gram_demo.zip_DEMO

function [X,Y,c_est]=gram_demo(STAN,UNKN,rank,opts) %Generalized Rank Annihilation Method as per Wilson, Sanchez, and Kowalski. % %INPUT % STAN: Standardized matrix of known analyte concentration. % UNKN: Mixture matrix of indeterminate constitution. % rank: Estimated rank of the concatenated STAN and UNKN matrices % opts: By default GRAM_WSK employs the concatenated matrices and [STAN;UNKN] % Setting options to any non-zero value employs the additive matrix [STAN+UNKN] for GRAM. % %Output: % X: Estimated, unit length, intrinsic profiles in the X order. % Y: Estimated, unit length, intrinsic profiles in the Y order. % c_est:Estimated relative constituent concentrations in UNKN. % % Initialization if nargin = = 3 opts = 0; end %Compute row space and column space if opts = = 0 [v,s,u]=svd([STAN,UNKN]',0); col_sp=u(:,1:rank); [u,s,v]=svd([STAN;UNKN],0); row_sp=v(:,1:rank); else [u,s,v]=svd([STAN+UNKN],0); col_sp=u(:,1:rank); row_sp=v:,1:rank); end %Reduce STAN and UNKN into square, full rank matrices and solve GEP STAN=col_sp'*STAN*row_sp; UNKN=col_sp'*UNKN*row_sp; [STAN_t,UNKN_t,q,z,Eig_vec]=qz(STAN,UNKN); %Calculate X, Y, and c_est Y=row_sp*pinv(Eig_vec)'; Y=Y./(ones(length(Y),1)*sum(Y.^2).^.5); X=col_sp*(STAN+UNKN)*Eig_vec; X=X./(ones(length(X),1)*sum(X.^2).^.5); c_est=diag(UNKN_t)./diag(STAN_t);