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Double integral on array

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Felicity Freeman
Felicity Freeman el 11 de Jul. de 2016
Comentada: Star Strider el 11 de Jul. de 2016
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!

Respuestas (1)

Star Strider
Star Strider el 11 de Jul. de 2016
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.
  3 comentarios
Felicity Freeman
Felicity Freeman el 11 de Jul. de 2016
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
Star Strider el 11 de Jul. de 2016
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.

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