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)
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Imported modules
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import LinearAlgebra
import Numeric
import pyclimate.pyclimateexcpt
import pyclimate.tools
import sys
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Functions
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center
congruence
correlationmatrix
covariancematrix
detrend
standardize
totalvariance
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center
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center ( dataset )
Returns a centered version (mean along first axis removed) of an array
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congruence
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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.
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correlationmatrix
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correlationmatrix ( X, Y )
Compute the (S-Mode) correlation matrix of two datasets
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Exceptions
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pex.MVSTLengthException(len( X ), len( Y ) )
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covariancematrix
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covariancematrix ( X, Y )
Compute the (S-Mode) covariance matrix of two datasets
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Exceptions
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pex.MVSTLengthException(len( X ), len( Y ) )
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detrend
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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)
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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 !!!
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standardize
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standardize ( dataset )
Standardized (centered and unit variance) version of an array
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totalvariance
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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.
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