Does anybody know what the exact meaning of the following command?

Does anybody know what the exact meaning of the following command?

       D = @(x,y)f(x,y).*(g(x ,y)>0);

If it possible, answer by an example.

Answer 1

[Matt J]

It defines an anonymous function of x,y. Everything after @(x,y) is the expression that will be evaluated. E.g.,

D=@(x,y) x+y;

D(1,0)

ans = 1

D(1,2)

ans = 3

D(10,13)

ans = 23

[Mehdi]

I mean this part. (g(x ,y)>0)

[Matt J]

It returns logical(1) if g(x,y)>0 and logical(0) otherwise, e.g.

g=@(x,y) x+y;

g(-5, 1)>0

ans = logical
   0

g(-5, 6)>0

ans = logical
   1

[Mehdi]

can we say that D defines f only within the domain of g>0 (limits f to the domain of g>0)?

[Walter Roberson]

Combining:

       D = @(x,y)f(x,y).*(g(x ,y)>0);

evaluates to:

• f(x,y) in locations where g(x,y) is > 0
• NaN in locations where f(x,y) is -inf or +inf and g(x,y) <= 0
• 0 in locations where f(x,y) is finite and g(x,y) <= 0

Most people forget about the inf -> nan problem: most people would summarize D as being 0 where g(x,y)<=0 and f(x,y) where g(x,y)>0 -- but that is wrong for the case of infinite f(x,y)

[Matt J]

can we say that D defines f only within the domain of g>0 (limits f to the domain of g>0)?

No, D is defined for all (x,y), in the sense that any (x,y) pair you give it as input will return a result. The g>0 part is simply to ensure that D=0 whenever g<=0 (assuming f(x,y) is finite for all x,y). Here is a 1D example that may make this clearer:

t=linspace(-1,1,25);
D=@(x) 2*(x>0);

plot(t,D(t),'--x'); axis padded %plot of a step fucntion

As you can see, D(t) returns plottable values for both positive and negative t. It is simply that D(t)=0 for negative t.