integral2 error message

Suppose I use

D=120, A=3,C=1

pdf = @(x,y) D*power(x,A)*power(1-y,C);

integral2(pdf, 0, 1, 0, 1)

(note that this pdf is defined on {X<Y})

then I get an error message

Error in ABC>@(x,y)D*power(x,A)*power(1-y,C)

Error in integral2Calc>integral2t/tensor (line 237)
            Z1 = FUN(X(VTSTIDX),Y(VTSTIDX)); NFE = NFE + 1;

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 106)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

Error in UPA (line 85)
integral2(pdf, 0, 1, 0, 1)

Please advise.

[Torsten]

Note that your function is separable such that

int = D*integral(@(x)x.^A,0,1)*integral(@(y)(1-y).^C,0,1)

Best wishes

Torsten.

[alpedhuez]

yes but the integral should be on {X<Y}. Please advise.

[Torsten]

D=120;
A=3;
C=1;
fun = @(x,y) D*x.^A.*(1-y).^C;
ymin = @(x) x;
q = integral2(fun,0,1,ymin,1)

Best wishes

Torsten.

[alpedhuez]

Thank you.

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/integral2.html

"The function fun must accept two arrays of the same size and return an array of corresponding values. It must perform element-wise operations."

However, the code line

pdf = @(x,y) D*power(x,A)*power(1-y,C);

does not do that. It does not do element-wise operations, and it fails if the two arrays do not happen to be square (which they typically are not.)

Remember that the * operator in MATLAB is algebraic matrix multiplication, not element-wise multiplication. Element-wise multiplication is the .* operator.

[alpedhuez]

Yes this is what I would like to understand. x, y, A, and C are all scalars. Why will it be a problem?

[Steven Lord]

A and C are scalars by the way you defined them. The x and y inputs with which integral2 calls your function may not be scalars. As Walter quoted from the documentation, with some emphasis added:

"The function fun must accept two arrays of the same size and return an array of corresponding values. It must perform element-wise operations."

integral2 may call your function with scalars. It may call your function with non-scalar vectors. I don't think it will call the function with matrices due to the way it's implemented, but if you've used element-wise operations like .*, ./, .^, etc. it shouldn't matter if it does now or at some point in the future.

[alpedhuez]

I see that the function does not see x and y are scalars at the time of definition. Then how about the restriction to the domain of the integration {X<Y}?

[Steven Lord]

See the "Integrate Triangular Region with Singularity at the Boundary" example on the integral2 documentation page. It shows how to compute the integral over a non-rectangular region.

[alpedhuez]

Let me work on it.

[Walter Roberson]

For X<Y you should reverse the order of integration,

pdf = @(y,x) D*power(x,A)*power(1-y,C);

and then use integral2() with

integral2(pdf, 0, 1, 0, @(y) y)

[alpedhuez]

Thank you very much.