Why integral2 won't work, is there a solution?

Hello everybody,

In the following code I don't understand why integral2 doesn't work. Could you suggest me a solution to achieve the integration? Currently I am calculating many values with vpa and then I use twice trapz to make it work but it takes really long and the accuracy is not very good...

Thank you in advance

   clear all

WaveFunction = @(x) exp(-x.^2./2)./pi.^(0.25);

expression1 = @(x,p,y) exp(-i.*p.*y).* WaveFunction(x-y./2).* conj(WaveFunction(x+y./2));
syms y
WignerFunction = @(x,p) 1/(2.*pi).* int(expression1(x,p,y),y,-Inf,Inf);

t = isa(WignerFunction,'function_handle') % outputs 1
%vpa(WignerFunction(1,1))                 % outputs the correct value

t = integral2(WignerFunction,-Inf,Inf,-Inf,Inf) % should output 1

Answer 1

[Walter Roberson]

int() returns a symbolic expression, which might or might not contain any free variables. integral() and integral2() can only work with numeric expressions, not symbolic expressions.

If your int() returns a symbolic expression that has no unbound variables, then you can use

WignerFunction = @(x,p) 1/(2.*pi).* double(int(expression1(x,p,y),y,-Inf,Inf));

Answer 2

[Dipak kumar Panigrahy]

clear

clc

syms rtstar

syms rt1 v delta R %or assign numeric values to the variables

p=10;

cdf1=p*tan(delta)*R^2;

cdf2=p*tan(delta)*R^2;

eqn = ss == (int(int(cdf1,rt,rt1,rtstar),e,0,v)-int(int(cdf2,rt,rtstar,rt2),e,0,v));

sol = solve(eqn, rtstar)

can any one tell me how to solve for rstar