Double integral on array

I have a function dependent on both xp and t, which I need integrated over a meshgrid of X,Z. This is a slightly simplified version of the equation:

z=-0.000150:0.000005:0;

x=0.000300:0.000005:0.000100;

[X,Z]=meshgrid(x,z);

syms xp

syms t

F=@(xp,t) ((1/t).*(exp((-1).*(((X-xp).^2)+(Z.^2))/(4.*t))));

I need to integrate t between 0 and 0.0002, and xp between 0 and 0.000100 across the X,Z array. I know I can make a single integral ArrayValued, but I can't work out the best way to do the double integral. All suggestions welcome! Thanks!

Answer 1

[Star Strider]

I would just use trapz:

z=-0.000150:0.000005:0;
x=0.000300:-0.000005:0.000100;

[X,Z]=meshgrid(x,z);

F=@(xp,t) ((1./t).*(exp((-1).*(((X-xp).^2)+(Z.^2))./(4.*t))));

Fmtx = F(X,Z);                                                  % Create Matrix 

Fint = trapz(trapz(~(isnan(Fmtx))));                            % Integrate

To use the Symbolic Toolbox, the correct function is int, not integral.

[Torsten]

I thought xp and t were the variables of integration whereas X and Z were constants ...

But maybe I'm mistaken.

Best wishes

Torsten.

[Felicity Freeman]

Torsten, You are right. X and Z are constants, whose values are defined in arrays. The integration variables are xp and t. Felicity

[Star Strider]

For 'ArrayValued' to work, the integrand has to be an actual array.

For example:

A = @(x,y) [x,x+y;x-y,y]; 

Q = integral(@(y) integral(@(x)A(x,y) ,0,2, 'ArrayValued',true), 3,5, 'ArrayValued',true)

That works.