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

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Hélène
Hélène 2023-6-20
回答： Hélène 2023-6-21
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!

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采纳的回答

Hélène
Hélène 2023-6-21
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)

更多回答（1 个）

Torsten
Torsten 2023-6-20
编辑：Torsten 2023-6-20
You forgot to initialize x as
x = []
in the second example.
  1 个评论
Hélène
Hélène 2023-6-21
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.

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