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maint: merge stable to default.
author John W. Eaton <jwe@octave.org>
date Wed, 10 Feb 2021 10:10:40 -0500
parents 90fea9cc9caa 0a5b15007766
children 363fb10055df
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1993-2021 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25 ##
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26 ## Original version by Paul Kienzle distributed as free software in the
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27 ## public domain.
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28
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29 ## -*- texinfo -*-
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30 ## @deftypefn {} {} hadamard (@var{n})
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31 ## Construct a Hadamard matrix (@nospell{Hn}) of size @var{n}-by-@var{n}.
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32 ##
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33 ## The size @var{n} must be of the form @math{2^k * p} in which p is one of
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34 ## 1, 12, 20 or 28. The returned matrix is normalized, meaning
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35 ## @w{@code{Hn(:,1) == 1}} and @w{@code{Hn(1,:) == 1}}.
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36 ##
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37 ## Some of the properties of Hadamard matrices are:
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38 ##
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39 ## @itemize @bullet
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40 ## @item
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41 ## @code{kron (Hm, Hn)} is a Hadamard matrix of size @var{m}-by-@var{n}.
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42 ##
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43 ## @item
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44 ## @code{Hn * Hn' = @var{n} * eye (@var{n})}.
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45 ##
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46 ## @item
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47 ## The rows of @nospell{Hn} are orthogonal.
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48 ##
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49 ## @item
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50 ## @code{det (@var{A}) <= abs (det (Hn))} for all @var{A} with
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51 ## @w{@code{abs (@var{A}(i, j)) <= 1}}.
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52 ##
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53 ## @item
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54 ## Multiplying any row or column by -1 and the matrix will remain a Hadamard
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55 ## matrix.
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56 ## @end itemize
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57 ## @seealso{compan, hankel, toeplitz}
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58 ## @end deftypefn
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59
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60 ## Reference [1] contains a list of Hadamard matrices up to n=256.
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61 ## See code for h28 in hadamard.m for an example of how to extend
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62 ## this function for additional p.
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63 ##
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64 ## Reference:
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65 ## [1] A Library of Hadamard Matrices, N. J. A. Sloane
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66 ## http://www.research.att.com/~njas/hadamard/
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67
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68 function h = hadamard (n)
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69
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70 if (nargin < 1)
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71 print_usage ();
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72 endif
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73
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74 ## Find k if n = 2^k*p.
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75 k = 0;
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76 while (n > 1 && fix (n/2) == n/2)
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77 k += 1;
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78 n /= 2;
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79 endwhile
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80
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81 ## Find base hadamard.
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82 ## Except for n=2^k, need a multiple of 4.
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83 if (n != 1)
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84 k -= 2;
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85 endif
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86
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87 ## Trigger error if not a multiple of 4.
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88 if (k < 0)
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89 n =- 1;
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90 endif
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91
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92 switch (n)
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93 case 1
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94 h = 1;
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95 case 3
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96 h = h12 ();
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97 case 5
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98 h = h20 ();
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99 case 7
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100 h = h28 ();
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101 otherwise
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102 error ("hadamard: N must be 2^k*p, for p = 1, 12, 20 or 28");
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103 endswitch
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104
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105 ## Build H(2^k*n) from kron(H(2^k),H(n)).
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106 h2 = [1,1;1,-1];
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107 while (true)
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108 if (fix (k/2) != k/2)
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109 h = kron (h2, h);
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110 endif
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111 k = fix (k/2);
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112 if (k == 0)
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113 break;
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114 endif
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115 h2 = kron (h2, h2);
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116 endwhile
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117
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118 endfunction
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119
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120 function h = h12 ()
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121 tu = [-1,+1,-1,+1,+1,+1,-1,-1,-1,+1,-1];
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122 tl = [-1,-1,+1,-1,-1,-1,+1,+1,+1,-1,+1];
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123 ## Note: assert (tu(2:end), tl(end:-1:2)).
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124 h = ones (12);
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125 h(2:end,2:end) = toeplitz (tu, tl);
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126 endfunction
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127
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128 function h = h20 ()
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129 tu = [+1,-1,-1,+1,+1,+1,+1,-1,+1,-1,+1,-1,-1,-1,-1,+1,+1,-1,-1];
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130 tl = [+1,-1,-1,+1,+1,-1,-1,-1,-1,+1,-1,+1,-1,+1,+1,+1,+1,-1,-1];
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131 ## Note: assert (tu(2:end), tl(end:-1:2)).
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132 h = ones (20);
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133 h(2:end,2:end) = fliplr (toeplitz (tu, tl));
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134 endfunction
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135
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136 function h = h28 ()
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137 ## Williamson matrix construction from
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138 ## http://www.research.att.com/~njas/hadamard/had.28.will.txt
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139 ## Normalized so that each row and column starts with +1
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140 h = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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141 1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
142 1 -1 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
143 1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
144 1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 1 -1 -1 -1 1 1 1 -1 1 -1 1 -1 -1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
145 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 1 1 1 1 1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
146 1 -1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 1 1 1 1 -1 1 -1 1 -1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
147 1 -1 1 1 1 1 -1 -1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 1 -1 -1 1 1 1 1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
148 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 -1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
149 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 -1 -1 1 1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
150 1 -1 1 1 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
151 1 -1 -1 1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 1 1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
152 1 -1 -1 -1 1 1 1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
153 1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 -1 -1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
154 1 1 -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 -1 1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
155 1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 -1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
156 1 1 -1 1 -1 1 1 1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
157 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
158 1 -1 1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
159 1 1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
160 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 1 1 -1 -1 -1 -1 -1 1 1 1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
161 1 1 1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
162 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 -1 1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
163 1 -1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
164 1 1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
165 1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 1 1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 -1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
166 1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 1
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
167 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 1 -1 -1 1 1 -1 -1 1 -1];
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
168 endfunction
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
169
13893
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
170
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
171 %!assert (hadamard (1), 1)
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
172 %!assert (hadamard (2), [1,1;1,-1])
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
173 %!test
13893
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
174 %! for n = [1,2,4,8,12,24,48,20,28,2^9]
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
175 %! h = hadamard (n);
13913
521adfd775be hadamard.m: Fix failing %!tests
Rik <octave@nomad.inbox5.com>
parents: 13893
diff changeset
176 %! assert (norm (h*h' - n*eye (n)), 0);
13893
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
177 %! endfor
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
178
28896
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28891
diff changeset
179 %!error <Invalid call> hadamard ()
13893
5b1ddcf5ede1 hadamard.m: Embed hadamard28 matrix as constant rather than computed value.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
180 %!error hadamard (1,2)
13913
521adfd775be hadamard.m: Fix failing %!tests
Rik <octave@nomad.inbox5.com>
parents: 13893
diff changeset
181 %!error <N must be 2\^k\*p> hadamard (5)