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Module: svd svd.py

SVD decomposition of two fields

Imported modules   
import LinearAlgebra
import Numeric
import Scientific.Statistics
import pyclimate.mctest
import pyclimate.mvarstatools
import pyclimate.pyclimateexcpt
import pyclimate.tools
import sys
import whrandom
Functions   
CSCF
SCF
getcoefcorrelations
getcoefs
getvector
heterogeneousmaps
homogeneousmaps
makemctest
numberofvectors
svd
  CSCF 
CSCF ( sigmas )

Cumulative squared covariance fraction

Argument:

sigmas
Covariances returned by svd()

Returns a Numeric Array with the Cumulative squared covariance fraction

  SCF 
SCF ( sigmas )

Get the squared covariance fraction of the modes

Argument:

sigmas
Covariances returned by svd()

Returns a Numeric array with the Squared covariance fraction

  getcoefcorrelations 
getcoefcorrelations ( scoefs,  zcoefs )

Correlation between the temporal expansion coefficients

  getcoefs 
getcoefs ( data,  svectors )

Temporal expansion coefficients

Arguments:

data
Data to project onto the singular vectors, usually the same NumPy used to get the vectors.
svectors
Singular vectors (left or right) as returned by svd()
  getvector 
getvector ( svectors,  ivect )

Get the ivect-eth singular vector.

Arguments:

svectors
Matrix of eigenvectors returned by svd (P or Q)
ivect
The order of the eigenvector that must be returned

Returns the ivect-ieth spatial pattern

  heterogeneousmaps 
heterogeneousmaps ( xdata,  ycoefs )

Heterogeneous correlation maps

Arguments:

xdata
Data to be represented as heterogeneous correlation
ycoefs
Temporal expansion coefs to correlate with xdata. To get an heterogeneous map they must be left-xdata and right-ycoefs or right-xdata and left-ycoefs.
  homogeneousmaps 
homogeneousmaps ( data,  svectors )

Homogeneus correlation maps

Arguments:

data
Data to be represented as homogeneous correlation
svectors
Correspondent singular vectors as returned by svd()
  makemctest 
makemctest (
        Umaster,
        Vmaster,
        ldata,
        rdata,
        itimes,
        ielems,
        )

Monte Carlo test on the congruence of the singular vectors

Arguments:

Umaster
Left singular vectors as returned by svd()
Vmaster
Right singular vectors as returned by svd()
ldata
Left data field
rdata
Right data field
itimes
Number of Monte Carlo runs
ielems
Number of records in each Monte Carlo subsample
Exceptions   
excpt.SVDSubsetLengthException(vectors, len(Vmaster [ 0 ] ) )
  numberofvectors 
numberofvectors ( svectors )

Number of eigenvectors according to our storage rules.

Arguments:

svectors
Matrix of eigenvectors returned by svd() (P or Q)
  svd 
svd ( sfield,  zfield )

Given two fields, get the SVD of their covariance matrix.

Arguments:

sfield
Input left field
zfield
Input right field

Returns a tuple (P,S,Q) with:

P
The left singular vectors.
S
The covariance of each of the modes.
Q
The right singular vectors
Exceptions   
excpt.SVDLengthException(len( sfield ), len( zfield ) )

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