How to convert symbolic expression to numeric?

Question

Jacob 2024-11-26

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2168993-how-to-convert-symbolic-expression-to-numeric

编辑： Torsten 2024-11-27

I am creating a distance function that I will need for convex optimization later. This distance function requires integrating a function of x, x', z, and z' so I am initially dealing with symbolic expressions. The code below produces the desired integrand as its ouput. However, I cannot seem to convert this 1x1 sym output into anything that I use numerically. double, matlabFunction, and sym2poly all just give errors. As a workaround, I've just manually transcriped the resulting formula but that is obviously not an ideal solution. What am I doing wrong here?

syms x y z k_1 k_2 k_3 k_4 k_5 k_6 k_7 k_8 y_0
x = k_1*(y^3) + k_2*(y^2) + k_3*y+k_4;
xprime = 3*k_1*(y^2) + 2*k_2*y + k_3;
% construction of approximate trajectory for z
z = k_5*(x^3) + k_6*(x^2) + k_7*x+k_8;
zprime = 3*k_5*(x^2) + 2*k_6*x + k_7;
integrand = sqrt(1+(zprime*xprime)^2+(xprime)^2);
% performance parameters
Isp = 300; % s
S = 12.56; % m^2
P_min = 540; % kN
P_max = 800; % kN
alpha_min = -10; % degrees
alpha_max = 10; % degrees
beta_min = -10; % degrees
beta_max = 10; % degrees
T_c = 0.7; % s
delta_T = 3; % s
maxdelta_P = 80; % kN
N = 200;
kappa = 0.5;
deltaT_L = 1.5; % s
V_0 = 335; % m/s
theta_0 = -65; % degrees
phi_0 = -6; % degrees
x_0 = 2500; % m
y_0 = 3698; % m
z_0 = 2500; % m
m_0 = 31200; % kg
% target terminal states
V_f = 0; % m/s 
theta_f = -90; % degrees
phi_f = 0; % degrees
x_f = 3232; % m
y_f = 0; % m
z_f = 2646; % m
Ax = [(y_0)^3 (y_0)^2 y_0 1;... 
     (y_f)^3 (y_f)^2 y_f 1;... 
     3*(y_0)^2 2*(y_0) 1 0;...
     3*(y_f)^2 2*(y_f) 1 0];
bx = [x_0; x_f; cos(phi_0)/tan(theta_0); cos(phi_f)/tan(theta_f)];
kx = Ax\bx;
k_1 = kx(1); k_2 = kx(2); k_3 = kx(3); k_4 = kx(4);
% construction of approximate trajectory for z
Az = [(x_0)^3 (x_0)^2 y_0 1;...
     (x_f)^3 (x_f)^2 x_f 1;...
     3*(x_0)^2 2*x_0 1 0;...
     3*(x_f)^2 2*x_f 1 0];
bz = [z_0; z_f; -tan(phi_0); -tan(phi_f)];
kz = Az\bz;
k_5 = kz(1); k_6 = kz(2); k_7 = kz(3); k_8 = kz(4);
integrand_num = matlabFunction(subs(simplify(integrand)))
integrand_num = function_handle with value:
    @(y)sqrt((y.*(-1.216549561249475e-3)+y.^2.*3.400868872575844e-7+5.012027833801532e-1).^2+(y.*(-1.216549561249475e-3)+y.^2.*3.400868872575844e-7+5.012027833801532e-1).^2.*(y.*1.800900185003124e-4-y.^2.*2.185626659078132e-7+y.^3.*4.073285028791622e-11-(y.*5.012027833801532e-1-y.^2.*6.082747806247377e-4+y.^3.*1.133622957525281e-7+3.232e+3).^2.*1.320420657586983e-7+1.379288179511788).^2+1.0)
%simplify(subs(integrand))