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annotate scripts/polynomial/conv.m @ 20828:a3b9ee5c040a

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Replace bsxfun with broadcasting for performance with complex inputs (bug #38628). cumtrapz.m, quadgk.m, trapz.m, center.m, zscore.m: Replace bsxfun with broadcasting for performance where inputs might be complex.
author Rik <rik@octave.org>
date Mon, 12 Oct 2015 21:28:32 -0700
parents 9fc020886ae9
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 1994-2015 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} = @qcode{"full"}
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33 ## Return the full convolution. (default)
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34 ##
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35 ## @item @var{shape} = @qcode{"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