How to set an axis with arbitrary, but equally spaced, scaling.

Hello,

I am attempting to replicate the following plot in a textbook using my own numerical solver. I am having trouble with replicating the x-axis in the plot for comparison since it is a bit odd. See the axes below:

I am aware that you can use Xtick to choose where ticks are located, but this does not affect the spacing of the ticks such that they are equally spaced like in the example above. The closest I am able to get is shown below:

Log scaling does slightly better, but is still not evenly spaced like I would hope:

Unfortunately I have not been able to find a way to change the scaling to be something other than linear or log. I am using MATLAB R2023a.

Does anyone know a way to create the evently spaced type of scaling seen in the first set of axes?

Answer 1

[John D'Errico]

You could not plot versus the numbers 0,1,2,3, but then set the x-tick labels as you wish?

x = [1/3 1/2 1 inf];
xfake = [0 1 2 3];

y = [2 3 5 7];

plot(xfake,y,'-or')
set(gca,Xtick = [0 1 2 3],XTickLabel = x)

[Zucrode]

Thank you for your response. This is very close to what I want and I am trying to figure out a way to get this to work with my data.

I have an x vector and y vector that are of length 180 and I don't actually have values that land where x is 1/3, 1/2, 1, or inf so I don't think I can just swap in an xfake unless I have a tick for every single datapoint. My range for x starts at 0.2 and goes to 3.2 so it doesnt actually fit with the axes that I am trying to stick it on.

With your method and XTickLabel = [x(1), x(round(length(x)*2/3)), x(round(length(x)*2/3)), x(end)] I get the axes below:

This gives me something evenly spaced, but does not give me the right bounds. I can fix the left hand side of this by limiting my data to only values above 1/3 which gives me this:

I am not sure now how to proceed currently since I cannot map (or more likely do not know how to map) the data directly to the tick values as was done in your example.

[John D'Errico]

Why not? Nothing stops you from plotting your data against any set of values, equally spaced or not, then choosing which of them gets a tick mark, and labeling it as you wish.

[William Rose]

@Zucrode,

You have 180 measured x-y pairs, and the x-values go from 0.2 to 3.2. You want to plot x-values from 0.333 to +Inf. I guess you not want to plot the data whose x-values are below 0.333.

Here is a modified version of @John D'Errico's solution. Measured x values are mapped to fake x values smoothly and monotomically with interp1(...,'pchip'). The y values are plotted versus fake-x-values. The desired ticks and labels are put in place using @John D'Errico's method.

x=linspace(.2,3.2,180); % measured x values
y=x.*x;                 % measured y values
xfake = [0 1 2 3];       % fake x tick mark positions 
xlbl = [1/3 1/2 1 inf]; % tick labels
% next: label values for interpolation purposes
xlblinterp=[1/3 1/2 1 10];
% next: map measured x values to fake x values
xfakeinterp=interp1(xlblinterp,xfake,x,'pchip');
plot(xfakeinterp,y,'-r.')   % plot the data
xlim([0,3])                 % set fake x axis limits
set(gca,Xtick = xfake,XTickLabel = xlbl) % set ticks & labels

Good luck.

[Zucrode]

@William Rose

This method got me what I needed. Thanks!

The plot is looking a bit wobbly, but I expect that is due to the way the non-uniform spacing of my data is interacting with the interpolation and not because of the method. Still pchip seems to work the best.

Thanks to you and @John D'Errico for your help.

[William Rose]

@Zucrode, you are welcome. pchip is smooth and spline is smooth, but spline can be non-monotonic (can go backward).

[Voss]

@Zucrode: A side note: to get the labels aligned to the ticks properly, specify labels as text (i.e., a string array or a cell array of chars) instead of numeric. (Notice how the '1' label appears to be quite a bit to the left of the corresponding tick in the plots above.)

ax = subplot(2,1,1);
x=linspace(.2,3.2,180);
xfake = [0 1 2 3];
xlbl = [1/3 1/2 1 inf]; % numeric labels
plot(interp1([1/3 1/2 1 10],xfake,x,'pchip'),x.*x,'-r.')
xlim([0,3])
set(gca,Xtick = xfake,XTickLabel = xlbl)
title('numeric tick labels (original)')

ax(2) = subplot(2,1,2);
x=linspace(.2,3.2,180);
xfake = [0 1 2 3];
xlbl = string([1/3 1/2 1 inf]); % string labels
plot(interp1([1/3 1/2 1 10],xfake,x,'pchip'),x.*x,'-r.')
xlim([0,3])
set(gca,Xtick = xfake,XTickLabel = xlbl)
title('text tick labels')

The problem is that numeric text labels are stored as a char array, which can add white space, affecting the apparent alignment:

ax(1).XTickLabels

ans = 4x8 char array
    '0.333333'
    '0.5     '
    '1       '
    'Inf     '

Specifying the tick labels as text doesn't have this problem:

ax(2).XTickLabels

ans = 4x1 cell array
    {'0.33333'}
    {'0.5'    }
    {'1'      }
    {'Inf'    }

Also, you may want to use text anyway to be able to do things like this:

figure
x=linspace(.2,3.2,180);
xfake = [0 1 2 3];
xlbl = ["1/3" "1/2" "1" "...Infinity"]; % string labels
plot(interp1([1/3 1/2 1 10],xfake,x,'pchip'),x.*x,'-r.')
xlim([0,3])
set(gca,Xtick = xfake,XTickLabel = xlbl)