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spm_Volterra.m
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spm_Volterra.m
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function [X,Xname,Fc] = spm_Volterra(U,bf,V)
% generalized convolution of inputs (U) with basis set (bf)
% FORMAT [X,Xname,Fc] = spm_Volterra(U,bf,V);
% U - input structure array
% bf - Basis functions
% V - [1 or 2] order of Volterra expansion [default = 1]
%
% X - Design Matrix
% Xname - names of regressors [columns] in X
% Fc(j).i - indices pertaining to input i (and interactions)
% Fc(j).name - names pertaining to input i (and interactions)
%___________________________________________________________________________
%
% For first order expansions spm_Volterra simply convolves the causes
% (e.g. stick functions) in U.u by the basis functions in bf to create
% a design matrix X. For second order expansions new entries appear
% in ind, bf and name that correspond to the interaction among the
% orginal causes. The basis functions for these efects are two dimensional
% and are used to assemble the second order kernel in spm_graph.m.
% Second order effects are computed for only the first column of U.u.
%___________________________________________________________________________
% @(#)spm_Volterra.m 2.3 Karl Friston 02/04/19
% 1st order terms
%---------------------------------------------------------------------------
if nargin == 2, V == 1; end
% Construct X
%===========================================================================
% 1st order terms
%---------------------------------------------------------------------------
X = [];
Xname = {};
ind = {};
Uname = {};
Fc = {};
for i = 1:length(U)
ind = [];
for k = 1:size(U(i).u,2)
for p = 1:size(bf,2)
x = U(i).u(:,k);
d = 1:length(x);
x = conv(full(x),bf(:,p));
x = x(d);
X = [X x];
% indices and regressor names
%-----------------------------------------------------------
str = sprintf('%s*bf(%i)',U(i).name{k},p);
Xname{end + 1} = str;
ind(end + 1) = size(X,2);
end
end
Fc(end + 1).i = ind;
Fc(end).name = U(i).name{1};
end
% return if first order
%---------------------------------------------------------------------------
if V == 1, return, end
% 2nd order terms
%---------------------------------------------------------------------------
for i = 1:length(U)
for j = i:length(U)
ind = [];
for p = 1:size(bf,2)
for q = 1:size(bf,2)
x = U(i).u(:,1);
y = U(j).u(:,1);
x = conv(full(x),bf(:,p));
y = conv(full(y),bf(:,q));
x = x(d);
y = y(d);
X = [X x.*y];
% indices and regressor names
%-----------------------------------------------------------
str = sprintf('%s*bf(%i)x%s*bf(%i)',...
U(i).name{1},p,...
U(j).name{1},q);
Xname{end + 1} = str;
ind(end + 1) = size(X,2);
end
end
Fc(end + 1).i = ind;
Fc(end).name = [U(i).name{1} 'x' U(j).name{1}];
end
end