Add a 45-degree line in a log-glog plot

Hi

I have a scatter plot as below:

scatter(log(X(:,1)),log(X(:,2)))

I want to add a 45-degree line here. I tried using refline(1,0) and got followint fig. Does it okay or refline can't be used in log-log plot. Please help.

Answer 1

[Voss]

Well, that's not a log-log plot; both axes are linear.

The line does indeed have slope 1. It may not be apparent that the slope is 1 because the x- and y-scales are different. (Notice that the distance from 19 to 20 on the x-axis is about twice as many screen pixels as the distance from 19 to 20 on the y-axis.)

[Md Mia]

Thanks for the clarification. I modified the code as below now:

scatter(log(matrix_f(:,1)),log(matrix_f(:,2)))

set(gca,'xscale','log')

set(gca,'yscale','log')

hold on

refline(1,0);

Now it looks like as below. Is it okay?

So, does the line represent a 45 degree line in the above figure? Or else what can be done. Thanks.

[Voss]

Yes, that is a line with slope 1.

There are infinitely many lines of slope 1 that you could plot. You have plotted the one whose y-intercept is zero, so that along that line, "bottom plate stress" is equal to "shell stress". Is that the one you want?

[John D'Errico]

@Md Mia - your confusion stems from the fact that IF the axis scaling is not the same for x and y, then a 45 degree line will not look like it is 45 degrees.

Let me give you an example.

x = [0 1];
y = [0 1];

Do you agree that the curve represented by those points MUST be a slope of 1? So the line would be perfectly 45 degrees? Now I'll plot those points TWICE, but I'll change the axes.

plot(x,y,'-')
xlim([-1 2])
ylim([0,1])

plot(x,y,'-')
xlim([0,1])
ylim([0,1])
axis equal
axis tight

The second plot was created to have the same spacing on the x and y axes. (Though, strangely, the y axis can sometimes have a different set of tick marks than x. Sigh.)

But do you agree that the first plot does not look remotely as if it has a 45 degree slope? In fact, it does have a perfectly 45 degree slope, but only when viewed properly. Screw around with the axis scaling, and nothing will look right. The data was the same on both plots.

Now, refline(1,0) DOES create a 45 degree line. But if you use it to plot a line on a set of axes where the units are differently scaled, then you get something that will look wrong, no matter what. That does not make it wrong. It is just your perception of wrong-ness that will be the problem.

[Md Mia]

Thanks for the clarifications. I understood now. Changed my scaling and look better although previously also it was okay. Thank you John D'Errico for your excellent explanations.