Nodal basis function 1D

Hello all, I coded a nodal basis function for 1D element from [-1,1]. the code is below:

 close all; clc; clearvars;
n=10;
x = linspace(-1,1,n);
for i=1:n

   a= x(i);
   for j=1:n
       b(j)=a.^(j-1);
          end
  v(i,:)=b';

end
vinv=inv(v);
for i=1:n
 k=zeros(1,n);
 k(i)=1;
 f=vinv*k'
p(:,i)=f;
 end
 for i=1:n

        g=@(x) p(1,i)+p(2,i).*x+p(3,i).*x.^2+p(4,i).*x.^3+p(5,i).*x.^4+p(6,i).*x.^5+p(7,i).*x.^6+p(8,i).*x.^7+p(9,i).*x.^8+ ....
        p(10,i).*x.^9;
legendInfo{i} = ['Phi ' num2str(i)]; 
fplot(g, [-1 1])
legend(legendInfo)
       hold on;
end

The code works already but my problem is in last "for loop" where I calculated "g" as a function handle. I want to instead of adding the terms from 1 to 10, use an automated calculation. Now, if I want to change number of nodes (n) from 10 to 20 I have to add 10 additional terms by hand. Moreover, Does somebody knows a better way to calculate nodal basis function for 1D element? Great thanks,

Answer 1

[KSSV]

Read about polyval

n=10;
x = linspace(-1,1,n);
for i=1:n
    a= x(i);
    for j=1:n
        b(j)=a.^(j-1);
    end
    v(i,:)=b';
end
vinv=inv(v);
for i=1:n
    k=zeros(1,n);
    k(i)=1;
    f=vinv*k'
    p(:,i)=f;
end
x = linspace(-1,1,1000) ;

for i=1:n
    r = flipud(p(:,i)) ;
    y = polyval(r,x) ;
     legendInfo{i} = ['Phi ' num2str(i)];
    plot(x,y)
    legend(legendInfo)
    hold on;
end

[mohamad hoseini]

Thanks for your response. The code works well by polyval. Do you know it is possible to make this polynomials by symbolic functions depend on (x)?

[KSSV]

Have a look on poly2sim

[mohamad hoseini]

Thanks

[KSSV]

Thanks is accepting and voting the answer..:)