50 lines
2.1 KiB
Mathematica
50 lines
2.1 KiB
Mathematica
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function [LoadingRate, StandardError, ConfidenceInterval] = jackknifeErrorEstimation(this, ovenObj, NumberOfLoadedAtoms)
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n = this.NumberOfAtoms;
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Autocorrelation = zeros(1, n);
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for i = 1:n-1
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FirstTerm = 0;
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SecondTerm = 0;
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for j = 1:n-i
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FirstTerm = FirstTerm + NumberOfLoadedAtoms(j) / j;
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SecondTerm = SecondTerm + (NumberOfLoadedAtoms(i+j)) / (i+j);
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Autocorrelation(i) = Autocorrelation(i) + ((NumberOfLoadedAtoms(j) / j) .*(NumberOfLoadedAtoms(i+j) / (i+j)));
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end
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Autocorrelation(i) = (1/(n-i)) * (Autocorrelation(i) - ((1/(n-i)) * FirstTerm * SecondTerm));
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end
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if Autocorrelation(1)~=0
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Autocorrelation = Autocorrelation./Autocorrelation(1);
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x = linspace(1,n,n);
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[FitParams,~] = fit(x',Autocorrelation',"exp(-x/tau)", 'Startpoint', 100);
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CorrelationFactor = FitParams.tau;
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SampleLength = 2*CorrelationFactor+1;
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NumberOfJackknifeSamples = floor(n/SampleLength);
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CaptureRatioInEachSample = zeros(1,NumberOfJackknifeSamples);
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SampleNumberLimit = min(NumberOfJackknifeSamples-1,5);
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for i=1:NumberOfJackknifeSamples-SampleNumberLimit
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CaptureRatioInEachSample(i) = NumberOfLoadedAtoms(n-ceil((i-1)*SampleLength))/(n-ceil((i-1)*SampleLength));
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end
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MeanCaptureRatio = sum(CaptureRatioInEachSample) / (NumberOfJackknifeSamples-SampleNumberLimit);
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LoadingRate = MeanCaptureRatio * ovenObj.ReducedFlux;
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Variance=0;
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for i=1:NumberOfJackknifeSamples-SampleNumberLimit
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Variance=Variance+(CaptureRatioInEachSample(i) - MeanCaptureRatio)^2;
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end
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StandardError = sqrt(Variance/(NumberOfJackknifeSamples-SampleNumberLimit));
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ConfidenceInterval = LoadingRate + 1.96*StandardError; % 95% Confidence Intervals
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else
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LoadingRate = nan;
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StandardError = nan;
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ConfidenceInterval = [nan nan];
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end
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end
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