substituting multiple values in symbolic formula?

I have this symbolic formula that is a variable of theta and phi, and I want to substitute the theta and phi with the following values in the following formula:

if true
  % code
end
theta = -pi/2:pi/180:pi/2;
phi   = -pi:pi/180:pi; 
U = abs(sin(pi*cos(phi)*sin(theta))*sin(pi*sin(phi)*sin(theta)))^2/(abs(sin((pi*cos(phi)*sin(theta))/2))^2*abs(sin((pi*sin(phi)*sin(theta))/2))^2);

[Ameer Hamza]

theta and phi have different lengths. For substitution, they must have equal lengths.

[Sharif Khalil]

if they have equal length, how to do the substitution?

Answer 1

[Walter Roberson]

First create the symbolic formula. Next create your vectors of values but give them a different name than the variables in the formula. Then use ndgrid to create a grid of values for the two variables and use different variable names still. Finally,

Output = subs(U, {theta, phi}, {thetaGrid, phiGrid}) ;

There is another possibility that does not require creating the grid but it involves two subs calls and being careful about row and column vectors.

[Sharif Khalil]

It also didn't work

syms theta phi real
Psi_x    = k*dx*sin(theta)*cos(phi) + Beta_x;
Psi_y    = k*dy*sin(theta)*sin(phi) + Beta_y;
AF_Field = (sin(Nx*Psi_x/2)/(sin(Psi_x/2)))*...
           (sin(Ny*Psi_y/2)/(sin(Psi_y/2)));
U        = abs((fi*AF_Field)).^2;
Theta    = -pi/2:pi/180:pi/2;       % Elevation Angle (radian)
Phi      = -pi:pi/180:pi;           % Azimuth Angle   (radian)
Urad = subs(U, {theta, phi}, {Theta, Phi}) ;

[Walter Roberson]

I do not see any call to ndgrid?

[Sharif Khalil]

could you please tell me how to do it

[Walter Roberson]

1) First create the symbolic formula.

syms theta phi real
Psi_x    = k*dx*sin(theta)*cos(phi) + Beta_x;
Psi_y    = k*dy*sin(theta)*sin(phi) + Beta_y;
AF_Field = (sin(Nx*Psi_x/2)/(sin(Psi_x/2)))*...
           (sin(Ny*Psi_y/2)/(sin(Psi_y/2)));
U        = abs((fi*AF_Field)).^2;

2) Next create your vectors of values but give them a different name than the variables in the formula.

Theta    = -pi/2:pi/180:pi/2;       % Elevation Angle (radian)
Phi      = -pi:pi/180:pi;           % Azimuth Angle   (radian)

3) Then use ndgrid to create a grid of values for the two variables and use different variable names still.

[thetaGrid, phiGrid] = ndgrid(Theta, Phi);

4) Finally,

Output = subs(U, {theta, phi}, {thetaGrid, phiGrid}) ;

[Sharif Khalil]

Thank you