allcrossings

Locate all intersections of a pair of functions f1 and f2, on a finite domain
2 Downloads
Updated 2 Mar 2023

View License

ALLCROSSINGS is a rootfinding tool , that is used to locate all points where a pair of functions cross in the plane. It solves for the locations x, where f1(x)==f2(x). As a simple example, here is the use of allcrossings, on the problem sin(x)==cos(x). We expect those solutions happen at the points (n+1/4)*pi. The search was done on the interval [-10,10].
xloc = allcrossings(@sin,@cos,[-10,10])
xloc =
-8.6394 -5.4978 -2.3562 0.7854 3.927 7.0686
If I now divide by pi, we should expect to see solutions that are all off from an integer by exactly 1/4.
xloc/pi
ans =
-2.75 -1.75 -0.75 0.25 1.25 2.25
The tool initially samples the supplied interval at equally spaced points, locating sub-intervals where a crossing must occur, then it uses fzero on that bracketed interval.
ALLCROSSINGS can also be used to identify crossings of a function with a constant. In this example, I used it to locate the points where y=2*x+tan(x) crosses the line y==1, on the interval [0,10].
xloc = allcrossings(@(x) 2*x + tan(x),1,[0,10])
xloc =
0.32919 1.5708 1.9113 4.7124 4.8274 7.854 7.9213
As one should expect though, the function here has singularities, where while it technically crosses the constant line y==1, they are not actually intersections. Those points are easily enough identified though, since wheere the function passes through a discontinuity, we see those points are clearly identified.
fun = @(x) 2*x + tan(x);
fun(xloc)
ans =
1 -1.2093e+15 1 3.5109e+14 1 2.5914e+14 1
I intentionally do not try to remove those locations, since they could technically be called a crossing point.

Cite As

John D'Errico (2024). allcrossings (https://www.mathworks.com/matlabcentral/fileexchange/125585-allcrossings), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2022b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
1.0.0