how to find the inflection point of a curve in matlab

hi....does anyone know how to find the inflection point of a curve in matlab? any suggestion is highly appreciated..

[Robert]

Is your function defined by an equation or a list of points? In other words, are you looking for an analytical or numeric approach?

[cloudy snow]

I'm very new to Matlab. I've some data about copper foil that are lists of points of potential(X) and current (Y) in excel . The purpose is to draw curves and find the inflection points of them..After finding the inflection points, the value of potential that can be used to get better quality of current will be defined for future use. I plotted the curves , but i don't know how to find the inflection points. Thank you.

[Image Analyst]

cloudy, you forgot to show us your data.

What Robert is asking is if you want to find the point off the digitized numerical data (array elements), or if you fitted your data to some kind of analytical equation, like a Boltzmann or a Cauchy curve or something like that. If you have parameters of a theoretical equation, you can sometime just get the inflection point from the mathematical equation of the second derivative of the curve.

[Star Strider]

‘cloudy’ included it in an Answer. I attached it (as ‘cloudy snow 30ppmGE.xlsx’) to my Comment to my Answer.

Answer 1

[Star Strider]

If your curve are data (not calculated by a function) I would use the gradient function to calculate the derivative. To find the zero-crossing of the derivative, you can either use a threshold test, or if appropriate for your derivative, the interp1 function.

[cloudy snow]

Thanks so much for your fast reply.. i did as you said by using gradient function and interp1 function...but I got an error message Error using griddedInterpolant The grid vectors are not strictly monotonic increasing.

Error in interp1 (line 186) F = griddedInterpolant(X,V,method); How could I solve it? Could you please help me to overcome it?... Thank you...

[Star Strider]

I would have to have your data to see what the problem is.

Use the ‘paperclip’ icon button to upload the file.

[Star Strider]

‘cloudy snow’s’ Answer moved here:

Here is the data I have got error.... Looking forward to your speedy reply...Thanks...

[Star Strider]

Even when I plot and analyse the derivatives on an interpolated version of your data, I don’t find any true inflection points in it:

[d,s,r] = xlsread('cloudy snow 30ppmGE.xlsx');
I = d(:,1);
E = d(:,2);

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector

Istats = [mean(diff(I))  std(diff(I))];                                 % Determine If Data Are Regularly Sampled

Iv = linspace(min(I), max(I), length(I)*100);
Ev = interp1(I, E, Iv, 'pchip');

dEdI = gradient(Ev, mean(diff(Iv)));
Iv_zci = zci(dEdI);
Iv_zc = dEdI(Iv_zci) < 0;

d2EdI2 = gradient(dEdI, mean(diff(Iv)));

figure(1)
plot(Iv,Ev);
hold on
plot(Iv, dEdI)
plot(Iv, d2EdI2)
hold off
grid
axis([xlim    -200  200])
legend('I(E)', '^{dI}/_{dE}', '^{d^2I}/_{dE^2}')

What do you want to do?

[cloudy snow]

 Thank you so much for your help...I' m very sorry I forget to say that the values of current must be changed into negative values from positive values... Actually, I don't know the properties of potential and current for copper foil production...My friend gave me  those data to find the inflection points and he said to change current values into negative before finding the points...Can Changing current into negative values change the result? I apologize for inconvenience.

[cloudy snow]

Sir, the figure I want is as shown in attached photo...I have many data files like I've sent to you...I did as your suggestion to use gradient and interp1 functions ... but I have got error message for that one..

[cloudy snow]

I'm sorry...I think there was no photo in previous comment...here is the photo...

[Star Strider]

The sign change does make a difference, in addition to which I now know the correct independent and dependent variables. (See: Draw tangent line in step response ?)

I have no idea how you chose that one point. I ran my previous analysis in the link with your data, and I still cannot identify any true inflection points that corresponds to that point. I did this even after using polyfit to smooth out the noise. (I got an acceptable fit, but this did not permit the identification of the point you plotted.)

This is the best I can do:

[d,s,r] = xlsread('cloudy snow 30ppmGE.xlsx');
I = -d(:,1);                                                    % Current
E = d(:,2);                                                     % Potential

t = E(E<=0);
y = I(E<=0);

[b,S,mu]  = polyfit(t, y, 6);
fy = polyval(b,t,S,mu);
y = fy;

d1y = gradient(y,t);                                            % Numerical Derivative
d2y = gradient(d1y,t);                                          % Numerical Second Derivative

t_infl = interp1(d1y, t, max(d1y));                             % Find ‘t’ At Maximum Of First Derivative
y_infl = interp1(t, y, t_infl);                                 % Find ‘y’ At Maximum Of First Derivative
slope  = interp1(t, d1y, t_infl);                               % Slope Defined Here As Maximum Of First Derivative
intcpt = y_infl - slope*t_infl;                                 % Calculate Intercept
tngt = slope*t + intcpt;                                        % Calculate Tangent Line

figure(1)
plot(t, y)
hold on
plot(t, fy)
plot(t, d1y, '-.m',    t, d2y, '--c')                           % Plot Derivatives (Optional)
plot(t, tngt, '-r', 'LineWidth',1)                              % Plot Tangent Line
plot(t_infl, y_infl, 'bp')                                      % Plot Maximum Slope
hold off
grid
legend('y(t)', 'y(t) Fit', 'dy/dt', 'd^2y/dt^2', 'Tangent', 'Location','E')
axis([xlim    min(min(y),intcpt)  ceil(max(y))])

Your data do not otherwise have anything that I can identify as an inflection point. If you have a mathematical model of the process that produced your data that you can fit to it using nonlinear regression techniques, that could provide a way to calculate the inflection points. I cannot do it from your data and get any point in the region of the red ‘*’.