How to make the below code with Symbolic variables run faster

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Fan Li 2018-12-5

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https://ww2.mathworks.cn/matlabcentral/answers/434098-how-to-make-the-below-code-with-symbolic-variables-run-faster

评论： Walter Roberson 2018-12-5

Dear matlab users

I have below code with Symbolic variables to evaluate a function. The a_n,b_n,c_n and d_n are numerical arrays which are calculated by a code which is not shown. And the variable "rho_interval" and "z_interval" are the numerical arrays as well. The most time consuming part is the loop and two matlabFunction. Are there any ways to make it run faster?

Thanks

syms zeta mu rho z eta
zeta=atanh(2*c.*z./(z.^2+rho.^2+c.^2));
% sin(eta)=(rho/z)*sinh(zeta);
cos(eta)=cosh(zeta)-(c/z)*sinh(zeta);
mu=cos(eta);
for n=0:N
   poly_syms(n+1,:) =(a_n(n+1,:)*cosh((n-1/2)*zeta)...
      +b_n(n+1,:)*sinh((n-1/2)*zeta)...
      +c_n(n+1,:)*cosh((n+3/2)*zeta)...
      +d_n(n+1,:)*sinh((n+3/2)*zeta))...
      .*gegenbauerC(n+1,-1/2,mu);
                                            
end
poly_syms_sum=sum(poly_syms);
str_func_syms=(cosh(zeta)-mu).^(-3/2)*poly_syms_sum;
poly_func=matlabFunction(poly_syms);
str_func_func=matlabFunction(str_func_syms);
[domain_rho,domain_z]=meshgrid(rho_interval,z_interval);
str_func=str_func_func(domain_rho,domain_z);

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Walter Roberson 2018-12-5

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The assignment can be vectorized. Instead of a for I suspect you can use

n = 0:N;
poly_syms = (a_n .* cosh((n-1/2)*zeta)...
      + b_n .* sinh((n-1/2)*zeta)...
      + c_n .* cosh((n+3/2)*zeta)...
      + d_n .* sinh((n+3/2)*zeta))...
      .* gegenbauerC(n+1,-1/2,mu);