How can I shade confidence intervals on a loglog plot?

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Heidi Hirsh on 9 Feb 2020
Commented: Star Strider on 10 Feb 2020
I am trying to plot frequency spectra with 95% confidence intervals (upper and lower bounds). I am using pwelch to calculate power spectra then plotting using loglog. But so far I can only figure out how to plot the confidence intervals at line. I would like to shade the intervals instead. I think I could do so by shading between the power line and the confidence interval lines. Any ideas? This is my current code and I have attached a figure.
Thank you!
figure
clear PxxU F PxxC; [PxxU,F,PxxC] = pwelch(detrend(fixgaps(PK1.zavg_pE(j,pkperiod))),[],[],nfft,288);
h=loglog(F,PxxU,F,PxxC,'--','color','k');
%h=loglog(F,PxxU);
hold on
grid on
set(gca,'fontsize',20)
xlabel('f (cpd)','fontsize',20)
ylabel('S_{along} (days)','fontsize',20)
title('Alongshore Velocity');
set(gca,'fontsize',16)
xlim([.1 10])
% legend('PK','PO','location','southwest')
legend('PK','PK upper','PK lower','location','southwest')

Hiro Yoshino on 10 Feb 2020
x = -10:0.1:10; % between intersections
yy1 =x.^2; %lower function
yy2 = -(x.^2-16); % upper function
x = [x,x]; % repeat x values
yy = [yy1,yy2]; % vector of upper & lower boundaries
fill(x,yy,'g') % fill area defined by x & yy in green
Hope this helps you out!

Heidi Hirsh on 10 Feb 2020
Thank you Hiro! I am wondering how I can apply this to a loglog plot? I think in my case yy = PxxC (the upper and lower confidence bounds).
I tried fill(loglog(F,PxxC,'g')) and loglog(fill(F,PxxC,'g'))
Neither works. Is there another way to combine the fill function with log axes?
Hiro Yoshino on 10 Feb 2020
I'm sure you can find a solution by referring to the documentation! Good luck.

Star Strider on 10 Feb 2020
Try this:
x = linspace(0.1, 10, 100); % Create Data
y = sin(2*pi*x/5)+1.5; % Create Data
err = [y+0.2; y-0.2]; % Create Data
figure
plot(x, y) % Mean
hold on
patch([x, fliplr(x)], [err(1,:), fliplr(err(2,:))], 'g', 'FaceAlpha',0.5) % Shaded Confidence Intervals
hold off
set(gca, 'XScale','log', 'YScale','log')
producing:

Heidi Hirsh on 10 Feb 2020
Thank you Star Strider! I'm getting closer! But something weird is happening for the my yaxis values between ~0.25 and 1.75 where it is shading outside the confidence intervals instead of inside. I'm not sure why.
I incorporated your code like this:
figure
sgtitle('Current Spectra, (August 9 - October 2, NFFT=8192)')
P = .95; %confidence interval
clear nfft; nfft = 8192;
jdo = 1;
j=jdo
hold on
clear PxxU F PxxC; [PxxU,F,PxxC] = pwelch(detrend(fixgaps(PK1.zavg_pE(j,pkperiod))),[],[],nfft,288);
% h=loglog(F,PxxU,F,PxxC,'--','color','k');
loglog(F,PxxU);
patch([F, fliplr(F)], [PxxC(:,1), fliplr(PxxC(:,2))],'g','FaceAlpha',0.5)
grid on
set(gca,'fontsize',20)
xlabel('f (cpd)','fontsize',20)
ylabel('S_{along} (days)','fontsize',20)
set(gca,'fontsize',16)
xlim([.1 10])
Star Strider on 10 Feb 2020
You can most likely resolve that problem by sorting all your data by the independent variable. It appears to be ‘wrapping’, so it returns to fhe first value at the end of the data.