26 lines
893 B
Matlab
26 lines
893 B
Matlab
function dy=glfdiff_fft(y,t,gam,p)
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% glfdiff_fft - evaluation of O(h^p) GL derivatives with FFT, not recommended
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%
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% dy=glfdiff_fft(y,t,gam,p)
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%
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% y - the samples of the function handle of the original function
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% t - the time vector
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% gam - the fractional order
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% p - the order for the precision setting
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% dy - the fractional-order derivatives, or integrals if gam<0
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% Copyright (c) Dingyu Xue, Northeastern University, China
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% Last modified 28 March, 2017
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% Last modified 18 May, 2022
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arguments, y(:,1), t(:,1), gam(1,1)
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p(1,1){mustBePositiveInteger}=5
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end
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[y,h,n]=fdiffcom(y,t); dy=zeros(n,1);
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g=double(genfunc(p)); T=2*pi/(n-1);
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if y(1)~=0 && gam>0, dy(1)=sign(y(1))*Inf; end
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tt=0:T:2*pi; F=g(1); f1=exp(1i*tt); f0=f1;
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for i=2:p+1, F=F+g(i)*f1; f1=f1.*f0; end
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w=real(fft(F.^gam))*T/2/pi;
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for k=2:n, dy(k)=w(1:k)*y(k:-1:1)/h^gam; end
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end
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