mwrgs_old.m

MDPSAS工具箱是马里兰大学开发的

function [psi] = mwrgs(f,w)

% mwrgs.m A Gram-Schmidt ortho-normalization procedure. The discretized set
%         of functions (phi) is made ortho-normal with with respect to the
%         discretized weight function (w) over the unit domain to produce
%         the set of functions (psi). Called as
%
%         [psi] = mwrgs(phi,w)
%
%        INPUT Variables: 
%                 phi : [: by m] array of m trial functions
%                 w   : weight array from pd.m
%
%        OUTPUT Variables:
%                 psi : ortho-normal result of phi w.r.t. w and the domain
%
%        EXAMPLE: Perform G.S. procedure on a series of function x^n where
%                 n is an integer from 0 to 4 in the cylindrical domain.
%                 The resulting functions (fct) are shown to be ortho-
%                 normal using the weighted inner product function (wip.m).
%
%                 [x w] = pd('cyln',25);
%                 fct   = mwrgs( gdf(x,'x.^n','x',{'n',[0:4]}), w );
%                 wip(fct,fct,w)

% Written by Raymond A. Adomaitis, Hsiao-Yung Chang, and Yi-hung Lin 
% as part of MWRtools, version 1.2.

% Copyright (c) by Raymond A. Adomaitis, 1998, 1999, 2000

[m n] = size(f);
psi   = zeros(m,n);

for i = 1 : n
  v = f(:,i);
  for j = 1 : i 
     v = v - wip(v,psi(:,j),w)*psi(:,j);
  end
  psi(:,i) = v/sqrt( wip(v,v,w) );
end