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1 ## Copyright (C) 2000, 2006, 2007 Kai Habel |
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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{x} =} gradient (@var{M}) |
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21 ## @deftypefnx {Function File} {[@var{x}, @var{y}, @dots{}] =} gradient (@var{M}) |
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22 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{M}, @var{s}) |
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23 ## @deftypefnx {Function File} {[@dots{}] =} gradient (@var{M}, @var{dx}, @var{dy}, @dots{}) |
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24 ## |
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25 ## Calculates the gradient. @code{@var{x} = gradient (@var{M})} |
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26 ## calculates the one dimensional gradient if @var{M} is a vector. If |
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27 ## @var{M} is a matrix the gradient is calculated for each row. |
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28 ## |
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29 ## @code{[@var{x}, @var{y}] = gradient (@var{M})} calculates the one |
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30 ## dimensional gradient for each direction if @var{M} if @var{M} is a |
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31 ## matrix. Additional return arguments can be use for multi-dimensional |
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32 ## matrices. |
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33 ## |
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34 ## Spacing values between two points can be provided by the |
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35 ## @var{dx}, @var{dy} or @var{h} parameters. If @var{h} is supplied it |
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36 ## is assumed to be the spacing in all directions. Otherwise, separate |
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37 ## values of the spacing can be supplied by the @var{dx}, etc variables. |
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38 ## A scalar value specifies an equidistant spacing, while a vector value |
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39 ## can be used to specify a variable spacing. The length must match |
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40 ## their respective dimension of @var{M}. |
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41 ## |
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42 ## At boundary points a linear extrapolation is applied. Interior points |
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43 ## are calculated with the first approximation of the numerical gradient |
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44 ## |
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45 ## @example |
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46 ## y'(i) = 1/(x(i+1)-x(i-1)) *(y(i-1)-y(i+1)). |
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47 ## @end example |
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48 ## |
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49 ## @end deftypefn |
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50 |
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51 ## Author: Kai Habel <kai.habel@gmx.de> |
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52 ## Modified: David Bateman <dbateman@free.fr> Added NDArray support |
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53 |
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54 function varargout = gradient (M, varargin) |
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55 |
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56 if (nargin < 1) |
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57 print_usage () |
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58 endif |
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59 |
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60 transposed = false; |
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61 if (isvector (M)) |
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62 ## Make a column vector. |
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63 transposed = (size (M, 2) == 1); |
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64 M = M(:)'; |
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65 endif |
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66 |
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67 nd = ndims (M); |
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68 sz = size (M); |
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69 if (nargin > 2 && nargin != nd + 1) |
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70 print_usage () |
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71 endif |
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72 |
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73 d = cell (1, nd); |
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74 if (nargin == 1) |
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75 for i = 1:nd |
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76 d{i} = ones (sz(i), 1); |
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77 endfor |
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78 elseif (nargin == 2) |
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79 if (isscalar (varargin{1})) |
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80 for i = 1:nd |
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81 d{i} = varargin{1} * ones (sz(i), 1); |
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82 endfor |
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83 else |
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84 for i = 1:nd |
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85 d{i} = varargin{1}; |
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86 endfor |
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87 endif |
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88 else |
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89 for i = 1:nd |
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90 if (isscalar (varargin{i})) |
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91 ## Why the hell did Matlab decide to swap these two values? |
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92 if (i == 1) |
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93 d{2} = varargin{1} * ones (sz(2), 1); |
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94 elseif (i == 2) |
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95 d{1} = varargin{2} * ones (sz(1), 1); |
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96 else |
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97 d{i} = varargin{i} * ones (sz(i), 1); |
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98 endif |
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99 else |
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100 ## Why the hell did Matlab decide to swap these two values? |
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101 if (i == 1) |
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102 d{2} = varargin{1}; |
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103 elseif (i == 2) |
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104 d{1} = varargin{2}; |
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105 else |
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106 d{i} = varargin{i}; |
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107 endif |
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108 endif |
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109 endfor |
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110 endif |
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111 |
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112 for i = 1:max (2, min (nd, nargout)) |
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113 mr = sz(i); |
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114 mc = prod ([sz(1:i-1), sz(i+1:nd)]); |
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115 Y = zeros (size (M), class (M)); |
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116 |
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117 if (mr > 1) |
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118 ## Top and bottom boundary. |
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119 Y(1,:) = diff (M(1:2,:)) / d{i}(1); |
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120 Y(mr,:) = diff (M(mr-1:mr,:)) / d{i}(mr-1); |
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121 endif |
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122 |
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123 if (mr > 2) |
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124 ## Interior points. |
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125 Y(2:mr-1,:) = (M(3:mr,:) .- M(1:mr-2,:)) ... |
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126 ./ kron (d{i}(1:mr-2) .+ d{i}(2:mr-1), ones (1, mc)); |
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127 endif |
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128 varargout{i} = ipermute (Y, [i:nd,1:i-1]); |
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129 M = permute (M, [2:nd,1]); |
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130 endfor |
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131 |
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132 ## Why the hell did Matlab decide to swap these two values? |
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133 tmp = varargout{1}; |
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134 varargout{1} = varargout{2}; |
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135 varargout{2} = tmp; |
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136 |
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137 if (transposed) |
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138 varargout{1} = varargout{1}.'; |
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139 endif |
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140 endfunction |
