Mercurial > octave
annotate scripts/general/cplxpair.m @ 31198:863730dd0f83 stable
nextpow2: Fix for input between 0.5 and 1 (bug #62947).
* scripts/general/nextpow2.m: Switch to a naïve implementation using log2 with
a single output argument and ceil.
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Wed, 24 Aug 2022 17:15:34 +0200 |
parents | 796f54d4ddbf |
children | 5d3faba0342e |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2000-2022 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/>. |
5820 | 7 ## |
8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
5820 | 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. |
5820 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
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. |
5820 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
7016 | 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 ######################################################################## |
5820 | 25 |
26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {} cplxpair (@var{z}) |
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28 ## @deftypefnx {} {} cplxpair (@var{z}, @var{tol}) |
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29 ## @deftypefnx {} {} cplxpair (@var{z}, @var{tol}, @var{dim}) |
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30 ## Sort the numbers @var{z} into complex conjugate pairs ordered by increasing |
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31 ## real part. |
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32 ## |
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33 ## The negative imaginary complex numbers are placed first within each pair. |
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34 ## All real numbers (those with |
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35 ## @code{abs (imag (@var{z})) / abs (@var{z}) < @var{tol}}) are placed after |
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36 ## the complex pairs. |
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37 ## |
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38 ## @var{tol} is a weighting factor in the range [0, 1) which determines the |
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39 ## tolerance of the matching. The default value is @code{100 * eps} and the |
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40 ## resulting tolerance for a given complex pair is |
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41 ## @code{@var{tol} * abs (@var{z}(i)))}. |
5820 | 42 ## |
43 ## By default the complex pairs are sorted along the first non-singleton | |
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44 ## dimension of @var{z}. If @var{dim} is specified, then the complex pairs are |
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45 ## sorted along this dimension. |
5820 | 46 ## |
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47 ## Signal an error if some complex numbers could not be paired. Signal an |
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48 ## error if all complex numbers are not exact conjugates (to within @var{tol}). |
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49 ## Note that there is no defined order for pairs with identical real parts but |
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50 ## differing imaginary parts. |
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51 ## @c Set example in small font to prevent overfull line |
5820 | 52 ## |
7031 | 53 ## @smallexample |
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54 ## cplxpair (exp (2i*pi*[0:4]'/5)) == exp (2i*pi*[3; 2; 4; 1; 0]/5) |
7031 | 55 ## @end smallexample |
5820 | 56 ## @end deftypefn |
57 | |
58 ## 2006-05-12 David Bateman - Modified for NDArrays | |
59 | |
60 function y = cplxpair (z, tol, dim) | |
61 | |
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62 if (nargin < 1) |
6046 | 63 print_usage (); |
5820 | 64 endif |
65 | |
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66 if (isempty (z)) |
5820 | 67 y = zeros (size (z)); |
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68 return; |
5820 | 69 endif |
70 | |
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71 cls = ifelse (isa (z, "single"), "single", "double"); |
5820 | 72 if (nargin < 2 || isempty (tol)) |
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73 tol = 100*eps (cls); |
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74 elseif (! isscalar (tol) || tol < 0 || tol >= 1) |
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75 error ("cplxpair: TOL must be a scalar number in the range 0 <= TOL < 1"); |
5820 | 76 endif |
77 | |
78 nd = ndims (z); | |
79 if (nargin < 3) | |
80 ## Find the first singleton dimension. | |
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81 sz = size (z); |
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82 (dim = find (sz > 1, 1)) || (dim = 1); |
5820 | 83 else |
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84 dim = floor (dim); |
5820 | 85 if (dim < 1 || dim > nd) |
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86 error ("cplxpair: invalid dimension DIM"); |
5820 | 87 endif |
88 endif | |
89 | |
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90 ## Move dimension to analyze to first position, and convert to a 2-D matrix. |
5820 | 91 perm = [dim:nd, 1:dim-1]; |
92 z = permute (z, perm); | |
93 sz = size (z); | |
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94 n = sz(1); |
5820 | 95 m = prod (sz) / n; |
96 z = reshape (z, n, m); | |
97 | |
8507 | 98 ## Sort the sequence in terms of increasing real values. |
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99 [~, idx] = sort (real (z), 1); |
5820 | 100 z = z(idx + n * ones (n, 1) * [0:m-1]); |
101 | |
8507 | 102 ## Put the purely real values at the end of the returned list. |
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103 [idxi, idxj] = find (abs (imag (z)) ./ (abs (z) + realmin (cls)) <= tol); |
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104 ## Force values detected to be real within tolerance to actually be real. |
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105 z(idxi + n*(idxj-1)) = real (z(idxi + n*(idxj-1))); |
5820 | 106 q = sparse (idxi, idxj, 1, n, m); |
107 nr = sum (q, 1); | |
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108 [~, idx] = sort (q, 1); |
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109 midx = idx + rows (idx) * ones (rows (idx), 1) * [0:columns(idx)-1]; |
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110 z = z(midx); |
5820 | 111 y = z; |
112 | |
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113 ## For each remaining z, place the value and its conjugate at the start of |
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114 ## the returned list, and remove them from further consideration. |
5820 | 115 for j = 1:m |
116 p = n - nr(j); | |
8507 | 117 for i = 1:2:p |
5820 | 118 if (i+1 > p) |
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119 error ("cplxpair: could not pair all complex numbers"); |
5820 | 120 endif |
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121 [v, idx] = min (abs (z(i+1:p,j) - conj (z(i,j)))); |
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122 if (v >= tol * abs (z(i,j))) |
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123 error ("cplxpair: could not pair all complex numbers"); |
5820 | 124 endif |
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125 ## For pairs, select the one with positive imaginary part and use it and |
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126 ## it's conjugate, but list the negative imaginary pair first. |
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127 if (imag (z(i,j)) > 0) |
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128 y([i, i+1],j) = [conj(z(i,j)), z(i,j)]; |
5820 | 129 else |
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130 y([i, i+1],j) = [conj(z(idx+i,j)), z(idx+i,j)]; |
5820 | 131 endif |
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132 z(idx+i,j) = z(i+1,j); |
5820 | 133 endfor |
134 endfor | |
135 | |
8507 | 136 ## Reshape the output matrix. |
5820 | 137 y = ipermute (reshape (y, sz), perm); |
138 | |
139 endfunction | |
140 | |
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141 |
5820 | 142 %!demo |
143 %! [ cplxpair(exp(2i*pi*[0:4]'/5)), exp(2i*pi*[3; 2; 4; 1; 0]/5) ] | |
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]) |
5820 | 153 |
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154 %!shared z,y |
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155 %! z = exp (2i*pi*[4; 3; 5; 2; 6; 1; 0]/7); |
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156 %! z(2) = conj (z(1)); |
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157 %! z(4) = conj (z(3)); |
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158 %! z(6) = conj (z(5)); |
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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 %! y = [ -1-1i; -1+1i;-3; -2; 1; 2; 3]; |
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166 %!assert (cplxpair ([z(randperm (7)), y(randperm (7))]), [z,y]) |
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167 %!assert (cplxpair ([z(randperm (7)), y(randperm (7)),z(randperm (7))]), |
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168 %! [z,y,z]) |
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169 |
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170 ## Test tolerance |
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171 %!assert (cplxpair ([2000 * (1+eps) + 4j; 2000 * (1-eps) - 4j]), |
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172 %! [(2000 - 4j); (2000 + 4j)], 100*eps(200)) |
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173 %!error <could not pair> |
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174 %! cplxpair ([2000 * (1+eps) + 4j; 2000 * (1-eps) - 4j], 0); |
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175 %!error <could not pair> |
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176 %! cplxpair ([2e6 + j; 2e6 - j; 1e-9 * (1 + j); 1e-9 * (1 - 2j)]); |
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177 |
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178 ## Test input validation |
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179 %!error <Invalid call> cplxpair () |
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180 %!error <cplxpair: TOL must be .* scalar number> cplxpair (1, ones (2,2)) |
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181 %!error <cplxpair: TOL must be .* in the range 0 <= TOL < 1> cplxpair (1, -1) |
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182 %!error <cplxpair: TOL must be .* in the range 0 <= TOL < 1> cplxpair (1, -1) |
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183 %!error <invalid dimension DIM> cplxpair (1, [], 3) |