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binoinv.m: Implement binary search algorithm for 28X performance increase (bug #34363). * binoinv.m: Call new functions scalar_binoinv or vector_binoinv to calculate binoinv. If there are still uncalculated values then call bin_search_binoinv to perform binary search for remaining values. Add more BIST tests. * binoinv.m (scalar_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000. * binoinv.m (vector_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000.
author Lachlan Andrew <lachlanbis@gmail.com>
date Sun, 11 Oct 2015 19:49:40 -0700
parents 2645f9ef8c88
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
19898
4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 1999-2015 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 3 of the License, or (at
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8 ## your option) 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, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} magic (@var{n})
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21 ##
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22 ## Create an @var{n}-by-@var{n} magic square.
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23 ##
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24 ## A magic square is an arrangement of the integers @code{1:n^2} such that the
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25 ## row sums, column sums, and diagonal sums are all equal to the same value.
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26 ##
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27 ## Note: @var{n} must be greater than 2 for the magic square to exist.
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28 ## @end deftypefn
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29
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30 function A = magic (n)
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31
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32 if (nargin != 1)
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33 print_usage ();
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34 endif
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35
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36 if (n != fix (n) || n < 0 || n == 2)
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37 error ("magic: N must be a positive integer not equal to 2");
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38 endif
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39
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40 if (n == 0)
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41
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42 A = [];
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43
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44 elseif (mod (n, 2) == 1)
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45
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46 shift = floor ((0:n*n-1)/n);
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47 c = mod ([1:n*n] - shift + (n-3)/2, n);
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48 r = mod ([n*n:-1:1] + 2*shift, n);
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49 A(c*n+r+1) = 1:n*n;
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50 A = reshape (A, n, n);
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51
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52 elseif (mod (n, 4) == 0)
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53
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54 A = reshape (1:n*n, n, n)';
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55 I = [1:4:n, 4:4:n];
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56 J = fliplr (I);
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57 A(I,I) = A(J,J);
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58 I = [2:4:n, 3:4:n];
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59 J = fliplr (I);
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60 A(I,I) = A(J,J);
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61
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62 elseif (mod (n, 4) == 2)
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63
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64 m = n/2;
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65 A = magic (m);
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66 A = [A, A+2*m*m; A+3*m*m, A+m*m];
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67 k = (m-1)/2;
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68 if (k > 1)
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69 I = 1:m;
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70 J = [2:k, n-k+2:n];
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71 A([I,I+m],J) = A([I+m,I],J);
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72 endif
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73 I = [1:k, k+2:m];
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74 A([I,I+m],1) = A([I+m,I],1);
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75 I = k + 1;
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76 A([I,I+m],I) = A([I+m,I],I);
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77
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78 endif
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79
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80 endfunction
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81
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82
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83 %!test
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84 %! for i = 3:30
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85 %! A = magic (i);
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86 %! assert (norm(diff([sum(diag(A)),sum(diag(flipud(A))),sum(A),sum(A')])),0);
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87 %! endfor
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88
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89 %!assert (isempty (magic (0)))
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90 %!assert (magic (1), 1)
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91
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92 ## Test input validation
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93 %!error magic ()
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94 %!error magic (1, 2)
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95 %!error <N must be a positive integer not equal to 2> magic (1.5)
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96 %!error <N must be a positive integer not equal to 2> magic (-1)
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97 %!error <N must be a positive integer not equal to 2> magic (2)
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98