Table of Contents

Class: SVDEOFs svdeofs.py

Class implementation of the EOF routines

Methods   
MCTest
__init__
bartlettTest
eigenvalues
eofs
eofsAsCorrelation
eofsAsExplainedVariance
northTest
pcs
projectField
reconstructedField
totalAnomalyVariance
unreconstructedField
varianceFraction
  MCTest 
MCTest (
        self,
        subsamples,
        length,
        neofs=None,
        )

Monte Carlo test for the temporal stability of the EOFs.

Parameters:

subsamples
Number of Monte Carlo subsamples to take
lenght
Length of each subsample (obviously less than the total number od time records)

Optional parameters:

neofs
Number of EOFs to perform the test on. Defaults to the number selected by a 70% variance stopping rule (See pyclimate.tools.getneofs).

Returns a NumPy array containing in each row the congruence coefficient of each subsample obtained patterns with those obtained for the whole dataset.

  __init__ 
__init__ ( self,  dataset )

Contructor for SVDEOFs

Argument:

dataset
NumPy array containing the data to be decomposed. Time must be the first dimension. Several channel dimensions are supported.
  bartlettTest 
bartlettTest ( self )

Performs the Bartlett test on the last p-k eigenvalues

It is a test on the last p-k eigenvalues being the same. It relies on the statistic:

/ SUM lambda_j \

-nu SUM log(lambda_j) + nu(p-k) log| -------------- |

\ p - k /

(SUMmation goes from j=k+1 to p) that is supposed to be distributed following the chi square distribution with nu=(p-k+1)(p-k+2)/2 degrees of freedom.

This method returns a tuple (chi,chiprob) with:

chi
A NumPy array with the Bartlett statistic for k = 1 to p. (length: p-1)
chiprob
the probability associated to that chi value
  eigenvalues 
eigenvalues ( self )

The decreasing variances associated to each EOF

  eofs 
eofs ( self,  pcscaling=0 )

Returns the empirical orthogonal functions

Optional argument:

pcscaling
Sets the scaling of the EOFs. Set to 0 for orthonormal EOFs. Set to 1 for non-dimensional EOFs. Defaults to 0.
Exceptions   
pex.ScalingError( pcscaling )
  eofsAsCorrelation 
eofsAsCorrelation ( self )

The EOFs scaled as the correlation of the PC with the original field

  eofsAsExplainedVariance 
eofsAsExplainedVariance ( self )

The EOFs scaled as fraction of explained variance of the original field

  northTest 
northTest ( self )

Performs the North test returning the estimated sampling errors

Details:

North et al. (1982) Sampling errors in the estimation of empirical orthogonal functions, Monthly Weather Review 110:699-706

  pcs 
pcs ( self,  pcscaling=0 )

Returns the principal components as the columns of an array

Optional argument:

pcscaling
Sets the scaling of the PCs. Set to 1 for standardized PCs. Defaults to 0.
Exceptions   
pex.ScalingError( pcscaling )
  projectField 
projectField (
        self,
        neofs,
        X=None,
        )

Projects a field X onto the neofs leading EOFs returning its coordinates in the EOF-space

  reconstructedField 
reconstructedField ( self,  neofs )

Reconstructs the original field using neofs EOFs

  totalAnomalyVariance 
totalAnomalyVariance ( self )

The total variance associated to the field of anomalies

  unreconstructedField 
unreconstructedField (
        self,
        neofs,
        X=None,
        )

Returns the part of the field NOT reconstructed by neofs EOFs

Argument:

neofs
number of EOFs for reconstructing the field

Optional argument:

X
The field to try to reconstruct. Defaults to the data field used to derive the EOFs.
  varianceFraction 
varianceFraction ( self )

The fraction of the total variance explained by each principal mode


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