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gallery.m: clean and vectorize part of qmult. * scripts/special-matrix/gallery.m: make qmult() follow Octave guidelines, vectorize last for loop in qmult().
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 28 May 2015 18:32:47 +0200
parents 33e706b6b7be
children 7503499a252b
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1 ## Copyright (C) 2015 Carnë Draug
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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} {@var{area} =} rectint (@var{a}, @var{b})
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21 ## Compute area or volume of intersection of rectangles or ND boxes.
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22 ##
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23 ## Compute the area of intersection of rectangles in @var{a} and
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24 ## rectangles in @var{b}. N dimensional boxes are supported in which
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25 ## case the volume, or hypervolume is computed according to the number
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26 ## of dimensions.
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27 ##
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28 ## 2 dimensional rectangles are defined as @code{[xpos ypos width height]}
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29 ## where xpos and ypos are the position of the bottom left corner.
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30 ## Higher dimensions are supported where the coordinates for the minimum
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31 ## value of each dimension follow the length of the box in that dimension,
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32 ## e.g., @code{[xpos ypos zpos kpos @dots{} width height depth k_length @dots{}]}.
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33 ##
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34 ## Each row of @var{a} and @var{b} define a rectangle, and if both define
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35 ## multiple rectangles, then the output, @var{area}, is a matrix where
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36 ## the i-th row corresponds to the i-th row of a and the j-th column
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37 ## corresponds to the j-th row of b.
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38 ##
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39 ## @seealso{polyarea}
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40 ## @end deftypefn
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41
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42 ## Author: 2015 Carnë Draug <carandraug@octave.org>
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43
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44 function dists = rectint (a, b)
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45
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46 if (nargin != 2)
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47 print_usage ();
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48 elseif (columns (a) != columns (b))
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49 error ("rectint: A and B must have same number of columns");
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50 elseif (ndims (a) > 2)
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51 error ("rectint: A and B must be 2-d arrays");
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52 elseif (mod (columns (a), 2))
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53 error ("rectint: number of columns of A and B must be a multiple of two");
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54 endif
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55
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56 nd = columns (a) / 2;
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57 na = rows (a);
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58 nb = rows (b);
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59
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60 a_start = a(:,1:nd);
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61 b_start = b(:,1:nd);
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62
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63 a_end = a_start + a(:,nd+1:end);
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64 b_end = b_start + b(:,nd+1:end);
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65
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66 a_start = reshape (a_start, [na 1 nd]);
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67 b_start = reshape (b_start, [1 nb nd]);
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68
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69 a_end = reshape (a_end, [na 1 nd]);
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70 b_end = reshape (b_end, [1 nb nd]);
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71
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72 ## We get a 3d matrix where each dimension is in the 3rd dimension
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73 dists = bsxfun (@min , a_end, b_end) - bsxfun (@max, a_start, b_start);
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74 dists(dists < 0) = 0;
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75 dists = prod (dists, 3);
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76
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77 endfunction
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78
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79 ## Exactly overlapping
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80 %!assert (rectint ([0 0 1 1], [0 0 1 1]), 1)
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81 ## rect2 completely enclosed by rect1
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82 %!assert (rectint ([-1 -1 3 3], [0 0 1 1]), 1)
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83 ## rect1 completely enclosed by rect2
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84 %!assert (rectint ([0 0 1 1], [-1 -1 3 3]), 1)
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85 ## rect1 right and top in rect2
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86 %!assert (rectint ([-1 -1 1.5 1.5], [0 0 1 1]), 0.25)
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87 ## rect2 right and top in rect1
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88 %!assert (rectint ([0 0 1 1], [-1 -1 1.5 1.5]), 0.25)
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89 ## no overlap - shared corner
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90 %!assert (rectint ([0 0 1 1], [1 1 2 2]), 0)
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91 ## no overlap - shared edge
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92 %!assert (rectint ([0 0 1 1], [0 1 2 2]), 0)
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93 ## Correct orientation of output
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94 %!assert (rectint ([0 0 1 1;0.5 0.5 1 1;-1 -1 2 2], [1 1 2 2]), [0;0.25;0])
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95 %!assert (rectint ([1 1 2 2], [0 0 1 1;0.5 0.5 1 1;-1 -1 2 2]), [0 0.25 0])
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96
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97 ## bug #44904
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98 %!assert (rectint ([0 0 5 5], [6 6 5 5]), 0)
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99 %!assert (rectint ([0 0 5 5], [0 6 5 5]), 0)
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100 %!assert (rectint ([0 0 5 5], [6 0 5 5]), 0)
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101 %!assert (rectint ([0 0 0 5 5 5], [0 0 6 5 5 5]), 0)
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102
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103 ## Test volumes
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104 %!shared r1, r2, r3, r4, r5
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105 %! r1 = [ 5 3 0 7 5 2];
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106 %! r2 = [ 2 5 0 4 2 2];
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107 %! r3 = [ 10 7 0 10 3 2];
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108 %! r4 = [ 10 -5 0 5 7 2];
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109 %! r5 = [-10 0 0 40 11 2];
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110
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111 %!assert (rectint (r5, r1), 70)
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112 %!assert (rectint (r5, r4), 20)
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113 %!assert (rectint (r5, [r1; r2; r3; r4]), [70 16 60 20])
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114
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115 ## Test multiple volumes in both A and B
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116 %!assert (rectint ([r2; r5], [r1; r3; r4]), [4 0 0; 70 60 20])