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all script files: untabify and strip trailing whitespace
author John W. Eaton <jwe@octave.org>
date Thu, 20 Jan 2011 17:35:29 -0500
parents fd0a3ac60b0e
children 72c96de7a403
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1 ## Copyright (C) 2000-2011 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. Place the negative imaginary complex number
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25 ## first within each pair. Place all the real numbers (those with
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26 ## @code{abs (imag (@var{z}) / @var{z}) < @var{tol})}) after the
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27 ## complex pairs.
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28 ##
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29 ## If @var{tol} is unspecified the default value is 100*@code{eps}.
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30 ##
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31 ## By default the complex pairs are sorted along the first non-singleton
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32 ## dimension of @var{z}. If @var{dim} is specified, then the complex
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33 ## pairs are sorted along this dimension.
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34 ##
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35 ## Signal an error if some complex numbers could not be paired. Signal an
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36 ## error if all complex numbers are not exact conjugates (to within
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37 ## @var{tol}). Note that there is no defined order for pairs with identical
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38 ## real parts but differing imaginary parts.
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39 ## @c Set example in small font to prevent overfull line
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40 ##
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41 ## @smallexample
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42 ## cplxpair (exp(2i*pi*[0:4]'/5)) == exp(2i*pi*[3; 2; 4; 1; 0]/5)
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43 ## @end smallexample
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44 ## @end deftypefn
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45
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46 ## FIXME: subsort returned pairs by imaginary magnitude
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47 ## FIXME: Why doesn't exp(2i*pi*[0:4]'/5) produce exact conjugates. Does
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48 ## FIXME: it in Matlab? The reason is that complex pairs are supposed
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49 ## FIXME: to be exact conjugates, and not rely on a tolerance test.
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50
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51 ## 2006-05-12 David Bateman - Modified for NDArrays
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52
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53 function y = cplxpair (z, tol, dim)
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54
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55 if nargin < 1 || nargin > 3
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56 print_usage ();
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57 endif
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58
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59 if (length (z) == 0)
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60 y = zeros (size (z));
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61 return;
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62 endif
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63
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64 if (nargin < 2 || isempty (tol))
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65 if (isa (z, "single"))
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66 tol = 100 * eps("single");
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67 else
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68 tol = 100*eps;
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69 endif
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70 endif
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71
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72 nd = ndims (z);
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73 orig_dims = size (z);
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74 if (nargin < 3)
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75 ## Find the first singleton dimension.
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76 dim = 0;
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77 while (dim < nd && orig_dims(dim+1) == 1)
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78 dim++;
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79 endwhile
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80 dim++;
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81 if (dim > nd)
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82 dim = 1;
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83 endif
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84 else
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85 dim = floor(dim);
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86 if (dim < 1 || dim > nd)
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87 error ("cplxpair: invalid dimension along which to sort");
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88 endif
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89 endif
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90
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91 ## Move dimension to treat first, and convert to a 2-D matrix.
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92 perm = [dim:nd, 1:dim-1];
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93 z = permute (z, perm);
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94 sz = size (z);
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95 n = sz (1);
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96 m = prod (sz) / n;
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97 z = reshape (z, n, m);
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98
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99 ## Sort the sequence in terms of increasing real values.
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100 [q, idx] = sort (real (z), 1);
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101 z = z(idx + n * ones (n, 1) * [0:m-1]);
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102
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103 ## Put the purely real values at the end of the returned list.
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104 cls = "double";
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105 if (isa (z, "single"))
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106 cls = "single";
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107 endif
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108 [idxi, idxj] = find (abs (imag (z)) ./ (abs (z) + realmin(cls)) < tol);
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109 q = sparse (idxi, idxj, 1, n, m);
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110 nr = sum (q, 1);
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111 [q, idx] = sort (q, 1);
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112 z = z(idx);
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113 y = z;
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114
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115 ## For each remaining z, place the value and its conjugate at the
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116 ## start of the returned list, and remove them from further
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117 ## consideration.
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118 for j = 1:m
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119 p = n - nr(j);
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120 for i = 1:2:p
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121 if (i+1 > p)
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122 error ("cplxpair: could not pair all complex numbers");
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123 endif
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124 [v, idx] = min (abs (z(i+1:p) - conj (z(i))));
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125 if (v > tol)
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126 error ("cplxpair: could not pair all complex numbers");
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127 endif
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128 if (imag (z(i)) < 0)
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129 y([i, i+1]) = z([i, idx+i]);
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130 else
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131 y([i, i+1]) = z([idx+i, i]);
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132 endif
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133 z(idx+i) = z(i+1);
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134 endfor
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135 endfor
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136
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137 ## Reshape the output matrix.
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138 y = ipermute (reshape (y, sz), perm);
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139
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140 endfunction
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141
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142 %!demo
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143 %! [ cplxpair(exp(2i*pi*[0:4]'/5)), exp(2i*pi*[3; 2; 4; 1; 0]/5) ]
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144
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145 %!assert (isempty(cplxpair([])));
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146 %!assert (cplxpair(1), 1)
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147 %!assert (cplxpair([1+1i, 1-1i]), [1-1i, 1+1i])
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148 %!assert (cplxpair([1+1i, 1+1i, 1, 1-1i, 1-1i, 2]), \
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149 %! [1-1i, 1+1i, 1-1i, 1+1i, 1, 2])
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150 %!assert (cplxpair([1+1i; 1+1i; 1; 1-1i; 1-1i; 2]), \
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151 %! [1-1i; 1+1i; 1-1i; 1+1i; 1; 2])
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152 %!assert (cplxpair([0, 1, 2]), [0, 1, 2]);
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153
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154 %!shared z
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155 %! z=exp(2i*pi*[4; 3; 5; 2; 6; 1; 0]/7);
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156 %!assert (cplxpair(z(randperm(7))), z);
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157 %!assert (cplxpair(z(randperm(7))), z);
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158 %!assert (cplxpair(z(randperm(7))), z);
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159 %!assert (cplxpair([z(randperm(7)),z(randperm(7))]),[z,z])
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160 %!assert (cplxpair([z(randperm(7)),z(randperm(7))],[],1),[z,z])
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161 %!assert (cplxpair([z(randperm(7)).';z(randperm(7)).'],[],2),[z.';z.'])
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162
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163 %!## tolerance test
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164 %!assert (cplxpair([1i, -1i, 1+(1i*eps)],2*eps), [-1i, 1i, 1+(1i*eps)]);