PNLEG_ALL Evaluates Legendre polynomials, from degree 0 to n
[p]=pnleg_all(x,n) returns the evaluation of the Legendre
polynomials of degree 0,1,...,N at x, using the three
term relation (2.3.3), pag. 75 CHQZ2.
Input: x = scalar or array
n = degree of Legendre polynomial to be evalueted
Output: p = 1-index (size(p)=size(x)) or
2-indexes (size(p)=[length(x),n+1])
array containing the
evaluation of L_0(x), L_1(x), .... L_n(x)
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 [p] = pnleg_all(x,n) 0002 %PNLEG_ALL Evaluates Legendre polynomials, from degree 0 to n 0003 % 0004 % [p]=pnleg_all(x,n) returns the evaluation of the Legendre 0005 % polynomials of degree 0,1,...,N at x, using the three 0006 % term relation (2.3.3), pag. 75 CHQZ2. 0007 % 0008 % Input: x = scalar or array 0009 % n = degree of Legendre polynomial to be evalueted 0010 % 0011 % Output: p = 1-index (size(p)=size(x)) or 0012 % 2-indexes (size(p)=[length(x),n+1]) 0013 % array containing the 0014 % evaluation of L_0(x), L_1(x), .... L_n(x) 0015 % 0016 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, 0017 % "Spectral Methods. Fundamentals in Single Domains" 0018 % Springer Verlag, Berlin Heidelberg New York, 2006. 0019 0020 % Written by Paola Gervasio 0021 % $Date: 2007/04/01$ 0022 0023 0024 nn=size(x); 0025 if nn==1 0026 if n==0 0027 p=1; 0028 elseif n==1 0029 p=[1,x]; 0030 else 0031 p1=1; p2=x; p3=p2; p=[p1,p2]; 0032 for k =1:n-1 0033 p3=((2*k+1)*x*p2-k*p1)/(k+1); 0034 p1=p2; 0035 p2=p3; 0036 p=[p,p3]; 0037 end 0038 end 0039 0040 else 0041 if n==0 0042 p=ones(nn); 0043 elseif n==1 0044 p=[ones(nn),x]; 0045 else 0046 p1=ones(nn); p2=x; p3=p2; p=[p1,p2]; 0047 for k =1:n-1 0048 p3=((2*k+1)*x.*p2-k*p1)/(k+1); 0049 p1=p2; 0050 p2=p3; 0051 p=[p,p3]; 0052 end 0053 end 0054 0055 end 0056 return