Multidimensional arrays in Matlab

1
Multidimensional arrays in Matlab

• Xanadu Halkias

2
Overview

• Creating/accessing/indexing multidimensional
  arrays
• Using and computing with multidimensional arrays
• Multidimensional cell arrays
• Multidimensional structure arrays

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Corpus hypercubus
Creating multidimensional arrays a 1 2 30 6
42 5 4 a(,,2) 4 2 10 5 16 3
2 a(,,3) 3 turning a into a
3x3x3x2 a(,,,2) ones(3,3,3) a(,,1,2) 4
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More on creating

• different way
• b repmat(2,3 3 3 2)
• c repmat(rand(2),3 1 2)
• one more
• d cat(4,1 4 2 3,5 82 3)

Memory try to pre-allocate eg. zeros or use
repmat for best performance
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A few good functions

• reshape and permute
• a bunch of data
• x rand(3,3,2)
• new_x reshape(x,6 3)
• tranx permute(x,2 1 3)
• Ind sub2ind(size(x),1,3,2)

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Working with them

• computing with multidimensional arrays
• x rand(3,3,3)
• s sum(x,3)
• d sin(x)
• e eig(x(,,2))
• ee eig(squeeze(x(2,,)))

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Multidimensional cell arrays

• multidimensional cells
• a 1 2 5 3 77 2 4 5, 110 rand(1,3), 2
• b 1215, rand(1,5) 1 0 0 1, 5
• c cat(3,a,b)
• D1 conv(c12)
• D2 conv(c1,1,)
• d cell2mat(D)
• for i1length(D1),
• m1(i) D1(i)
• end
• for i1length(D2),
• m2(i) D2(i)
• end
• m m1, m2

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Multidimensional structure arrays

• multidimensional structures
• dolphin(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)

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Multidimensional structures more

• computing some stuff
• s sum(dolphin.sampfreq)
• b1 fft(dolphin(1,1,1).signal)
• dolphin(1,1,1).fourier b

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Murphys mhmm_em.m

• each page gets its own cell
• if iscell(data)
• data num2cell(data, 1 2)
• end
• numex length(data) num of pages is number
• mixtures
• O size(data1,1) getting the dimensionality
• Q length(prior) number of states
• if isempty(mixmat)number of mixtures
• mixmat ones(Q,1)
• end
• M size(mixmat,2)
• if M 1
• adj_mix 0
• end

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Murphys more-EM

• while (num_iter lt max_iter) converged
• E step
• loglik, exp_num_trans, exp_num_visits1,
  postmix, m, ip, op ...
• ess_mhmm(prior, transmat, mixmat, mu,
  Sigma, data)
• M step
• if verbose, fprintf(1, 'iteration d, loglik
  f\n', num_iter, loglik) end
• num_iter num_iter 1
• converged em_converged(loglik,previous_loglik,
  thresh)
• previous_loglik loglik
• LL LL loglik
• end

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The E of EM

• function loglik, exp_num_trans, exp_num_visits1,
  postmix, m, ip, op ... ess_mhmm(prior,
  transmat, mixmat, mu, Sigma, data)
• Loglik likelihood of the model
• Exp_num_trans expected number of transitions is
  the transition matrix
• Exp_num_visits1 expected number of visits to
  each state is our priors
• Postmix is the mixing matrix
• M is the weighted observations
• Ip is the weighted inner product of the
  observations
• Op is the weighted outer product of the
  observations

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More on E

• initialization
• verbose 0
• numex length(data)
• O size(data1,1)
• 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 (Mgt1)

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One more on expectation

• loglik 0
• if verbose, fprintf(1, 'forwards-backwards
  example ') end
• for ex1numex
• if verbose, fprintf(1, 'd ', ex) end
• obs dataex
• 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

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Almost done

• loglik 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

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Last one

• for i1Q
• for k1M
• 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
• end
• end
• if verbose, fprintf(1, '\n') end