plot a tangent line of zero point

Hi all,

I am kinda new to matlab.. I have a x-y data and would like to plot a zero-point tangent to the curve which I have...

I have checked several old codes, but not working with my data,

Could anyone please help me ?

I already attched the data and code (which I already got it from here, but have no idea why it is not giving me what I wanna ??

Thanks,

clearvars
clc; 
close all 
%% READ DATA FROM EXCEL 
data    =   xlsread('matlab_1.xlsx','Sheet2');
x    =   data(:,1); 
y    =   data(:,2);  
%% PLOTTING TANGENT 
h = mean(diff(x));
dy = gradient(y, x);                                         % Numerical Derivative
[~,idx] = max(dy)                                          % Index Of Maximum
idx-1
b = [x([idx,idx+1]) ones(2,1)] \ y([idx,idx+1]);            % Regression Line Around Maximum Derivative
tv = [-b(2)/b(1); (1-b(2))/b(1)];                               % Independent Variable Range For Tangent Line Plot
f = [tv ones(2,1)] * b;                                         % Calculate Tangent Line
figure 
plot(x,y);
hold on
plot(tv, f, '-r')                                               % Tangent Line
plot(x(idx), y(idx), '.r')                                      % Maximum Vertical
hold off
grid

[Star Strider]

These variables don’t exist:

plot(disp(idx), load(idx), '.r') % Maximum Vertical

If they’re important to the code, please define them.

They also overshadow the disp and load functions, so it would be best to rename them as well.

[Walter Roberson]

dy = gradient(y, h);                                         % Numerical Derivative

No, that is wrong. You should be using

dy = gradient(y, x);                                         % Numerical Derivative

If you want to then make this into something equally spaced, then use interp1() on dy

[Mark Sc]

@Walter Roberson

Thank you so much,however still give me wrong curve at all, as attached two pictures( old presents the current codewith red line

instead, I would like to have the blue line in the neww_plot figure...

Hope you could guide or recommend me with something that could work with any data

[Star Strider]

@Mark Sc — Your data are extremely noisy, and your code happens to choose the maximum slope of the noise. (They are also not sampled even close to uniformly.) The maximum slope is not actually an inflection point, since the data appeare to be approximately linear, simply the maximum slope of a noisy signal. After using resample on the signal (with a sampling frequency of 400) and filtering out the noise (lowpass with a cutoff of 8 and choosing an elliptic filter), the maximum slope is part of the initial transient response at the third data pair. I doubt that there is any other inflection point in the signal, or that the initial transient response could be considered an inflection point, however I do not know what the data are or what you want to do with them.

[Mark Sc]

@Star Strider

Thanks for your reply.

Actually it is a data from experimental work... I just wanna to draw a tangent line

I tried the following code and it seems ok.. I just wanna a bit of translation of the tangent line as attached titled desired_fig

Hope you could understand what I wanna and help me!

Wanna the same line but a bit translated (as presented in the bold blue line)

Looking to hearing from you

slopp=polyfit(x,y,1)
x1=x;
y1=polyval(slopp,x1)
figure
plot(x,y,'-')
hold on
plot(x1,y1)
hold off

Thanks,

Answer 1

[Star Strider]

That should work, and it appears to be appropriate.

Try something like this —

clearvars
clc; 
close all 
%% READ DATA FROM EXCEL 
data    =   xlsread('matlab_1.xlsx','Sheet2');
x    =   data(:,1); 
y    =   data(:,2);  
%% PLOTTING TANGENT 
h = mean(diff(x));
dy = gradient(y, x);                                         % Numerical Derivative
[~,idx] = max(dy)                                          % Index Of Maximum

idx = 1508

idx-1

ans = 1507

b = [x([idx,idx+1]) ones(2,1)] \ y([idx,idx+1]);            % Regression Line Around Maximum Derivative
tv = [-b(2)/b(1); (1-b(2))/b(1)];                               % Independent Variable Range For Tangent Line Plot
f = [tv ones(2,1)] * b;                                         % Calculate Tangent Line
% figure 
% plot(x,y);
% hold on
% plot(tv, f, '-r')                                               % Tangent Line
% plot(x(idx), y(idx), '.r')                                      % Maximum Vertical
% hold off
% grid

slopp=polyfit(x,y,1)

slopp = 1×2

3.4580 0.6735

x1=x;
y1=polyval(slopp,x1);
figure
plot(x,y,'-')
hold on
plot(x1,y1)
hold off
title('Original')

ofst = 1;                                                   % Choose Appropriate Value For 'ofst' ('Offset')

figure
plot(x,y,'-')
hold on
plot(x1,y1+ofst)
hold off
title('Offset')

.

[Mark Sc]

@Star Strider

Thank you so much.. it works fine now, however, May I ask the possbility to have the tangent curve starts from from zero,

I tried with your previous post slope =x(:)\y(:)

but gives me only a horizontal line

[Star Strider]

Sure!

All that is necessary is to concatenate 0 to ‘x1’ in the polyval and plot calls —

% clearvars
% clc; 
% close all 
%% READ DATA FROM EXCEL 
data    =   xlsread('matlab_1.xlsx','Sheet2');
x    =   data(:,1); 
y    =   data(:,2);  
%% PLOTTING TANGENT 
h = mean(diff(x));
dy = gradient(y, x);                                         % Numerical Derivative
[~,idx] = max(dy)                                          % Index Of Maximum

idx = 1508

idx-1

ans = 1507

b = [x([idx,idx+1]) ones(2,1)] \ y([idx,idx+1]);            % Regression Line Around Maximum Derivative
tv = [-b(2)/b(1); (1-b(2))/b(1)];                               % Independent Variable Range For Tangent Line Plot
f = [tv ones(2,1)] * b;                                         % Calculate Tangent Line
% figure 
% plot(x,y);
% hold on
% plot(tv, f, '-r')                                               % Tangent Line
% plot(x(idx), y(idx), '.r')                                      % Maximum Vertical
% hold off
% grid

slopp=polyfit(x,y,1)

slopp = 1×2

3.4580 0.6735

x1=x;
y1=polyval(slopp,[0;x1]);
figure
plot(x,y,'-')
hold on
plot([0;x1],y1)
hold off
title('Original')

ofst = 1;                                                   % Choose Appropriate Value For 'ofst' ('Offset')

figure
plot(x,y,'-')
hold on
plot([0;x1],y1+ofst)
hold off
title('Offset')

If you want the regression to begin at the origin, that requires a slightly different approach —

B = x\y                                 % Force Origin Intercept

B = 3.6013

x1 = [0;x];
y1 = B*x1;

figure
plot(x,y,'-')
hold on
plot(x1,y1)
hold off
title('Original (Origin Intercept)')

figure
plot(x,y,'-')
hold on
plot(x1,y1+ofst)
hold off
title('Offset')

Obviously, the ‘Offset’ line is not going to go through (0,0).

Also, the easiest way to calculate the numerical derivative (in the context that you are using it here) is:

dydx = gradient(y) ./ gradient(x);

That automatically accounts for the intervals of ‘x’ not being constant.

.