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makenergymat.m
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makenergymat.m
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function E = makenergymat ( n , ca , c , d0 )
%
% E = makenergymat ( n , ca , c , d0 )
%
% MET Analysis Kit, pre-processing. After initial clustering, the next
% step in spike sorting (Fee et al. 1996) is to compute the interface-
% energy matrix, which tabulates the interface energy between every pair of
% spike clusters. The un-normalised energy matrix is returned, as this can
% be easily updated when clusters are later merged. Hence, it is necessary
% to compute connection strengths from these raw energy values.
%
%
% Input
%
% n - Vector of the number of spikes assigned to each cluster. n( i ) is
% the number of spikes in the ith cluster.
%
% ca - Vector of cluster assignments for each spike. ca( i ) returns the
% cluster assignment of the ith spike.
%
% c - S x N matrix of spike waveform components. Spikes are indexed
% across columns, and components over rows. Hence c( : , i ) is the set
% of components for the ith spike waveform.
%
% d0 - Scalar value , the scaling term returned by makspkclust.
%
%
% Output
%
% E - Nc x Nc matrix , where Nc is the number of initial spike clusters.
% Values are tabulated in the upper-triangular section of the matrix
% and along the diagonal. Thus E( i , j ), where i <= j, is the raw
% interface energy between spike clusters i and j.
%
%
% References:
%
% Fee MS, Mitra PP, Kleinfeld D. J Neurosci Methods. 1996 Nov;69(2):175-88.
% Hill DN, Mehta SB, Kleinfeld D. J Neurosci. 2011 Jun 15;31(24):8699-705.
% UltraMegaSort2000, https://neurophysics.ucsd.edu/software.php
%
%
% Written by Jackson Smith - January 2018 - DPAG , University of Oxford
%
%%% Preparation %%%
% The number of clusters
cnum = numel ( n ) ;
% Group spikes by cluster number , for distribution of data in parfor
% loop
C = arrayfun ( @( i ) c( : , ca == i )' , ...
1 : cnum , 'UniformOutput' , false ) ;
% Make vectors of cluster data in the order that they're needed to
% compute energies
npairs = ( cnum ^ 2 - cnum ) / 2 + cnum ;
C1 = cell ( npairs , 1 ) ;
C2 = cell ( npairs , 1 ) ;
k = 0 ;
% In this order, we fill in each row of the upper-triangular portion of
% the energy matrix
for i = 1 : cnum
for j = i : cnum
k = k + 1 ;
C1{ k } = C{ i } ;
C2{ k } = C{ j } ;
end
end
%%% Raw interface Energy %%%
parfor k = 1 : npairs
% Pairwise distances between all spikes in cluster i with those in
% cluster j
d = pdist2 ( C1{ k } , C2{ k } ) ;
% Compute interface energy
e( k ) = sum ( exp( - double( d( : ) ) / d0 ) ) ;
end
% Reshape from a vector into a square matrix , first allocate a matrix
E = zeros ( cnum ) ;
% Then get logical index that fills lower triangular portion. Since
% Matlab indexing is columns first, we will transpose the result to get
% the final energy matrix.
i = tril ( true( cnum ) ) ;
% Assign values
E( i ) = e ;
% And transpose
E = E' ;
%%% Correction %%%
% Index vector of diagonal elements
i = find ( eye( cnum ) ) ;
% Correction of terms , following UltraMegaSort2000's recipe in ss_energy
E( i ) = ( E( i ) - double( n' ) ) / 2 ;
end % makenergymat