[566] | 1 | function [strout, rgrsout, statistics] = straux1(L, d, nu, L0, d0, nu0, belief, nbest, max_nrep, lambda, order_k); |
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| 2 | % structure estimation based on LD decomposition |
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| 3 | % |
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| 4 | % This m/mex file is internally called by facstr, IT IS NOT TO BE CALLED |
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| 5 | % BY USER!! Documentation guiven for reference. |
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| 6 | % |
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| 7 | % |
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| 8 | % [strout, rgrsout, statistics] = straux1(L, d, nu, L0, d0, nu0, belief, nbest, max_nrep, lambda, order_k); |
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| 9 | % |
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| 10 | % L : Actual LD decomposition based on data |
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| 11 | % d : Actual LD decomposition based on data |
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| 12 | % nu : Actual data amount |
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| 13 | % L0 : prior information |
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| 14 | % d0 : prior information |
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| 15 | % nu0 : prior data amount |
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| 16 | % belief: user's belief on maximum structure items |
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| 17 | % (1 items must be present, 2 items are probably present |
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| 18 | % 4 items must not be present, 3 items are probably not present) |
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| 19 | % 2 and 3 is the same |
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| 20 | % nbest : how many "best" regressors are maintained |
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| 21 | % strout : structure estimated (of the regressor, richest is 2:length(d) |
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| 22 | % max_nrep : maximal number of random starts in search for the best |
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| 23 | % structure |
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| 24 | % lambda : stooping rule threshold |
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| 25 | % order_k : order of k |
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| 26 | % |
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| 27 | % Design : L. Tesar |
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| 28 | % Updated : Feb-Apr 2003 |
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| 29 | % Project : post-ProDaCTool |
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| 30 | % References: (only local inline functions) |
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| 31 | % |
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| 32 | % Todo: in add_new, we need to implement structure comparison, instead of |
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| 33 | % loglikelihood comparison: ~any(logliks == new.loglik) |
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| 34 | |
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| 35 | % randun seed stuff: |
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| 36 | %global SEED |
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| 37 | %SEED = randn('seed'); |
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| 38 | |
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| 39 | % Argument's checking: |
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| 40 | if nargin<8; |
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| 41 | if nargout>=2; |
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[571] | 42 | nbest = 2; |
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[566] | 43 | else |
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| 44 | % If we don't need the second parameter it is better to avoid |
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| 45 | % calculating it at all, because it is very costly (5x slowdown). |
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| 46 | nbest = 1; |
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| 47 | end; |
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| 48 | end; |
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| 49 | |
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| 50 | if nargin< 6, error('Incorrect number of input parameters in straux1'); end; |
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| 51 | if nargin< 7, belief = []; end; % Don't belive anybody. |
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[571] | 52 | if nargin< 9, max_nrep = 3; end; |
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[566] | 53 | if nargin<10, lambda = 0.75; end; |
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| 54 | if nargin<11, order_k = 2; end; |
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| 55 | % Arguments were just checked. |
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| 56 | |
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| 57 | n_data = length(d); |
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| 58 | |
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| 59 | belief_out = find(belief==4)+1; % we are avoiding to put this into regressor |
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| 60 | belief_in = find(belief==1)+1; % we are instantly keeping this in regressor |
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| 61 | |
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| 62 | full.d0 = d0; |
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| 63 | full.nu0 = nu0; |
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| 64 | full.L0 = L0; |
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| 65 | full.L = L; |
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| 66 | full.d = d; |
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| 67 | full.nu = nu; |
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| 68 | full.strL = 1:n_data; % Current structure of L and d |
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| 69 | full.strRgr = 2:n_data; % Structure elements currently inside regressor (after regressand) |
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| 70 | full.strMis = []; % structure elements, that are currently outside regressor (before regressand) |
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| 71 | full.posit1 = 1; % regressand position |
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| 72 | full.nbits = floor(log2(bitmax))-1; % number of bits available in double |
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| 73 | full.bitstr = str_bitset(zeros(1,floor(n_data/full.nbits)+1),full.strRgr,full.nbits); |
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| 74 | full.loglik = seloglik1(full); % loglikelihood |
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| 75 | |
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| 76 | % construct full and empty structure |
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| 77 | full = sestrremove(full,belief_out); |
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| 78 | empty = sestrremove(full,setdiff(full.strRgr,belief_in)); |
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| 79 | |
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| 80 | % stopping rule calculation: |
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| 81 | local_max = []; |
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| 82 | muto = 0; |
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| 83 | |
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| 84 | % statistics: |
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| 85 | cputime0 = cputime; |
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| 86 | if nargout>=3; |
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| 87 | mutos = zeros(1,max_nrep+2); |
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| 88 | maxmutos = zeros(1,max_nrep+2); |
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| 89 | end; |
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| 90 | % ---------------------- |
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| 91 | |
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| 92 | % For stopping-rule calculation |
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| 93 | %so = 2^(n_data -1-length(belief_in)- length(belief_out)); % do we use this ? |
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| 94 | % ---------------------- |
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| 95 | |
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| 96 | all_str = 1:n_data; |
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| 97 | |
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| 98 | global_best = full; |
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| 99 | |
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| 100 | % MAIN LOOP is here. |
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| 101 | for n_start = -1:max_nrep; |
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| 102 | to = n_start+2; |
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| 103 | |
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| 104 | if n_start == -1; |
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| 105 | % start from the full structure |
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| 106 | last = full; |
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| 107 | elseif n_start == 0; |
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| 108 | % start from the empty structure |
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| 109 | last = empty; |
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| 110 | else |
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| 111 | % start from random structure |
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| 112 | last_str = find([ 0 floor(2*randun(1,n_data-1))]); % this creates random vector consisting of indexes, and sorted |
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| 113 | last = sestrremove(full,setdiff(all_str,[1 last_str empty.strRgr])); |
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| 114 | end; |
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| 115 | |
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| 116 | % DEBUGging print: |
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| 117 | %fprintf('STRUCTURE generated in loop %2i was %s\n', n_start, strPrintstr(last)); |
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| 118 | |
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| 119 | % The loop is repeated until likelihood stops growing (break condition |
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| 120 | % used at the end; |
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| 121 | while 1; |
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| 122 | |
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| 123 | % This structure is going to hold the best elements |
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| 124 | best = last; |
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| 125 | % Nesting by removing elements (enpoorment) |
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| 126 | for removed_item = setdiff(last.strRgr,belief_in); |
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| 127 | new = sestrremove(last,removed_item); |
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| 128 | if nbest>1; |
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| 129 | global_best = add_new(global_best,new,nbest); |
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| 130 | end; |
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| 131 | if new.loglik>best.loglik; |
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| 132 | best = new; |
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| 133 | end; |
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| 134 | end; |
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| 135 | % Nesting by adding elements (enrichment) |
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| 136 | for added_item = setdiff(last.strMis,belief_out); |
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| 137 | new = sestrinsert(last,added_item); |
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| 138 | if nbest>1; |
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| 139 | global_best = add_new(global_best,new,nbest); |
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| 140 | end; |
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| 141 | if new.loglik>best.loglik; |
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| 142 | best = new; |
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| 143 | end; |
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| 144 | end; |
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| 145 | |
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| 146 | % Break condition if likelihood does not change. |
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| 147 | if best.loglik <= last.loglik; |
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| 148 | break; |
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| 149 | else |
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| 150 | % Making best structure last structure. |
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| 151 | last = best; |
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| 152 | end; |
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| 153 | |
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| 154 | end; |
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| 155 | |
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| 156 | % DEBUGging print: |
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| 157 | %fprintf('STRUCTURE found (local maxima) in loop %2i was %s randun_seed=%11lu randun_counter=%4lu\n', n_start, strPrintstr(best), randn('seed'), RANDUN_COUNTER); |
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| 158 | |
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| 159 | % Collecting of the best structure in case we don't need the second parameter |
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| 160 | if nbest<=1; |
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| 161 | if best.loglik>global_best.loglik; |
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| 162 | global_best = best; |
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| 163 | end; |
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| 164 | end; |
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| 165 | |
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| 166 | % uniqueness of the structure found |
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| 167 | if ~ismember(best.bitstr,local_max,'rows'); |
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| 168 | local_max = [local_max ; best.bitstr]; |
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| 169 | muto = muto + 1; |
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| 170 | end; |
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| 171 | |
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| 172 | % stopping rule: |
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| 173 | maxmuto = (to-order_k-1)/lambda-to+1; |
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| 174 | if to>2; |
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| 175 | if maxmuto>=muto; |
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| 176 | % fprintf('*'); |
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| 177 | break; |
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| 178 | end; |
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| 179 | end; |
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| 180 | |
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| 181 | % do statistics if necessary: |
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| 182 | if nargout>=3; |
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| 183 | mutos(to) = muto; |
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| 184 | maxmutos(to) = maxmuto; |
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| 185 | end; |
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| 186 | end; |
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| 187 | |
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| 188 | % Aftermath: The best structure was in: global_best |
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| 189 | |
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| 190 | % Updating loglikelihoods: we have to add the constant stuff |
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| 191 | for f=1:length(global_best); |
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| 192 | global_best(f).loglik = global_best(f).loglik + seloglik2(global_best(f)); |
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| 193 | end; |
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| 194 | |
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| 195 | % Making first output parameter: |
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| 196 | [lik i] = max([global_best.loglik]); |
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| 197 | best = global_best(i); |
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| 198 | strout = best.strRgr; |
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| 199 | |
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| 200 | % Making the second output parameter |
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| 201 | [lik i] = sort([global_best.loglik]); |
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| 202 | rgrsout = global_best(i(length(i):-1:1)); |
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| 203 | |
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| 204 | if (nargout>=3); |
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| 205 | statistics.allstrs = 2^(n_data -1-length(belief_in) - length(belief_out)); |
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| 206 | statistics.nrand = to-2; |
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| 207 | statistics.unique = muto; |
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| 208 | statistics.to = to; |
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| 209 | statistics.cputime_seconds = cputime - cputime0; |
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| 210 | statistics.itemspeed = statistics.to / statistics.cputime_seconds; |
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| 211 | statistics.muto = muto; |
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| 212 | statistics.mutos = mutos; |
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| 213 | statistics.maxmutos = maxmutos; |
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| 214 | end; |
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| 215 | |
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| 216 | % randun seed stuff: |
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| 217 | %randn('seed',SEED); |
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| 218 | |
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| 219 | % --------------------- END of MAIN program -------------------- |
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| 220 | |
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| 221 | % This is needed for bitstr manipulations |
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| 222 | function out = str_bitset(in,ns,nbits) |
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| 223 | out = in; |
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| 224 | for n = ns; |
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| 225 | index = 1+floor((n-2)/nbits); |
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| 226 | bitindex = 1+rem(n-2,nbits); |
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| 227 | out(index) = bitset(out(index),bitindex); |
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| 228 | end; |
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| 229 | function out = str_bitres(in,ns,nbits) |
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| 230 | out = in; |
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| 231 | for n = ns; |
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| 232 | index = 1+floor((n-2)/nbits); |
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| 233 | bitindex = 1+rem(n-2,nbits); |
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| 234 | mask = bitset(0,bitindex); |
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| 235 | out(index) = bitxor(bitor(out(index),mask),mask); |
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| 236 | end; |
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| 237 | |
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| 238 | function out = strPrintstr(in) |
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| 239 | out = '0'; |
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| 240 | nbits = in.nbits; |
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| 241 | for f = 2:length(in.d0); |
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| 242 | index = 1+floor((f-2)/nbits); |
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| 243 | bitindex = 1+rem(f-2,nbits); |
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| 244 | if bitget(in.bitstr(index),bitindex); |
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| 245 | out(f) = '1'; |
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| 246 | else; |
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| 247 | out(f) = '0'; |
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| 248 | end; |
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| 249 | end; |
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| 250 | |
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| 251 | function global_best_out = add_new(global_best,new,nbest) |
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| 252 | % Eventually add to global best, but do not go over nbest values |
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| 253 | % Also avoids repeating things, which makes this function awfully slow |
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| 254 | if length(global_best)>=nbest; |
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| 255 | logliks = [global_best.loglik]; |
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| 256 | [loglik i] = min(logliks); |
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| 257 | global_best_out = global_best; |
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| 258 | if loglik<new.loglik; |
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| 259 | % if ~any(logliks == new.loglik); |
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| 260 | addit=1; |
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| 261 | for f = [global_best.bitstr]; |
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| 262 | if f == new.bitstr; |
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| 263 | addit = 0; |
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| 264 | break; |
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| 265 | end; |
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| 266 | end; |
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| 267 | if addit; |
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| 268 | global_best_out(i) = new; |
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| 269 | % DEBUGging print: |
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| 270 | % fprintf('ADDED structure, add_new: %s, loglik=%g\n', strPrintstr(new), new.loglik); |
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| 271 | end; |
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| 272 | end; |
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| 273 | else; |
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| 274 | global_best_out = [global_best new]; |
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| 275 | end; |
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| 276 | |
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| 277 | function out = sestrremove(in,removed_elements); |
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| 278 | % Removes elements from regressor |
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| 279 | n_strL = length(in.strL); |
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| 280 | out = in; |
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| 281 | for f=removed_elements; |
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| 282 | posit1 = find(out.strL==1); |
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| 283 | positf = find(out.strL==f); |
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| 284 | for g=(positf-1):-1:posit1; |
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| 285 | % BEGIN: We are swapping g and g+1 NOW!!!! |
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| 286 | [out.L, out.d] = seswapudl(out.L, out.d, g); |
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| 287 | [out.L0, out.d0] = seswapudl(out.L0, out.d0, g); |
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| 288 | out.strL([g g+1]) = [out.strL(g+1) out.strL(g)]; |
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| 289 | % END |
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| 290 | end; |
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| 291 | end; |
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| 292 | out.posit1 = find(out.strL==1); |
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| 293 | out.strRgr = out.strL((out.posit1+1):n_strL); |
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| 294 | out.strMis = out.strL(1:(out.posit1-1)); |
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| 295 | out.bitstr = str_bitres(out.bitstr,removed_elements,out.nbits); |
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| 296 | out.loglik = seloglik1(out); |
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| 297 | |
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| 298 | function out = sestrinsert(in,inserted_elements); |
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| 299 | % Moves elements into regressor |
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| 300 | n_strL = length(in.strL); |
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| 301 | out = in; |
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| 302 | for f=inserted_elements; |
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| 303 | posit1 = find(out.strL==1); |
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| 304 | positf = find(out.strL==f); |
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| 305 | for g=positf:(posit1-1); |
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| 306 | % BEGIN: We are swapping g and g+1 NOW!!!! |
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| 307 | [out.L, out.d] = seswapudl(out.L, out.d, g); |
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| 308 | [out.L0, out.d0] = seswapudl(out.L0, out.d0, g); |
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| 309 | out.strL([g g+1]) = [out.strL(g+1) out.strL(g)]; |
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| 310 | % END |
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| 311 | end; |
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| 312 | end; |
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| 313 | out.posit1 = find(out.strL==1); |
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| 314 | out.strRgr = out.strL((out.posit1+1):n_strL); |
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| 315 | out.strMis = out.strL(1:(out.posit1-1)); |
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| 316 | out.bitstr = str_bitset(out.bitstr,inserted_elements,out.nbits); |
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| 317 | out.loglik = seloglik1(out); |
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| 318 | |
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| 319 | % |
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| 320 | % seloglik_real = seloglik1 + seloglik2 |
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| 321 | % |
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| 322 | |
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| 323 | function l = seloglik1(in) |
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| 324 | % This is the loglikelihood (non-constant part) - this should be used in |
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| 325 | % frequent computation |
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| 326 | len = length(in.d); |
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| 327 | p1 = in.posit1; |
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| 328 | |
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| 329 | i1 = -0.5*in.nu *log(in.d (p1)) -0.5*sum(log(in.d ((p1+1):len))); |
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| 330 | i0 = -0.5*in.nu0*log(in.d0(p1)) -0.5*sum(log(in.d0((p1+1):len))); |
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| 331 | l = i1-i0; |
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| 332 | |
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| 333 | % DEBUGGing print: |
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| 334 | % fprintf('SELOGLIK1: str=%s loglik=%g\n', strPrintstr(in), l); |
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| 335 | |
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| 336 | |
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| 337 | function l = seloglik2(in) |
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| 338 | % This is the loglikelihood (constant part) - this should be added to |
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| 339 | % everything at the end. It needs some computation, so it is useless to |
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| 340 | % make it for all the stuff |
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| 341 | logpi = log(pi); |
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| 342 | |
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| 343 | i1 = gammaln(in.nu /2) - 0.5*in.nu *logpi; |
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| 344 | i0 = gammaln(in.nu0/2) - 0.5*in.nu0*logpi; |
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| 345 | l = i1-i0; |
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| 346 | |
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| 347 | |
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| 348 | function [Lout, dout] = seswapudl(L,d,i); |
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| 349 | %SESWAPUDL swaps information matrix in decomposition V=L^T diag(d) L |
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| 350 | % |
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| 351 | % [Lout, dout] = seswapudl(L,d,i); |
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| 352 | % |
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| 353 | % L : lower triangular matrix with 1's on diagonal of the decomposistion |
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| 354 | % d : diagonal vector of diagonal matrix of the decomposition |
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| 355 | % i : index of line to be swapped with the next one |
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| 356 | % Lout : output lower triangular matrix |
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| 357 | % dout : output diagional vector of diagonal matrix D |
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| 358 | % |
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| 359 | % Description: |
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| 360 | % Lout' * diag(dout) * Lout = P(i,i+1) * L' * diag(d) * L * P(i,i+1); |
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| 361 | % |
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| 362 | % Where permutation matrix P(i,j) permutates columns if applied from the |
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| 363 | % right and line if applied from the left. |
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| 364 | % |
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| 365 | % Note: naming: |
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| 366 | % se = structure estimation |
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| 367 | % lite = light, simple |
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| 368 | % udl = U*D*L, or more precisely, L'*D*L, also called as ld |
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| 369 | % |
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| 370 | % Design : L. Tesar |
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| 371 | % Updated : Feb 2003 |
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| 372 | % Project : post-ProDaCTool |
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| 373 | % Reference: sedydr |
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| 374 | |
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| 375 | j = i+1; |
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| 376 | |
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| 377 | pomd = d(i); |
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| 378 | d(i) = d(j); |
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| 379 | d(j) = pomd; |
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| 380 | |
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| 381 | pomL = L(i,:); |
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| 382 | L(i,:) = L(j,:); |
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| 383 | L(j,:) = pomL; |
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| 384 | |
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| 385 | pomL = L(:,i); |
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| 386 | L(:,i) = L(:,j); |
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| 387 | L(:,j) = pomL; |
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| 388 | |
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| 389 | % We must be working with LINES of matrix L ! |
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| 390 | |
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| 391 | r = L(i,:)'; |
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| 392 | f = L(j,:)'; |
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| 393 | Dr = d(i); |
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| 394 | Df = d(j); |
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| 395 | |
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| 396 | [r, f, Dr, Df] = sedydr(r, f, Dr, Df, j); |
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| 397 | |
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| 398 | r0 = r(i); |
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| 399 | Dr = Dr*r0*r0; |
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| 400 | r = r/r0; |
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| 401 | |
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| 402 | L(i,:) = r'; |
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| 403 | L(j,:) = f'; |
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| 404 | d(i) = Dr; |
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| 405 | d(j) = Df; |
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| 406 | |
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| 407 | L(i,i) = 1; |
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| 408 | L(j,j) = 1; |
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| 409 | |
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| 410 | Lout = L; |
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| 411 | dout = d; |
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| 412 | |
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| 413 | function [rout, fout, Drout, Dfout, kr] = sedydr(r,f,Dr,Df,R,jl,jh); |
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| 414 | %SEDYDR dyadic reduction, performs transformation of sum of 2 dyads |
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| 415 | % |
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| 416 | % [rout, fout, Drout, Dfout, kr] = sedydr(r,f,Dr,Df,R,jl,jh); |
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| 417 | % [rout, fout, Drout, Dfout] = sedydr(r,f,Dr,Df,R); |
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| 418 | % |
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| 419 | % Description: dyadic reduction, performs transformation of sum of |
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| 420 | % 2 dyads r*Dr*r'+ f*Df*f' so that the element of r pointed by R is zeroed |
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| 421 | % |
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| 422 | % r : column vector of reduced dyad |
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| 423 | % f : column vector of reducing dyad |
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| 424 | % Dr : scalar with weight of reduced dyad |
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| 425 | % Df : scalar with weight of reducing dyad |
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| 426 | % R : scalar number giving 1 based index to the element of r, |
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| 427 | % which is to be reduced to |
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| 428 | % zero; the corresponding element of f is assumed to be 1. |
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| 429 | % jl : lower index of the range within which the dyads are |
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| 430 | % modified (can be omitted, then everything is updated) |
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| 431 | % jh : upper index of the range within which the dyads are |
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| 432 | % modified (can be omitted then everything is updated) |
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| 433 | % rout,fout,Drout,dfout : resulting two dyads |
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| 434 | % kr : coefficient used in the transformation of r |
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| 435 | % rnew = r + kr*f |
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| 436 | % |
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| 437 | % Description: dyadic reduction, performs transformation of sum of |
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| 438 | % 2 dyads r*Dr*r'+ f*Df*f' so that the element of r indexed by R is zeroed |
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| 439 | % Remark1: Constant mzero means machine zero and should be modified |
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| 440 | % according to the precision of particular machine |
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| 441 | % Remark2: jl and jh are, in fact, obsolete. It takes longer time to |
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| 442 | % compute them compared to plain version. The reason is that we |
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| 443 | % are doing vector operations in m-file. Other reason is that |
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| 444 | % we need to copy whole vector anyway. It can save half of time for |
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| 445 | % c-file, if you use it correctly. (please do tests) |
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| 446 | % |
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| 447 | % Note: naming: |
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| 448 | % se = structure estimation |
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| 449 | % dydr = dyadic reduction |
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| 450 | % |
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| 451 | % Original Fortran design: V. Peterka 17-7-89 |
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| 452 | % Modified for c-language: probably R. Kulhavy |
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| 453 | % Modified for m-language: L. Tesar 2/2003 |
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| 454 | % Updated: Feb 2003 |
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| 455 | % Project: post-ProDaCTool |
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| 456 | % Reference: none |
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| 457 | |
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| 458 | if nargin<6; |
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| 459 | update_whole=1; |
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| 460 | else |
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| 461 | update_whole=0; |
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| 462 | end; |
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| 463 | |
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| 464 | mzero = 1e-32; |
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| 465 | |
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| 466 | if Dr<mzero; |
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| 467 | Dr=0; |
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| 468 | end; |
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| 469 | |
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| 470 | r0 = r(R); |
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| 471 | kD = Df; |
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| 472 | kr = r0 * Dr; |
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| 473 | Dfout = kD + r0 * kr; |
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| 474 | |
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| 475 | if Dfout > mzero; |
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| 476 | kD = kD / Dfout; |
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| 477 | kr = kr / Dfout; |
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| 478 | else; |
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| 479 | kD = 1; |
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| 480 | kr = 0; |
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| 481 | end; |
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| 482 | |
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| 483 | Drout = Dr * kD; |
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| 484 | |
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| 485 | % Try to uncomment marked stuff (*) if in numerical problems, but I don't |
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| 486 | % think it can make any difference for normal healthy floating-point unit |
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| 487 | if update_whole; |
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| 488 | rout = r - r0*f; |
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| 489 | % rout(R) = 0; % * could be needed for some nonsense cases(or numeric reasons?), normally not |
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| 490 | fout = f + kr*rout; |
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| 491 | % fout(R) = 1; % * could be needed for some nonsense cases(or numeric reasons?), normally not |
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| 492 | else; |
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| 493 | rout = r; |
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| 494 | fout = f; |
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| 495 | rout(jl:jh) = r(jl:jh) - r0 * f(jl:jh); |
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| 496 | rout(R) = 0; |
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| 497 | fout(jl:jh) = f(jl:jh) + kr * rout(jl:jh); |
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| 498 | end; |
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| 499 | |
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| 500 | |
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| 501 | |
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| 502 | |
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| 503 | |
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| 504 | |
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