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1 ## Copyright (C) 2000 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 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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {@var{x} = } gradient (@var{M}) |
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22 ## @deftypefnx {Function File} {[@var{x}, @var{y}, @dots{}] = } gradient (@var{M}) |
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23 ## @deftypefnx {Function File} {[@dots{}] = } gradient (@var{M}, @var{s}) |
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24 ## @deftypefnx {Function File} {[@dots{}] = } gradient (@var{M}, @var{dx}, @var{dy}, @dots{}) |
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25 ## |
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26 ## Calculates the gradient. @code{@var{x} = gradient (@var{M})} |
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27 ## calculates the one dimensional gradient if @var{M} is a vector. If |
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28 ## @var{M} is a matrix the gradient is calculated for each row. |
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29 ## |
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30 ## @code{[@var{x}, @var{y}] = gradient (@var{M})} calculates the one |
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31 ## dimensional gradient for each direction if @var{M} if @var{M} is a |
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32 ## matrix. Additional return arguments can be use for multi-dimensional |
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33 ## matrices. |
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34 ## |
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35 ## Spacing values between two points can be provided by the |
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36 ## @var{dx}, @var{dy} or @var{h} parameters. If @var{h} is supplied it |
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37 ## is assumed to be the spacing in all directions. Otherwise, seperate |
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38 ## values of the spacing can be supplied by the @var{dx}, etc variables. |
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39 ## A scalar value specifies an equidistant spacing, while a vector value |
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40 ## can be used to specify a variable spacing. The length must match |
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41 ## their respective dimension of @var{M}. |
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42 ## |
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43 ## At boundary points a linear extrapolation is applied. Interior points |
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44 ## are calculated with the first approximation of the numerical gradient |
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45 ## |
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46 ## @example |
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47 ## y'(i) = 1/(x(i+1)-x(i-1)) *(y(i-1)-y(i+1)). |
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48 ## @end example |
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49 ## |
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50 ## @end deftypefn |
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51 |
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52 ## Author: Kai Habel <kai.habel@gmx.de> |
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53 ## Modified: David Bateman <dbateman@free.fr> Added NDArray support |
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54 |
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55 function [varargout] = gradient (M, varargin) |
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56 |
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57 if (nargin < 1) |
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58 print_usage () |
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59 endif |
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60 |
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61 transposed = false; |
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62 if (isvector (M)) |
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63 ## make a column vector |
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64 transposed = (size (M, 2) == 1); |
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65 M = M(:)'; |
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66 endif |
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67 |
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68 nd = ndims (M); |
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69 sz = size (M); |
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70 if (nargin > 2 && nargin != nd + 1) |
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71 print_usage () |
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72 endif |
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73 |
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74 d = cell (1, nd); |
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75 if (nargin == 1) |
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76 for i=1:nd |
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77 d{i} = ones (sz(i), 1); |
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78 endfor |
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79 elseif (nargin == 2) |
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80 if (isscalar (varargin{1})) |
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81 for i = 1:nd |
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82 d{i} = varargin{1} * ones (sz(i), 1); |
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83 endfor |
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84 else |
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85 for i = 1:nd |
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86 d{i} = varargin{1}; |
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87 endfor |
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88 endif |
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89 else |
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90 for i=1:nd |
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91 if (isscalar (varargin{1})) |
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92 d{i} = varargin{i} * ones (sz(i), 1); |
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93 else |
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94 d{i} = varargin{i}; |
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95 endif |
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96 endfor |
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97 |
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98 ## Why the hell did matlab decide to swap these two values? |
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99 tmp = d{1}; |
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100 d{1} = d{2}; |
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101 d{2} = tmp; |
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102 endif |
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103 |
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104 for i = 1:max (2, min (nd, nargout)) |
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105 mr = sz(i); |
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106 mc = prod ([sz(1:i-1), sz(i+1:nd)]); |
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107 Y = zeros (size (M), class (M)); |
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108 |
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109 if (mr > 1) |
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110 ## top and bottom boundary |
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111 Y(1,:) = diff (M(1:2,:)) / d{i}(1); |
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112 Y(mr,:) = diff (M(mr-1:mr,:)) / d{i}(mr-1); |
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113 endif |
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114 |
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115 if (mr > 2) |
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116 ## interior points |
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117 Y(2:mr-1,:) = (M(3:mr,:) .- M(1:mr-2,:)) ... |
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118 ./ kron (d{i}(1:mr-2) .+ d{i}(2:mr-1), ones (1, mc)); |
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119 endif |
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120 varargout{i} = ipermute (Y, [i:nd,1:i-1]); |
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121 M = permute (M, [2:nd,1]); |
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122 endfor |
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123 |
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124 ## Why the hell did matlab decide to swap these two values? |
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125 tmp = varargout{1}; |
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126 varargout{1} = varargout{2}; |
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127 varargout{2} = tmp; |
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128 |
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129 if (transposed) |
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130 varargout{1} = varargout{1}.'; |
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131 endif |
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132 endfunction |
