-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Statistics
--   
--   Purely functional interface for statistics based on hmatrix and
--   hmatrix-gsl-stats
--   
--   When hmatrix is installed with -fvector, the vector type is
--   Data.Vector.Storable from the vector package and compatible with the
--   <a>statistics</a> package
--   &lt;http:<i></i>hackage.haskell.org<i>package</i>statistics
--   
--   Feature requests, suggestions, and bug fixes welcome.
@package hstatistics
@version 0.2.2.7


-- | Methods for tests using surrogate data
module Numeric.Statistics.Surrogate

-- | perform an analysis using surrogate data
surrogate :: Int -> Int -> (Array Int (Vector Double) -> a) -> Array Int (Vector Double) -> Array Int a


-- | create histograms from density functions
module Numeric.Statistics.Histogram
cumulativeToHistogram :: (Double -> Double) -> Vector Double -> Histogram
gaussianHistogram :: Double -> Double -> Vector Double -> Histogram


-- | Probability Distribution Function interface
module Numeric.Statistics.PDF

-- | a probability distribution function
--   
--   a PDF interface
data PDFFunction a
class PDF b a
probability :: PDF b a => b -> Vector a -> Vector Double

-- | create a PDF from an arbtrary function f :-&gt; [0,1]
pdfFromFunction :: (a -> Double) -> PDFFunction a
instance PDF Histogram2D (Double, Double)
instance PDF Histogram Double
instance Storable b => PDF (PDFFunction b) b


-- | Shannon entropy
module Numeric.Statistics.Information

-- | the entropy sum p_i lln{p_i} of a sequence
entropy :: PDF a Double => a -> Vector Double -> Double

-- | the mutual information sum_x sum_y p(x,y) ln{frac{p(x,y)}{p(x)p(y)}}
mutual_information :: (PDF a Double, PDF b (Double, Double)) => b -> a -> a -> (Vector Double, Vector Double) -> Double


-- | Useful statistical functions
module Numeric.Statistics
type Sample a = Vector a
type Samples a = Array Int (Vector a)

-- | the covariance matrix
covarianceMatrix :: Samples Double -> Matrix Double

-- | the mean of a list of vectors
meanList :: (Container Vector a, Num (Vector a)) => [Sample a] -> Sample a

-- | the mean of an array of vectors
meanArray :: (Container Vector a, Num (Vector a)) => Samples a -> Sample a

-- | the mean of a matrix with data series in rows
meanMatrix :: (Container Vector a, Num (Vector a), Element a) => Matrix a -> Sample a

-- | the variance of a list of vectors
varianceList :: (Container Vector a, Floating (Vector a)) => [Sample a] -> Sample a

-- | the variance of an array of vectors
varianceArray :: (Container Vector a, Floating (Vector a)) => Samples a -> Sample a

-- | the variance of a matrix with data series in rows
varianceMatrix :: (Container Vector a, Floating (Vector a), Element a) => Matrix a -> Sample a


-- | Principal Components Analysis
module Numeric.Statistics.PCA

-- | find the n principal components of multidimensional data
pca :: Array Int (Vector Double) -> Double -> Matrix Double

-- | perform a PCA transform of the original data (remove mean) | Final =
--   M^T Data^T
pcaTransform :: Array Int (Vector Double) -> Matrix Double -> Array Int (Vector Double)

-- | perform a dimension-reducing PCA modification
pcaReduce :: Array Int (Vector Double) -> Double -> Array Int (Vector Double)


-- | Independent Components Analysis
--   
--   implements the FastICA algorithm found in:
--   
--   <ul>
--   <li>Aapo Hyvrinen and Erkki Oja, Independent Component Analysis:
--   Algorithms and Applications, <i>Neural Networks</i>, 13(4-5):411-430,
--   2000</li>
--   </ul>
--   
--   
--   <a>http://www.google.com/url?sa=t&amp;source=web&amp;cd=2&amp;ved=0CBgQFjAB&amp;url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.79.7003%26rep%3Drep1%26type%3Dpdf&amp;ei=RQozTJb6L4_fcbCV6cMD&amp;usg=AFQjCNGClLIB9MAvbrEj45SyUx9cYubLyA&amp;sig2=hg5Wnfy3dLPkoIc1hqSfjg</a>
module Numeric.Statistics.ICA

-- | sigmoid transfer function
sigmoid :: Double -> Double

-- | derivative of sigmoid transfer function
sigmoid' :: Double -> Double

-- | remove the mean from data
demean :: Array Int (Vector Double) -> (Array Int (Vector Double), Vector Double)

-- | whiten data
whiten :: Array Int (Vector Double) -> Double -> (Array Int (Vector Double), Matrix Double)

-- | perform an ICA transform
ica :: Int -> (Double -> Double) -> (Double -> Double) -> NormType -> Double -> Int -> Array Int (Vector Double) -> (Array Int (Vector Double), Matrix Double)

-- | ICA with default values: no dimension reduction, euclidean norms, 16
--   sample groups, sigmoid
icaDefaults :: Int -> Array Int (Vector Double) -> (Array Int (Vector Double), Matrix Double)