not enough input arguments when using symbolic

Dear all,

I am using the symbolic function to calculate the derivative of functions and convert the derivative results by "matlabFunction" . After that, I want to obtain the specific value of the derivatives at initial given points, but the error message "not enough input arguments" appear. How can I fix it? I can input the initial value directly and it works, but it looks waste of time.

Besides, How can I simplify the codes where I calculate F11-F71? Does the loop like "for" possibly work?

Thanks a lot!

%clear

%Parameters
t_0     = 1.8;
phi   = 1.2;
eta_S = 1;
eta_N = eta_S*phi;
sigma = 3.5;
L_S   = 1000;
H_S   = 500;
L_N   = 800;
H_N   = 1600;
z_N_up = 1;
z_S_up = 0.9;

%Derivative 
syms z_S z_N p_S p_N w_S_H w_N_L w_N_H t

x = [z_S,z_N,p_S,p_N,w_S_H,w_N_L,w_N_H,t];

I_N   = w_N_H*H_N + w_N_L*L_N;
I_S   = w_S_H*H_S + L_S;

g1N = [(1-sigma)*log(w_S_H)-1]*[(1-sigma)*log(w_S_H)]^(-2)*[w_S_H^((1-sigma)*(1-z_N))-w_S_H^(1-sigma)];
g1S = [(1-sigma)*log(w_S_H)-1]*[(1-sigma)*log(w_S_H)]^(-2)*[w_S_H^((1-sigma)*(1-z_S))-w_S_H^(1-sigma)];

g2N = [(1-sigma)*log(w_S_H)]^(-1)*[(1-z_N)*(w_S_H)^((1-sigma)*z_N)-1]+[(1-sigma)*log(w_S_H)]^(-2)*[w_S_H^((1-sigma)*z_N)-1];
g2S = [(1-sigma)*log(w_S_H)]^(-1)*[(1-z_S)*(w_S_H)^((1-sigma)*z_S)-1]+[(1-sigma)*log(w_S_H)]^(-2)*[w_S_H^((1-sigma)*z_S)-1];

g3N = [(1-sigma)*log(w_N_H/w_N_L)-1]*[(1-sigma)*log(w_N_H/w_N_L)]^(-2)*[(w_N_H/w_N_L)^((1-sigma)*(1-z_N_up))-(w_N_H/w_N_L)^((1-sigma)*(1-z_N))];
g3S = [(1-sigma)*log(w_N_H/w_N_L)-1]*[(1-sigma)*log(w_N_H/w_N_L)]^(-2)*[(w_N_H/w_N_L)^((1-sigma)*(1-z_S_up))-(w_N_H/w_N_L)^((1-sigma)*(1-z_S))];

g4N = [(1-sigma)*log(w_N_H/w_N_L)]^(-1)*[(1-z_N_up)*(w_N_H/w_N_L)^((1-sigma)*z_N_up)-(1-z_N)*(w_N_H/w_N_L)^((1-sigma)*z_N)]+[(1-sigma)*log(w_N_H/w_N_L)]^(-2)*[(w_N_H/w_N_L)^((1-sigma)*z_N_up)-(w_N_H/w_N_L)^((1-sigma)*z_N)];
g4S = [(1-sigma)*log(w_N_H/w_N_L)]^(-1)*[(1-z_S_up)*(w_N_H/w_N_L)^((1-sigma)*z_S_up)-(1-z_S)*(w_N_H/w_N_L)^((1-sigma)*z_S)]+[(1-sigma)*log(w_N_H/w_N_L)]^(-2)*[(w_N_H/w_N_L)^((1-sigma)*z_S_up)-(w_N_H/w_N_L)^((1-sigma)*z_S)];

F1(x)  = z_N*log(w_S_H*w_N_L/w_N_H) - [log(w_N_L)-log(t)-sigma*(sigma-1)^(-1)*log(phi)];

F2(x)  = z_S*log(w_S_H*w_N_L/w_N_H) - [log(w_N_L)-log(t)-sigma*(sigma-1)^(-1)*log(phi)];

F3(x)  = p_N^(1-sigma) - eta_S^(sigma)*t^(1-sigma)*[(1-sigma)*log(w_S_H)]^(-1)*[w_S_H^(z_N*(1-sigma))-1] - eta_N^(sigma)*w_N_L^(1-sigma)*[(1-sigma)*log(w_N_H/w_N_L)]^(-1)*[(w_N_H/w_N_L)^(1-sigma)-(w_N_H/w_N_L)^(z_N*(1-sigma))];

F4(x)  = p_S^(1-sigma) - eta_S^(sigma)*[(1-sigma)*log(w_S_H)]^(-1)*[w_S_H^(z_S*(1-sigma))-1] - eta_N^(sigma)*t^(1-sigma)*w_N_L^(1-sigma)*[(1-sigma)*log(w_N_H/w_N_L)]^(-1)*[(w_N_H/w_N_L)^(1-sigma)-(w_N_H/w_N_L)^(z_S*(1-sigma))];

F5(x)  = L_S*w_S_H^(1-sigma)*[I_N*p_N^(sigma-1)*t^(-sigma)*g1N+I_S*p_S^(sigma-1)*g1S] - H_S*w_S_H*[I_N*p_N^(sigma-1)*t^(-sigma)*g2N+I_S*p_S^(sigma-1)*g2S];

F6(x)  = L_N*w_N_L*w_N_H^(1-sigma)*[I_N*p_N^(sigma-1)*g3N+I_S*p_S^(sigma-1)*t^(-sigma)*g3S] - H_N*w_N_H*w_N_L^(1-sigma)*[I_N*p_N^(sigma-1)*g4N+I_S*p_S^(sigma-1)*t^(-sigma)*g4S];

F7(x)  = L_S*phi^(sigma)*w_N_L^(1-sigma)*[I_N*p_N^(sigma-1)*g4N+I_S*p_S^(sigma-1)*t^(-sigma)*g4S] - L_N*w_N_L*[I_N*p_N^(sigma-1)*t^(-sigma)*g2N+I_S*p_S^(sigma-1)*g2S];

% Partial Differential respect to endogenous variables: z_S   
F11 = matlabFunction(diff(F1,z_S));
F21 = matlabFunction(diff(F2,z_S));
F31 = matlabFunction(diff(F3,z_S));
F41 = matlabFunction(diff(F4,z_S));
F51 = matlabFunction(diff(F5,z_S));
F61 = matlabFunction(diff(F6,z_S));
F71 = matlabFunction(diff(F7,z_S));

% the value of derivatives at specific given points
x_0 = [0.0210    0.2429    1.5721    0.9723    1.5823    2.3639    1.7306    1.8000];
F21(x_0)
F21(0.0210,0.2429,1.5721,0.9723,1.5823,2.3639,1.7306,1.8000)

Answer 1

[Payas Bahade]

Hi,

For the first part of the question, following code can be used to pass multiple input arguments to function using cell array:

x_0 = {0.0210    0.2429    1.5721    0.9723    1.5823    2.3639    1.7306    1.8000};
F21(x_0{:})

For second part of question, below lines of code illustrates the use of ‘for’ loop for calculating F11 to F71 which gets stored in variable Fxx:

size=7;
Fx=cell(size,1);
x_0 = {0.0210    0.2429    1.5721    0.9723    1.5823    2.3639    1.7306    1.8000};
for i=1:size
    Fi =strcat('F', num2str(i));
    Fx{i}= matlabFunction(diff(eval(Fi),z_S));
    Fxx{i}=Fx{i}(x_0{:});
end

Hope this helps!