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1 ## Copyright (C) 1995, 1996 Kurt Hornik |
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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} {} diff (@var{x}, @var{k}, @var{dim}) |
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21 ## If @var{x} is a vector of length @var{n}, @code{diff (@var{x})} is the |
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22 ## vector of first differences |
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23 ## @iftex |
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24 ## @tex |
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25 ## $x_2 - x_1, \ldots{}, x_n - x_{n-1}$. |
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26 ## @end tex |
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27 ## @end iftex |
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28 ## @ifinfo |
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29 ## @var{x}(2) - @var{x}(1), @dots{}, @var{x}(n) - @var{x}(n-1). |
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30 ## @end ifinfo |
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31 ## |
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32 ## If @var{x} is a matrix, @code{diff (@var{x})} is the matrix of column |
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33 ## differences along the first non-singleton dimension. |
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34 ## |
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35 ## The second argument is optional. If supplied, @code{diff (@var{x}, |
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36 ## @var{k})}, where @var{k} is a nonnegative integer, returns the |
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37 ## @var{k}-th differences. It is possible that @var{k} is larger than |
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38 ## then first non-singleton dimension of the matrix. In this case, |
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39 ## @code{diff} continues to take the differences along the next |
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40 ## non-singleton dimension. |
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41 ## |
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42 ## The dimension along which to take the difference can be explicitly |
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43 ## stated with the optional variable @var{dim}. In this case the |
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44 ## @var{k}-th order differences are calculated along this dimension. |
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45 ## In the case where @var{k} exceeds @code{size (@var{x}, @var{dim})} |
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46 ## then an empty matrix is returned. |
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47 ## @end deftypefn |
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48 |
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49 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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50 ## Created: 2 February 1995 |
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51 ## Adapted-By: jwe |
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52 |
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53 function x = diff (x, k, dim) |
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54 |
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55 if (nargin < 1 || nargin > 3) |
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56 print_usage (); |
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57 endif |
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58 |
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59 if (nargin < 2 || isempty(k)) |
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60 k = 1; |
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61 else |
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62 if (! (isscalar (k) && k == round (k) && k >= 0)) |
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63 error ("diff: k must be a nonnegative integer"); |
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64 elseif (k == 0) |
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65 return; |
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66 endif |
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67 endif |
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68 |
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69 nd = ndims (x); |
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70 sz = size (x); |
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71 if (nargin != 3) |
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72 %% Find the first non-singleton dimension |
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73 dim = 1; |
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74 while (dim < nd + 1 && sz (dim) == 1) |
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75 dim = dim + 1; |
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76 endwhile |
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77 if (dim > nd) |
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78 dim = 1; |
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79 endif |
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80 else |
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81 if (! (isscalar (dim) && dim == round (dim)) && dim > 0 && |
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82 dim < (nd + 1)) |
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83 error ("diff: dim must be an integer and valid dimension"); |
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84 endif |
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85 endif |
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86 |
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87 if (ischar (x)) |
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88 error ("diff: symbolic differentiation not (yet) supported"); |
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89 endif |
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90 |
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91 |
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92 if (nargin == 3) |
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93 if (sz (dim) <= k) |
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94 sz(dim) = 0; |
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95 x = zeros (sz); |
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96 else |
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97 n = sz (dim); |
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98 idx1 = cell (); |
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99 for i = 1:nd |
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100 idx1 {i} = 1:sz(i); |
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101 endfor |
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102 idx2 = idx1; |
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103 for i = 1 : k; |
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104 idx1 {dim} = 2 : (n - i + 1); |
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105 idx2 {dim} = 1 : (n - i); |
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106 x = x (idx1 {:}) - x (idx2 {:}); |
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107 endfor |
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108 endif |
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109 else |
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110 if (sum (sz - 1) < k) |
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111 x = []; |
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112 else |
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113 idx1 = cell (); |
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114 for i = 1:nd |
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115 idx1 {i} = 1:sz(i); |
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116 endfor |
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117 idx2 = idx1; |
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118 while (k) |
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119 n = sz (dim); |
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120 for i = 1 : min (k, n - 1) |
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121 idx1 {dim} = 2 : (n - i + 1); |
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122 idx2 {dim} = 1 : (n - i); |
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123 x = x (idx1 {:}) - x (idx2 {:}); |
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124 endfor |
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125 idx1 {dim} = idx2 {dim} = 1; |
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126 k = k - min (k, n - 1); |
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127 dim = dim + 1; |
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128 endwhile |
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129 endif |
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130 endif |
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131 |
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132 endfunction |
