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<div class="title">matrix_scaler.h</div> </div>
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<a href="matrix__scaler_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// The SparseMatrixScaler class provides tools to scale a SparseMatrix, i.e.</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// reduce the range of its coefficients and make for each column and each row</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// the maximum magnitude of its coefficients equal to 1.</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// In the case there are bounds or costs on the columns or a right-hand side</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// related to each row, SparseMatrixScaler provides the tools to scale those</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// appropriately.</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// More precisely, suppose we have the Linear Program:</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// min c.x</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// s.t A.x = b</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// with l <= x <= u</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// The rows of A are scaled by left-multiplying it by a diagonal matrix R</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// whose elements R_ii correspond to the scaling factor of row i.</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// The columns of A are scaled by right-multiplying it by a diagonal matrix C</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// whose elements C_jj correspond to the scaling factor of column j.</span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// We obtain a matrix A' = R.A.C.</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// We wish to scale x, c, b, l, u so as to work on the scaled problem:</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// min c'.x'</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// s.t A'.x' = b'</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// with l' <= x' <= u'</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// The right-hand side b needs to be left-multiplied by R, the cost function c</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// needs to be right-multiplied by C. Finally, x, and its lower- and upper-bound</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// vectors l and u need to be left-multiplied by C^-1.</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// Note also that the dual vector y is scaled as follows:</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// y'.R = y, thus y' = y.R^-1.</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// The complete transformation is thus:</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// A' = R.A.C,</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// b' = R.b,</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// c' = c.C,</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// x' = C^-1.x,</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// l' = C^-1.l,</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// u' = C^-1.u,</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// y' = y.R^-1.</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// The validity of the above transformation can be checked by computing:</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// c'.x' = c.C.C^-1.x = c.x.</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// and:</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// A'.x' = R.A.C.C^-1.x = R.A.x = R.b = b'.</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  </div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="preprocessor">#ifndef OR_TOOLS_LP_DATA_MATRIX_SCALER_H_</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="preprocessor">#define OR_TOOLS_LP_DATA_MATRIX_SCALER_H_</span></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  </div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="preprocessor">#include "<a class="code" href="macros_8h.html">ortools/base/macros.h</a>"</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="preprocessor">#include "<a class="code" href="parameters_8pb_8h.html">ortools/glop/parameters.pb.h</a>"</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="preprocessor">#include "<a class="code" href="revised__simplex_8h.html">ortools/glop/revised_simplex.h</a>"</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="preprocessor">#include "<a class="code" href="status_8h.html">ortools/glop/status.h</a>"</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="preprocessor">#include "<a class="code" href="lp__data_8h.html">ortools/lp_data/lp_data.h</a>"</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="preprocessor">#include "<a class="code" href="lp__types_8h.html">ortools/lp_data/lp_types.h</a>"</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  </div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">namespace </span>glop {</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  </div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="keyword">class </span>SparseMatrix;</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  </div>
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<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html"> 78</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html">SparseMatrixScaler</a> {</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa5d52693bed51c5fb6e84c99a23799b5">SparseMatrixScaler</a>();</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  </div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// Initializes the object with the SparseMatrix passed as argument.</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// The row and column scaling factors are all set to 1.0 (i.e. no scaling.)</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// In terms of matrices, R and C are set to identity matrices.</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a2dd7d09e2fe8d71850baa854b0edbf27">Init</a>(<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>* matrix);</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  </div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="comment">// Clears the object, and puts it back into the same state as after being</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="comment">// constructed.</span></div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// The column col of the matrix was multiplied by ColScalingFactor(col). The</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// variable bounds and objective coefficient at the same columsn where DIVIDED</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">// by that same factor. If col is outside the matrix size, this returns 1.0.</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a0fda0916591d196bc6a237a40c89dc2b">ColScalingFactor</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  </div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// The constraint row of the matrix was multiplied by RowScalingFactor(row),</span></div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="comment">// same for the constraint bounds (which is not the same as for the variable</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// bounds for a column!). If row is outside the matrix size, this returns 1.0.</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a00be4687c662ab91018b1901422968ef">RowScalingFactor</a>(RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  </div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// The inverse of both factor above (this is how we keep them) so this</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">// direction should be faster to query (no 1.0 / factor).</span></div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ac9e0ca12adc5a8695b7c203049ae6f56">ColUnscalingFactor</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ada52fc5d004939ec0a71b5302434af02">RowUnscalingFactor</a>(RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  </div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="comment">// TODO(user): rename function and field to col_scales (and row_scales)</span></div>
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<div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a08e7c50887a37fd89b09ab1c1b60e7aa"> 107</a></span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a08e7c50887a37fd89b09ab1c1b60e7aa">col_scale</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> col_scale_; }</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  </div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">// Scales the matrix.</span></div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#abc0a90242ca4f46222e707202f7918b0">Scale</a>(GlopParameters::ScalingAlgorithm method);</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  </div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">// Solves the scaling problem as a linear program.</span></div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <a class="code" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a4eedd0e414498a0b6bc4f2ce2143da72">LPScale</a>();</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  </div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">// Unscales the matrix.</span></div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aebfa385cb902145ed371b68ce3bf579d">Unscale</a>();</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  </div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// Scales a row vector up or down (depending whether parameter up is true or</span></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// false) using the scaling factors determined by Scale().</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// Scaling up means multiplying by the scaling factors, while scaling down</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// means dividing by the scaling factors.</span></div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a57b3fbbeb1e0b5a127cc94694aad586e">ScaleRowVector</a>(<span class="keywordtype">bool</span> up, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* row_vector) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  </div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// Scales a column vector up or down (depending whether parameter up is true</span></div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="comment">// or false) using the scaling factors determined by Scale().</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">// Scaling up means multiplying by the scaling factors, while scaling down</span></div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="comment">// means dividing by the scaling factors.</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a150a7b18071b89f90d47aa00b679edc9">ScaleColumnVector</a>(<span class="keywordtype">bool</span> up, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* column_vector) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  </div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="comment">// Computes the variance of the non-zero coefficients of the matrix.</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="comment">// Used by Scale() do decide when to stop.</span></div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#af9524ee82f45fb16c26a3e6eb6f32ef3">VarianceOfAbsoluteValueOfNonZeros</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  </div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="comment">// Scales the rows. Returns the number of rows that have been scaled.</span></div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">// Helper function to Scale().</span></div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aeaa021fae3560c48754bc32bfc54978c">ScaleRowsGeometrically</a>();</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  </div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="comment">// Scales the columns. Returns the number of columns that have been scaled.</span></div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// Helper function to Scale().</span></div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a8b4373d64f8f8f3a6480e9ae4e2a6a2e">ScaleColumnsGeometrically</a>();</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  </div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="comment">// Equilibrates the rows. Returns the number of rows that have been scaled.</span></div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// Helper function to Scale().</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a89b5d413f7e1aa8426e85143a37b54dc">EquilibrateRows</a>();</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  </div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">// Equilibrates the Columns. Returns the number of columns that have been</span></div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// scaled. Helper function to Scale().</span></div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a6a8ddd97065e27d7f8e5013aaa59fb24">EquilibrateColumns</a>();</div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  </div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">// Convert the matrix to be scaled into a linear program.</span></div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordtype">void</span> GenerateLinearProgram(<a class="code" href="classoperations__research_1_1glop_1_1_linear_program.html">LinearProgram</a>*);</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  </div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// Scales the row indexed by row by 1/factor.</span></div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// Used by ScaleMatrixRowsGeometrically and EquilibrateRows.</span></div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  RowIndex ScaleMatrixRows(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& factors);</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  </div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="comment">// Scales the column index by col by 1/factor.</span></div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">// Used by ScaleColumnsGeometrically and EquilibrateColumns.</span></div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordtype">void</span> ScaleMatrixColumn(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> factor);</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  </div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// Looks up the index to the scale factor variable for this matrix row, in the</span></div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="comment">// LinearProgram, or creates it. Note lp_ must be initialized first.</span></div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  ColIndex GetRowScaleIndex(RowIndex row_num);</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  </div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="comment">// As above, but for the columns of the matrix.</span></div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  ColIndex GetColumnScaleIndex(ColIndex col_num);</div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  </div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="comment">// Returns a string containing information on the progress of the scaling</span></div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// algorithm. This is not meant to be called in an optimized mode as it takes</span></div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// some time to compute the displayed quantities.</span></div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  std::string DebugInformationString() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  </div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="comment">// Pointer to the matrix to be scaled.</span></div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>* matrix_;</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  </div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="comment">// Member pointer for convenience, in particular for GetRowScaleIndex and</span></div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="comment">// GetColumnScaleIndex.</span></div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <a class="code" href="classoperations__research_1_1glop_1_1_linear_program.html">LinearProgram</a>* lp_;</div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  </div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="comment">// Array of scaling factors for each row. Indexed by row number.</span></div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> row_scale_;</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  </div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="comment">// Array of scaling factors for each column. Indexed by column number.</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a> col_scale_;</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  DISALLOW_COPY_AND_ASSIGN(<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html">SparseMatrixScaler</a>);</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> };</div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  </div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> } <span class="comment">// namespace glop</span></div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_LP_DATA_MATRIX_SCALER_H_</span></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_linear_program_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_linear_program.html">operations_research::glop::LinearProgram</a></div><div class="ttdef"><b>Definition:</b> <a href="lp__data_8h_source.html#l00055">lp_data.h:55</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html">operations_research::glop::SparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00061">sparse.h:61</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html">operations_research::glop::SparseMatrixScaler</a></div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8h_source.html#l00078">matrix_scaler.h:78</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a00be4687c662ab91018b1901422968ef"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a00be4687c662ab91018b1901422968ef">operations_research::glop::SparseMatrixScaler::RowScalingFactor</a></div><div class="ttdeci">Fractional RowScalingFactor(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00057">matrix_scaler.cc:57</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a08e7c50887a37fd89b09ab1c1b60e7aa"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a08e7c50887a37fd89b09ab1c1b60e7aa">operations_research::glop::SparseMatrixScaler::col_scale</a></div><div class="ttdeci">const DenseRow & col_scale() const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8h_source.html#l00107">matrix_scaler.h:107</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a0fda0916591d196bc6a237a40c89dc2b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a0fda0916591d196bc6a237a40c89dc2b">operations_research::glop::SparseMatrixScaler::ColScalingFactor</a></div><div class="ttdeci">Fractional ColScalingFactor(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00061">matrix_scaler.cc:61</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a150a7b18071b89f90d47aa00b679edc9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a150a7b18071b89f90d47aa00b679edc9">operations_research::glop::SparseMatrixScaler::ScaleColumnVector</a></div><div class="ttdeci">void ScaleColumnVector(bool up, DenseColumn *column_vector) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00176">matrix_scaler.cc:176</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a2dd7d09e2fe8d71850baa854b0edbf27"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a2dd7d09e2fe8d71850baa854b0edbf27">operations_research::glop::SparseMatrixScaler::Init</a></div><div class="ttdeci">void Init(SparseMatrix *matrix)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00034">matrix_scaler.cc:34</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a4eedd0e414498a0b6bc4f2ce2143da72"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a4eedd0e414498a0b6bc4f2ce2143da72">operations_research::glop::SparseMatrixScaler::LPScale</a></div><div class="ttdeci">Status LPScale()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00358">matrix_scaler.cc:358</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a57b3fbbeb1e0b5a127cc94694aad586e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a57b3fbbeb1e0b5a127cc94694aad586e">operations_research::glop::SparseMatrixScaler::ScaleRowVector</a></div><div class="ttdeci">void ScaleRowVector(bool up, DenseRow *row_vector) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00171">matrix_scaler.cc:171</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a6a8ddd97065e27d7f8e5013aaa59fb24"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a6a8ddd97065e27d7f8e5013aaa59fb24">operations_research::glop::SparseMatrixScaler::EquilibrateColumns</a></div><div class="ttdeci">ColIndex EquilibrateColumns()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00290">matrix_scaler.cc:290</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a89b5d413f7e1aa8426e85143a37b54dc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a89b5d413f7e1aa8426e85143a37b54dc">operations_research::glop::SparseMatrixScaler::EquilibrateRows</a></div><div class="ttdeci">RowIndex EquilibrateRows()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00268">matrix_scaler.cc:268</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a8b4373d64f8f8f3a6480e9ae4e2a6a2e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a8b4373d64f8f8f3a6480e9ae4e2a6a2e">operations_research::glop::SparseMatrixScaler::ScaleColumnsGeometrically</a></div><div class="ttdeci">ColIndex ScaleColumnsGeometrically()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00240">matrix_scaler.cc:240</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aa5d52693bed51c5fb6e84c99a23799b5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa5d52693bed51c5fb6e84c99a23799b5">operations_research::glop::SparseMatrixScaler::SparseMatrixScaler</a></div><div class="ttdeci">SparseMatrixScaler()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00031">matrix_scaler.cc:31</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::SparseMatrixScaler::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00041">matrix_scaler.cc:41</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_abc0a90242ca4f46222e707202f7918b0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#abc0a90242ca4f46222e707202f7918b0">operations_research::glop::SparseMatrixScaler::Scale</a></div><div class="ttdeci">void Scale(GlopParameters::ScalingAlgorithm method)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00090">matrix_scaler.cc:90</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_ac9e0ca12adc5a8695b7c203049ae6f56"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ac9e0ca12adc5a8695b7c203049ae6f56">operations_research::glop::SparseMatrixScaler::ColUnscalingFactor</a></div><div class="ttdeci">Fractional ColUnscalingFactor(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00052">matrix_scaler.cc:52</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_ada52fc5d004939ec0a71b5302434af02"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ada52fc5d004939ec0a71b5302434af02">operations_research::glop::SparseMatrixScaler::RowUnscalingFactor</a></div><div class="ttdeci">Fractional RowUnscalingFactor(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00047">matrix_scaler.cc:47</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aeaa021fae3560c48754bc32bfc54978c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aeaa021fae3560c48754bc32bfc54978c">operations_research::glop::SparseMatrixScaler::ScaleRowsGeometrically</a></div><div class="ttdeci">RowIndex ScaleRowsGeometrically()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00212">matrix_scaler.cc:212</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aebfa385cb902145ed371b68ce3bf579d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aebfa385cb902145ed371b68ce3bf579d">operations_research::glop::SparseMatrixScaler::Unscale</a></div><div class="ttdeci">void Unscale()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00342">matrix_scaler.cc:342</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_af9524ee82f45fb16c26a3e6eb6f32ef3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#af9524ee82f45fb16c26a3e6eb6f32ef3">operations_research::glop::SparseMatrixScaler::VarianceOfAbsoluteValueOfNonZeros</a></div><div class="ttdeci">Fractional VarianceOfAbsoluteValueOfNonZeros() const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00182">matrix_scaler.cc:182</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html">operations_research::glop::Status</a></div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00024">status.h:24</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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