value of type 'sym' is not convertible to 'double'

Hey,

I am trying to let the following code run but I always get the same error:

Unable to perform assignment because value of type 'sym' is not convertible to 'double'.

Error in spdiags>makeSparseGeneral (line 225)

V(offset) = B(i + d(k), k);

Error in spdiags (line 125)

res1 = makeSparseGeneral(B, d, A);

Error in Combined_Model>spdiag (line 157)

x = spdiags(v,0,rv,rv);

Error in Combined_Model (line 76)

Js = spdiag(f(kc, kp) - (delta+n)*kc)*d1Mx*theta - ...

Caused by: Error using symengine. Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables.

Can anyone help me with this?

%% COMBINED MODEL

clear; close all; clc;

%% Parameters

rho = 0.04;
theta = 1.5;

nu = 0.35;
delta = 0.05;

A=1;
L=1;
alpha = 0.5;
gamma = 0.5; 
n = 0.01;

%% Functions

syms kc
Ec = (A*kc.^gamma*L.^(1-gamma)) ;

syms kp
Ep = (A*kp.^gamma*L.^(1-gamma)) ; 

E = Ec + Ep;

fs = A*(E.^gamma)*(L.^(1-gamma));
f_p1s_c = diff(fs, kc);
f_p1s_p = diff(fs, kp);

f = matlabFunction(fs,'vars',{kc kp});
f_p1_c = matlabFunction(f_p1s_c,'vars',{kc kp});
f_p1_p = matlabFunction(f_p1s_p,'vars',{kc kp});


u = @(c) (integral(exp(-(p-n))*c.^(1-theta)/(1-theta)));0;inf ;


% %% Steady state
% % SS for Ramsey, GR for Solow
% % Numerical solution using unidimensional Newton-Raphson
% 
% metric=1; i=0; kSS=1;
% while (metric>=1e-10)
%     kSS = ((delta +rho)/(A*alpha)).^(1/alpha - 1) ;
%     metric = ((delta +rho)/(A*alpha)).^(1/alpha - 1); i=i+1;
% end
% cSS = f(kSS) - (delta+n)*kSS;

kSS_c = ((delta +rho)/(A*gamma)).^(1/(gamma - 1)) ;
kSS_p = ((delta +rho)/(A*gamma)).^(1/(gamma - 1)) ;

%kSS = [kSS_c kSS_p]
cSS = f(kSS_c, kSS_p) - (delta+n)*kSS_c ; 
%% Grid, differentiation operators

Ik = 2000; kmin = 1e-5*kSS_c; kmax = 5*kSS_c;
k = linspace(kmin,kmax,Ik)';

dk = (kmax-kmin)/Ik;

d1Mx = spdiags(repmat([-1 sparse(1,1) 1],Ik,1),-1:1,Ik,Ik)/2;
d1Mx(1,1)=-1; d1Mx(1,2)=1; d1Mx(Ik,Ik-1)=-1; d1Mx(Ik,Ik)=1;
d1Mx = d1Mx/dk;

%% Main loop - Euler equation + Newton-Raphson (modified reflection method)
% Initialisation
metric=1; i=0;

c=k;


% Static (c-independent) component of the Jacobian
Js = spdiag(f(kc, kp) - (delta+n)*kc)*d1Mx*theta - ...
     spdiag(f_p1_c(kc, kp)-delta - rho);

Unable to perform assignment because value of type 'sym' is not convertible to 'double'.

Error in spdiags>makeSparseGeneral (line 225)
V(offset) = B(i + d(k), k);

Error in spdiags (line 125)
res1 = makeSparseGeneral(B, d, A);

Error in solution>spdiag (line 112)
x = spdiags(v,0,rv,rv);

Caused by:
Error using symengine
Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables.

Jd = sparse(Ik,Ik);

tic
while metric > 1e-10
    % Dynamic (c-dependent) component of the Jacobian
%     Jd = spdiags([-0.5*c [0; 0.5*(c(1:N-2)-c(3:N)); 0] 0.5*c],-1:1,N,N)';
%     Jd(1,1) = 2*c(1)-c(2); Jd(1,2) = -c(1);
%     Jd(N,N-1) = c(N); Jd(N,N) = c(N-1) - 2*c(N);
    Jd = -(spdiag(d1Mx*c)+spdiag(c)*d1Mx)*theta;
    
    % Merit function/Error vector (from the Euler equation)
    err = (d1Mx*c).*(f(k) - (delta+n)*k - c)*theta - ...
        (f_p1(k)-delta - rho).*c;
    
    c = c - (Js+Jd)\err;
    metric = max(abs(err));
    i=i+1;
end
toc

if metric<=1e-10
    fprintf('Solver converged in %d iterations.\n',i);
else
    fprintf('Solver failed to converge in %d iterations!\n',i);
    return;
end

s = f(k) - (delta+n)*k - c;

%% Simple sparse diagonalisation
function[x] = spdiag(v)
    [rv,cv] = size(v);
    
    if (cv==1)
        x = spdiags(v,0,rv,rv);
        return;
    elseif (rv==1)
        x = spdiags(v',0,cv,cv);
        return;
    else x=v; return;
    end
end

Answer 1

[Steven Lord]

You cannot create a sparse matrix that contains a symbolic expression. Either store the symbolic expression in a symbolic matrix or convert the symbolic expression into a numeric value and store that in the sparse matrix.

syms x
y = x.^2 % symbolic expression

y = 

S = sym(zeros(4)) % symbolic matrix

S = 

S(2, 3) = y % Assign a symbolic expression into a symbolic matrix

S = 

y2 = subs(y, x, 3) % numeric value

y2 = 

9

A = zeros(4) % numeric matrix

A = 4×4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

A(2, 3) = y2 % Assign a numeric value into a numeric matrix

A = 4×4

0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0

You can store a numeric value in a symbolic array (which will automatically convert the numeric value into a symbolic expression) but storing a symbolic expression in a numeric array will not work unless the symbolic expression can be converted into a numeric value.

S(4, 1) = y2 % Storing a numeric value into a symbolic matrix works

S = 

A(4, 1) = y % Storing a symbolic expression in a numeric matrix does not work

Unable to perform assignment because value of type 'sym' is not convertible to 'double'.

Caused by:
Error using symengine
Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables.

[Sabrina Haumann]

Hello, thanks for your answer! But what lines do I then have to edit in my code? Sorry, I am completely new to MATLAB.