Mercurial > hg > octave-nkf
annotate scripts/general/cplxpair.m @ 10412:d2ac9433cd09
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 15 Mar 2010 16:56:14 -0400 |
| parents | 761fc0d3d980 |
| children | 95c3e38098bf |
| rev | line source |
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| 8920 | 1 ## Copyright (C) 2000, 2006, 2007, 2008, 2009 Paul Kienzle |
| 5820 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 5820 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 5820 | 18 |
| 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}) |
| 5820 | 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}. |
| 5820 | 30 ## |
| 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 |
| 5820 | 33 ## pairs are sorted along this dimension. |
| 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. |
| 5820 | 39 ## |
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40 ## @c Set example in small font to prevent overfull line |
| 7031 | 41 ## @smallexample |
| 5831 | 42 ## cplxpair (exp(2i*pi*[0:4]'/5)) == exp(2i*pi*[3; 2; 4; 1; 0]/5) |
| 7031 | 43 ## @end smallexample |
| 5820 | 44 ## @end deftypefn |
| 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. |
| 5820 | 50 |
| 51 ## 2006-05-12 David Bateman - Modified for NDArrays | |
| 52 | |
| 53 function y = cplxpair (z, tol, dim) | |
| 54 | |
| 55 if nargin < 1 || nargin > 3 | |
| 6046 | 56 print_usage (); |
| 5820 | 57 endif |
| 58 | |
| 59 if (length (z) == 0) | |
| 60 y = zeros (size (z)); | |
| 61 return; | |
| 62 endif | |
| 63 | |
| 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 |
| 5820 | 70 endif |
| 71 | |
| 72 nd = ndims (z); | |
| 73 orig_dims = size (z); | |
| 74 if (nargin < 3) | |
| 75 ## Find the first singleton dimension. | |
| 76 dim = 0; | |
| 77 while (dim < nd && orig_dims(dim+1) == 1) | |
| 78 dim++; | |
| 79 endwhile | |
| 80 dim++; | |
| 81 if (dim > nd) | |
| 82 dim = 1; | |
| 83 endif | |
| 84 else | |
| 85 dim = floor(dim); | |
| 86 if (dim < 1 || dim > nd) | |
| 87 error ("cplxpair: invalid dimension along which to sort"); | |
| 88 endif | |
| 89 endif | |
| 90 | |
| 8507 | 91 ## Move dimension to treat first, and convert to a 2-D matrix. |
| 5820 | 92 perm = [dim:nd, 1:dim-1]; |
| 93 z = permute (z, perm); | |
| 94 sz = size (z); | |
| 95 n = sz (1); | |
| 96 m = prod (sz) / n; | |
| 97 z = reshape (z, n, m); | |
| 98 | |
| 8507 | 99 ## Sort the sequence in terms of increasing real values. |
| 5820 | 100 [q, idx] = sort (real (z), 1); |
| 101 z = z(idx + n * ones (n, 1) * [0:m-1]); | |
| 102 | |
| 8507 | 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 |
| 8507 | 108 [idxi, idxj] = find (abs (imag (z)) ./ (abs (z) + realmin(cls)) < tol); |
| 5820 | 109 q = sparse (idxi, idxj, 1, n, m); |
| 110 nr = sum (q, 1); | |
| 111 [q, idx] = sort (q, 1); | |
| 112 z = z(idx); | |
| 113 y = z; | |
| 114 | |
| 115 ## For each remaining z, place the value and its conjugate at the | |
| 116 ## start of the returned list, and remove them from further | |
| 117 ## consideration. | |
| 118 for j = 1:m | |
| 119 p = n - nr(j); | |
| 8507 | 120 for i = 1:2:p |
| 5820 | 121 if (i+1 > p) |
| 122 error ("cplxpair could not pair all complex numbers"); | |
| 123 endif | |
| 124 [v, idx] = min (abs (z(i+1:p) - conj (z(i)))); | |
| 125 if (v > tol) | |
| 126 error ("cplxpair could not pair all complex numbers"); | |
| 127 endif | |
| 128 if (imag (z(i)) < 0) | |
| 129 y([i, i+1]) = z([i, idx+i]); | |
| 130 else | |
| 131 y([i, i+1]) = z([idx+i, i]); | |
| 132 endif | |
| 133 z(idx+i) = z(i+1); | |
| 134 endfor | |
| 135 endfor | |
| 136 | |
| 8507 | 137 ## Reshape the output matrix. |
| 5820 | 138 y = ipermute (reshape (y, sz), perm); |
| 139 | |
| 140 endfunction | |
| 141 | |
| 142 %!demo | |
| 143 %! [ cplxpair(exp(2i*pi*[0:4]'/5)), exp(2i*pi*[3; 2; 4; 1; 0]/5) ] | |
| 144 | |
| 145 %!assert (isempty(cplxpair([]))); | |
| 146 %!assert (cplxpair(1), 1) | |
| 147 %!assert (cplxpair([1+1i, 1-1i]), [1-1i, 1+1i]) | |
| 148 %!assert (cplxpair([1+1i, 1+1i, 1, 1-1i, 1-1i, 2]), \ | |
| 149 %! [1-1i, 1+1i, 1-1i, 1+1i, 1, 2]) | |
| 150 %!assert (cplxpair([1+1i; 1+1i; 1; 1-1i; 1-1i; 2]), \ | |
| 151 %! [1-1i; 1+1i; 1-1i; 1+1i; 1; 2]) | |
| 152 %!assert (cplxpair([0, 1, 2]), [0, 1, 2]); | |
| 153 | |
| 154 %!shared z | |
| 155 %! z=exp(2i*pi*[4; 3; 5; 2; 6; 1; 0]/7); | |
| 156 %!assert (cplxpair(z(randperm(7))), z); | |
| 157 %!assert (cplxpair(z(randperm(7))), z); | |
| 158 %!assert (cplxpair(z(randperm(7))), z); | |
| 159 %!assert (cplxpair([z(randperm(7)),z(randperm(7))]),[z,z]) | |
| 160 %!assert (cplxpair([z(randperm(7)),z(randperm(7))],[],1),[z,z]) | |
| 161 %!assert (cplxpair([z(randperm(7)).';z(randperm(7)).'],[],2),[z.';z.']) | |
| 162 | |
| 163 %!## tolerance test | |
| 164 %!assert (cplxpair([1i, -1i, 1+(1i*eps)],2*eps), [-1i, 1i, 1+(1i*eps)]); |