Module: mvarstatools mvarstatools.py

### Some statistical tools used in multivariate analysis

Utility routines used in several other routines

WARNING!!!!!

These routines are designed on the assumption that the input dataset is arranged as a matrix NxM, with N=samples and M=channels This functions depend critically on the arrangement of the input datasets. This order has been chosen due to an easier implementation of the code:

The datasets are arranged as arrays NxM, where N (rows) is the number of samples and M (rows in the array) is the number of channels (spatial grid cells, for instance)

Imported modules
import LinearAlgebra
import Numeric
import pyclimate.pyclimateexcpt
import pyclimate.tools
import sys
Functions
center
congruence
correlationmatrix
covariancematrix
detrend
standardize
totalvariance
center
center ( dataset )



Returns a centered version (mean along first axis removed) of an array

congruence
congruence ( p1,  p2 )



### Get the congruence coefficient of two spatial patterns

They must be provided as 1-dimensional arrays. If several dimensions are found it returns an array with the congruence along the first dimension.

correlationmatrix
correlationmatrix ( X,  Y )



Compute the (S-Mode) correlation matrix of two datasets

Exceptions
pex.MVSTLengthException(len( X ), len( Y ) )
covariancematrix
covariancematrix ( X,  Y )



Compute the (S-Mode) covariance matrix of two datasets

Exceptions
pex.MVSTLengthException(len( X ), len( Y ) )
detrend
detrend (
dataset,
tvalues,
order=1,
)



### Removes polinomial trends

Given a linear input dataset, detrend it removing a polynomial of order N of type trend(t)=\sum_{i=0}^N a_i t^i

#### Arguments:

dataset
Numpy array with the data to be detrended (along its first dimension)
tvalues
Numpy array with the values of the time coordinate. Its length must be that of the first dimension of dataset

#### Optional arguments:

order
The order of the polinomial to be removed. Defaults to 1 (linear)

The function returns the detrended (LINEAR) dataset and the parameters of the trend in a tuple. Of course, when removing a polynomial of the mentioned type, the mean is also removed !!!

standardize
standardize ( dataset )



Standardized (centered and unit variance) version of an array

totalvariance
totalvariance ( field )



### Returns the total variance of an array

Again, variances along the first dimension of the array are calculated and the variances obtained are added together.