4d integral in matlab - matlab

Question

I'm trying to evaluate the integral using MATLAB with an equation containing 4 related random variables, thus the boundaries of the integrals are not constant.
There are 2 exponential pdfs, and 2 other hyper exponential , and 1 Reyleigh CDF all multiplied together and with (x - y - z).
I'm trying to evaluate it using integral Q = (#(w) integral3(#(x,y,z,w),xmin,xmax,ymin,ymax,zmin,zmax),wmin,wmax);
I'm getting an error always. this is my code down here :
u_x = 10; % rate!
x_th = .3;
sigma = 1.33;
u_y = 10;
u_w = 100;
a= 1;
fun = #(x,y,z,w) (x - y - z )*u_x*exp(-u_x*x)*u_y*exp(-u_y*y)*((a/(a+1))*(a*u_w)*exp(-a*u_w*w)+((1/(a+1))*(u_w/a))*exp(-u_w*w/a))*((a/(a+1))*(a*u_w)*exp(-a*u_w*z)+((1/(a+1))*(u_w/a))*exp(-u_w*z/a))*(1-exp(-x_th/sigma^2))
xmin = #(y)y;
xmax = #(y,w)y + w;
ymin = 0;
ymax = inf;
zmin = 0;
zmax = #(w) w;
wmin = 0;
wmax = inf;
Q = integral(#(w) integral3(fun,xmin,xmax,ymin,ymax,zmin,zmax),wmin,wmax);
ERROR MESSAGE :
Error using integral3 (line 63)
XMIN must be a floating point scalar.
Error in numerical_int>#(w)integral3(fun,xmin,xmax,ymin,ymax,zmin,zmax)
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 83)
[q,errbnd] = vadapt(#AToInfInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);
Error in numerical_int (line 28)
Q = integral(#(w) integral3(fun,xmin,xmax,ymin,ymax,zmin,zmax),wmin,wmax);

Answer 1

integral3() requires all the lower bounds to be real
number
int() does not, but need to use syms function instead of function
handle
For element-wise calculation use the dot. operator followed by the
concerned operator like
1) * ---> .* 2) / ---> ./ 3) ^ ---> .^
Read this for more information on how to use int() for nd
integral
The code is as follows
syms x y z w
u_x = 10; % rate!
x_th = .3;
sigma = 1.33;
u_y = 10;
u_w = 100;
a= 1;
fun = (x - y - z ).*u_x.*exp(-u_x*x).*u_y.*exp(-u_y.*y)...
.*((a./(a+1)).*(a.*u_w).*exp(-a.*u_w.*w)+((1./(a+1)).*(u_w./a))...
.*exp(-u_w.*w./a)).*((a./(a+1)).*(a*u_w)*exp(-a.*u_w.*z)...
+((1./(a+1)).*(u_w./a))*exp(-u_w.*z./a)).*(1-exp(-x_th./sigma.^2));
xmin = y;
xmax = y + w;
ymin = 0;
ymax = inf;
zmin = 0;
zmax = w;
wmin = 0;
wmax = inf;
% Integrate along x
intx = int(fun, x, xmin, xmax);
% Integrate along y
intxy = int(intx, y, ymin, ymax);
% Integrate along z
intxyz = int(intxy, z, zmin, zmax);
% Integrate along w
intxyzw = int(intxyz, w, wmin, wmax);
value = vpa(intxyzw, 3);
% 2.14e-5