Need advise: Is my implementation good ?

Hi, is my MATLAB code (please look below in my EDIT) good for solving this problem?

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This was the original question:

Hello, I have a question concerning differentiation and integration of multivariate functions. I am tryling to implement this in MATLAB:

1) We have a function in two variables, for example f(x,y):= x^2 exp( -(x-y)^2 )

2) First I want to differentiate it several times wrt to the second variable, lets say g(x,y) := (d/dy)^5 f(x,y)

3) Afterwards I fix y and integrate wrt to x. For example integrate g(x,0) over (-\infty,\infty)

My approach was to calculate the function g by hand and do the integration wrt to x with quadgk. Due to the fact that I need many different orders of derivatives this is really ineffective ... Can anyone please help me out ? Thanks !!

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EDIT: The way I think it should work. MATLAB-Code:

syms x y;

fun =  x.^2 exp( -(x-y).^2 );

for j=0:10;
    FUNC = inline(diff(fun,y,j));
    L = @(x) FUNC(x,0);
    quadgk(L, -inf, inf,'RelTol',1e-8,'AbsTol',1e-12)
end;

Is this a good way? Any opinions of advanced MATLAB users ? Thanks

Answer 1

[Alan Weiss]

Do you have Symbolic Math Toolbox?

If not, are you supposed to differentiate and integrate numerically or symbolically?

Alan Weiss

MATLAB mathematical toolbox documentation

[Oscar]

Hello,

I have MATLAB 7.8.0 ... I only used symbolic differentiation in this way A=inline(diff(f,z,4)). Due to the fact that I bought a MATLAB version from my university, I think that it is only a standard student edition.

In my case, the derivative of the function is not hard to calculate by hand. The function f(x,y):= x^2 exp( -(x-y)^2 ) serves as a good example. The case that I am working has a similar structure, but it is not possible to find a recursion formula for the derivatives. So lets stick to the function f as defined above.

I have to integrate the y-derivatives (of order 1 to N ) evaluated at y=0 over the whole real line. That is why I thougt it would be better to do symbolic differentiation at first. I want to proceed like this:

1) We put: f = @(x,y) x.^2 exp( -(x-y).^2 )

2) We put: g_k(x,y) := (d/dy)^k f(x,y)

3) We define the integrad like this: INTk = @(x) g_k(x,0)

4) We do the integration: quadgk(INTk, -inf, inf,'AbsTol',1e-12)

This is all really informal and I just can't get a working code ... Is the idea ok, or would you do it differently? Due to the fact that I have very little experience in using MATLAB I would be very thankful, if anyone could help me to implement this procedure.

With best regards, Oscar