How do you do a numerical integration of a delta function in MATLAB?

Say I have a function f(x,y) and a number A. My function g(x,y)=1 when A-f(x,y)>0 and 0 when A-f(x,y)<0 and 0 when A-f(x,y)=0. I would like to do a double integral over x and y (x goes from 0 to 1, and y goes from x-1 to -x+1) of the delta-like function g(x,y).

I am trying to use integral2, but I don't know what function in matlab I could use for g(x,y).

Thanks!

Answer 1

[Star Strider]

You seem to have defined a step (Heaviside) function, not a delta function. The easiest way to do the integration is to integrate separately for ‘A-f(x,y)>0’ and ‘A-f(x,y)<=0’, then sum them.

I don’t understand what ‘g(x,y)’ is doing, because it only appears qualitatively in your description, so I didn’t include it.

[Sonia]

Oh great, thank you, yes it is a heaviside function. I meant say g(x,y) is the heaviside function. I am not sure why I would need to do the integration separately though?

I am using the code (Say my function 'f(x,y) = x^2+y^2):

fun = @(x,y) heaviside(A-(x^2+y^2))
ymax = @(x) 1 - x;
ymin = @(x) -1 + x;

q = integral2(fun,0,1,ymin,ymax)

This seems to work I think.

Thank you!

[Walter Roberson]

Heaviside and Dirac Delta have discontinuities. The integral2() function is not designed to deal with discontinuities. The integral() function can handle some forms of discontinuity provided that you supply waypoints

[Star Strider]

@Sonia — My pleasure!

@Walter — Thank you!

Answer 2

[Walter Roberson]

Sometimes you need to rewrite integral2 in terms of nested integral() so that you can pass in the waypoints option