double calculateJointEntropy(double *firstVector, double *secondVector, int vectorLength)
{
double jointEntropy = 0.0;
double tempValue = 0.0;
int i;
JointProbabilityState state = calculateJointProbability(firstVector,secondVector,vectorLength);
/*H(XY) = - sumx sumy p(xy) log p(xy)*/
for (i = 0; i < state.numJointStates; i++)
{
tempValue = state.jointProbabilityVector[i];
if (tempValue > 0)
{
jointEntropy -= tempValue * log(tempValue);
}
}
jointEntropy /= log(2.0);
FREE_FUNC(state.firstProbabilityVector);
state.firstProbabilityVector = NULL;
FREE_FUNC(state.secondProbabilityVector);
state.secondProbabilityVector = NULL;
FREE_FUNC(state.jointProbabilityVector);
state.jointProbabilityVector = NULL;
return jointEntropy;
}/*calculateJointEntropy(double *, double *, int)*/
double calculateMutualInformation(double *dataVector, double *targetVector, int vectorLength)
{
double mutualInformation = 0.0;
int firstIndex,secondIndex;
int i;
JointProbabilityState state = calculateJointProbability(dataVector,targetVector,vectorLength);
/*
** I(X;Y) = sum sum p(xy) * log (p(xy)/p(x)p(y))
*/
for (i = 0; i < state.numJointStates; i++)
{
firstIndex = i % state.numFirstStates;
secondIndex = i / state.numFirstStates;
if ((state.jointProbabilityVector[i] > 0) && (state.firstProbabilityVector[firstIndex] > 0) && (state.secondProbabilityVector[secondIndex] > 0))
{
/*double division is probably more stable than multiplying two small numbers together
** mutualInformation += state.jointProbabilityVector[i] * log(state.jointProbabilityVector[i] / (state.firstProbabilityVector[firstIndex] * state.secondProbabilityVector[secondIndex]));
*/
mutualInformation += state.jointProbabilityVector[i] * log(state.jointProbabilityVector[i] / state.firstProbabilityVector[firstIndex] / state.secondProbabilityVector[secondIndex]);
}
}
mutualInformation /= log(2.0);
FREE_FUNC(state.firstProbabilityVector);
state.firstProbabilityVector = NULL;
FREE_FUNC(state.secondProbabilityVector);
state.secondProbabilityVector = NULL;
FREE_FUNC(state.jointProbabilityVector);
state.jointProbabilityVector = NULL;
return mutualInformation;
}/*calculateMutualInformation(double *,double *,int)*/
double calculateJointRenyiEntropy(double alpha, double *firstVector, double *secondVector, int vectorLength)
{
double jointEntropy = 0.0;
double tempValue = 0.0;
int i;
JointProbabilityState state = calculateJointProbability(firstVector,secondVector,vectorLength);
/*H_\alpha(XY) = 1/(1-alpha) * log(2)(sum p(xy)^alpha)*/
for (i = 0; i < state.numJointStates; i++)
{
tempValue = state.jointProbabilityVector[i];
if (tempValue > 0)
{
jointEntropy += pow(tempValue,alpha);
}
}
jointEntropy = log(jointEntropy);
jointEntropy /= log(2.0);
jointEntropy /= (1.0-alpha);
FREE_FUNC(state.firstProbabilityVector);
state.firstProbabilityVector = NULL;
FREE_FUNC(state.secondProbabilityVector);
state.secondProbabilityVector = NULL;
FREE_FUNC(state.jointProbabilityVector);
state.jointProbabilityVector = NULL;
return jointEntropy;
}/*calculateJointRenyiEntropy(double,double*,double*,int)*/
double calcJointEntropy(uint *firstVector, uint *secondVector, int vectorLength) {
JointProbabilityState state = calculateJointProbability(firstVector, secondVector, vectorLength);
double h = jointEntropy(state);
freeJointProbabilityState(state);
return h;
}/*calcJointEntropy(uint *, uint *, int)*/
double calcConditionalEntropy(uint *dataVector, uint *conditionVector, int vectorLength) {
JointProbabilityState state = calculateJointProbability(dataVector, conditionVector, vectorLength);
double h = condEntropy(state);
freeJointProbabilityState(state);
return h;
}/*calcConditionalEntropy(uint *, uint *, int)*/
double calculateConditionalEntropy(double *dataVector, double *conditionVector, int vectorLength)
{
/*
** Conditional entropy
** H(X|Y) = - sumx sumy p(xy) log p(xy)/p(y)
*/
double condEntropy = 0.0;
double jointValue = 0.0;
double condValue = 0.0;
int i;
JointProbabilityState state = calculateJointProbability(dataVector,conditionVector,vectorLength);
/*H(X|Y) = - sumx sumy p(xy) log p(xy)/p(y)*/
/* to index by numFirstStates use modulus of i
** to index by numSecondStates use integer division of i by numFirstStates
*/
for (i = 0; i < state.numJointStates; i++)
{
jointValue = state.jointProbabilityVector[i];
condValue = state.secondProbabilityVector[i / state.numFirstStates];
if ((jointValue > 0) && (condValue > 0))
{
condEntropy -= jointValue * log(jointValue / condValue);
}
}
condEntropy /= log(2.0);
FREE_FUNC(state.firstProbabilityVector);
state.firstProbabilityVector = NULL;
FREE_FUNC(state.secondProbabilityVector);
state.secondProbabilityVector = NULL;
FREE_FUNC(state.jointProbabilityVector);
state.jointProbabilityVector = NULL;
return condEntropy;
}/*calculateConditionalEntropy(double *, double *, int)*/
/*******************************************************************************
**entry point for the mex call
**nlhs - number of outputs
**plhs - pointer to array of outputs
**nrhs - number of inputs
**prhs - pointer to array of inputs
*******************************************************************************/
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
/*****************************************************************************
** this function takes a flag and a variable number of arguments
** depending on the value of the flag and returns either a construct
** containing probability estimates, a merged vector or a double value
** representing an entropy or mutual information
*****************************************************************************/
int flag, i, numberOfSamples, checkSamples, thirdCheckSamples, numberOfFeatures, checkFeatures, thirdCheckFeatures;
int numArities, errorTest;
double *dataVector, *condVector, *targetVector, *firstVector, *secondVector, *output, *numStates;
double *matrix, *mergedVector, *arities;
int *outputIntVector, *intArities;
double *jointOutput, *numJointStates, *firstOutput, *numFirstStates, *secondOutput, *numSecondStates;
ProbabilityState state;
JointProbabilityState jointState;
/*if (nlhs != 1)
{
printf("Incorrect number of output arguments\n");
}//if not 1 output
*/
switch (nrhs)
{
case 2:
{
/*printf("Must be H(X), calculateProbability(X), merge(X), normaliseArray(X)\n");*/
break;
}
case 3:
{
/*printf("Must be H(XY), H(X|Y), calculateJointProbability(XY), I(X;Y)\n");*/
break;
}
case 4:
{
/*printf("Must be I(X;Y|Z)\n");*/
break;
}
default:
{
printf("Incorrect number of arguments, format is MIToolbox(\"FLAG\",varargin)\n");
break;
}
}
/* number to function map
** 1 = calculateProbability
** 2 = calculateJointProbability
** 3 = mergeArrays
** 4 = H(X)
** 5 = H(XY)
** 6 = H(X|Y)
** 7 = I(X;Y)
** 8 = I(X;Y|Z)
** 9 = normaliseArray
*/
flag = *mxGetPr(prhs[0]);
switch (flag)
{
case 1:
{
/*
**calculateProbability
*/
numberOfSamples = mxGetM(prhs[1]);
dataVector = (double *) mxGetPr(prhs[1]);
/*ProbabilityState calculateProbability(double *dataVector, int vectorLength);*/
state = calculateProbability(dataVector,numberOfSamples);
plhs[0] = mxCreateDoubleMatrix(state.numStates,1,mxREAL);
plhs[1] = mxCreateDoubleMatrix(1,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
numStates = (double *) mxGetPr(plhs[1]);
*numStates = state.numStates;
for (i = 0; i < state.numStates; i++)
{
output[i] = state.probabilityVector[i];
}
break;
}/*case 1 - calculateProbability*/
case 2:
{
/*
**calculateJointProbability
*/
numberOfSamples = mxGetM(prhs[1]);
firstVector = (double *) mxGetPr(prhs[1]);
secondVector = (double *) mxGetPr(prhs[2]);
/*JointProbabilityState calculateJointProbability(double *firstVector, double *secondVector int vectorLength);*/
jointState = calculateJointProbability(firstVector,secondVector,numberOfSamples);
plhs[0] = mxCreateDoubleMatrix(jointState.numJointStates,1,mxREAL);
plhs[1] = mxCreateDoubleMatrix(1,1,mxREAL);
plhs[2] = mxCreateDoubleMatrix(jointState.numFirstStates,1,mxREAL);
plhs[3] = mxCreateDoubleMatrix(1,1,mxREAL);
plhs[4] = mxCreateDoubleMatrix(jointState.numSecondStates,1,mxREAL);
plhs[5] = mxCreateDoubleMatrix(1,1,mxREAL);
jointOutput = (double *)mxGetPr(plhs[0]);
numJointStates = (double *) mxGetPr(plhs[1]);
firstOutput = (double *)mxGetPr(plhs[2]);
numFirstStates = (double *) mxGetPr(plhs[3]);
secondOutput = (double *)mxGetPr(plhs[4]);
numSecondStates = (double *) mxGetPr(plhs[5]);
*numJointStates = jointState.numJointStates;
*numFirstStates = jointState.numFirstStates;
*numSecondStates = jointState.numSecondStates;
for (i = 0; i < jointState.numJointStates; i++)
{
jointOutput[i] = jointState.jointProbabilityVector[i];
}
for (i = 0; i < jointState.numFirstStates; i++)
{
firstOutput[i] = jointState.firstProbabilityVector[i];
}
for (i = 0; i < jointState.numSecondStates; i++)
{
secondOutput[i] = jointState.secondProbabilityVector[i];
}
break;
}/*case 2 - calculateJointProbability */
case 3:
{
/*
**mergeArrays
*/
numberOfSamples = mxGetM(prhs[1]);
numberOfFeatures = mxGetN(prhs[1]);
numArities = 0;
if (nrhs > 2)
{
numArities = mxGetN(prhs[2]);
/*printf("arities = %d, features = %d, samples = %d\n",numArities,numberOfFeatures,numberOfSamples);*/
}
plhs[0] = mxCreateDoubleMatrix(0,0,mxREAL);
if (numArities == 0)
{
/*
**no arities therefore compress output
*/
if ((numberOfFeatures > 0) && (numberOfSamples > 0))
{
matrix = (double *) mxGetPr(prhs[1]);
mergedVector = (double *) mxCalloc(numberOfSamples,sizeof(double));
plhs[0] = mxCreateDoubleMatrix(numberOfSamples,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
/*int mergeMultipleArrays(double *inputMatrix, double *outputVector, int matrixWidth, int vectorLength)*/
mergeMultipleArrays(matrix, mergedVector, numberOfFeatures, numberOfSamples);
for (i = 0; i < numberOfSamples; i++)
{
output[i] = mergedVector[i];
}
mxFree(mergedVector);
mergedVector = NULL;
}
}
else if (numArities == numberOfFeatures)
{
if ((numberOfFeatures > 0) && (numberOfSamples > 0))
{
matrix = (double *) mxGetPr(prhs[1]);
mergedVector = (double *) mxCalloc(numberOfSamples,sizeof(double));
arities = (double *) mxGetPr(prhs[2]);
intArities = (int *) mxCalloc(numberOfFeatures,sizeof(int));
for (i = 0; i < numArities; i++)
{
intArities[i] = (int) floor(arities[i]);
}
/*int mergeMultipleArrays(double *inputMatrix, double *outputVector, int matrixWidth, int *arities, int vectorLength);*/
errorTest = mergeMultipleArraysArities(matrix, mergedVector, numberOfFeatures, intArities, numberOfSamples);
if (errorTest != -1)
{
plhs[0] = mxCreateDoubleMatrix(numberOfSamples,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
for (i = 0; i < numberOfSamples; i++)
{
output[i] = mergedVector[i];
}
}
else
{
printf("Incorrect arities supplied. More states in data than specified\n");
}
mxFree(mergedVector);
mergedVector = NULL;
}
}
else
{
printf("Number of arities does not match number of features, arities should be a row vector\n");
}
break;
}/*case 3 - mergeArrays*/
case 4:
{
/*
**H(X)
*/
numberOfSamples = mxGetM(prhs[1]);
numberOfFeatures = mxGetN(prhs[1]);
dataVector = (double *) mxGetPr(prhs[1]);
plhs[0] = mxCreateDoubleMatrix(1,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
if (numberOfFeatures == 1)
{
/*double calculateEntropy(double *dataVector, int vectorLength);*/
*output = calculateEntropy(dataVector,numberOfSamples);
}
else
{
printf("No columns in input\n");
*output = -1.0;
}
break;
}/*case 4 - H(X)*/
case 5:
{
/*
**H(XY)
*/
numberOfSamples = mxGetM(prhs[1]);
checkSamples = mxGetM(prhs[2]);
numberOfFeatures = mxGetN(prhs[1]);
checkFeatures = mxGetN(prhs[2]);
firstVector = mxGetPr(prhs[1]);
secondVector = mxGetPr(prhs[2]);
plhs[0] = mxCreateDoubleMatrix(1,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
if ((numberOfFeatures == 1) && (checkFeatures == 1))
{
if ((numberOfSamples == 0) && (checkSamples == 0))
{
*output = 0.0;
}
else if (numberOfSamples == 0)
{
*output = calculateEntropy(secondVector,numberOfSamples);
}
else if (checkSamples == 0)
{
*output = calculateEntropy(firstVector,numberOfSamples);
}
else if (numberOfSamples == checkSamples)
{
/*double calculateJointEntropy(double *firstVector, double *secondVector, int vectorLength);*/
*output = calculateJointEntropy(firstVector,secondVector,numberOfSamples);
}
else
{
printf("Vector lengths do not match, they must be the same length\n");
*output = -1.0;
}
}
else
{
printf("No columns in input\n");
*output = -1.0;
}
break;
}/*case 5 - H(XY)*/
case 6:
{
/*
**H(X|Y)
*/
numberOfSamples = mxGetM(prhs[1]);
checkSamples = mxGetM(prhs[2]);
numberOfFeatures = mxGetN(prhs[1]);
checkFeatures = mxGetN(prhs[2]);
dataVector = mxGetPr(prhs[1]);
condVector = mxGetPr(prhs[2]);
plhs[0] = mxCreateDoubleMatrix(1,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
if ((numberOfFeatures == 1) && (checkFeatures == 1))
{
if (numberOfSamples == 0)
{
*output = 0.0;
}
else if (checkSamples == 0)
{
*output = calculateEntropy(dataVector,numberOfSamples);
}
else if (numberOfSamples == checkSamples)
{
/*double calculateConditionalEntropy(double *dataVector, double *condVector, int vectorLength);*/
*output = calculateConditionalEntropy(dataVector,condVector,numberOfSamples);
}
else
{
printf("Vector lengths do not match, they must be the same length\n");
*output = -1.0;
}
}
else
{
printf("No columns in input\n");
*output = -1.0;
}
break;
}/*case 6 - H(X|Y)*/
case 7:
{
/*
**I(X;Y)
*/
numberOfSamples = mxGetM(prhs[1]);
checkSamples = mxGetM(prhs[2]);
numberOfFeatures = mxGetN(prhs[1]);
checkFeatures = mxGetN(prhs[2]);
firstVector = mxGetPr(prhs[1]);
secondVector = mxGetPr(prhs[2]);
plhs[0] = mxCreateDoubleMatrix(1,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
if ((numberOfFeatures == 1) && (checkFeatures == 1))
{
if ((numberOfSamples == 0) || (checkSamples == 0))
{
*output = 0.0;
}
else if (numberOfSamples == checkSamples)
{
/*double calculateMutualInformation(double *firstVector, double *secondVector, int vectorLength);*/
*output = calculateMutualInformation(firstVector,secondVector,numberOfSamples);
}
else
{
printf("Vector lengths do not match, they must be the same length\n");
*output = -1.0;
}
}
else
{
printf("No columns in input\n");
*output = -1.0;
}
break;
}/*case 7 - I(X;Y)*/
case 8:
{
/*
**I(X;Y|Z)
*/
numberOfSamples = mxGetM(prhs[1]);
checkSamples = mxGetM(prhs[2]);
thirdCheckSamples = mxGetM(prhs[3]);
numberOfFeatures = mxGetN(prhs[1]);
checkFeatures = mxGetN(prhs[2]);
thirdCheckFeatures = mxGetN(prhs[3]);
firstVector = mxGetPr(prhs[1]);
targetVector = mxGetPr(prhs[2]);
condVector = mxGetPr(prhs[3]);
plhs[0] = mxCreateDoubleMatrix(1,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
if ((numberOfFeatures == 1) && (checkFeatures == 1))
{
if ((numberOfSamples == 0) || (checkSamples == 0))
{
*output = 0.0;
}
else if ((thirdCheckSamples == 0) || (thirdCheckFeatures != 1))
{
*output = calculateMutualInformation(firstVector,targetVector,numberOfSamples);
}
else if ((numberOfSamples == checkSamples) && (numberOfSamples == thirdCheckSamples))
{
/*double calculateConditionalMutualInformation(double *firstVector, double *targetVector, double *condVector, int vectorLength);*/
*output = calculateConditionalMutualInformation(firstVector,targetVector,condVector,numberOfSamples);
}
else
{
printf("Vector lengths do not match, they must be the same length\n");
*output = -1.0;
}
}
else
{
printf("No columns in input\n");
*output = -1.0;
}
break;
}/*case 8 - I(X;Y|Z)*/
case 9:
{
/*
**normaliseArray
*/
numberOfSamples = mxGetM(prhs[1]);
dataVector = (double *) mxGetPr(prhs[1]);
outputIntVector = (int *) mxCalloc(numberOfSamples,sizeof(int));
plhs[0] = mxCreateDoubleMatrix(numberOfSamples,1,mxREAL);
plhs[1] = mxCreateDoubleMatrix(1,1,mxREAL);
output = (double *)mxGetPr(plhs[0]);
numStates = (double *) mxGetPr(plhs[1]);
/*int normaliseArray(double *inputVector, int *outputVector, int vectorLength);*/
*numStates = normaliseArray(dataVector, outputIntVector, numberOfSamples);
for (i = 0; i < numberOfSamples; i++)
{
output[i] = outputIntVector[i];
}
break;
}/*case 9 - normaliseArray*/
default:
{
printf("Unrecognised flag\n");
break;
}/*default*/
}/*switch(flag)*/
return;
}/*mexFunction()*/
