%CreateOmega.m
%Math 128B Spring 2005
%Returns W(i,j)=Wjk(Xi)
% Wjk=j'th linear function with W(knots(j))=0,W(knot(j+k-1))=1

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function	w	= CreateOmega(t, knots, K)
%t = discretization of domain
%knots = row vector of knot locations
%returns w(i,j)=Wjk(Ti)
N	= length(knots);
M	= length(t);
k	= K-1;		%	degree
TT	= repmat(t', 1, N-k);
KNOTS	= repmat(knots, M, 1);

%w numerator = x - t(j)
wNum	= TT - KNOTS(:,1:N-k);

%w denominator = t(j+k) - t(j)
wDen	= KNOTS(:,1+k:N) - KNOTS(:,1:N-k);

%replace zero entries in wDen (multiplicity > 1)
wDen(find(~wDen))	= 1;

%Wjk = quotient
w	= wNum./wDen;

return