How do you find the intersection points of two functions?

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Dan Teep
Dan Teep am 7 Nov. 2013
Kommentiert: Elina Nikolopoulou am 28 Dez. 2021
My problem tells me to plot and then find and print the points of intersection for x=[2:7]. I already sought help and they explained that I should use 'find' and then the '==' to find where the output match. Sounded simple enough but I'm getting "Empty Matrix: 1-by-0" as the answer. Any one know what I'm doing wrong or a better way?
Also, any idea how I'd then go about using a "for - while" loop to find every intersection? I'm taking it one problem at a time though.
Here's my script so far:
% clear all windows and variables
clc
% Declare an array for the values of x
x=[2:7];
% Input the given functions
f1=@(x) 90.*exp(-x);
f2=@(x) 3*sin(2*pi*x);
% Graph the functions in the same window
fplot(f1,[2,7],'b')
hold on
fplot(f2,[2,7],'r')
grid on
title('Finding Intersections of Functions')
xlabel('Input Values (x)')
ylabel('Ouput Values (f)')
% Find the first intersection
f1a=90.*exp(-x);
f2a=3*sin(2*pi*x);
find(f1a==f2a)
  2 Kommentare
ankit kumar
ankit kumar am 5 Apr. 2018
is there anyway i can give a txt file including x and y axis value and can find how many times a curve is crossing through a threshold and also to note down the x values.
Elina Nikolopoulou
Elina Nikolopoulou am 28 Dez. 2021
How do i keep the Y and the X coordinates of the intersections in separate arrays (one for the X and one for the Y coordinates) ???

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Antworten (3)

Andrei Bobrov
Andrei Bobrov am 7 Nov. 2013
Bearbeitet: Andrei Bobrov am 7 Nov. 2013
EDIT
f1=@(x) 90.*exp(-x);
f2=@(x) 3*sin(2*pi*x);
f = @(x)f1(x)-f2(x);
xx = 2:.1:7;
t = f(xx) > 0;
i0 = find(diff(t(:))~=0);
i0 = [i0(:)';i0(:)'+1];
n = size(i0,2);
xout = zeros(n,1);
for jj = 1:n
xout(jj) = fzero(f,xx(i0(:,jj)));
end
  2 Kommentare
Mathijs Frenken
Mathijs Frenken am 27 Nov. 2018
Thank you for your answer. However, you realize you are not the only one that reads your code right? It's actually unreadable.

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Alexander Efremov
Alexander Efremov am 7 Nov. 2013
Bearbeitet: Alexander Efremov am 7 Nov. 2013
There is a fancy contribution on "File Exchange" which appeared in the Pick of the week. This should help.
Syed Riza
Syed Riza am 31 Jul. 2016
Bearbeitet: Walter Roberson am 31 Jul. 2016
Hello Dan Teep; you can find your answer in this modified code
% Declare an array for the values of x
x=linspace(2,7,1200);
% Input the given functions
f1=@(x) 90.*exp(-x);
f2=@(x) 3*sin(2*pi*x);
% Graph the functions in the same window
fplot(f1,[2,7],'b')
hold on
fplot(f2,[2,7],'r')
grid on
title('Finding Intersections of Functions')
xlabel('Input Values (x)')
ylabel('Ouput Values (f)')
% Find the x-cordinates of intersecting points
f1a=90.*exp(-x);
f2a=3*sin(2*pi*x);
Intersections=find(abs(f1a-f2a)<=(0.05));
X_Values=x(Intersections)
  2 Kommentare
Maya Priveetra
Maya Priveetra am 9 Mär. 2017
Hi can I know why you (abs(fla-f2a)<=(0.05))
Like what does it do especially the 0.05
Adeel Yousuf
Adeel Yousuf am 13 Feb. 2019
He has used a tolerance value of 0.05 as the dataset contains floating point values. We can keep tolerance as small as it seems suitable (like: 1e-4). It's meant to "detect" the closeness of 2 floating point values. Moreover in simple words, we need to make MATLAB determine if 60.2745 is the same as 60.274 or not? So for that we can use threshold/tolerance of 0.001.

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