Multidimensional arrays in MatlabXanadu Halkias

OverviewCreating/accessing/indexing multidimensional arraysUsing and computing with multidimensional arraysMultidimensional cell arraysMultidimensional structure arrays

Corpus hypercubus

%Creating multidimensional arraysa = [1 2 3;0 6 4;2 5 4];a(:,:,2) = [4 2 1;0 5 1;6 3 2];a(:,:,3) = 3;%turning a into a 3x3x3x2a(:,:,:,2) = ones(3,3,3);a(:,:,1,2) = 4;

More on creating%different wayb = repmat(2,[3 3 3 2]);c = repmat(rand(2),[3 1 2]);

%one mored = cat(4,[1 4; 2 3],[5 8;2 3]);Memory: try to pre-allocate eg. zeros or use repmat for best performance

A few good functions%reshape and permute

%a bunch of datax = rand(3,3,2);new_x = reshape(x,[6 3]);tranx = permute(x,[2 1 3]);Ind = sub2ind(size(x),1,3,2);

Working with them%computing with multidimensional arraysx = rand(3,3,3);s = sum(x,3);d = sin(x);e = eig(x(:,:,2));ee = eig(squeeze(x(2,:,:)));

Multidimensional cell arrays%multidimensional cells

a = {[1 2 5 3 77 2 4 5], 1:10; rand(1,3), 2};b = {1:2:15, rand(1,5); [1 0 0 1], 5;}c = cat(3,a,b);[D{1}] = conv(c{1:2});[D{2}] = conv(c{1,1,:});d = cell2mat(D);for i=1:length(D{1}), m1(i) = D{1}(i); endfor i=1:length(D{2}), m2(i) = D{2}(i); endm = [m1, m2];

Multidimensional structure arrays%multidimensional structuresdolphin(1,1,1).species = 'bottlenose';dolphin(1,1,1).sampfreq = 44100;dolphin(1,1,1).signal = rand(1,100);dolphin(1,2,1).species = 'atlantic';dolphin(1,2,1).sampfreq = 44100;dolphin(1,2,1).signal = rand(1,100);dolphin(1,1,2).species = 'pink';dolphin(1,1,2).sampfreq = 44100;dolphin(1,1,2).signal = rand(1,100);dolphin(1,2,2).species = 'riso';dolphin(1,2,2).sampfreq = 44100;dolphin(1,2,2).signal = rand(1,100);

Multidimensional structures more %computing some stuff

s = sum([dolphin.sampfreq]);[b{1}] = fft(dolphin(1,1,1).signal);dolphin(1,1,1).fourier = b;

Murphys mhmm_em.m%each page gets its own cellif ~iscell(data) data = num2cell(data, [1 2]); endnumex = length(data); %num of pages is numbermixturesO = size(data{1},1); %getting the dimensionalityQ = length(prior); %number of statesif isempty(mixmat)%number of mixtures mixmat = ones(Q,1);endM = size(mixmat,2);if M == 1 adj_mix = 0;end

Murphys more-EMwhile (num_iter

The E of EMfunction [loglik, exp_num_trans, exp_num_visits1, postmix, m, ip, op] = ... ess_mhmm(prior, transmat, mixmat, mu, Sigma, data)Loglik: likelihood of the modelExp_num_trans: expected number of transitions is the transition matrixExp_num_visits1: expected number of visits to each state is our priorsPostmix: is the mixing matrixM: is the weighted observationsIp: is the weighted inner product of the observationsOp: is the weighted outer product of the observations

More on E%initializationverbose = 0;numex = length(data);O = size(data{1},1);Q = length(prior);M = size(mixmat,2);exp_num_trans = zeros(Q,Q);exp_num_visits1 = zeros(Q,1);postmix = zeros(Q,M);m = zeros(O,Q,M);op = zeros(O,O,Q,M);ip = zeros(Q,M);mix = (M>1);

One more on expectationloglik = 0;if verbose, fprintf(1, 'forwards-backwards example # '); endfor ex=1:numex if verbose, fprintf(1, '%d ', ex); end obs = data{ex}; T = size(obs,2); if mix %if you have mixtures [B, B2] = mixgauss_prob(obs, mu, Sigma, mixmat); [alpha, beta, gamma, current_loglik, xi, gamma2] = ...fwdback(prior, transmat, B, 'obslik2', B2, 'mixmat', mixmat); else %one single gaussian as an emission B = mixgauss_prob(obs, mu, Sigma); [alpha, beta, gamma, current_loglik, xi] = fwdback(prior, transmat, B); end

Almost doneloglik = loglik + current_loglik; if verbose, fprintf(1, 'll at ex %d = %f\n', ex, loglik); end

exp_num_trans = exp_num_trans + sum(xi,3); exp_num_visits1 = exp_num_visits1 + gamma(:,1); if mix postmix = postmix + sum(gamma2,3); else postmix = postmix + sum(gamma,2); gamma2 = reshape(gamma, [Q 1 T]); end

Last onefor i=1:Q for k=1:M w = reshape(gamma2(i,k,:), [1 T]); % w(t) = w(i,k,t,l) wobs = obs .* repmat(w, [O 1]); % wobs(:,t) = w(t) * obs(:,t) m(:,i,k) = m(:,i,k) + sum(wobs, 2); % m(:) = sum_t w(t) obs(:,t) op(:,:,i,k) = op(:,:,i,k) + wobs * obs'; % op(:,:) = sum_t w(t) * obs(:,t) * obs(:,t)' ip(i,k) = ip(i,k) + sum(sum(wobs .* obs, 2)); % ip = sum_t w(t) * obs(:,t)' * obs(:,t) end endendif verbose, fprintf(1, '\n'); end