intlag_lg

 INTLAG_LG  Computes matrix "a" to evaluate 1D Lagrange interpolant at LG 

  (Legendre Gauss) nodes in [-1,1] at another mesh x_new in [-1,1]

  [a]=intlag_lg(x_lg, w_lg, x_new)

 Input: x_lg = array of np_lg LG nodes in [-1,1]
        w_lg = array of np_lg LG weights in [-1,1]
        x_new = array of np_new another set in [-1,1]

 Output: a = matrix of size (np_new,np_lg) 

       If u_lg is the array with evaluations  of a function u at nodes
          x_lg, it holds:  u_new = a * u_lg, i.e. u_new=u(x_new)

 Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
                    "Spectral Methods. Fundamentals in Single Domains"
                    Springer Verlag, Berlin Heidelberg New York, 2006.

0001 function [a]=intlag_lg(x_lg, w_lg, x_new);
0002 % INTLAG_LG  Computes matrix "a" to evaluate 1D Lagrange interpolant at LG
0003 %
0004 %  (Legendre Gauss) nodes in [-1,1] at another mesh x_new in [-1,1]
0005 %
0006 %  [a]=intlag_lg(x_lg, w_lg, x_new)
0007 %
0008 % Input: x_lg = array of np_lg LG nodes in [-1,1]
0009 %        w_lg = array of np_lg LG weights in [-1,1]
0010 %        x_new = array of np_new another set in [-1,1]
0011 %
0012 % Output: a = matrix of size (np_new,np_lg)
0013 %
0014 %       If u_lg is the array with evaluations  of a function u at nodes
0015 %          x_lg, it holds:  u_new = a * u_lg, i.e. u_new=u(x_new)
0016 %
0017 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0018 %                    "Spectral Methods. Fundamentals in Single Domains"
0019 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0020 
0021 %   Written by Paola Gervasio
0022 %   $Date: 2007/04/01$
0023 
0024 np_lg=length(x_lg);
0025 np_new=length(x_new);
0026 n_lg=np_lg-1;
0027 a=zeros(np_new,np_lg);
0028 
0029 pn=pnleg_all([x_lg;x_new],n_lg);
0030 pn1=pn(np_lg+1:np_lg+np_new,:);
0031 pn=pn(1:np_lg,:);
0032 nor=0.5+(0:n_lg);
0033 for i=1:np_new
0034 for j=1:np_lg
0035 a(i,j)=sum(nor.*pn(j,:).*pn1(i,:))*w_lg(j);
0036 end
0037 end
0038 
0039 return