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annotate scripts/general/cplxpair.m @ 20509:c5a8eff5a05d

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gallery: add very basic tests (check output size) for all matrix types.
author Carnë Draug <carandraug@octave.org>
date Fri, 03 Jul 2015 16:53:08 +0100
parents 7503499a252b
children 4c2e76cbdc7d
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) 2000-2015 Paul Kienzle
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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} {} cplxpair (@var{z})
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21 ## @deftypefnx {Function File} {} cplxpair (@var{z}, @var{tol})
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22 ## @deftypefnx {Function File} {} cplxpair (@var{z}, @var{tol}, @var{dim})
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23 ## Sort the numbers @var{z} into complex conjugate pairs ordered by
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24 ## increasing real part.
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25 ##
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26 ## The negative imaginary complex numbers are placed first within each pair.
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27 ## All real numbers (those with
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28 ## @code{abs (imag (@var{z}) / @var{z}) < @var{tol}}) are placed after the
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29 ## complex pairs.
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30 ##
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31 ## If @var{tol} is unspecified the default value is 100*@code{eps}.
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32 ##
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33 ## By default the complex pairs are sorted along the first non-singleton
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34 ## dimension of @var{z}. If @var{dim} is specified, then the complex pairs are
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35 ## sorted along this dimension.
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36 ##
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37 ## Signal an error if some complex numbers could not be paired. Signal an
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38 ## error if all complex numbers are not exact conjugates (to within @var{tol}).
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39 ## Note that there is no defined order for pairs with identical real parts but
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40 ## differing imaginary parts.
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41 ## @c Set example in small font to prevent overfull line
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42 ##
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43 ## @smallexample
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44 ## cplxpair (exp(2i*pi*[0:4]'/5)) == exp(2i*pi*[3; 2; 4; 1; 0]/5)
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45 ## @end smallexample
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46 ## @end deftypefn
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47
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48 ## FIXME: subsort returned pairs by imaginary magnitude
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49 ## FIXME: Why doesn't exp (2i*pi*[0:4]'/5) produce exact conjugates. Does
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50 ## FIXME: it in Matlab? The reason is that complex pairs are supposed
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51 ## FIXME: to be exact conjugates, and not rely on a tolerance test.
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52
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53 ## 2006-05-12 David Bateman - Modified for NDArrays
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54
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55 function y = cplxpair (z, tol, dim)
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56
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57 if (nargin < 1 || nargin > 3)
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58 print_usage ();
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59 endif
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60
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61 if (length (z) == 0)
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62 y = zeros (size (z));
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63 return;
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64 endif
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65
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66 if (nargin < 2 || isempty (tol))
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67 if (isa (z, "single"))
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68 tol = 100 * eps("single");
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69 else
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70 tol = 100*eps;
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71 endif
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72 endif
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73
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74 nd = ndims (z);
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75 orig_dims = size (z);
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76 if (nargin < 3)
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77 ## Find the first singleton dimension.
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78 dim = 0;
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79 while (dim < nd && orig_dims(dim+1) == 1)
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80 dim++;
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81 endwhile
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82 dim++;
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83 if (dim > nd)
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84 dim = 1;
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85 endif
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86 else
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87 dim = floor (dim);
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88 if (dim < 1 || dim > nd)
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89 error ("cplxpair: invalid dimension along which to sort");
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90 endif
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91 endif
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92
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93 ## Move dimension to treat first, and convert to a 2-D matrix.
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94 perm = [dim:nd, 1:dim-1];
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95 z = permute (z, perm);
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96 sz = size (z);
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97 n = sz(1);
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98 m = prod (sz) / n;
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99 z = reshape (z, n, m);
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100
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101 ## Sort the sequence in terms of increasing real values.
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102 [q, idx] = sort (real (z), 1);
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103 z = z(idx + n * ones (n, 1) * [0:m-1]);
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104
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105 ## Put the purely real values at the end of the returned list.
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106 cls = "double";
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107 if (isa (z, "single"))
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108 cls = "single";
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109 endif
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110 [idxi, idxj] = find (abs (imag (z)) ./ (abs (z) + realmin (cls)) < tol);
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111 q = sparse (idxi, idxj, 1, n, m);
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112 nr = sum (q, 1);
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113 [q, idx] = sort (q, 1);
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114 z = z(idx);
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115 y = z;
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116
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117 ## For each remaining z, place the value and its conjugate at the
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118 ## start of the returned list, and remove them from further
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119 ## consideration.
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120 for j = 1:m
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121 p = n - nr(j);
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122 for i = 1:2:p
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123 if (i+1 > p)
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124 error ("cplxpair: could not pair all complex numbers");
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125 endif
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126 [v, idx] = min (abs (z(i+1:p) - conj (z(i))));
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127 if (v > tol)
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128 error ("cplxpair: could not pair all complex numbers");
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129 endif
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130 if (imag (z(i)) < 0)
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131 y([i, i+1]) = z([i, idx+i]);
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132 else
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133 y([i, i+1]) = z([idx+i, i]);
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134 endif
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135 z(idx+i) = z(i+1);
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136 endfor
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137 endfor
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138
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139 ## Reshape the output matrix.
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140 y = ipermute (reshape (y, sz), perm);
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141
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142 endfunction
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143
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145 %!demo
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146 %! [ cplxpair(exp(2i*pi*[0:4]'/5)), exp(2i*pi*[3; 2; 4; 1; 0]/5) ]
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148 %!assert (isempty (cplxpair ([])))
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149 %!assert (cplxpair (1), 1)
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150 %!assert (cplxpair ([1+1i, 1-1i]), [1-1i, 1+1i])
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151 %!assert (cplxpair ([1+1i, 1+1i, 1, 1-1i, 1-1i, 2]), ...
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152 %! [1-1i, 1+1i, 1-1i, 1+1i, 1, 2])
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153 %!assert (cplxpair ([1+1i; 1+1i; 1; 1-1i; 1-1i; 2]), ...
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154 %! [1-1i; 1+1i; 1-1i; 1+1i; 1; 2])
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155 %!assert (cplxpair ([0, 1, 2]), [0, 1, 2])
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157 %!shared z
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158 %! z = exp (2i*pi*[4; 3; 5; 2; 6; 1; 0]/7);
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159 %!assert (cplxpair (z(randperm (7))), z)
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160 %!assert (cplxpair (z(randperm (7))), z)
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161 %!assert (cplxpair (z(randperm (7))), z)
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162 %!assert (cplxpair ([z(randperm(7)),z(randperm(7))]), [z,z])
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163 %!assert (cplxpair ([z(randperm(7)),z(randperm(7))],[],1), [z,z])
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164 %!assert (cplxpair ([z(randperm(7)).';z(randperm(7)).'],[],2), [z.';z.'])
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165
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166 ## tolerance test
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167 %!assert (cplxpair ([1i, -1i, 1+(1i*eps)],2*eps), [-1i, 1i, 1+(1i*eps)])
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