integrate function

Hi!!!

I would like to ask if anyone knows what's the appropriate way to calculate the integral of this function

function out = Gr(u,x,Kt,i)

out= exp(-(u.^2)).*frustration_function2(u,x,Kt,i);

end

The integrating variable is u, and the limits are [1e-4,1e4]

Thanks!!

Answer 1

[Andrei Bobrov]

variant

x = ...;
Kt = ...;
i = ...;

quad(@(u)exp(-(u.^2)).*frustration_function2(u,x,Kt,i),
1e-4,1e4)

[kostas]

The problem is that the frustration_function2(u,x,Kt,i) is also an integral of another function and matlab gives error..

the problem simplified is something like that:

function out =d(x,Kt,i)

out=quad(@(u) u+x+Kt+i,0,1);

end

function out=intd(Kt,i)

out=quad(@(x) exp(x).*d(x,Kt,i),0,1);

end

Matlab gives error when i try to calculate function intd(Kt,i)

[Walter Roberson]

What error does it give?

Are you taking in to account that for quad(), "The function y = fun(x) should accept a vector argument x and return a vector result y, the integrand evaluated at each element of x." ?

[kostas]

the error in the example functions above is

??? Error using ==> plus

Matrix dimensions must agree.

the problem as i think is in the calculation of an integral which contains another integral...

[Walter Roberson]

As I noted above, quad() will pass in vectors for the first argument and expect a vector result. quad() does not, however, define how long the vector will be; it could even be different lengths on different calls.

Your anonymous function in intd will be passed a vector, which it will pass in as "x" to d(). d() will then call quad, which will pass a vector in to the anonymous function there, dummy variable "u". But you have no reason to expect that the length of the vector quad created for "u" will be the same as the length of the vector quad created in the outer call for "x".

You would also run in to problems if Kt or i are not scalars.

You are going to have to recode d, such as to

d = @(x,Kt,i) arrayfun(@(X) quad(@u) u+X+Kt+i,0,1), x);

[kostas]

all the variables are scalars not vectors and i want quad to give just one result..How can i have it?

[Andrei Bobrov]

Hi Walter! Your last comment - the correct answer.

Bellow example, with use Maple Toolbox.

>> intd=@(Kt,i1)quad(@(x)exp(x).*arrayfun(@(X)quad(@(u)u+X+Kt+i1,0,1),x),0,1)

intd =

@(Kt,i1)quad(@(x)exp(x).*arrayfun(@(X)quad(@(u)u+X+Kt+i1,0,1),x),0,1)

>> intd(3,3)

ans =

12.169

>> syms Kt i1 x u

int(exp(x)*int(u+x+Kt+i1,u,0,1),x,0,1)

ans =

1/2 - Kt - i1 + 1/2 exp(1) + exp(1) Kt + exp(1) i1

>> double(subs(ans,[Kt,i1],[3,3]))

ans =

12.169

>>

[Walter Roberson]

Ah good... it was around 4 AM when I wrote that, so I'm glad to see that I didn't do much worse than miss a "(" in the inner anonymous function!

Answer 2

[kostas]

i mean that the result of the quad need to be scalar

[Walter Roberson]

The results of the quad cannot be scalar. My sentence "The function y = fun(x) should accept a vector argument x and return a vector result y, the integrand evaluated at each element of x." was a direct quote from the reference documentation for quad. quad does not just do one evaluation at a time: it selects a number of x and requests that the fun do the evaluation with respect to each of them and return the vector of corresponding answers.