úÎZVE6      !"#$%&'()*+,-./012345,(c) Alexander Vivian Hugh McPhail 2010, 2014BSD3+haskell.vivian.mcphail <at> gmail <dot> com provisionalportableNone(perform an analysis using surrogate data random seednumber of repetitionsthe evaluation functionthe dataythe results, with the evaluated real data in position 1 and the rest of the array containing the evaluated surrogate data678678(c) A. V. H. McPhail 2010, 2014BSD3+haskell.vivian.mcphail <at> gmail <dot> com provisionalportableNone9;<=calculate a probability#a probability distribution functiona PDF interface2create a PDF from an arbtrary function f :-> [0,1]99%(c) A. V. H. McPhail 2010, 2014, 2017BSD3+haskell.vivian.mcphail <at> gmail <dot> com provisionalportableNoneVfind the principal components of multidimensional data greater than the threshhold efind N greatest principal components of multidimensional data according to size of the eigenvalue Tperform a PCA transform of the original data (remove mean) | Final = M^T Data^T Sperform a dimension-reducing PCA modification, using an eigenvalue threshhold Aperform a dimension-reducing PCA modification, using N components  :;<=> the datathe principal componentsthe transformed data the dataeigenvalue thresholdthe reduced data the dataN, the number of components-the reduced data, with n principal components   :;<=> (c) A. V. H. McPhail 2010, 2014BSD3+haskell.vivian.mcphail <at> gmail <dot> com provisionalportableNone: *the entropy sum p_i lln{p_i} of a sequenceDthe mutual information sum_x sum_y p(x,y) ln{frac{p(x,y)}{p(x)p(y)}}?@ the underlying distribution the sequence the entropythe underlying distribution the first dimension distribution!the second dimension distribution the sequencethe mutual information  ?@ (c) A. V. H. McPhail 2010, 2014BSD3+haskell.vivian.mcphail <at> gmail <dot> com provisionalportableNoneA.the cumulative distribution function D(x <= X)the binsthe resulting histogrammeanstandard deviationthe binsthe resulting histogramA%(c) A. V. H. McPhail 2010, 2012, 2014BSD3+haskell.vivian.mcphail <at> gmail <dot> com provisionalportableNone:the covariance matrix8the correlation coefficient: (cov x y) / (std x) (std y)the mean of a list of vectorsthe 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 vectors1the variance of a matrix with data series in rows$centre the data to 0: (x - (mean x))Hcomplementary log-log function cloglog :: Vector Double -> Vector Double1corcoeff = covariance x / (std dev x * std dev y)Ccut numerical data into intervals, data must fall inside the bounds¡return the rank of each element of the vector multiple identical entries result in the average rank of those entries ranks :: Vector Double -> Vector Double kendall's rank correlation Ä!@(logit p) = log(p/(1-p)) logit :: Vector Double -> Vector Double"|the Mahalanobis D-square distance between samples columns are components and rows are observations (uses pseudoinverse)#a list of element frequencies$the p'th moment of a vector%£ordinary least squares estimation for the multivariate model Y = X B + e rows are observations, columns are elements mean e = 0, cov e = kronecker s I&compute quantiles in percent';the difference between the maximum and minimum of the input(2count the number of runs greater than or equal to n in the data)'Spearman's rank correlation coefficient*centre and normalise a vector8the dimensions of data (each vector being one dimension)the symmetric covariance matrix intervalsdata indexed by bin !" the data set5(Just sample) to be measured or use mean when NothingD^2 #$momentcalculate central momentcalculate absolute momentdata%XY9(OLS estimator for B, OLS estimator for s, OLS residuals)&percentile (0 - 100)dataresult'(longest run to countdata (run length,count))* !"#$%&'()* !"#$%&'()* !"#$%&'()*(c) A. V. H. McPhail 2010, 2014BSD3+haskell.vivian.mcphail <at> gmail <dot> com provisionalportableNone:0sigmoid transfer function1'derivative of sigmoid transfer function2remove the mean from data3 whiten data4perform an ICA transform5[ICA with default values: no dimension reduction, euclidean norms, 16 sample groups, sigmoid+,-./B012the data(demeaned data,mean)3the dataeigenvalue threshold(whitened data,transform)CDEFGHI-transfer function (tanh,u exp(u^2/2), etc...)derivative of transfer function/type of normalisation: Infinity, PNorm1, PNorm2)convergence tolerance for feature vectors weight matrixinput data in chunksica transform (weight matrix)4 random seed-transfer function (tanh,u exp(u^2/2), etc...)derivative of transfer function/type of normalisation: Infinity, PNorm1, PNorm2cconvergence tolerance for feature vectors -> Int -- ^ output dimensions3sampling size (must be smaller than length of data)datatransformed data, ica transform5 random seeddatatransformed data, ica transform +,-./012345 012345+,-./+,-./B0123CDEFGHI45J      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQR&hstatistics-0.3-HNx3URJIs9B2lGJVaVG43RNumeric.Statistics.SurrogateNumeric.Statistics.PDFNumeric.Statistics.PCANumeric.Statistics.InformationNumeric.Statistics.HistogramNumeric.StatisticsNumeric.Statistics.ICA surrogatePDF probability PDFFunctionpdfFromFunction$fPDFHistogram2D(,)$fPDFHistogramDouble$fPDFPDFFunctionbpcapcaN pcaTransform pcaReduce pcaReduceNentropymutual_informationcumulativeToHistogramgaussianHistogramSamplesSamplecovarianceMatrixcorrelationCoefficientMatrixmeanList meanArray meanMatrix varianceList varianceArrayvarianceMatrixcentrecloglogcorcoeffcutrankskendalllogit mahalanobismodemomentols percentilerange run_countspearman studentizeNormTypeNormZeroNormOneNormTwoNormInfsigmoidsigmoid'demeanwhitenica icaDefaults surrogate' randomList permute_dataP_Funcv1v2v3ab zeroToOnelogEvectorToTuplespnormunconcat random_vectorupdate decorrelate normalise convergedica'