How to represent function which is defined on different interval?

I'm trying to plot function that defined on different intervals like following.

Let

phi_i(x)=M*(x-(i-1)/M) on [(i-1)/M,i/M] and M*((i+1)/M-x) on [i/M,(i+1)/M] and 0 on other values.

I got values u_1, u_2 ...u_(M-1) and note u(x)=u_1 phi_1(x)+u_2 phi_2(x) +...+u_(M-1) phi(x)

How to plot u(x)?

Answer 1

[Rik]

You can use a for-loop to compose the function out of the parts using anonymous functions:

phi_part_i=@(x,i) ...
    M*(x-(i-1)/M)*( (i-1)/M <x & x<     i/M ) + ...
    M*((i+1)/M-x)*(     i/M <x & x< (i+1)/M );

phi_1=@(x) phi_part_i(x,1);

phi_1_10=@(x) 0;
for m=1:10
    phi_1_10=@(x) phi_1_10(x) + phi_part_i(x,m);
end

[Jinman Park]

Wow!! I've never seen code like this before!!

Thanks for your comment

[Jinman Park]

Can I ask you another question?

I wrote code

j=1;
g=@(x) 0;
phi_part_i=@(x,i) N*(x-(i-1)/N)*( ((i-1)/N <x) & (x<i/N) ) + N*((i+1)/N-x)*((i/N <x) & (x<(i+1)/N));
while(j<=(N-1))
  g=@(x) g(x)+u(j,1)*phi_part_i(x,j);
  j=j+1;
end
fplot(@(x) g(x),@(x) sin(pi*x),[0,1])

But, I got error

 > In matlab.graphics.function.ParameterizedFunctionLine>getFunction
  In matlab.graphics.function.ParameterizedFunctionLine/set.XFunction
  In matlab.graphics.function.ParameterizedFunctionLine
  In fplot>singleFplot (line 243)
  In fplot>@(f1,f2)singleFplot(cax,{f1,f2},limits,extraOpts,args) (line 201)
  In fplot>vectorizeFplot (line 201)
  In fplot (line 163)
  In week6_1_3 (line 27)

Can you give me an advice?

[Walter Roberson]

phi_part_i = @(x,i) N*(x-(i-1)/N).*( ((i-1)/N <x) & (x<i/N) ) + N*((i+1)/N-x).*((i/N <x) & (x<(i+1)/N));

[Jinman Park]

Thanks.

Additionally, I found another mistake that I made.

I modified last part of my code to

   fplot(g(x),@(x) sin(pi*x),[0,1])

[Jinman Park]

Well, I'm really sorry to ask you another one.

I wrote similar code and I followed your advice.

j=1;
g=@(x) 0;
phi_odd_i=@(x,i)-4*(N^2)*((x-((i-1)/(2*N)))*(x-((i+1)/(2*N)))).*( ((i-1)/(2*N) <x) & (x<=(i+1)/(2*N)) );
phi_even_i=@(x,i) 2*(N^2)*((x-((i-2)/(2*N)))*(x-((i-1)/(2*N)))).*( ((i-2)/(2*N) <x) & (x<=i/(2*N)) ) + 2*(N^2)*((x-((i+2)/(2*N)))*(x-((i+1)/(2*N)))).*((i/(2*N) <x) & (x<=(i+2)/(2*N)));
while(j<=(2*N-1))
  if(mod(j,2)==0)
      g=@(x) g(x)+u(j,1)*phi_even_i(x,j);
  else
      g=@(x) g(x)+u(j,1)*phi_odd_i(x,j);
  end
  j=j+1;
end
fplot(g,[0,1],'b')
hold on
fplot(@(x) sin(pi*x),[0,1],'r')
hold off
end

But, I face the same error. Can you give me one more advice?

[Walter Roberson]

Notice how I change the * operators into .* operators in my response to you before. You need to do the same thing.

[Jinman Park]

Thanks.

Your advice worked!!