Plot the integral of a discrete function

Good morning, I have to plot the integral of a discrete function (t,df/dt) defined in a file *.txt. I want to plot (t,f). f is an angle. I've tried with the command trapz but it gives only the numeric value of the area. Thanks

Answer 1

[Youssef Khmou]

Trapz function returns a scalar value, numeric primitive can be calculated using the following function :

 function itg=integral(f,dx,smooth);
% INTEGRAL  ANS=INTEGRAL(F,DX) 
%           This function computes the integral of F(X)DX where the integrand
%           is specified at discrete points F spaced DX apart (F is a vector,
%           DX is a scalar).  Simpsons Rule is used, so that the error
%           is O(dx^5*F4). (F4 is the 4th derivative of F).
%
%           If F is a matrix, then the integration is done for each column.
%
%           If F is really spiky, then INTEGRAL(F,DX,'smooth') may
%           provide a better looking result (the result is smoothed
%           with a 3 point triangular filter).
%   

 % Author: RP (WHOI) 15/Aug/92        
 [N,M]=size(f);

 if (N==1 | M==1),

   N=max(size(f));

   itg=zeros(size(f));
   itg(1)=0;                                    % first element
   itg(2)=(5*f(1)+8*f(2)-f(3))*dx/12;           % Parabolic approx to second
   itg(3:N)=(f(1:N-2)+4*f(2:N-1)+f(3:N))*dx/3;  % Simpsons rule for 2-segment 
                                                % intervals

   itg(1:2:N)=cumsum(itg(1:2:N));    % Sum up 2-seg integrals
   itg(2:2:N)=cumsum(itg(2:2:N));

   if (nargin>2),                    % ... apply smoothing
      itg(2:N-1)=(itg(1:N-2)+2*itg(2:N-1)+itg(3:N))/4;
      itg(N)= (itg(N-1)+itg(N))/2;
   end;

 else

   itg=zeros(size(f));
   itg(1,:)=zeros(1,M);                                         
   itg(2,:)=(5*f(1,:)+8*f(2,:)-f(3,:))*dx/12;  
   itg(3:N,:)=(f(1:N-2,:)+4*f(2:N-1,:)+f(3:N,:))*dx/3;  

   itg(1:2:N,:)=cumsum(itg(1:2:N,:));    % Sum up 2-seg integrals
   itg(2:2:N,:)=cumsum(itg(2:2:N,:));

   if (nargin>2),                    % ... apply smoothing
         itg(2:N-1,:)=(itg(1:N-2,:)+2*itg(2:N-1,:)+itg(3:N,:))/4;
         itg(N,:)= (itg(N-1,:)+itg(N,:))/2;
   end;

 end;

Example :

 t=0:0.1:10;
 y=sin(t);
 z=integral(y,0.1);
 figure; plot(t,y,t,z);

Answer 2

[Antonio]

Thanks for the answer.

The code gives me the error

In an assignment A(I) = B, the number of elements in B and I must be the same.

could you apply your code to the real case of study I've attached here?

I need to plot f.

load data_hw1.txt

dx = data_hw1(:,1)

F = data_hw1(:,3) % F=df/dx

ps my homework suggests the trapezoidal integration.

[Youssef Khmou]

the sampling rate is :

DX=dx(300)-dx(299);
FF=integral(F,DX);
figure; plot(dx,F,dx,FF),legend(' F','\int F');

[Antonio]

It gives me error :( I've tried with this code (I need to plot angle in the interval 0deg:360deg. is it correct?

load data_hw1.txt

dx = data_hw1(:,1)

f = data_hw1(:,3);

FF=cumsum(f)

a=FF./10;

for n = 1:1:length(dx)

if a(n,1) < -360

   FF(n)=(a(n,1)+720)

else

   FF(n)=(a(n,1)+360)

end

end

figure(1)

plot(dx,f,dx,FF)