmbeddingDelay,
int sourceHistoryEmbeddingLength, int sourceEmbeddingDelay, int delay) {
boolean paramsChanged = (this.alphabetSize != base) || (k != destHistoryEmbedLength) ||
(this.destEmbeddingDelay != destEmbeddingDelay) || (this.sourceHistoryEmbedLength != sourceHistoryEmbeddingLength) ||
(this.sourceEmbeddingDelay != sourceEmbeddingDelay) || (this.delay != delay);
super.initialise(base, destHistoryEmbedLength);
if (paramsChanged) {
updateParameters(base, destHistoryEmbedLength, destEmbeddingDelay,
sourceHistoryEmbeddingLength, sourceEmbeddingDelay, delay);
}
if (paramsChanged || (sourceNextPastCount == null)) {
// Create new storage for extra counts of observations
try {
sourceNextPastCount = new int[base_power_l][base][base_power_k];
sourcePastCount = new int[base_power_l][base_power_k];
} catch (OutOfMemoryError e) {
// Allow any Exceptions to be thrown, but catch and wrap
// Error as a RuntimeException
throw new RuntimeException("Requested memory for the base " +
base + ", k=" + k + ", l=" + sourceHistoryEmbedLength +
" is too large for the JVM at this time", e);
}
} else {
MatrixUtils.fill(sourceNextPastCount, 0);
MatrixUtils.fill(sourcePastCount, 0);
}
estimateComputed = false;
}
@Override
public void initialise(){
initialise(this.alphabetSize, k, destEmbeddingDelay, sourceHistoryEmbedLength,
sourceEmbeddingDelay, delay);
}
@Override
public void addObservations(int[] source, int[] dest) {
addObservations(source, dest, 0, dest.length-1);
}
/**
* Add observations for a single source-destination pair
* to our estimates of the pdfs.
* Start and end time are the (inclusive) indices within which to add the observations.
* The start time is from the earliest of the k historical values of the destination (inclusive),
* the end time is the last destination time point to add in.
*
* @param source source time-series
* @param dest destination time-series.
* Must be same length as source
* @param startTime earliest time that we may extract embedded history from
* @param endTime last destination (next) time point to add in
*
*/
public void addObservations(int[] source, int[] dest, int startTime, int endTime) {
if ((endTime - startTime) - startObservationTime + 1 <= 0) {
// No observations to add
return;
}
if ((endTime >= dest.length) || (endTime >= source.length)) {
throw new ArrayIndexOutOfBoundsException(
String.format("endTime (%d) must be <= length of input arrays (dest: %d, source: %d)",
endTime, dest.length, source.length));
}
// increment the count of observations:
observations += (endTime - startTime) - startObservationTime + 1;
// Initialise and store the current previous values;
// one for each phase of the embedding delay.
// First for the destination:
int[] pastVal = new int[destEmbeddingDelay];
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[d] += dest[startTime + startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay];
pastVal[d] *= this.alphabetSize;
}
}
// Next for the source:
int[] sourcePastVal = new int[sourceEmbeddingDelay];
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[d] += source[startTime + startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay];
sourcePastVal[d] *= this.alphabetSize;
}
}
// 1. Count the tuples observed
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
for (int r = startTime + startObservationTime; r <= endTime; r++) {
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[destEmbeddingPhase] += dest[r-1];
}
sourcePastVal[sourceEmbeddingPhase] += source[r-delay];
// Add to the count for this particular transition:
// (cell's assigned as above)
destVal = dest[r];
int thisPastVal = pastVal[destEmbeddingPhase];
int thisSourceVal = sourcePastVal[sourceEmbeddingPhase];
sourceNextPastCount[thisSourceVal][destVal][thisPastVal]++;
sourcePastCount[thisSourceVal][thisPastVal]++;
nextPastCount[destVal][thisPastVal]++;
pastCount[thisPastVal]++;
nextCount[destVal]++;
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[destEmbeddingPhase] -= maxShiftedValue[dest[r-1-(k-1)*destEmbeddingDelay]];
pastVal[destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[sourceEmbeddingPhase] -=
maxShiftedSourceValue[
source[r-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay]];
sourcePastVal[sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
}
/**
* Add observations for a single source-destination pair
* to our estimates of the pdfs.
*
* @param source source time-series
* @param dest destination time-series.
* Must be same length as source
* @param valid time-series of whether the signals
* at the given time should be considered valid
* and added to our PDFs. We don't include any embedding vectors which
* stretch across any invalid points, even if these invalid points
* are not specifically sampled for the embedding vector.
*/
public void addObservations(int[] source, int[] dest, boolean[] valid) {
int rows = dest.length;
if (dest.length - startObservationTime <= 0) {
// No observations to add
return;
}
// Initialise and store the current previous values;
// one for each phase of the embedding delay.
// First for the destination:
int[] pastVal = new int[destEmbeddingDelay];
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[d] += dest[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay];
pastVal[d] *= this.alphabetSize;
}
}
// We can take an observation if timeSinceLastDestInvalid >= minDestLengthRequired
int minDestLengthRequired = (k>0) ? (k-1)*destEmbeddingDelay + 1 : 0;
// And initialise the time since last valid dest observation:
int timeSinceLastDestInvalid = minDestLengthRequired;
for (int t = startObservationTime - 1; t >= 0; t--) {
if (!valid[t]) {
timeSinceLastDestInvalid = startObservationTime - t - 1;
break;
}
}
// Next for the source:
int[] sourcePastVal = new int[sourceEmbeddingDelay];
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[d] += source[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay];
sourcePastVal[d] *= this.alphabetSize;
}
}
// We can take an observation if timeSinceLastSourceInvalid >= minSourceLengthRequired
int minSourceLengthRequired = (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay + 1;
// And initialise the time since last valid source observation:
int timeSinceLastSourceInvalid = minSourceLengthRequired;
for (int t = startObservationTime - delay; t >= 0; t--) {
if (!valid[t]) {
timeSinceLastSourceInvalid = startObservationTime - t - 1;
break;
}
}
// 1. Count the tuples observed
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
for (int r = startObservationTime; r < rows; r++) {
timeSinceLastDestInvalid++;
timeSinceLastSourceInvalid++;
// First update the embedding values for the current
// phases of the embeddings:
// Pre-condition now:
// timeSinceLastDestInvalid holds the time from r back to
// the last invalid destination point (not including current destination)
// timeSinceLastSourceInvalid holds the time from r back to
// the last invalid source point (not including new source value)
// Update embedded values
if (k > 0) {
pastVal[destEmbeddingPhase] += dest[r-1];
}
sourcePastVal[sourceEmbeddingPhase] += source[r-delay];
// Now check validity of new entrants here:
if (!valid[r]) {
timeSinceLastDestInvalid = 0;
}
if (!valid[r-delay]) {
timeSinceLastSourceInvalid = 0;
}
if ((timeSinceLastDestInvalid > minDestLengthRequired) &&
(timeSinceLastSourceInvalid >= minSourceLengthRequired)) {
// We have enough of both source and dest valid to continue
// Note the >= on source only (because dest must have next value as
// valid as well.
// Add to the count for this particular transition:
// (cell's assigned as above)
destVal = dest[r];
int thisPastVal = pastVal[destEmbeddingPhase];
int thisSourceVal = sourcePastVal[sourceEmbeddingPhase];
sourceNextPastCount[thisSourceVal][destVal][thisPastVal]++;
sourcePastCount[thisSourceVal][thisPastVal]++;
nextPastCount[destVal][thisPastVal]++;
pastCount[thisPastVal]++;
nextCount[destVal]++;
observations++; // Need to increment number of observations explicitly here
}
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[destEmbeddingPhase] -= maxShiftedValue[dest[r-1-(k-1)*destEmbeddingDelay]];
pastVal[destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[sourceEmbeddingPhase] -=
maxShiftedSourceValue[
source[r-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay]];
sourcePastVal[sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
}
/**
* Add observations in to our estimates of the PDFs,
* from a multivariate time-series.
* This call suitable only for homogeneous variables, as all
* variable pairs separated by j column will contribute to the PDFs.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i: we
* compute transfer is j cells to the right, using observations
* across all column pairs separated by j)
*/
public void addObservations(int states[][], int j) {
int timeSteps = states.length;
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return;
}
int variables = states[0].length;
// increment the count of observations:
if (periodicBoundaryConditions) {
observations += (timeSteps - startObservationTime)*variables;
} else {
observations += (timeSteps - startObservationTime)*(variables - Math.abs(j));
}
// Initialise and store the current previous values for each column;
// one for each phase of the embedding delay.
// First for the destination:
int[][] pastVal = new int[variables][destEmbeddingDelay];
for (int c = 0; c < variables; c++) {
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[c][d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[c][d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][c];
pastVal[c][d] *= this.alphabetSize;
}
}
}
// Next for the source:
int[][] sourcePastVal = new int[variables][sourceEmbeddingDelay];
for (int c = 0; c < variables; c++) {
int sourceVariable = c-j;
if ((sourceVariable < 0) || (sourceVariable >= variables)) {
// Source variable is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceVariable = (sourceVariable+variables) % variables;
} else {
// Don't add this to our observations
continue;
}
}
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[c][d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[c][d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceVariable];
sourcePastVal[c][d] *= this.alphabetSize;
}
}
}
// 1. Count the tuples observed
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
for (int r = startObservationTime; r < timeSteps; r++) {
for (int c = 0; c < variables; c++) {
// Add to the count for this particular transition:
// (cell's assigned as above)
int sourceVariable = c-j;
if ((sourceVariable < 0) || (sourceVariable >= variables)) {
// Source variable is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceVariable = (sourceVariable+variables) % variables;
} else {
// Don't add this to our observations
continue;
}
}
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[c][destEmbeddingPhase] += states[r-1][c];
}
sourcePastVal[c][sourceEmbeddingPhase] += states[r-delay][sourceVariable];
// Add to the count for this particular transition:
// (cell's assigned as above)
destVal = states[r][c];
int thisPastVal = pastVal[c][destEmbeddingPhase];
int thisSourceVal = sourcePastVal[c][sourceEmbeddingPhase];
sourceNextPastCount[thisSourceVal][destVal][thisPastVal]++;
sourcePastCount[thisSourceVal][thisPastVal]++;
nextPastCount[destVal][thisPastVal]++;
pastCount[thisPastVal]++;
nextCount[destVal]++;
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[c][destEmbeddingPhase] -= maxShiftedValue[states[r-1-(k-1)*destEmbeddingDelay][c]];
pastVal[c][destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[c][sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[r-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceVariable]];
sourcePastVal[c][sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
}
/**
* Add observations in to our estimates of the PDFs,
* from a multivariate time-series.
* This call suitable only for homogeneous agents, as all
* variable pairs separated by h rows and j columns
* will contribute to the PDFs.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param h - number of rows to compute transfer entropy across
* (i.e. source is in row i-h, dest is column i)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i)
*/
public void addObservations(int states[][][], int h, int j) {
int timeSteps = states.length;
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return;
}
int agentRows = states[0].length;
if (agentRows == 0) {
return;
}
int agentColumns = states[0][0].length;
// increment the count of observations:
if (periodicBoundaryConditions) {
observations += (timeSteps - startObservationTime) * agentRows * agentColumns;
} else {
observations += (timeSteps - startObservationTime) * (agentRows - Math.abs(h)) * (agentColumns - Math.abs(j));
}
// Initialise and store the current previous values for each variable;
// one for each phase of the embedding delay.
// First for the destination:
int[][][] pastVal = new int[agentRows][agentColumns][destEmbeddingDelay];
for (int r = 0; r < agentRows; r++) {
for (int c = 0; c < agentColumns; c++) {
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[r][c][d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[r][c][d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][r][c];
pastVal[r][c][d] *= this.alphabetSize;
}
}
}
}
// Next for the source:
int[][][] sourcePastVal = new int[agentRows][agentColumns][sourceEmbeddingDelay];
for (int r = 0; r < agentRows; r++) {
for (int c = 0; c < agentColumns; c++) {
int sourceAgentRow = r-h;
if ((sourceAgentRow < 0) || (sourceAgentRow >= agentRows)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentRow = (sourceAgentRow+agentRows) % agentRows;
} else {
// Don't add this to our observations
continue;
}
}
int sourceAgentColumn = c-j;
if ((sourceAgentColumn < 0) || (sourceAgentColumn >= agentColumns)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentColumn = (sourceAgentColumn+agentColumns) % agentColumns;
} else {
// Don't add this to our observations
continue;
}
}
// Now initialise the embedding
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[r][c][d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[r][c][d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceAgentRow][sourceAgentColumn];
sourcePastVal[r][c][d] *= this.alphabetSize;
}
}
}
}
// 1. Count the tuples observed
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
for (int t = startObservationTime; t < timeSteps; t++) {
for (int r = 0; r < agentRows; r++) {
for (int c = 0; c < agentColumns; c++) {
// Add to the count for this particular transition:
// (cell's assigned as above)
int sourceAgentRow = r-h;
if ((sourceAgentRow < 0) || (sourceAgentRow >= agentRows)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentRow = (sourceAgentRow+agentRows) % agentRows;
} else {
// Don't add this to our observations
continue;
}
}
int sourceAgentColumn = c-j;
if ((sourceAgentColumn < 0) || (sourceAgentColumn >= agentColumns)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentColumn = (sourceAgentColumn+agentColumns) % agentColumns;
} else {
// Don't add this to our observations
continue;
}
}
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[r][c][destEmbeddingPhase] += states[t-1][r][c];
}
sourcePastVal[r][c][sourceEmbeddingPhase] += states[t-delay][sourceAgentRow][sourceAgentColumn];
// Add to the count for this particular transition:
// (cell's assigned as above)
destVal = states[t][r][c];
int thisPastVal = pastVal[r][c][destEmbeddingPhase];
int thisSourceVal = sourcePastVal[r][c][sourceEmbeddingPhase];
sourceNextPastCount[thisSourceVal][destVal][thisPastVal]++;
sourcePastCount[thisSourceVal][thisPastVal]++;
nextPastCount[destVal][thisPastVal]++;
pastCount[thisPastVal]++;
nextCount[destVal]++;
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[r][c][destEmbeddingPhase] -= maxShiftedValue[states[t-1-(k-1)*destEmbeddingDelay][r][c]];
pastVal[r][c][destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[r][c][sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[t-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceAgentRow][sourceAgentColumn]];
sourcePastVal[r][c][sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
}
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
}
/**
* Add observations for a single source-destination pair of the multi-agent system
* to our estimates of the pdfs.
* This call should be made as opposed to {@link #addObservations(int[][], int)}
* for computing TE for heterogeneous agents.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param sourceIndex source variable index in states
* @param destIndex destination variable index in states
*/
public void addObservations(int states[][], int sourceIndex, int destIndex) {
int timeSteps = states.length;
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return;
}
// increment the count of observations:
observations += timeSteps - startObservationTime;
// Initialise and store the current previous values;
// one for each phase of the embedding delay.
// First for the destination:
int[] pastVal = new int[destEmbeddingDelay];
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][destIndex];
pastVal[d] *= this.alphabetSize;
}
}
// Next for the source:
int[] sourcePastVal = new int[sourceEmbeddingDelay];
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceIndex];
sourcePastVal[d] *= this.alphabetSize;
}
}
// 1. Count the tuples observed
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
for (int r = startObservationTime; r < timeSteps; r++) {
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[destEmbeddingPhase] += states[r-1][destIndex];
}
sourcePastVal[sourceEmbeddingPhase] += states[r-delay][sourceIndex];
// Add to the count for this particular transition:
// (cell's assigned as above)
destVal = states[r][destIndex];
int thisPastVal = pastVal[destEmbeddingPhase];
int thisSourceVal = sourcePastVal[sourceEmbeddingPhase];
sourceNextPastCount[thisSourceVal][destVal][thisPastVal]++;
sourcePastCount[thisSourceVal][thisPastVal]++;
nextPastCount[destVal][thisPastVal]++;
pastCount[thisPastVal]++;
nextCount[destVal]++;
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[destEmbeddingPhase] -= maxShiftedValue[states[r-1-(k-1)*destEmbeddingDelay][destIndex]];
pastVal[destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[r-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceIndex]];
sourcePastVal[sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
}
/**
* Add observations for a single source-destination pair of the multi-agent system
* to our estimates of the pdfs.
* This call should be made as opposed to {@link #addObservations(int[][][], int, int)}
* for computing TE for heterogeneous agents.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param sourceRowIndex source variable row index in states
* @param sourceColumnIndex source variable column index in states
* @param destRowIndex destination variable row index in states
* @param destColumnIndex destination variable column index in states
*/
public void addObservations(int states[][][], int sourceRowIndex, int sourceColumnIndex,
int destRowIndex, int destColumnIndex) {
int timeSteps = states.length;
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return;
}
// increment the count of observations:
observations += timeSteps - startObservationTime;
// Initialise and store the current previous values;
// one for each phase of the embedding delay.
// First for the destination:
int[] pastVal = new int[destEmbeddingDelay];
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][destRowIndex][destColumnIndex];
pastVal[d] *= this.alphabetSize;
}
}
// Next for the source:
int[] sourcePastVal = new int[sourceEmbeddingDelay];
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceRowIndex][sourceColumnIndex];
sourcePastVal[d] *= this.alphabetSize;
}
}
// 1. Count the tuples observed
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
for (int r = startObservationTime; r < timeSteps; r++) {
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[destEmbeddingPhase] += states[r-1][destRowIndex][destColumnIndex];
}
sourcePastVal[sourceEmbeddingPhase] += states[r-delay][sourceRowIndex][sourceColumnIndex];
// Add to the count for this particular transition:
// (cell's assigned as above)
destVal = states[r][destRowIndex][destColumnIndex];
int thisPastVal = pastVal[destEmbeddingPhase];
int thisSourceVal = sourcePastVal[sourceEmbeddingPhase];
sourceNextPastCount[thisSourceVal][destVal][thisPastVal]++;
sourcePastCount[thisSourceVal][thisPastVal]++;
nextPastCount[destVal][thisPastVal]++;
pastCount[thisPastVal]++;
nextCount[destVal]++;
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[destEmbeddingPhase] -= maxShiftedValue[states[r-1-(k-1)*destEmbeddingDelay][destRowIndex][destColumnIndex]];
pastVal[destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[r-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceRowIndex][sourceColumnIndex]];
sourcePastVal[sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
}
/**
*
* Returns the count of observations of the supplied past state
* pastVal.
* The past state is indicated by a unique discrete integer representing the joint variable
* of the k past states: (dest[n-k+1],dest[n-k+2],...,dest[n-1],dest[n]).
* The integer is computed as:<br/>
* pastVal = dest[n-k+1] * base^(k-1) + dest[n-k+2] * base^(k-2) + ... + dest[n-1] * base + dest[n]
*
*
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return count of observations of this given past state
*/
public int getPastCount(int pastVal) {
return pastCount[pastVal];
}
/**
* Returns the probability of the supplied past state
* pastVal.
* See {@link #getPastCount(int)} for how the joint value representing the past is calculated.
*
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return probability of the given past state
*/
public double getPastProbability(int pastVal) {
return (double) pastCount[pastVal] / (double) observations;
}
/**
* Returns the count of observations of the past given past state and next value.
*
* See {@link #getPastCount(int)} for how the joint value representing the past is calculated.
*
* @param destVal next state of the destination dest[n+1]
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return count of observations of the given past state and next state
*/
public int getNextPastCount(int destVal, int pastVal) {
return nextPastCount[destVal][pastVal];
}
/**
* Returns the probability of the past given past state and next value.
*
* See {@link #getPastCount(int)} for how the joint value representing the past is calculated.
*
* @param destVal next state of the destination dest[n+1]
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return probability of the given past state and next state
*/
public double getNextPastProbability(int destVal, int pastVal) {
return (double) nextPastCount[destVal][pastVal] / (double) observations;
}
/**
* Returns the count of observations of the past given state dest[n]^k and the source state source[n]^l.
*
* See {@link #getPastCount(int)} for how the joint values representing the past states are calculated.
*
* @param sourceVal int representing the joint state of the source source[n]^l
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return count of observations of the given past state and the source state
*/
public int getSourcePastCount(int sourceVal, int pastVal) {
return sourcePastCount[sourceVal][pastVal];
}
/**
* Returns the probability of the past given state dest[n]^k and the source state source[n]^l.
*
* See {@link #getPastCount(int)} for how the joint values representing the past states are calculated.
*
* @param sourceVal int representing the joint state of the source source[n]^l
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return probability of the given past state and the source state
*/
public double getSourcePastProbability(int sourceVal, int pastVal) {
return (double) sourcePastCount[sourceVal][pastVal] / (double) observations;
}
/**
* Returns the count of observations of the past given state dest[n]^k,
* the next state of the destination dest[n+1] and the source state source[n]^l.
*
* See {@link #getPastCount(int)} for how the joint values representing the past states are calculated.
*
* @param sourceVal int representing the joint state of the source source[n]^l
* @param nextVal next state of the destination dest[n+1]
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return count of observations of the given past state, next state of destination and the source state
*/
public int getSourceNextPastCount(int sourceVal, int destVal, int pastVal) {
return sourceNextPastCount[sourceVal][destVal][pastVal];
}
/**
* Returns the probability of the past given state dest[n]^k,
* the next state of the destination dest[n+1] and the source state source[n]^l.
*
* See {@link #getPastCount(int)} for how the joint values representing the past states are calculated.
*
* @param sourceVal int representing the joint state of the source source[n]^l
* @param nextVal next state of the destination dest[n+1]
* @param pastVal int representing the joint state of the past of the destination dest[n]^k
* @return probability of the given past state, next state of destination and the source state
*/
public double getSourceNextPastProbability(int sourceVal, int destVal, int pastVal) {
return (double) sourceNextPastCount[sourceVal][destVal][pastVal] / (double) observations;
}
/**
* Returns the count of observations of the next state dest[n+1].
*
* @param nextVal next state of the destination dest[n+1]
* @return count of observations of the given next state
*/
public int getNextCount(int destVal) {
return nextCount[destVal];
}
/**
* Returns the probability of the next state dest[n+1].
*
* @param nextVal state of the next destination dest[n+1]
* @return probability of the given next state
*/
public double getNextProbability(int destVal) {
return (double) nextCount[destVal] / (double) observations;
}
@Override
public double computeAverageLocalOfObservations() {
double te = 0.0;
double teCont = 0.0;
max = 0;
min = 0;
double meanSqLocals = 0;
for (int pastVal = 0; pastVal < base_power_k; pastVal++) {
// compute p(past)
// double p_past = (double) pastCount[pastVal] / (double) observations;
if (pastCount[pastVal] == 0) {
continue;
}
for (int destVal = 0; destVal < this.alphabetSize; destVal++) {
// compute p(dest,past)
// double p_dest_past = (double) destPastCount[destVal][pastVal] / (double) observations;
if (nextPastCount[destVal][pastVal] == 0) {
continue;
}
double denom = (double) nextPastCount[destVal][pastVal] / (double) pastCount[pastVal];
for (int sourceVal = 0; sourceVal < base_power_l; sourceVal++) {
// Compute TE contribution:
if (sourceNextPastCount[sourceVal][destVal][pastVal] != 0) {
/* Double check: should never happen
if ((sourcePastCount[sourceVal][pastVal] == 0) ||
(destPastCount[destVal][pastVal] == 0) ||
(pastCount[pastVal] == 0)) {
throw new RuntimeException("one subcount was zero!!");
}
*/
// compute p(source,dest,past)
double p_source_dest_past = (double) sourceNextPastCount[sourceVal][destVal][pastVal] / (double) observations;
// compute p(source,past)
// double p_source_past = (double) sourcePastCount[sourceVal][pastVal] / (double) observations;
double logTerm = ((double) sourceNextPastCount[sourceVal][destVal][pastVal] / (double) sourcePastCount[sourceVal][pastVal]) /
(denom);
double localValue = Math.log(logTerm); // We'll / log_2 later, to save a floating pt op;
teCont = p_source_dest_past * localValue;
if (localValue > max) {
max = localValue;
} else if (localValue < min) {
min = localValue;
}
// Add this contribution to the mean
// of the squared local values
meanSqLocals += teCont * localValue;
} else {
teCont = 0.0;
}
te += teCont;
}
}
}
te /= log_2;
max /= log_2;
min /= log_2;
meanSqLocals /= (log_2 * log_2);
average = te;
std = Math.sqrt(meanSqLocals - average * average);
estimateComputed = true;
return te;
}
/**
* Returns the average active information storage from
* the observed values which have been passed in previously.
*
* @see ActiveInformationCalculatorDiscrete
*/
public double computeAverageActiveInfoStorageOfObservations() {
double active = 0.0;
double activeCont = 0.0;
for (int nextVal = 0; nextVal < this.alphabetSize; nextVal++) {
// compute p_next
double p_next = (double) nextCount[nextVal] / (double) observations;
for (int prevVal = 0; prevVal < base_power_k; prevVal++) {
// Compute MI contribution:
if (nextPastCount[nextVal][prevVal] != 0) {
double logTerm = (double) nextPastCount[nextVal][prevVal] /
(double) pastCount[prevVal] /
p_next;
double localValue = Math.log(logTerm) / log_2;
activeCont = (nextPastCount[nextVal][prevVal] /
(double) observations) * localValue;
} else {
activeCont = 0.0;
}
active += activeCont;
}
}
return active;
}
/**
* Dump a debug print of the PDFs of our observations
*/
public void debugPrintObservations() {
System.out.println("Src\tDst\tPast\tc(s,d,p)\tc(s,p)\tc(d,p)\tc(p)");
for (int pastVal = 0; pastVal < base_power_k; pastVal++) {
for (int destVal = 0; destVal < this.alphabetSize; destVal++) {
for (int sourceVal = 0; sourceVal < base_power_l; sourceVal++) {
// Compute TE contribution:
System.out.println(sourceVal + "\t" + destVal + "\t" + pastVal + "\t" +
sourceNextPastCount[sourceVal][destVal][pastVal] + "\t\t" +
sourcePastCount[sourceVal][pastVal] + "\t" +
nextPastCount[destVal][pastVal] + "\t" +
pastCount[pastVal]);
}
}
}
}
@Override
public EmpiricalMeasurementDistribution computeSignificance(int numPermutationsToCheck) {
RandomGenerator rg = new RandomGenerator();
// (Not necessary to check for distinct random perturbations)
int[][] newOrderings = rg.generateRandomPerturbations(observations, numPermutationsToCheck);
return computeSignificance(newOrderings);
}
@Override
public EmpiricalMeasurementDistribution computeSignificance(int[][] newOrderings) {
double actualTE = computeAverageLocalOfObservations();
int numPermutationsToCheck = newOrderings.length;
// Reconstruct the *joint* source values (not necessarily in order, but using joint values retains their l-tuples)
int[] sourceValues = new int[observations];
int t_s = 0;
for (int sourceVal = 0; sourceVal < base_power_l; sourceVal++) {
// Count up the number of times this joint source value was observed:
int numberOfSamples = 0;
for (int pastVal = 0; pastVal < base_power_k; pastVal++) {
numberOfSamples += sourcePastCount[sourceVal][pastVal];
}
// Now add all of these as unordered observations:
MatrixUtils.fill(sourceValues, sourceVal, t_s, numberOfSamples);
t_s += numberOfSamples;
}
// And construct unordered (dest,past) tuples.
// It doesn't matter that we've appeared to destroy the ordering here because
// the joint distribution nextPastCount is actually preserved in
// our construction of pastVal and destValues together here.
int[] destValues = new int[observations];
int[] pastValues = new int[observations];
int t_d = 0;
int t_p = 0;
for (int pastVal = 0; pastVal < base_power_k; pastVal++) {
MatrixUtils.fill(pastValues, pastVal, t_p, pastCount[pastVal]);
t_p += pastCount[pastVal];
for (int destVal = 0; destVal < this.alphabetSize; destVal++) {
MatrixUtils.fill(destValues, destVal, t_d, nextPastCount[destVal][pastVal]);
t_d += nextPastCount[destVal][pastVal];
}
}
// If we want a calculator just like this one, we should provide all of
// the same parameters:
TransferEntropyCalculatorDiscrete ate2 =
new TransferEntropyCalculatorDiscrete(this.alphabetSize, k, destEmbeddingDelay,
sourceHistoryEmbedLength, sourceEmbeddingDelay, delay);
ate2.initialise();
ate2.observations = observations;
ate2.pastCount = pastCount;
ate2.nextPastCount = nextPastCount;
int countWhereTeIsMoreSignificantThanOriginal = 0;
EmpiricalMeasurementDistribution measDistribution = new EmpiricalMeasurementDistribution(numPermutationsToCheck);
for (int p = 0; p < numPermutationsToCheck; p++) {
// Generate a new re-ordered data set for the source
int[] newSourceData = MatrixUtils.extractSelectedTimePoints(sourceValues, newOrderings[p]);
// compute the joint probability distributions
MatrixUtils.fill(ate2.sourceNextPastCount, 0);
MatrixUtils.fill(ate2.sourcePastCount, 0);
for (int t = 0; t < observations; t++) {
// This looks like we're doing no source embedding --
// but we're already using joint source values in newSourceData
ate2.sourcePastCount[newSourceData[t]][pastValues[t]]++;
ate2.sourceNextPastCount[newSourceData[t]][destValues[t]][pastValues[t]]++;
}
// And get a TE value for this realisation:
double newTe = ate2.computeAverageLocalOfObservations();
measDistribution.distribution[p] = newTe;
if (newTe >= actualTE) {
countWhereTeIsMoreSignificantThanOriginal++;
}
}
// And return the significance
measDistribution.pValue = (double) countWhereTeIsMoreSignificantThanOriginal / (double) numPermutationsToCheck;
measDistribution.actualValue = actualTE;
return measDistribution;
}
@Override
public AnalyticMeasurementDistribution computeSignificance()
throws Exception {
if (!estimateComputed) {
computeAverageLocalOfObservations();
}
return new ChiSquareMeasurementDistribution(average,
observations,
(base_power_l - 1)*(this.alphabetSize - 1)*(base_power_k));
}
/**
* Computes local transfer entropy for the given values
*
* See {@link #getPastCount(int)} for how the joint values representing the past are calculated.
*
* @param sourceCurrent int representing the joint state of the source source[n]^l
* @param destNext next state of the destination dest[n+1]
* @param destPast int representing the joint state of the past of the destination dest[n]^k
*
* @return local TE for the given observation
*/
public double computeLocalFromPreviousObservations(int sourceCurrent, int destNext, int destPast){
double logTerm = ((double) sourceNextPastCount[sourceCurrent][destNext][destPast] / (double) sourcePastCount[sourceCurrent][destPast]) /
((double) nextPastCount[destNext][destPast] / (double) pastCount[destPast]);
return Math.log(logTerm) / log_2;
}
/**
* Computes local apparent transfer entropy for the given
* states, using PDFs built up from observations previously
* sent in via the addObservations method.
*
* @param source source time-series
* @param dest destination time-series.
* Must be same length as source
* @return time-series of local TE values
*/
public double[] computeLocalFromPreviousObservations(int source[], int dest[]){
int timeSteps = dest.length;
// Allocate for all rows even though we'll leave the first ones as zeros
double[] localTE = new double[timeSteps];
average = 0;
max = 0;
min = 0;
if (timeSteps - startObservationTime <= 0) {
// No observations to compute locals for
return localTE;
}
// Initialise and store the current previous values;
// one for each phase of the embedding delay.
// First for the destination:
int[] pastVal = new int[destEmbeddingDelay];
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[d] += dest[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay];
pastVal[d] *= this.alphabetSize;
}
}
// Next for the source:
int[] sourcePastVal = new int[sourceEmbeddingDelay];
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[d] += source[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay];
sourcePastVal[d] *= this.alphabetSize;
}
}
// now compute the local values
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
double logTerm;
for (int t = startObservationTime; t < timeSteps; t++) {
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[destEmbeddingPhase] += dest[t-1];
}
sourcePastVal[sourceEmbeddingPhase] += source[t-delay];
destVal = dest[t];
int thisPastVal = pastVal[destEmbeddingPhase];
int thisSourceVal = sourcePastVal[sourceEmbeddingPhase];
// Now compute the local value
logTerm = ((double) sourceNextPastCount[thisSourceVal][destVal][thisPastVal] /
(double) sourcePastCount[thisSourceVal][thisPastVal]) /
((double) nextPastCount[destVal][thisPastVal] / (double) pastCount[thisPastVal]);
localTE[t] = Math.log(logTerm) / log_2;
average += localTE[t];
if (localTE[t] > max) {
max = localTE[t];
} else if (localTE[t] < min) {
min = localTE[t];
}
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[destEmbeddingPhase] -= maxShiftedValue[dest[t-1-(k-1)*destEmbeddingDelay]];
pastVal[destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[sourceEmbeddingPhase] -=
maxShiftedSourceValue[
source[t-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay]];
sourcePastVal[sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
average = average/(double) (timeSteps - startObservationTime);
return localTE;
}
/**
* Computes local transfer for the given
* multivariate states, using pdfs built up from observations previously
* sent in via the addObservations method.
* This call suitable only for homogeneous agents, as all
* variable pairs separated by j column will
* have their local TE computed.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i: we
* compute transfer is j cells to the right, using observations
* across all column pairs separated by j)
* @return multivariate time series of local TE values
* (first index is time, second index is destination variable)
*/
public double[][] computeLocalFromPreviousObservations(int states[][], int j){
int timeSteps = states.length;
if ((timeSteps == 0) || (states[0] == null)) {
// No variables supplied
return new double[timeSteps][];
}
int variables = states[0].length;
// Allocate for all rows even though we'll leave the first ones as zeros
double[][] localTE = new double[timeSteps][variables];
average = 0;
max = 0;
min = 0;
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return localTE;
}
// Initialise and store the current previous values for each column;
// one for each phase of the embedding delay.
// First for the destination:
int[][] pastVal = new int[variables][destEmbeddingDelay];
for (int c = 0; c < variables; c++) {
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[c][d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[c][d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][c];
pastVal[c][d] *= this.alphabetSize;
}
}
}
// Next for the source:
int[][] sourcePastVal = new int[variables][sourceEmbeddingDelay];
for (int c = 0; c < variables; c++) {
int sourceVariable = c-j;
if ((sourceVariable < 0) || (sourceVariable >= variables)) {
// Source variable is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceVariable = (sourceVariable+variables) % variables;
} else {
// Don't add this to our observations
continue;
}
}
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[c][d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[c][d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceVariable];
sourcePastVal[c][d] *= this.alphabetSize;
}
}
}
// now compute the local values
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
double logTerm;
for (int t = startObservationTime; t < timeSteps; t++) {
for (int c = 0; c < variables; c++) {
int sourceVariable = c-j;
if ((sourceVariable < 0) || (sourceVariable >= variables)) {
// Source variable is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceVariable = (sourceVariable+variables) % variables;
} else {
// Don't compute a local value for this one
continue;
}
}
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[c][destEmbeddingPhase] += states[t-1][c];
}
sourcePastVal[c][sourceEmbeddingPhase] += states[t-delay][sourceVariable];
destVal = states[t][c];
int thisPastVal = pastVal[c][destEmbeddingPhase];
int thisSourceVal = sourcePastVal[c][sourceEmbeddingPhase];
// Now compute the local value
logTerm = ((double) sourceNextPastCount[thisSourceVal][destVal][thisPastVal] /
(double) sourcePastCount[thisSourceVal][thisPastVal]) /
((double) nextPastCount[destVal][thisPastVal] / (double) pastCount[thisPastVal]);
localTE[t][c] = Math.log(logTerm) / log_2;
average += localTE[t][c];
if (localTE[t][c] > max) {
max = localTE[t][c];
} else if (localTE[t][c] < min) {
min = localTE[t][c];
}
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[c][destEmbeddingPhase] -= maxShiftedValue[states[t-1-(k-1)*destEmbeddingDelay][c]];
pastVal[c][destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[c][sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[t-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceVariable]];
sourcePastVal[c][sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
if (periodicBoundaryConditions) {
average = average/(double) ((timeSteps - startObservationTime) * variables);
} else {
average = average/(double) ((timeSteps - startObservationTime) * (variables - Math.abs(j)));
}
return localTE;
}
/**
* Computes local transfer for the given
* states, using pdfs built up from observations previously
* sent in via the addObservations method.
* This call suitable only for homogeneous agents, as all
* variable pairs separated by h rows and j columns
* will have their local TE computed.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param h - number of rows to compute transfer entropy across
* (i.e. source is in row i-h, dest is column i)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i)
* @return multivariate time series of local TE values
* (first index is time, second index is destination variable
* row number, third is destination variable column number)
*/
public double[][][] computeLocalFromPreviousObservations(int states[][][], int h, int j){
int timeSteps = states.length;
if ((timeSteps == 0) || (states[0] == null)) {
// No variables supplied
return new double[timeSteps][][];
}
int agentRows = states[0].length;
if (agentRows == 0) {
return new double[timeSteps][agentRows][];
}
int agentColumns = states[0][0].length;
if (agentRows == 0) {
return new double[timeSteps][agentRows][agentColumns];
}
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return new double[timeSteps][][];
}
// Allocate for all rows even though we'll leave the first ones as zeros
double[][][] localTE = new double[timeSteps][agentRows][agentColumns];
average = 0;
max = 0;
min = 0;
// Initialise and store the current previous values for each variable;
// one for each phase of the embedding delay.
// First for the destination:
int[][][] pastVal = new int[agentRows][agentColumns][destEmbeddingDelay];
for (int r = 0; r < agentRows; r++) {
for (int c = 0; c < agentColumns; c++) {
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[r][c][d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[r][c][d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][r][c];
pastVal[r][c][d] *= this.alphabetSize;
}
}
}
}
// Next for the source:
int[][][] sourcePastVal = new int[agentRows][agentColumns][sourceEmbeddingDelay];
for (int r = 0; r < agentRows; r++) {
for (int c = 0; c < agentColumns; c++) {
int sourceAgentRow = r-h;
if ((sourceAgentRow < 0) || (sourceAgentRow >= agentRows)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentRow = (sourceAgentRow+agentRows) % agentRows;
} else {
// Don't add this to our observations
continue;
}
}
int sourceAgentColumn = c-j;
if ((sourceAgentColumn < 0) || (sourceAgentColumn >= agentColumns)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentColumn = (sourceAgentColumn+agentColumns) % agentColumns;
} else {
// Don't add this to our observations
continue;
}
}
// Now initialise the embedding
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[r][c][d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[r][c][d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceAgentRow][sourceAgentColumn];
sourcePastVal[r][c][d] *= this.alphabetSize;
}
}
}
}
// Now compute the local values
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
double logTerm;
for (int t = startObservationTime; t < timeSteps; t++) {
for (int r = 0; r < agentRows; r++) {
for (int c = 0; c < agentColumns; c++) {
int sourceAgentRow = r-h;
if ((sourceAgentRow < 0) || (sourceAgentRow >= agentRows)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentRow = (sourceAgentRow+agentRows) % agentRows;
} else {
// Don't compute a local value here
continue;
}
}
int sourceAgentColumn = c-j;
if ((sourceAgentColumn < 0) || (sourceAgentColumn >= agentColumns)) {
// Source agent is out of bounds unless we are using periodic boundary conditions
if (periodicBoundaryConditions) {
sourceAgentColumn = (sourceAgentColumn+agentColumns) % agentColumns;
} else {
// Don't compute a local value here
continue;
}
}
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[r][c][destEmbeddingPhase] += states[t-1][r][c];
}
sourcePastVal[r][c][sourceEmbeddingPhase] += states[t-delay][sourceAgentRow][sourceAgentColumn];
// Add to the count for this particular transition:
// (cell's assigned as above)
destVal = states[t][r][c];
int thisPastVal = pastVal[r][c][destEmbeddingPhase];
int thisSourceVal = sourcePastVal[r][c][sourceEmbeddingPhase];
// Now compute the local value
logTerm = ((double) sourceNextPastCount[thisSourceVal][destVal][thisPastVal] /
(double) sourcePastCount[thisSourceVal][thisPastVal]) /
((double) nextPastCount[destVal][thisPastVal] / (double) pastCount[thisPastVal]);
localTE[t][r][c] = Math.log(logTerm) / log_2;
average += localTE[t][r][c];
if (localTE[t][r][c] > max) {
max = localTE[t][r][c];
} else if (localTE[t][r][c] < min) {
min = localTE[t][r][c];
}
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[r][c][destEmbeddingPhase] -= maxShiftedValue[states[t-1-(k-1)*destEmbeddingDelay][r][c]];
pastVal[r][c][destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[r][c][sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[t-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceAgentRow][sourceAgentColumn]];
sourcePastVal[r][c][sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
}
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
if (periodicBoundaryConditions) {
average = average/(double) ((timeSteps - startObservationTime) * agentRows * agentColumns);
} else {
average = average/(double) ((timeSteps - startObservationTime) * (agentRows - Math.abs(h)) *
(agentColumns - Math.abs(j)));
}
return localTE;
}
/**
* Computes local transfer for the given
* single source-destination pair of the multi-agent system,
* using pdfs built up from observations previously
* sent in via the addObservations methods.
* This call should be made as opposed to {@link #addObservations(int[][], int)}
* for computing local TE for heterogeneous agents.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param sourceIndex source variable index in states
* @param destIndex destination variable index in states
* @return time-series of local TE values between the series
*/
public double[] computeLocalFromPreviousObservations(int states[][], int sourceIndex, int destIndex){
int timeSteps = states.length;
// Allocate for all rows even though we'll leave the first ones as zeros
double[] localTE = new double[timeSteps];
average = 0;
max = 0;
min = 0;
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return localTE;
}
// Initialise and store the current previous values;
// one for each phase of the embedding delay.
// First for the destination:
int[] pastVal = new int[destEmbeddingDelay];
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][destIndex];
pastVal[d] *= this.alphabetSize;
}
}
// Next for the source:
int[] sourcePastVal = new int[sourceEmbeddingDelay];
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceIndex];
sourcePastVal[d] *= this.alphabetSize;
}
}
// Now compute the local values
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
double logTerm;
for (int r = startObservationTime; r < timeSteps; r++) {
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[destEmbeddingPhase] += states[r-1][destIndex];
}
sourcePastVal[sourceEmbeddingPhase] += states[r-delay][sourceIndex];
destVal = states[r][destIndex];
int thisPastVal = pastVal[destEmbeddingPhase];
int thisSourceVal = sourcePastVal[sourceEmbeddingPhase];
// Now compute the local value
logTerm = ((double) sourceNextPastCount[thisSourceVal][destVal][thisPastVal] /
(double) sourcePastCount[thisSourceVal][thisPastVal]) /
((double) nextPastCount[destVal][thisPastVal] / (double) pastCount[thisPastVal]);
localTE[r] = Math.log(logTerm) / log_2;
average += localTE[r];
if (localTE[r] > max) {
max = localTE[r];
} else if (localTE[r] < min) {
min = localTE[r];
}
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[destEmbeddingPhase] -= maxShiftedValue[states[r-1-(k-1)*destEmbeddingDelay][destIndex]];
pastVal[destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[r-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceIndex]];
sourcePastVal[sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
average = average/(double) (timeSteps - startObservationTime);
return localTE;
}
/**
* Computes local transfer for the given
* single source-destination pair of the multi-agent system,
* using pdfs built up from observations previously
* sent in via the addObservations method.
* This call should be made as opposed to {@link #addObservations(int[][][], int, int)}
* for computing local TE for heterogeneous agents.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param sourceRowIndex source variable row index in states
* @param sourceColumnIndex source variable column index in states
* @param destRowIndex destination variable row index in states
* @param destColumnIndex destination variable column index in states
* @return time-series of local TE values between the series
*/
public double[] computeLocalFromPreviousObservations(int states[][][],
int sourceRowIndex, int sourceColumnIndex, int destRowIndex, int destColumnIndex){
int timeSteps = states.length;
// Allocate for all rows even though we'll leave the first ones as zeros
double[] localTE = new double[timeSteps];
average = 0;
max = 0;
min = 0;
if (timeSteps - startObservationTime <= 0) {
// No observations to add
return localTE;
}
// Initialise and store the current previous values;
// one for each phase of the embedding delay.
// First for the destination:
int[] pastVal = new int[destEmbeddingDelay];
for (int d = 0; d < destEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
pastVal[d] = 0;
for (int p = 0; p < k-1; p++) {
pastVal[d] += states[startObservationTime + d - 1
- (k-1)*destEmbeddingDelay
+ p*destEmbeddingDelay][destRowIndex][destColumnIndex];
pastVal[d] *= this.alphabetSize;
}
}
// Next for the source:
int[] sourcePastVal = new int[sourceEmbeddingDelay];
for (int d = 0; d < sourceEmbeddingDelay; d++) {
// Compute the current previous values for
// phase d of the embedding delay, but leave
// out the most recent value (we'll add those in
// in the main loop)
sourcePastVal[d] = 0;
for (int p = 0; p < sourceHistoryEmbedLength - 1; p++) {
sourcePastVal[d] += states[startObservationTime + d - delay
- (sourceHistoryEmbedLength-1)*sourceEmbeddingDelay
+ p*sourceEmbeddingDelay][sourceRowIndex][sourceColumnIndex];
sourcePastVal[d] *= this.alphabetSize;
}
}
// Now compute the local values
int destVal, destEmbeddingPhase = 0, sourceEmbeddingPhase = 0;
double logTerm;
for (int r = startObservationTime; r < timeSteps; r++) {
// First update the embedding values for the current
// phases of the embeddings:
if (k > 0) {
pastVal[destEmbeddingPhase] += states[r-1][destRowIndex][destColumnIndex];
}
sourcePastVal[sourceEmbeddingPhase] += states[r-delay][sourceRowIndex][sourceColumnIndex];
destVal = states[r][destRowIndex][destColumnIndex];
int thisPastVal = pastVal[destEmbeddingPhase];
int thisSourceVal = sourcePastVal[sourceEmbeddingPhase];
// Now compute the local value
logTerm = ((double) sourceNextPastCount[thisSourceVal][destVal][thisPastVal] /
(double) sourcePastCount[thisSourceVal][thisPastVal]) /
((double) nextPastCount[destVal][thisPastVal] / (double) pastCount[thisPastVal]);
localTE[r] = Math.log(logTerm) / log_2;
average += localTE[r];
if (localTE[r] > max) {
max = localTE[r];
} else if (localTE[r] < min) {
min = localTE[r];
}
// Now, update the combined embedding values and phases,
// for this phase we back out the oldest value which we'll no longer need:
if (k > 0) {
pastVal[destEmbeddingPhase] -= maxShiftedValue[states[r-1-(k-1)*destEmbeddingDelay][destRowIndex][destColumnIndex]];
pastVal[destEmbeddingPhase] *= this.alphabetSize; // and shift the others up
}
sourcePastVal[sourceEmbeddingPhase] -=
maxShiftedSourceValue[
states[r-delay-(sourceHistoryEmbedLength-1)*sourceEmbeddingDelay][sourceRowIndex][sourceColumnIndex]];
sourcePastVal[sourceEmbeddingPhase] *= this.alphabetSize; // and shift the others up
// then update the phase
destEmbeddingPhase = (destEmbeddingPhase + 1) % destEmbeddingDelay;
sourceEmbeddingPhase = (sourceEmbeddingPhase + 1) % sourceEmbeddingDelay;
}
average = average/(double) (timeSteps - startObservationTime);
return localTE;
}
/**
* Standalone routine to
* compute local transfer entropy between two time series
* Return a time series of local values.
* First max(k,l) values are zeros since TE is not defined there
*
* @param sourceStates source time-series
* @param destStates destination time-series.
* Must be same length as sourceStates
* @return time-series of local TE values
*/
public double[] computeLocal(int sourceStates[], int destStates[]) {
initialise();
addObservations(sourceStates, destStates);
return computeLocalFromPreviousObservations(sourceStates, destStates);
}
/**
* Standalone routine to
* compute local transfer entropy across a 2D spatiotemporal
* array of the states of homogeneous agents.
* Return a 2D spatiotemporal array of local values.
* First max(k,l) values are zeros since TE is not defined there.
* This call suitable only for homogeneous agents, as all
* variable pairs separated by j column will
* have their local TE computed.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i: we
* compute transfer is j cells to the right, using observations
* across all column pairs separated by j)
* @return multivariate time series of local TE values
* (first index is time, second index is destination variable)
*/
public double[][] computeLocal(int states[][], int j) {
initialise();
addObservations(states, j);
return computeLocalFromPreviousObservations(states, j);
}
/**
* Standalone routine to
* compute local transfer entropy across a 3D spatiotemporal
* array of the states of homogeneous agents.
* Return a 3D spatiotemporal array of local values.
* First max(k,l) values are zeros since TE is not defined there.
* This call suitable only for homogeneous agents, as all
* variable pairs separated by h rows and j columns
* will have their local TE computed.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param h - number of rows to compute transfer entropy across
* (i.e. source is in row i-h, dest is column i)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i)
* @return multivariate time series of local TE values
* (first index is time, second index is destination variable
* row number, third is destination variable column number)
*/
public double[][][] computeLocal(int states[][][], int h, int j) {
initialise();
addObservations(states, h, j);
return computeLocalFromPreviousObservations(states, h, j);
}
/**
* Standalone routine to
* compute average local transfer entropy across a 2D spatiotemporal
* array of the states of homogeneous agents
* Return the average TE.
* This call suitable only for homogeneous agents, as all
* variable pairs separated by j column will
* have their local TE computed.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i: we
* compute transfer is j cells to the right, using observations
* across all column pairs separated by j)
* @return average TE across j variables to the right
*/
public double computeAverageLocal(int states[][], int j) {
initialise();
addObservations(states, j);
return computeAverageLocalOfObservations();
}
/**
* Standalone routine to
* compute average local transfer entropy across a 3D spatiotemporal
* array of the states of homogeneous agents
* Return the average.
* This call suitable only for homogeneous agents, as all
* variable pairs separated by h rows and j columns
* will have their PDFs combined.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param h - number of rows to compute transfer entropy across
* (i.e. source is in row i-h, dest is column i)
* @param j - number of columns to compute transfer entropy across
* (i.e. source is column i-j, dest is column i)
* @return
*/
public double computeAverageLocal(int states[][][], int h, int j) {
initialise();
addObservations(states, h, j);
return computeAverageLocalOfObservations();
}
/**
* Standalone routine to
* compute local transfer entropy between specific variables in
* a 2D spatiotemporal multivariate time-series.
* First max(k,l) values are zeros since TE is not defined there.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param sourceCol source variable index in states
* @param destCol destination variable index in states
* @return time-series of local TE values between the series
*/
public double[] computeLocal(int states[][], int sourceCol, int destCol) {
initialise();
addObservations(states, sourceCol, destCol);
return computeLocalFromPreviousObservations(states, sourceCol, destCol);
}
/**
* Standalone routine to
* computes local transfer for the given
* single source-destination pair of the 3D multi-agent system.
* This method suitable for heterogeneous variables.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param sourceRowIndex source variable row index in states
* @param sourceColumnIndex source variable column index in states
* @param destRowIndex destination variable row index in states
* @param destColumnIndex destination variable column index in states
* @return time-series of local TE values between the series
*/
public double[] computeLocal(int states[][][], int sourceRowIndex, int sourceColumnIndex,
int destRowIndex, int destColumnIndex) {
initialise();
addObservations(states, sourceRowIndex, sourceColumnIndex, destRowIndex, destColumnIndex);
return computeLocalFromPreviousObservations(states, sourceRowIndex, sourceColumnIndex,
destRowIndex, destColumnIndex);
}
/**
* Standalone routine to
* compute local transfer entropy between specific variables in
* a 2D spatiotemporal multivariate time-series.
* Returns the average.
* This method suitable for heterogeneous agents.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable number)
* @param sourceCol source variable index in states
* @param destCol destination variable index in states
* @return average TE for the given pair
*/
public double computeAverageLocal(int states[][], int sourceCol, int destCol) {
initialise();
addObservations(states, sourceCol, destCol);
return computeAverageLocalOfObservations();
}
/**
* Standalone routine to
* compute local transfer entropy between specific variables in
* a 3D spatiotemporal multivariate time-series.
* Returns the average.
* This method suitable for heterogeneous agents.
*
* @param states multivariate time series
* (1st index is time, 2nd index is variable row number,
* 3rd is variable column number)
* @param sourceRowIndex source variable row index in states
* @param sourceColumnIndex source variable column index in states
* @param destRowIndex destination variable row index in states
* @param destColumnIndex destination variable column index in states
* @return average TE for the given pair
*/
public double computeAverageLocal(int states[][][], int sourceRowIndex, int sourceColumnIndex,
int destRowIndex, int destColumnIndex) {
initialise();
addObservations(states, sourceRowIndex, sourceColumnIndex, destRowIndex, destColumnIndex);
return computeAverageLocalOfObservations();
}
/**
* Whether we assume periodic boundary conditions in the calls
* for homogeneous variables.
*
* @return as above
*/
public boolean isPeriodicBoundaryConditions() {
return periodicBoundaryConditions;
}
/**
* set whether we assume periodic boundary conditions in the calls
* for homogeneous variables.
*
* @param periodicBoundaryConditions as above
*/
public void setPeriodicBoundaryConditions(boolean periodicBoundaryConditions) {
this.periodicBoundaryConditions = periodicBoundaryConditions;
}
}
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