function [A, B, exitflag, output]= tfarma_est_mle(y, Aml0, Bml0, re_im, opts)% function [A, B, exitflag, output]= tfarma_est_mle(y, Aml0, Bml0, re_im, opts)%   This file is part of the TFPM toolbox v1.0 (c)%   michael.jachan@tuwien.ac.at and underlies the GPL.% % Exact ML estimator for TFARMA(MAR, LAR; MMA, LMA; N; 1/2)% models. %%TODO: % The switch re_im decides how the parameters are% optimized! Formulated such that all parameters to be optimized% are real-valued! (cf. tfar_llfe.m)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clear;tfpm;N    = 128;MAR  =   2;LAR  =   2;MMA  =   1;LMA  =   1;re_im= 'r';mo_no= 'm';tfpm_file_gen;%-------------beta = 1/2;MC= 2*(MAR+MMA);LC= 2*(LAR+LMA);Amlref= Aml;Bmlref= Bml;y= tfarma_gen(randn(N, 1), Aml, Bml, beta);qyy= corr_est(y, y, MC, 1/2);ayy= fft(qyy);ayy= [ayy(N/2+1:N, :); ayy(1:N/2, :)];ayy= ayy(N/2+1-3*LC:N/2+1+3*LC, :);Psi= tf_multiwin(N, MC, LC, 5, 1, 1);psi= Psi(N/2+1-3*LC:N/2+1+3*LC, N/2+1-MC:N/2+1+MC);[Aml0, Bml0, INSTAB]= gkmu(ayy.*conj(psi), N, MAR, LAR, MMA, LMA);opts= optimset('MaxIter', 1000, 'MaxFunEvals', 100000);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Dimensions:[MAR, LAR]= param_dim(Aml0);[MMA, LMA]= param_dim(Bml0);% Combine the parameters, do not contain a_{0, l}!theta_AB= [param_stack_ml(Aml0(:, 2:end)); param_stack_ml(Bml0)];% Call fminunc:[X, lX, exitflag, output]= fminunc('tfarma_llfe', theta_AB, opts, y, MAR, LAR, MMA, LMA, re_im);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Call fmincon:[X, lX, exitflag, output]= fmincon('tfarma_llfe', theta_AB, [], [], [], [], -3*ones(size(theta_AB)), 3*ones(size(theta_AB)), [], opts, y, MAR, LAR, MMA, LMA, re_im);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%theta_A= X(1:MAR*(2*LAR+1));theta_B= X(MAR*(2*LAR+1)+1:end);Aml= [[zeros(LAR, 1); 1; zeros(LAR, 1)] param_destack_ml(theta_A, MAR-1, LAR)];Bml= param_destack_ml(theta_B, MMA, LMA);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%[param_norm(Aml, Amlref, 0) param_norm(Aml0, Amlref, 0)][param_norm(Bml, Bmlref, 1) param_norm(Bml0, Bmlref, 1)]%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clear;tfpm;N    = 256;MAR  =   2;LAR  =   2;MMA  =   0;LMA  = LAR;re_im= 'r';mo_no= 'n';tfpm_file_gen;%-------------beta = 1/2;B0l= Bml;MM= 20;opts= optimset('MaxIter', 300, 'MaxFunEvals', 10000, 'Diagnostics', 'off', 'Display', 'off');AMLyw= zeros(2*LAR+1, MAR+2, MM);AMLml= zeros(2*LAR+1, MAR+2, MM);Iter= [];NFun= [];EFLG= [];for mm= 1:MM   mm   y= tfarma_gen(randn(N, 1), Aml, B0l, beta);   qyy= corr_est(y, y, MAR, 1/2);   ayy= fft(qyy);   ayy= [ayy(N/2+1:N, :); ayy(1:N/2, :)];   ayy= ayy(N/2+1-3*LAR:N/2+1+3*LAR, :);   [AA, BB]= tfar_est_tfywu(ayy, N);   Aml0= AA(:, :, end);   B0l0= BB(:, :, end);   [A, B, exitflag, output]= tfar_est_mle(y, Aml0, B0l0, re_im, opts);   Iter= [Iter; output.iterations];   NFun= [NFun; output.funcCount];   EFLG= [EFLG; exitflag];   figure(1);clf;plot(Iter);drawnow   figure(2);clf;plot(NFun);drawnow   AMLyw(:, :, mm)= [Aml0 B0l0];   AMLml(:, :, mm)= [A B];end;[mean(Iter) mean(NFun)][Myw, Vyw, Byw]= param_mse(AMLyw, [Aml B0l])[Mml, Vml, Bml]= param_mse(AMLml, [Aml B0l])[norm(Myw) norm(Mml)]mean(AMLyw, 3)mean(AMLml, 3)sum(EFLG)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%