GradSimplex2DP.m

function [dmodedr, dmodeds] = GradSimplex2DP(a,b,id,jd)

% function [dmodedr, dmodeds] = GradSimplex2DP(a,b,id,jd)
% Purpose: Return the derivatives of the modal basis (id,jd) on the 2D simplex at (a,b).   

fa = JacobiP(a, 0, 0, id);     dfa = GradJacobiP(a, 0, 0, id);
gb = JacobiP(b, 2*id+1,0, jd); dgb = GradJacobiP(b, 2*id+1,0, jd);

% r-derivative
% d/dr = da/dr d/da + db/dr d/db = (2/(1-s)) d/da = (2/(1-b)) d/da
dmodedr = dfa.*gb;
if(id>0)
  dmodedr = dmodedr.*((0.5*(1-b)).^(id-1));
end

% s-derivative
% d/ds = ((1+a)/2)/((1-b)/2) d/da + d/db
dmodeds = dfa.*(gb.*(0.5*(1+a)));
if(id>0)
 dmodeds = dmodeds.*((0.5*(1-b)).^(id-1));
end

tmp = dgb.*((0.5*(1-b)).^id);
if(id>0)
  tmp = tmp-0.5*id*gb.*((0.5*(1-b)).^(id-1));
end
dmodeds = dmodeds+fa.*tmp;

% Normalize
dmodedr = 2^(id+0.5)*dmodedr; dmodeds = 2^(id+0.5)*dmodeds;
return;