how to check the direction of a plot (monotonicity)

I would like to check the percentage of data going forward instead of going backward in a data. For example in the following images:

the data should go from left to right, but for the second image, we can see that few data goes backward before it goes forward again.

1) I would like to check the percentage of the data forward in the overall data to check the monotonicity of the plot.

2) i would like to set a reference line, at different angle. for example, the below image can be seen at 0 degree from x axis. i would like to be able to set the reference line to perhaps 45 degree and see if teh monotinicity value of the plot would change if i change the angle. (because by rotating the axis, the monotonicity behaviour will change, where the data will look like it goes in forward direction instead of backward again

Answer 1

[John D'Errico]

Assuming that x is in increasing order, then something like this:

sum(diff(y) >= 0)/(numel(y) - 1)

will suffice to yield the relative fraction of points on the curve that lie in increasing order. Easily fixed if the points are not sorted for increasing x.

[Sharah]

x and y is not in increasing order. it will be either decreasing or increasing depending on the performance. so here basically what need to be checked of the relationship between y-x is always in increasing order or not

[John D'Errico]

So whats the problem?

Just compute

d = diff(y)./diff(x);

If ANY of diff(x) == 0, then the curve is never monotone anyway. So you need for all of the elements of d to have the same sign and to be finite.

Test that all the elements of d are positive, OR they are all negative, AND they are all finite (not either inf or nan).

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