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- function f = projectionmatrix(X)
- % function f = projectionmatrix(X)
- %
- % <X> is samples x parameters
- %
- % what we want to do is to perform a regression using <X>
- % and subtract out the fit. this is accomplished by
- % y-X*inv(X'*X)*X'*y = (I-X*inv(X'*X)*X')*y = f*y
- % where y is the data (samples x cases).
- %
- % what this function does is to return <f> which has
- % dimensions samples x samples. to accomplish this,
- % we rely heavily on olsmatrix.m.
- %
- % if <X> has no parameters, the output of this function is 1.
- %
- % history:
- % - 2013/08/18 - in the cases of empty <X>, we now return 1 instead of [].
- %
- % example:
- % x = sort(randn(100,1));
- % x2 = projectionmatrix(constructpolynomialmatrix(100,0:1))*x;
- % figure; hold on; plot(x,'r-'); plot(x2,'g-');
- % handle corner case
- if isempty(X)
- f = 1;
- return;
- end
- % do it
- f = eye(size(X,1)) - X*olsmatrix(X);
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