Research of inflexion point - Index exceeds the number of array elements.

Hello

As part of a data analysis project, I've written a function to calculate the inflection points of a curve using its derivatives.

The program consists of two functions and a main code. A first basic function calculates the derivatives :

        function F1 = derivee(x1, x2, y1, y2)
            F1 = (y2-y1)/(x2-x1);
            
        end

A second function calculates inflection points using the signs of left, center and right derivatives:

        function [outputArray] = inflexion_point(x, y)
    dg = [];
    dd = [];
    dc = [];
    n = length(x);
    
    dd(1) = derivee(x(2), x(1), y(2), y(1));
    dg(1) = derivee(x(1), x(2), y(1), y(2));
    dc(1) = derivee(x(1), x(3), y(1), y(3));
    
    for i = 2:(n-1)
        dd(i) = derivee(x(i), x(i+1), y(i), y(i+1));
        dg(i) = derivee(x(i-1), x(i+1), y(i-1), y(i+1));
        dc(i) = derivee(x(i-1), x(i+1), y(i-1), y(i+1));
    end
    
    dg(n) = derivee(x(n-1), x(n), y(n-1), y(n));
    
    inflex = [];
    plat = [];
    
    for i = 2:(n-1)
        if dg(i) * dg(i+1) == 0 && y(i) == y(i+1)
            j = i + 1;
            while j < n && dg(j) == 0 && y(j) == y(j+1)
                plat = [plat j];
                j = j + 1;
            end
        elseif dg(i) * dg(i+1) < 0 || dd(i) * dd(i+1) < 0 || dc(i) * dc(i+1) < 0
            inflex = [inflex i];
        end
    end
    
    xinflex = x(inflex);
    yinflex = y(inflex);
    dg  %This six lines are just to try to figure out where the problem is
    dc
    dd
    a=length(dd)
    b=length(dc)
    c=length(dd)
    
    outputArray = [xinflex', yinflex'];
end

I made a first test with a basic data set in my main file:

x=[]
y = [10,9,8,7,6,5,5,6,8,8,7,5,4,3,4,5,6,6,5,5,4,3,2,1,1,1,1,1];
for i = 1 : length(y)
    x = [x i]; %ici, pour construire les x
end
[outputArray] = inflexion_point(x,y);
xinflex = outputArray(:,1);
yinflex = outputArray(:,2);


figure(1)
plot(x,y)
hold on
scatter(xinflex, yinflex)

In the real case, my data are data vectors (X,Y) of length 199, so I created a random vector to generate data for a more consistent test. And then, when I compile, I get the error

Index exceeds the number of array elements. Index must not exceed 198.

lowerBound = 0;  
upperBound = 800;  
y = (upperBound - lowerBound) * rand(1, 199) + lowerBound;
for i = 1 : length(y)
x = [x i]; %ici, pour construire les x
end
[outputArray] = inflexion_point(x,y);
xinflex = outputArray(:,1);
yinflex = outputArray(:,2);
figure(1)
plot(x,y)
hold on
scatter(xinflex, yinflex)

is displayed. In the inflexion_point function, I tried to modify the end indices of the for and while loops by stopping at the previous point, but this didn't change anything and the error "adapted" by becoming :

Index exceeds the number of array elements. Index must not exceed 197.

I don't understand why this code works for one lambda data set and not for another.

Is there a step I've missed or a glaring error in my code?

Thank you in advance for your help!

Answer 1

[Hélène]

Ok I found what the problem was, this line

dg(n) = derivee(x(n-1), x(n), y(n-1), y(n));

was adding an extra term to dg, so dc dd and dg were not the same length. Moreover, in this for loop :

    for i = 2:(n-1)
        if dg(i) * dg(i+1) == 0 && y(i) == y(i+1)
        ...
        end

the loop went to index n-1, but the if condition was looking for the n-th term of dg which didn't exist. I solved the problem by modifiying the last index of the for loop :

        for i = 2:(n-2)

Answer 2

[Torsten]

You forgot to initialize x as

x = []

in the second example.

[Hélène]

Hello,

Thanks for your reply but no, it's initialized, I just forgot this line in the copy/paste of the code I put here.