# ITE / code / shared / MA_polynomial.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 function [H] = MA_polynomial(Dx,De,MA) %Generates a MA polynomial H[z] of dimension Dx x De (H[z]\in R[z]^{Dx x De}) and length L, to an uMA-IPA/complete MA-IPA problem. % %INPUT: % MA.type: % 1)'randn' ('rand'): the coordinates of H are i.i.d. standard normal (uniform = U[0,1]) variables. % 2)'stable': H corresponds to the polynomail matrix H[z] = [\prod_{k=1}^L(I-lambda O_i z^{-1})]H_0: O_i,H_0:random orthogonal, |MAparameters.lambda|<1. % MA.L: length of the convolution; H_0,...,H_{L}: L+1 H_j matrices. %OUTPUT: % H = [H_0,...,H_L], where H[z] = \sum_{l=0}^L H_l z^{-l}. %EXAMPLE: % %uMA-IPA: % MA.type = 'randn'; % H = MA_polynomial(4,2,3,MA); % %MA-IPA: % MA.type = 'stable'; % MA.lambda = 0.4; % H = MA_polynomial(4,2,3,MA); % %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu") % %This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox. % %ITE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by %the Free Software Foundation, either version 3 of the License, or (at your option) any later version. % %This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of %MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. % %You should have received a copy of the GNU General Public License along with ITE. If not, see . switch MA.type case 'randn'%uMA-IPA H = randn(Dx,De*(MA.L+1)); case 'rand'%uMA-IPA H = rand(Dx,De*(MA.L+1)); case 'stable'%MA-IPA (Dx=De) if Dx==De MA_L = MA.L; MA_lambda = MA.lambda; %Hz = [\prod_{k=1}^L(I-lambda O_i z^{-1})]: O_i:random orthogonal. Hz = {eye(De)}; for k = 1 : MA_L Hznew = {}; Hznew{1}= eye(De); Hznew{2} = -MA_lambda * random_orthogonal(De); Hz = multiply_polynomial_matrices(Hz,Hznew); end %xH0, H_0: orthogonal. H0 = random_orthogonal(De); H = zeros(De,De*(MA_L+1));%preallocation for k = 1 : length(Hz) H(:,(k-1)*De+1:k*De) = Hz{k} * H0; end else error('dim(x) must be equal to dim(e), i.e., we are focusing on complete systems!'); end otherwise error('MA type=?'); end 
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