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1 ## Copyright (C) 2000 Paul Kienzle |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} ismember(@var{A}, @var{S}) |
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22 ## |
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23 ## Return a matrix the same shape as @var{A} which has 1 if |
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24 ## @code{A(i,j)} is in @var{S} or 0 if it isn't. |
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25 ## |
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26 ## @end deftypefn |
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27 ## @seealso{unique, union, intersect, setxor, setdiff} |
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28 |
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29 ## Author: Paul Kienzle |
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30 ## Adapted-by: jwe |
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31 |
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32 function c = ismember (a, S) |
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33 |
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34 if (nargin != 2) |
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35 usage ("ismember (A, S)"); |
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36 endif |
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37 |
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38 [ra, ca] = size (a); |
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39 if (isempty (a) || isempty (S)) |
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40 c = zeros (ra, ca); |
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41 else |
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42 S = unique (S(:)); |
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43 lt = length (S); |
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44 if (lt == 1) |
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45 c = (a == S); |
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46 elseif (ra*ca == 1) |
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47 c = any (a == S); |
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48 else |
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49 ## Magic: the following code determines for each a, the index i |
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50 ## such that S(i)<= a < S(i+1). It does this by sorting the a |
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51 ## into S and remembering the source index where each element came |
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52 ## from. Since all the a's originally came after all the S's, if |
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53 ## the source index is less than the length of S, then the element |
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54 ## came from S. We can then do a cumulative sum on the indices to |
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55 ## figure out which element of S each a comes after. |
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56 ## E.g., S=[2 4 6], a=[1 2 3 4 5 6 7] |
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57 ## unsorted [S a] = [ 2 4 6 1 2 3 4 5 6 7 ] |
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58 ## sorted [ S a ] = [ 1 2 2 3 4 4 5 6 6 7 ] |
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59 ## source index p = [ 4 1 5 6 2 7 8 3 9 10 ] |
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60 ## boolean p<=l(S) = [ 0 1 0 0 1 0 0 1 0 0 ] |
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61 ## cumsum(p<=l(S)) = [ 0 1 1 1 2 2 2 3 3 3 ] |
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62 ## Note that this leaves a(1) coming after S(0) which doesn't |
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63 ## exist. So arbitrarily, we will dump all elements less than |
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64 ## S(1) into the interval after S(1). We do this by dropping S(1) |
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65 ## from the sort! E.g., S=[2 4 6], a=[1 2 3 4 5 6 7] |
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66 ## unsorted [S(2:3) a] =[4 6 1 2 3 4 5 6 7 ] |
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67 ## sorted [S(2:3) a] = [ 1 2 3 4 4 5 6 6 7 ] |
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68 ## source index p = [ 3 4 5 1 6 7 2 8 9 ] |
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69 ## boolean p<=l(S)-1 = [ 0 0 0 1 0 0 1 0 0 ] |
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70 ## cumsum(p<=l(S)-1) = [ 0 0 0 1 1 1 2 2 2 ] |
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71 ## Now we can use Octave's lvalue indexing to "invert" the sort, |
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72 ## and assign all these indices back to the appropriate A and S, |
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73 ## giving S_idx = [ -- 1 2], a_idx = [ 0 0 0 1 1 2 2 ]. Add 1 to |
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74 ## a_idx, and we know which interval S(i) contains a. It is |
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75 ## easy to now check membership by comparing S(a_idx) == a. This |
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76 ## magic works because S starts out sorted, and because sort |
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77 ## preserves the relative order of identical elements. |
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78 [v, p] = sort ([S(2:lt); a(:)]); |
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79 idx(p) = cumsum (p <= lt-1) + 1; |
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80 idx = idx(lt:lt+ra*ca-1); |
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81 c = (a == reshape (S(idx), size (a))); |
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82 endif |
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83 endif |
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84 |
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85 endfunction |
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86 |
