What is wrong with my matlab codes

i wrote this matlab script to solve a system of nonlinear equations

function F = myfun (x)

format long

clear

syms k

%values of parameter and vector x

n=5;

m(k)=[6 12 18 24 30];

tol = 10.^-4; %tol is a convergence tolerance

%initial guess or values b=0.002;

a=0.0002;

l=0.0002;

r=0.00002;

xnew = [b;a;l;r];

xold = zeros(size(xnew))

iter=0; %iterations

xnew = [100;100;100];

while norm(xnew - x0) > tol

    iter = iter + 1;

    xold = xnew;

    % update b, a, l, and r

    b = xold(1);

    a = xold(2);

    l = xold(3);

    r = xold(4);

    %Defining the functions for b, a, l, and r
    f= n-sum(b*m(k)^a*exp(l*m(k)),k,1,n)-2*sum(b*r*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);
    g= sum(log(m(k)),1,n)+sum(1/(a+l*m(k)),k,1,n)-sum(b*m(k)^a*exp(l*m(k))*log(m(k)),k,1,n)-2*sum(a*r*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*log(m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);
    h= sum(m(k)/(a+l*m(k)),k,1,n)-sum(b*m(k)^(a+1)*exp(l*m(k)),k,1,n)-sum(m(k),k,1,n)-2*sum(b*r*m(k)^(a+1)*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);
    q= n/(1-r)-2*sum(exp(b*m(k)^a*exp(l*m(k)))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);

    %Partial derivatives in terms of b, a, l, and r
    dfdb = -sum(m(k)^a*exp(l*m(k)),k,1,n)-2*sum(r*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n)-2*sum(b*r*m(k)^(2*a)*exp(-b*m(k)^a*exp(l*m(k))+(2*l*m(k)))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dfda = -sum(b*m(k)^a*exp(l*m(k))*log(m(k)),k,1,n)+2*sum(b*r*m(k)^a*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*log(m(k))*(b*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))+r-exp(-b*m(k)^a*exp(l*x(k))+l*m(k)))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);
    dfdl = -sum(b*m(k)^(a+1)*exp(l*m(k)),k,1,n)-2*sum((b*r)^2*m(k)^(2*a+1)*exp(-2*(b*m(k)^a*exp(l*m(k))+l*m(k)))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n)-2*sum(b*r*m(k)^(a+1)*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-b*m(k)^a*exp(l*m(k)))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);
    dfdr = -2*sum(b*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n)-2*sum(b*r*m(k)^a*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);

    dgdb = -sum(b*m(k)^a*exp(l*m(k))*log(m(k)),k,1,n)+2*sum(a*(r)^2*m(k)^(2*a)*exp(-2*(b*m(k)^a*exp(l*m(k))+l*m(k)))*log(m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n)+2*sum(b*r*m(k)^(2*a)*exp(-b*m(k)^a*exp(l*m(k))+2*l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);
    dgda = -2*sum(r*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*log(m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n)-sum(b*m(k)^a*exp(l*m(k))*(log(m(k)))^2,k,1,n)-sum(1/(a+l*m(k))^2,k,1,n)+2*sum(a*r*m(k)^a*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*(log(m(k)))^2*(b*exp(b*m(k)^a*exp(l*m(k))+l*m(k))+r-exp(b*m(k)^a*exp(l*m(k))))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dgdl = -sum(b*m(k)^(a+1)*exp(l*m(k))*log(m(k)),k,1,n)-sum(m(k)/(a+l*m(k)^2),k,1,n)+2*sum(a*r*m(k)^(a+1)*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*log(m(k))*(b*m(k)^a*exp(b*m(k)^a*exp(l*m(k))+l*m(k))+r-exp(b*m(k)^a*exp(l*m(k))))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dgdr = -2*sum(a*r*m(k)^a*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*log(m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n)-2*sum(b*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*log(m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n);

    dhdb = -sum(m(k)^(a+1)*exp(l*m(k)),k,1,n)-2*sum(r*m(k)^(a+1)*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n)+2*sum(b*r*m(k)^(2*a+1)*exp(-b*m(k)^a*exp(l*m(k))+2*l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dhda = -sum(b*m(k)^(a+1)*exp(l*m(k))*log(m(k)),k,1,n)-sum(m(k)/(a+l*m(k)^2),k,1,n)+2*sum(b*r*m(k)^(a+1)*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*(b*m(k)^a*exp(b*m(k)^a*exp(l*m(k))+l*m(k))+r-exp(b*m(k)^a*exp(l*m(k))))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dhdl = -sum(b*m(k)^(a+2)*exp(l*m(k))*log(m(k)),k,1,n)-sum(m(k)^2/(a+l*m(k)^2),k,1,n)+2*sum(b*r*m(k)^(a+2)*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*(b*m(k)^a*exp(b*m(k)^a*exp(l*m(k))+l*m(k))+r-exp(b*m(k)^a*exp(l*m(k))))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dhdr = -2*sum(b*m(k)^(a+1)*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-1),k,1,n)-2*sum(b*r*m(k)^(a+1)*exp(-2*b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);

    dqdb = -2*sum(m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dqda = -2*sum(b*m(k)^a*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*log(m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dqdl = -2*symsum(b*m(k)^(a+1)*exp(-b*m(k)^a*exp(l*m(k))+l*m(k))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);
    dqdr = -(n/(1-r)^2)-2*sum(exp(-2*b*m(k)^a*exp(l*m(k)))*(1-r*exp(-b*m(k)^a*exp(l*m(k))))^(-2),k,1,n);

    %Jacobian matrix
    J = [dfdb dfda dfdl dfdr; dgdb dgda dgdl dgdr; dhdb dhda dhdl dhdr; dqdb dqda dqdl dqdr];
    % Applying the Newton-Raphson method
    xnew = x0- J\[f;g;h;q];
    disp(sprintf('iter=%6.15f, b=%6.15f, a=%6.15f, h=%6.15f, q=%6.15f', iter,xnew));
end

But the answer I got after running was;

??? Undefined function or method 'syms' for input arguments of type 'char'.

Error in ==> symsum at 5 syms k

Please, I wish to know where I went wrong. Thank you.

Answer 1

[Walter Roberson]

You appear to have stored this in a file named symsum.m . If you had gotten further you would have had recursion errors because the function needs the routine MATLAB symsum to work. Do not use routine names that are the same as something you need to call upon.

Then you appear to not have a license for the symbolic toolbox, or else do not have it installed.