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annotate scripts/polynomial/conv.m @ 15063:36cbcc37fdb8

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Refactor configure.ac to make it more understandable. Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests. * configure.ac, m4/acinclude.m4: Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests.
author Rik <rik@octave.org>
date Tue, 31 Jul 2012 10:28:51 -0700
parents f3d52523cde1
children bc924baa2c4e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 1994-2012 John W. Eaton
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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} {} conv (@var{a}, @var{b})
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21 ## @deftypefnx {Function File} {} conv (@var{a}, @var{b}, @var{shape})
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22 ## Convolve two vectors @var{a} and @var{b}.
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23 ##
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24 ## The output convolution is a vector with length equal to
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25 ## @code{length (@var{a}) + length (@var{b}) - 1}.
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26 ## When @var{a} and @var{b} are the coefficient vectors of two polynomials, the
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27 ## convolution represents the coefficient vector of the product polynomial.
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28 ##
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29 ## The optional @var{shape} argument may be
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30 ##
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31 ## @table @asis
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32 ## @item @var{shape} = "full"
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33 ## Return the full convolution. (default)
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34 ##
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35 ## @item @var{shape} = "same"
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36 ## Return the central part of the convolution with the same size as @var{a}.
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37 ## @end table
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38 ##
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39 ## @seealso{deconv, conv2, convn, fftconv}
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40 ## @end deftypefn
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41
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42 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
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43 ## Created: June 1994
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44 ## Adapted-By: jwe
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45
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46 function y = conv (a, b, shape = "full")
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47
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48 if (nargin < 2 || nargin > 3)
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49 print_usage ();
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50 endif
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51
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52 if (! (isvector (a) && isvector (b)))
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53 error ("conv: both arguments A and B must be vectors");
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54 elseif (nargin == 3 && ! any (strcmpi (shape, {"full", "same", "valid"})))
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55 error ('conv: SHAPE argument must be "full", "same", or "valid"');
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56 endif
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57
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58 la = la_orig = length (a);
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59 lb = lb_orig = length (b);
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60
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61 ly = la + lb - 1;
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62
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63 if (ly == 0)
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64 y = zeros (1, 0);
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65 return;
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66 endif
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67
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68 ## Use shortest vector as the coefficent vector to filter.
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69 if (la > lb)
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70 [a, b] = deal (b, a); # Swap vectors
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71 lb = la;
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72 endif
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73 x = b;
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74
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75 ## Pad longer vector to convolution length.
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76 if (ly > lb)
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77 x(end+1:end+ly-lb) = 0;
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78 endif
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79
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80 y = filter (a, 1, x);
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81
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82 if (strcmpi (shape, "same"))
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83 idx = ceil ((ly - la) / 2);
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84 y = y(idx+1:idx+la);
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85 elseif (strcmpi (shape, "valid"))
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86 len = la_orig - lb_orig;
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87 y = y(lb_orig:lb_orig+len);
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88 endif
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89
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90 endfunction
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91
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92
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93 %!test
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94 %! x = ones (3,1);
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95 %! y = ones (1,3);
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96 %! b = 2;
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97 %! c = 3;
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98 %! assert (conv (x, x), [1; 2; 3; 2; 1]);
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99 %! assert (conv (y, y), [1, 2, 3, 2, 1]);
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100 %! assert (conv (x, y), [1, 2, 3, 2, 1]);
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101 %! assert (conv (y, x), [1; 2; 3; 2; 1]);
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102 %! assert (conv (c, x), [3; 3; 3]);
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103 %! assert (conv (c, y), [3, 3, 3]);
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104 %! assert (conv (x, c), [3; 3; 3]);
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105 %! assert (conv (y, c), [3, 3, 3]);
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106 %! assert (conv (b, c), 6);
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107
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108 %!shared a,b
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109 %!test
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110 %! a = 1:10;
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111 %! b = 1:3;
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112 %!assert (size (conv (a,b)), [1, numel(a)+numel(b)-1])
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113 %!assert (size (conv (b,a)), [1, numel(a)+numel(b)-1])
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114
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115 %!test
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116 %! a = (1:10).';
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117 %!assert (size (conv (a,b)), [numel(a)+numel(b)-1, 1])
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118 %!assert (size (conv (b,a)), [numel(a)+numel(b)-1, 1])
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119
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120 %!test
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121 %! a = 1:10;
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122 %! b = (1:3).';
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123 %!assert (size (conv (a,b)), [1, numel(a)+numel(b)-1])
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124 %!assert (size (conv (b,a)), [1, numel(a)+numel(b)-1])
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125
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126 %!test
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127 %! a = 1:10;
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128 %! b = 1:3;
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129
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130 %!assert (conv (a,b,"full"), conv (a,b))
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131 %!assert (conv (b,a,"full"), conv (b,a))
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132
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133 %!assert (conv (a,b,"same"), [4, 10, 16, 22, 28, 34, 40, 46, 52, 47])
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134 %!assert (conv (b,a,"same"), [28, 34, 40])
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135
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136 %!assert (conv (a,b,"valid"), [10, 16, 22, 28, 34, 40, 46, 52])
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137 %!assert (conv (b,a,"valid"), zeros (1,0))
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138
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139
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140 %% Test input validation
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141 %!error conv (1)
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142 %!error conv (1,2,3,4)
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143 %!error <A and B must be vectors> conv ([1, 2; 3, 4], 3)
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144 %!error <A and B must be vectors> conv (3, [1, 2; 3, 4])
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145 %!error <SHAPE argument must be> conv (2, 3, "INVALID_SHAPE")
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146