substituting multiple values in symbolic formula?

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Sharif Khalil
Sharif Khalil 2018-6-29
编辑： Walter Roberson 2018-6-30
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);
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Ameer Hamza
Ameer Hamza 2018-6-30
theta and phi have different lengths. For substitution, they must have equal lengths.
Sharif Khalil
Sharif Khalil 2018-6-30
if they have equal length, how to do the substitution?

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Walter Roberson
Walter Roberson 2018-6-30
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.
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Walter Roberson
Walter Roberson 2018-6-30
编辑：Walter Roberson 2018-6-30
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}) ;

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