gistfile1.matlab

% Zachary Wolfe
% wolfe.zach@gmail.com
% CMPSC 456 SPR 2013

function [aQR, rQR, aMGS, rMGS, aCHOL, rCHOL] = fit()
   t = 0:0.05:1;
   V = vander(t);
   X = V(:,17:21);
   b = sin(pi*t);
   b = b'; % make b a column vector


   %mQ, mR are Q,R from Matlab's QR factorization
   [mQ, mR] = qr(X);
   [aQR, rQR] = mgs_solve(mQ, mR,b);


   %gQ, gR are from modified Gram - Schmidt defined in mgs.m
   [gQ, gR] = mgs(X);
   [aMGS,rMGS]= mgs_solve(gQ, gR,b);

   % To solve least squares using cholesky
   %  First find the cholesky decomposition of X'X, then solve
   %  cR'cR*yLS = X'b
   cR = chol(X'*X);
   aCHOL = (X'*b)\(cR'*cR);
   aCHOL = inv(cR'*cR)*(X'*b);
   rCHOL = b - X*aCHOL;
endfunction