úÎ4{2’     portable provisional+haskell.vivian.mcphail <at> gmail <dot> com)perform an analysis using surrogate data  random seed number of repetitions the evaluation function  the data zthe results, with the evaluated real data in position 1 and the rest of the array containing the evaluated surrogate data portable provisional+haskell.vivian.mcphail <at> gmail <dot> com)the cumulative distribution function D(x <= X)  the bins the resulting histogram mean standard deviation  the bins the resulting histogram portable provisional+haskell.vivian.mcphail <at> gmail <dot> comcalculate a probability $a probability distribution function a PDF interface 1create a PDF from an arbtrary function f :-> [0,1] portable provisional+haskell.vivian.mcphail <at> gmail <dot> com the entropy sum p_i lln{p_i} of a sequence the underlying distribution  the sequence  the entropy the mutual information sum_x s um_y p(x,y) ln{frac{p(x,y)}{p(x)p(y)}} the underlying distribution !the first dimension distribution "the second dimension distribution  the sequence the mutual information portable provisional+haskell.vivian.mcphail <at> gmail <dot> com the covariance matrix 9the dimensions of data (each vector being one dimension)  the symmetric covariance matrix the mean of a list of vectors  the mean of an array of vectors .the mean of a matrix with data series in rows "the variance of a list of vectors $the variance of an array of vectors 2the variance of a matrix with data series in rows   portable provisional+haskell.vivian.mcphail <at> gmail <dot> com9find the n principal components of multidimensional data ;perform a PCA transform of the original data (remove mean)  | Final = M^T Data^T  the data the principal components the transformed data .perform a dimension-reducing PCA modification  the data eigenvalue threshold .the reduced data, with n principal components portable provisional+haskell.vivian.mcphail <at> gmail <dot> com sigmoid transfer function (derivative of sigmoid transfer function remove the mean from data  the data (demeaned data,mean)  whiten data  the data eigenvalue threshold (whitened data,transform)  !"#$!transfer function (tanh,u exp(u^2/ 2), etc...)  derivative of transfer function 0type of normalisation: Infinity, PNorm1, PNorm2 *convergence tolerance for feature vectors weight matrix input data in chunks ica transform (weight matrix) perform an ICA transform  random seed !transfer function (tanh,u exp(u^2/ 2), etc...)  derivative of transfer function 0type of normalisation: Infinity, PNorm1, PNorm2 *convergence tolerance for feature vectors : -> Int -- ^ output dimensions 4sampling size (must be smaller than length of data) data  transformed data, ica transform \ICA with default values: no dimension reduction, euclidean norms, 16 sample groups, sigmoid  random seed data  transformed data, ica transform %      !"#$%&'()*+,-hstatistics-0.2.2.8Numeric.Statistics.SurrogateNumeric.Statistics.HistogramNumeric.Statistics.PDFNumeric.Statistics.InformationNumeric.StatisticsNumeric.Statistics.PCANumeric.Statistics.ICA surrogatecumulativeToHistogramgaussianHistogramPDF probability PDFFunctionpdfFromFunctionentropymutual_informationSamplesSamplecovarianceMatrixmeanList meanArray meanMatrix varianceList varianceArrayvarianceMatrixpca pcaTransform pcaReducesigmoidsigmoid'demeanwhitenica icaDefaults surrogate' randomList permute_dataP_Func random_vectorupdate decorrelate normalise convergedica'