Numerical integration while keeping the parameters

I have a function which is like f(a,b,x). I want to numerically integrate it with respect to x, for example using quad function and plot the result of integration with respect to parameters a and b. Can someone share how can I achieve this?

[Andrew Newell]

What interval do you want to integrate it over?

[Azar Bakili]

It is a definite integral from zero to infinity, for this reason I started with quadgk.

Answer 1

[Matt Tearle]

Or, if it's actually a function of x with two parameters, and integrated over a fixed interval, then a variation of Andrew's answer will do it

f = @(x,a,b) sin(a*x+b);
x1 = 0;
x2 = pi;
[a,b] = meshgrid(-1:0.1:1);
z = zeros(size(a));
for k = 1:numel(a)
  g = @(x) f(x,a(k),b(k)); 
  z(k) = quad(g,x1,x2);
end
surf(a,b,z)

[Azar Bakili]

Thank you very much, it was really helpful...

[Andrew Newell]

You won the "guess what the problem really is" lottery!

[Matt Tearle]

Hah, sorry. I feel a bit cheap ripping off your solution (although if it's any consolation, I was basically thinking the same approach as you anyway). I upvoted your second answer so it's more visible (given that it's the best answer for this specific question, in the end)

[Andrew Newell]

Don't worry, I don't mind. I think a lot of us get tired waiting to find out what the problem really is and just start offering solutions. We could call it extra content!

[Andrew Newell]

I should add that I didn't think you were ripping off my solution - I assumed that you were just thinking along the same lines as me. And your answer really is the best choice because it is more general. So I voted yours up!

Answer 2

[Andrew Newell]

Now that we know that you are integrating a function f(a,b,x) from zero to infinity, you can do something like this:

f = @(p1,p2,y) exp(-p1.*y.^2-p2.*y);
a = 0.1:.1:1;
b = 0.1:.1:1;
[a,b] = meshgrid(a,b);
g = 0*a;

for i = 1:numel(a)
  fab = @(x) f(a(i),b(i),x);
  g(i) = quadgk(fab,0,Inf);
end
surf(a,b,g)

Answer 3

[John D'Errico]

A numerical integration (i.e., quad) does not allow you to keep some of the parameters symbolic. It would not be a numerical integration if it did would it? And since adaptive routines like quad are designed to use the shape of the function to decide where to put the points, they cannot leave parameters unknown.

So if you really want to keep those parameters unknown, then use the symbolic toolbox for the integration.

Of course, nothing stops you from setting the values of parameters a and b to some fixed values, then doing the integral. Use an anonymous function to do this. Then you could loop over the values of those parameters, and build a plot as you desire.

Answer 4

[Andrew Newell]

I am going to assume that the function you want to integrate is really just a function of x, e.g., g(x), and f(a,b) is the integral of g(x) over the interval [a,b]. Then a code like this would do what you want:

g = @(x) exp(x);

a = -1:.1:1;
b = -1:.1:1;
[a,b] = meshgrid(a,b);
f = 0*a;

for i = 1:numel(a)
   f(i) = quadl(g,a(i),b(i));
end
surf(a,b,f)