# How do I plot logarithmic error?

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Niek Blikslager on 17 Aug 2020
Commented: J. Alex Lee on 19 Aug 2020
I have data that I want to plot on a log y-scale because it's not linear. When I plot the error, the bars are not of equal length (lower error looks larger) because of the log y-scale. How do I transform the error so it becomes the relative error and I get error bars of equal lengths above and below the datapoints?
I want to plot the error as a shaded area around the main data, so I need not plot a line above and below the main data. How do I calculate these two lines?
I don't calculate the logarithm of my data, I just plot it, and then change the y-axis through:
set(gca,'YScale','log');
Edit:
For clarity a figure of the problem. The dotted lines is the 'data + error', and the 'data - error'. Because of the log scale, the error seems way lager for the 'data - error', eventhough the error margin is equal above and below the data line. How do I transform the error so it has an equal distance between the error above and below the data line? I Hope this is more clear now.
data = [1.0 1.4 1.5 2.6 1.9 1.9 3.6 4.3 9.5 9.2];
error = [1.2 1.1 1.4 2.0 1.5 1.2 2.2 2.6 0.6 0.7];
dataPlus = data + error;
dataMin = data - error; J. Alex Lee on 18 Aug 2020
In log space, spacing is multiplicative, not additive, so you want to express your top and bottom curves as multiples of your base curve
clc;
close all;
clear;
data = [1.0 1.4 1.5 2.6 1.9 1.9 3.6 4.3 9.5 9.2];
err = [1.2 1.1 1.4 2.0 1.5 1.2 2.2 2.6 0.6 0.7];
% above
dataPlus = data + err;
dataPlusMult = dataPlus./data;
% below
dataMinus = data ./ dataPlusMult;
figure(1); cla; hold on;
plot(data,'-')
plot(dataPlus,'--')
plot(dataMinus,'--')
set(gca,'YScale','log')

Niek Blikslager on 19 Aug 2020
This is exactly what I wanted, thanks a lot for the help!
J. Alex Lee on 19 Aug 2020
Just to comment that your plot no longer reflects what you actually wanted to convey, if what you wanted to convey is data +/- err.

J. Alex Lee on 17 Aug 2020
use the log10() function? The question isn't super clear...

Niek Blikslager on 18 Aug 2020
I added some information, I hope the question is more clear now.
J. Alex Lee on 18 Aug 2020
the plot of the data is what it is, you can't change how it looks without changing the error values themselves...