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<divclass="title">matrix_utils.h</div></div>
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<ahref="matrix__utils_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aname="l00001"></a><spanclass="lineno"> 1</span> <spanclass="comment">// Copyright 2010-2018 Google LLC</span></div>
<divclass="line"><aname="l00002"></a><spanclass="lineno"> 2</span> <spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
<divclass="line"><aname="l00003"></a><spanclass="lineno"> 3</span> <spanclass="comment">// you may not use this file except in compliance with the License.</span></div>
<divclass="line"><aname="l00004"></a><spanclass="lineno"> 4</span> <spanclass="comment">// You may obtain a copy of the License at</span></div>
<divclass="line"><aname="l00008"></a><spanclass="lineno"> 8</span> <spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<divclass="line"><aname="l00009"></a><spanclass="lineno"> 9</span> <spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
<divclass="line"><aname="l00010"></a><spanclass="lineno"> 10</span> <spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<divclass="line"><aname="l00011"></a><spanclass="lineno"> 11</span> <spanclass="comment">// See the License for the specific language governing permissions and</span></div>
<divclass="line"><aname="l00012"></a><spanclass="lineno"> 12</span> <spanclass="comment">// limitations under the License.</span></div>
<divclass="line"><aname="l00023"></a><spanclass="lineno"> 23</span> <spanclass="comment">// Finds the proportional columns of the given matrix: all the pairs of columns</span></div>
<divclass="line"><aname="l00024"></a><spanclass="lineno"> 24</span> <spanclass="comment">// such that one is a non-zero scalar multiple of the other. The returned</span></div>
<divclass="line"><aname="l00025"></a><spanclass="lineno"> 25</span> <spanclass="comment">// mapping for a given column will either be:</span></div>
<divclass="line"><aname="l00026"></a><spanclass="lineno"> 26</span> <spanclass="comment">// - The index of the first column which is proportional with this one.</span></div>
<divclass="line"><aname="l00027"></a><spanclass="lineno"> 27</span> <spanclass="comment">// - Or kInvalidCol if this column is not proportional to any other.</span></div>
<divclass="line"><aname="l00029"></a><spanclass="lineno"> 29</span> <spanclass="comment">// Because of precision errors, two columns are declared proportional if the</span></div>
<divclass="line"><aname="l00030"></a><spanclass="lineno"> 30</span> <spanclass="comment">// multiples (>= 1.0) defined by all the couple of coefficients of the same row</span></div>
<divclass="line"><aname="l00031"></a><spanclass="lineno"> 31</span> <spanclass="comment">// are equal up to the given absolute tolerance.</span></div>
<divclass="line"><aname="l00033"></a><spanclass="lineno"> 33</span> <spanclass="comment">// The complexity is in most cases O(num entries of the matrix). However,</span></div>
<divclass="line"><aname="l00034"></a><spanclass="lineno"> 34</span> <spanclass="comment">// compared to the less efficient algorithm below, it is highly unlikely but</span></div>
<divclass="line"><aname="l00035"></a><spanclass="lineno"> 35</span> <spanclass="comment">// possible that some pairs of proportional columns are not detected.</span></div>
<divclass="line"><aname="l00039"></a><spanclass="lineno"> 39</span> <spanclass="comment">// A simple version of FindProportionalColumns() that compares all the columns</span></div>
<divclass="line"><aname="l00040"></a><spanclass="lineno"> 40</span> <spanclass="comment">// pairs one by one. This is slow, but here for reference. The complexity is</span></div>
<divclass="line"><aname="l00045"></a><spanclass="lineno"> 45</span> <spanclass="comment">// Returns true iff the two given matrices have exactly the same first num_rows</span></div>
<divclass="line"><aname="l00046"></a><spanclass="lineno"> 46</span> <spanclass="comment">// entries on the first num_cols columns. The two given matrices must be ordered</span></div>
<divclass="line"><aname="l00047"></a><spanclass="lineno"> 47</span> <spanclass="comment">// by rows (this is DCHECKed, but only for the first one at this point).</span></div>
<divclass="line"><aname="l00052"></a><spanclass="lineno"> 52</span> <spanclass="comment">// Returns true iff the rightmost square matrix is an identity matrix.</span></div>
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