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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">/* $NoKeywords: $ */</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment">//</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment">// Copyright (c) 1993-2012 Robert McNeel &amp; Associates. All rights reserved.</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment">// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment">// McNeel &amp; Associates.</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment">// THIS SOFTWARE IS PROVIDED &quot;AS IS&quot; WITHOUT EXPRESS OR IMPLIED WARRANTY.</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<span class="comment">// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="comment">// MERCHANTABILITY ARE HEREBY DISCLAIMED.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="comment">// </span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="comment">// For complete openNURBS copyright information see &lt;http://www.opennurbs.org&gt;.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="comment">//</span><span class="comment"></span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="comment">////////////////////////////////////////////////////////////////</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="comment"></span>*/</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="preprocessor">#if !defined(ON_MATRIX_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#define ON_MATRIX_INC_</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;</div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;<span class="keyword">class </span><a class="code" href="../../d3/d13/class_o_n___xform.html">ON_Xform</a>;</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;</div><div class="line"><a name="l00022"></a><span class="lineno"><a class="line" href="../../d7/d20/class_o_n___matrix.html"> 22</a></span>&#160;<span class="keyword">class </span>ON_CLASS <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160;{</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>();</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>( </div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="keywordtype">int</span> row_count,</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordtype">int</span> col_count</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; );</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>( <span class="comment">// see ON_Matrix::Create(int,int,int,int) for details</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// first valid row index</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// last valid row index</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// first valid column index</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordtype">int</span> <span class="comment">// last valid column index</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; );</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>( <span class="keyword">const</span> <a class="code" href="../../d3/d13/class_o_n___xform.html">ON_Xform</a>&amp; );</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>( <span class="keyword">const</span> <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; );</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160;<span class="preprocessor">#if defined(ON_HAS_RVALUEREF)</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="comment">// rvalue copy constructor</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>(<a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp;&amp;) ON_NOEXCEPT;</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="comment">// The rvalue assignment operator calls ON_Object::operator=(ON_Object&amp;&amp;)</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="comment">// which could throw exceptions. See the implementation of</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="comment">// ON_Object::operator=(ON_Object&amp;&amp;) for details.</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; operator=(<a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp;&amp;);</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;<span class="preprocessor">#endif</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;<span class="comment"> This constructor is for experts who have storage for a matrix</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;<span class="comment"> and need to use it in ON_Matrix form.</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;<span class="comment"> row_count - [in]</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;<span class="comment"> col_count - [in]</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160;<span class="comment"> M - [in]</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="comment"> bDestructorFreeM - [in]</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="comment"> If true, ~ON_Matrix will call onfree(M).</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="comment"> If false, caller is managing M&#39;s memory.</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160;<span class="comment"> ON_Matrix functions that increase the value of row_count or col_count</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;<span class="comment"> will fail on a matrix created with this constructor.</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>(</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordtype">int</span> row_count,</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordtype">int</span> col_count,</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordtype">double</span>** M,</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordtype">bool</span> bDestructorFreeM</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; );</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160;</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160;<span class="comment"> A row_count X col_count martix on the heap that can be </span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;<span class="comment"> deleted by calling ON_Matrix::Deallocate().</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keyword">static</span> <span class="keywordtype">double</span>** Allocate(</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> row_count,</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> col_count</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; );</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="keyword">static</span> <span class="keywordtype">void</span> Deallocate(</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordtype">double</span>** M</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; );</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keyword">virtual</span> ~<a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>();</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="keywordtype">void</span> EmergencyDestroy(); <span class="comment">// call if memory pool used matrix by becomes invalid</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="comment">// ON_Matrix[i][j] = value at row i and column j</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="comment">// 0 &lt;= i &lt; RowCount()</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="comment">// 0 &lt;= j &lt; ColCount()</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keywordtype">double</span>* operator[](<span class="keywordtype">int</span>);</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* operator[](<span class="keywordtype">int</span>) <span class="keyword">const</span>;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160;</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; operator=(<span class="keyword">const</span> <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp;);</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; operator=(<span class="keyword">const</span> <a class="code" href="../../d3/d13/class_o_n___xform.html">ON_Xform</a>&amp;);</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordtype">bool</span> IsValid() <span class="keyword">const</span>;</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordtype">int</span> IsSquare() <span class="keyword">const</span>; <span class="comment">// returns 0 for no and m_row_count (= m_col_count) for yes</span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="keywordtype">int</span> RowCount() <span class="keyword">const</span>;</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordtype">int</span> ColCount() <span class="keyword">const</span>;</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="keywordtype">int</span> MinCount() <span class="keyword">const</span>; <span class="comment">// smallest of row and column count</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="keywordtype">int</span> MaxCount() <span class="keyword">const</span>; <span class="comment">// largest of row and column count</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160;</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UnsignedRowCount() <span class="keyword">const</span>;</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UnsignedColCount() <span class="keyword">const</span>;</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UnsignedMinCount() <span class="keyword">const</span>; <span class="comment">// smallest of row and column count</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UnsignedMaxCount() <span class="keyword">const</span>; <span class="comment">// largest of row and column count</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160;</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordtype">void</span> RowScale(<span class="keywordtype">int</span>,<span class="keywordtype">double</span>); </div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <span class="keywordtype">void</span> ColScale(<span class="keywordtype">int</span>,<span class="keywordtype">double</span>);</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <span class="keywordtype">void</span> RowOp(<span class="keywordtype">int</span>,<span class="keywordtype">double</span>,<span class="keywordtype">int</span>);</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <span class="keywordtype">void</span> ColOp(<span class="keywordtype">int</span>,<span class="keywordtype">double</span>,<span class="keywordtype">int</span>);</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <span class="keywordtype">bool</span> Create(</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// number of rows</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keywordtype">int</span> <span class="comment">// number of columns</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; );</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160;</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <span class="keywordtype">bool</span> Create( <span class="comment">// E.g., Create(1,5,1,7) creates a 5x7 sized matrix that with</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <span class="comment">// &quot;top&quot; row = m[1][1],...,m[1][7] and &quot;bottom&quot; row</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <span class="comment">// = m[5][1],...,m[5][7]. The result of Create(0,m,0,n) is</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <span class="comment">// identical to the result of Create(m+1,n+1).</span></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// first valid row index</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// last valid row index</span></div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// first valid column index</span></div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="keywordtype">int</span> <span class="comment">// last valid column index</span></div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; );</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;<span class="comment"> This constructor is for experts who have storage for a matrix</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;<span class="comment"> and need to use it in ON_Matrix form.</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;<span class="comment"> row_count - [in]</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160;<span class="comment"> col_count - [in]</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160;<span class="comment"> M - [in]</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160;<span class="comment"> bDestructorFreeM - [in]</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160;<span class="comment"> If true, ~ON_Matrix will call onfree(M).</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160;<span class="comment"> If false, caller is managing M&#39;s memory.</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160;<span class="comment"> ON_Matrix functions that increase the value of row_count or col_count</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160;<span class="comment"> will fail on a matrix created with this constructor.</span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; <span class="keywordtype">bool</span> Create(</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; <span class="keywordtype">int</span> row_count,</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <span class="keywordtype">int</span> col_count,</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; <span class="keywordtype">double</span>** M,</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; <span class="keywordtype">bool</span> bDestructorFreeM</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; );</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160;</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160; <span class="keywordtype">void</span> Destroy();</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160;</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; <span class="keywordtype">void</span> Zero();</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160;</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; <span class="keywordtype">void</span> SetDiagonal(<span class="keywordtype">double</span>); <span class="comment">// sets diagonal value and zeros off diagonal values</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; <span class="keywordtype">void</span> SetDiagonal(<span class="keyword">const</span> <span class="keywordtype">double</span>*); <span class="comment">// sets diagonal values and zeros off diagonal values</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; <span class="keywordtype">void</span> SetDiagonal(<span class="keywordtype">int</span>, <span class="keyword">const</span> <span class="keywordtype">double</span>*); <span class="comment">// sets size to count x count and diagonal values and zeros off diagonal values</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <span class="keywordtype">void</span> SetDiagonal(<span class="keyword">const</span> <a class="code" href="../../dc/dfe/class_o_n___simple_array.html">ON_SimpleArray&lt;double&gt;</a>&amp;); <span class="comment">// sets size to length X lengthdiagonal values and zeros off diagonal values</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160;</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; <span class="keywordtype">bool</span> Transpose();</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160;</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; <span class="keywordtype">bool</span> SwapRows( <span class="keywordtype">int</span>, <span class="keywordtype">int</span> ); <span class="comment">// ints are row indices to swap</span></div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; <span class="keywordtype">bool</span> SwapCols( <span class="keywordtype">int</span>, <span class="keywordtype">int</span> ); <span class="comment">// ints are col indices to swap</span></div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <span class="keywordtype">bool</span> Invert( </div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; <span class="keywordtype">double</span> <span class="comment">// zero tolerance</span></div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; );</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160;</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160;<span class="comment"> Set this = A*B.</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160;<span class="comment"> A - [in]</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160;<span class="comment"> (Can be this)</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160;<span class="comment"> B - [in]</span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160;<span class="comment"> (Can be this)</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160;<span class="comment"> True when A is an mXk matrix and B is a k X n matrix; in which case</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160;<span class="comment"> &quot;this&quot; will be an mXn matrix = A*B.</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160;<span class="comment"> False when A.ColCount() != B.RowCount().</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; <span class="keywordtype">bool</span> Multiply( <span class="keyword">const</span> <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; A, <span class="keyword">const</span> <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; B );</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160;</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160;<span class="comment"> Set this = A+B.</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160;<span class="comment"> A - [in]</span></div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160;<span class="comment"> (Can be this)</span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160;<span class="comment"> B - [in]</span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160;<span class="comment"> (Can be this)</span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160;<span class="comment"> True when A and B are mXn matrices; in which case</span></div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160;<span class="comment"> &quot;this&quot; will be an mXn matrix = A+B.</span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160;<span class="comment"> False when A and B have different sizes.</span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; <span class="keywordtype">bool</span> Add( <span class="keyword">const</span> <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; A, <span class="keyword">const</span> <a class="code" href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a>&amp; B );</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160;</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160;</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160;<span class="comment"> Set this = s*this.</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160;<span class="comment"> s - [in]</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160;<span class="comment"> True when A and s are valid.</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160; <span class="keywordtype">bool</span> Scale( <span class="keywordtype">double</span> s );</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160;</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160;</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160; <span class="comment">// Description:</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160; <span class="comment">// Row reduce a matrix to calculate rank and determinant.</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160; <span class="comment">// Parameters:</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160; <span class="comment">// zero_tolerance - [in] (&gt;=0.0) zero tolerance for pivot test</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160; <span class="comment">// If the absolute value of a pivot is &lt;= zero_tolerance,</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160; <span class="comment">// then the pivot is assumed to be zero.</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160; <span class="comment">// determinant - [out] value of determinant is returned here.</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160; <span class="comment">// pivot - [out] value of the smallest pivot is returned here</span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160; <span class="comment">// Returns:</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; <span class="comment">// Rank of the matrix.</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; <span class="comment">// Remarks:</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160; <span class="comment">// The matrix itself is row reduced so that the result is</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160; <span class="comment">// an upper triangular matrix with 1&#39;s on the diagonal.</span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160; <span class="keywordtype">int</span> RowReduce( <span class="comment">// returns rank</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// zero_tolerance</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160; <span class="keywordtype">double</span>&amp;, <span class="comment">// determinant</span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160; <span class="keywordtype">double</span>&amp; <span class="comment">// pivot</span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160; ); </div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160;</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160; <span class="comment">// Description:</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160; <span class="comment">// Row reduce a matrix as the first step in solving M*X=B where</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160; <span class="comment">// B is a column of values.</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160; <span class="comment">// Parameters:</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160; <span class="comment">// zero_tolerance - [in] (&gt;=0.0) zero tolerance for pivot test</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160; <span class="comment">// If the absolute value of a pivot is &lt;= zero_tolerance,</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160; <span class="comment">// then the pivot is assumed to be zero.</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160; <span class="comment">// B - [in/out] an array of m_row_count values that is row reduced</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160; <span class="comment">// with the matrix.</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160; <span class="comment">// determinant - [out] value of determinant is returned here.</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160; <span class="comment">// pivot - [out] If not nullptr, then the value of the smallest </span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160; <span class="comment">// pivot is returned here</span></div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160; <span class="comment">// Returns:</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160; <span class="comment">// Rank of the matrix.</span></div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160; <span class="comment">// Remarks:</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160; <span class="comment">// The matrix itself is row reduced so that the result is</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160; <span class="comment">// an upper triangular matrix with 1&#39;s on the diagonal.</span></div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; <span class="comment">// Example:</span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; <span class="comment">// Solve M*X=B;</span></div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; <span class="comment">// double B[m] = ...;</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; <span class="comment">// double B[n] = ...;</span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160; <span class="comment">// ON_Matrix M(m,n) = ...;</span></div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; <span class="comment">// M.RowReduce(ON_ZERO_TOLERANCE,B); // modifies M and B</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160; <span class="comment">// M.BackSolve(m,B,X); // solution is in X</span></div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160; <span class="comment">// See Also: </span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; <span class="comment">// ON_Matrix::BackSolve</span></div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; <span class="keywordtype">int</span> RowReduce(</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// zero_tolerance</span></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// B</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160; <span class="keywordtype">double</span>* = <span class="keyword">nullptr</span> <span class="comment">// pivot</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160; ); </div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160;</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160; <span class="comment">// Description:</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160; <span class="comment">// Row reduce a matrix as the first step in solving M*X=B where</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160; <span class="comment">// B is a column of 3d points</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160; <span class="comment">// Parameters:</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160; <span class="comment">// zero_tolerance - [in] (&gt;=0.0) zero tolerance for pivot test</span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; <span class="comment">// If the absolute value of a pivot is &lt;= zero_tolerance,</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; <span class="comment">// then the pivot is assumed to be zero.</span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; <span class="comment">// B - [in/out] an array of m_row_count 3d points that is </span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160; <span class="comment">// row reduced with the matrix.</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160; <span class="comment">// determinant - [out] value of determinant is returned here.</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; <span class="comment">// pivot - [out] If not nullptr, then the value of the smallest </span></div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; <span class="comment">// pivot is returned here</span></div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; <span class="comment">// Returns:</span></div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <span class="comment">// Rank of the matrix.</span></div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; <span class="comment">// Remarks:</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160; <span class="comment">// The matrix itself is row reduced so that the result is</span></div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160; <span class="comment">// an upper triangular matrix with 1&#39;s on the diagonal.</span></div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; <span class="comment">// See Also: </span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160; <span class="comment">// ON_Matrix::BackSolve</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160; <span class="keywordtype">int</span> RowReduce(</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// zero_tolerance</span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160; <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>*, <span class="comment">// B</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160; <span class="keywordtype">double</span>* = <span class="keyword">nullptr</span> <span class="comment">// pivot</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160; ); </div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160;</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160; <span class="comment">// Description:</span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160; <span class="comment">// Row reduce a matrix as the first step in solving M*X=B where</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160; <span class="comment">// B is a column arbitrary dimension points.</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160; <span class="comment">// Parameters:</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160; <span class="comment">// zero_tolerance - [in] (&gt;=0.0) zero tolerance for pivot test</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160; <span class="comment">// If a the absolute value of a pivot is &lt;= zero_tolerance,</span></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160; <span class="comment">// then the pivoit is assumed to be zero.</span></div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160; <span class="comment">// pt_dim - [in] dimension of points</span></div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160; <span class="comment">// pt_stride - [in] stride between points (&gt;=pt_dim)</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160; <span class="comment">// pt - [in/out] array of m_row_count*pt_stride values.</span></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160; <span class="comment">// The i-th point is</span></div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160; <span class="comment">// (pt[i*pt_stride],...,pt[i*pt_stride+pt_dim-1]).</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>&#160; <span class="comment">// This array of points is row reduced along with the </span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>&#160; <span class="comment">// matrix.</span></div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>&#160; <span class="comment">// pivot - [out] If not nullptr, then the value of the smallest </span></div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>&#160; <span class="comment">// pivot is returned here</span></div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>&#160; <span class="comment">// Returns:</span></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>&#160; <span class="comment">// Rank of the matrix.</span></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>&#160; <span class="comment">// Remarks:</span></div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>&#160; <span class="comment">// The matrix itself is row reduced so that the result is</span></div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>&#160; <span class="comment">// an upper triangular matrix with 1&#39;s on the diagonal.</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>&#160; <span class="comment">// See Also: </span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>&#160; <span class="comment">// ON_Matrix::BackSolve</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>&#160; <span class="keywordtype">int</span> RowReduce( <span class="comment">// returns rank</span></div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// zero_tolerance</span></div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// pt_dim</span></div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// pt_stride</span></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// pt</span></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>&#160; <span class="keywordtype">double</span>* = <span class="keyword">nullptr</span> <span class="comment">// pivot</span></div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>&#160; ); </div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>&#160;</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>&#160; <span class="comment">// Description:</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>&#160; <span class="comment">// Solve M*X=B where M is upper triangular with a unit diagonal and</span></div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>&#160; <span class="comment">// B is a column of values.</span></div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>&#160; <span class="comment">// Parameters:</span></div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>&#160; <span class="comment">// zero_tolerance - [in] (&gt;=0.0) used to test for &quot;zero&quot; values in B</span></div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>&#160; <span class="comment">// in under determined systems of equations.</span></div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>&#160; <span class="comment">// Bsize - [in] (&gt;=m_row_count) length of B. The values in</span></div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>&#160; <span class="comment">// B[m_row_count],...,B[Bsize-1] are tested to make sure they are</span></div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>&#160; <span class="comment">// &quot;zero&quot;.</span></div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>&#160; <span class="comment">// B - [in] array of length Bsize.</span></div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>&#160; <span class="comment">// X - [out] array of length m_col_count. Solutions returned here.</span></div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>&#160; <span class="comment">// Remarks:</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>&#160; <span class="comment">// Actual values M[i][j] with i &lt;= j are ignored. </span></div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>&#160; <span class="comment">// M[i][i] is assumed to be one and M[i][j] i&lt;j is assumed to be zero.</span></div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>&#160; <span class="comment">// For square M, B and X can point to the same memory.</span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>&#160; <span class="comment">// See Also:</span></div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>&#160; <span class="comment">// ON_Matrix::RowReduce</span></div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>&#160; <span class="keywordtype">bool</span> BackSolve(</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// zero_tolerance</span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// Bsize</span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// B</span></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// X</span></div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160; ) <span class="keyword">const</span>;</div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160;</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>&#160; <span class="comment">// Description:</span></div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160; <span class="comment">// Solve M*X=B where M is upper triangular with a unit diagonal and</span></div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160; <span class="comment">// B is a column of 3d points.</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span>&#160; <span class="comment">// Parameters:</span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160; <span class="comment">// zero_tolerance - [in] (&gt;=0.0) used to test for &quot;zero&quot; values in B</span></div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160; <span class="comment">// in under determined systems of equations.</span></div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160; <span class="comment">// Bsize - [in] (&gt;=m_row_count) length of B. The values in</span></div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160; <span class="comment">// B[m_row_count],...,B[Bsize-1] are tested to make sure they are</span></div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160; <span class="comment">// &quot;zero&quot;.</span></div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160; <span class="comment">// B - [in] array of length Bsize.</span></div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>&#160; <span class="comment">// X - [out] array of length m_col_count. Solutions returned here.</span></div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>&#160; <span class="comment">// Remarks:</span></div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>&#160; <span class="comment">// Actual values M[i][j] with i &lt;= j are ignored. </span></div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>&#160; <span class="comment">// M[i][i] is assumed to be one and M[i][j] i&lt;j is assumed to be zero.</span></div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>&#160; <span class="comment">// For square M, B and X can point to the same memory.</span></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>&#160; <span class="comment">// See Also:</span></div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>&#160; <span class="comment">// ON_Matrix::RowReduce</span></div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>&#160; <span class="keywordtype">bool</span> BackSolve(</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// zero_tolerance</span></div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// Bsize</span></div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>*, <span class="comment">// B</span></div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>&#160; <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>* <span class="comment">// X</span></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>&#160; ) <span class="keyword">const</span>;</div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>&#160;</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>&#160; <span class="comment">// Description:</span></div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span>&#160; <span class="comment">// Solve M*X=B where M is upper triangular with a unit diagonal and</span></div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>&#160; <span class="comment">// B is a column of points</span></div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>&#160; <span class="comment">// Parameters:</span></div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>&#160; <span class="comment">// zero_tolerance - [in] (&gt;=0.0) used to test for &quot;zero&quot; values in B</span></div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span>&#160; <span class="comment">// in under determined systems of equations.</span></div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>&#160; <span class="comment">// pt_dim - [in] dimension of points</span></div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>&#160; <span class="comment">// Bsize - [in] (&gt;=m_row_count) number of points in B[]. The points</span></div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>&#160; <span class="comment">// correspoinding to indices m_row_count, ..., (Bsize-1)</span></div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>&#160; <span class="comment">// are tested to make sure they are &quot;zero&quot;.</span></div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>&#160; <span class="comment">// Bpt_stride - [in] stride between B points (&gt;=pt_dim)</span></div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>&#160; <span class="comment">// Bpt - [in/out] array of m_row_count*Bpt_stride values.</span></div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160; <span class="comment">// The i-th B point is</span></div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160; <span class="comment">// (Bpt[i*Bpt_stride],...,Bpt[i*Bpt_stride+pt_dim-1]).</span></div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160; <span class="comment">// Xpt_stride - [in] stride between X points (&gt;=pt_dim)</span></div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>&#160; <span class="comment">// Xpt - [out] array of m_col_count*Xpt_stride values.</span></div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>&#160; <span class="comment">// The i-th X point is</span></div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>&#160; <span class="comment">// (Xpt[i*Xpt_stride],...,Xpt[i*Xpt_stride+pt_dim-1]).</span></div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span>&#160; <span class="comment">// Remarks:</span></div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>&#160; <span class="comment">// Actual values M[i][j] with i &lt;= j are ignored. </span></div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>&#160; <span class="comment">// M[i][i] is assumed to be one and M[i][j] i&lt;j is assumed to be zero.</span></div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>&#160; <span class="comment">// For square M, B and X can point to the same memory.</span></div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>&#160; <span class="comment">// See Also:</span></div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span>&#160; <span class="comment">// ON_Matrix::RowReduce</span></div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>&#160; <span class="keywordtype">bool</span> BackSolve(</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// zero_tolerance</span></div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// pt_dim</span></div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// Bsize</span></div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// Bpt_stride</span></div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*,<span class="comment">// Bpt</span></div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// Xpt_stride</span></div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// Xpt</span></div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; ) <span class="keyword">const</span>;</div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160;</div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160; <span class="keywordtype">bool</span> IsRowOrthoganal() <span class="keyword">const</span>;</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>&#160; <span class="keywordtype">bool</span> IsRowOrthoNormal() <span class="keyword">const</span>;</div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span>&#160;</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>&#160; <span class="keywordtype">bool</span> IsColOrthoganal() <span class="keyword">const</span>;</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>&#160; <span class="keywordtype">bool</span> IsColOrthoNormal() <span class="keyword">const</span>;</div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160;</div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160;</div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160; <span class="keywordtype">double</span>** m = <span class="keyword">nullptr</span>; <span class="comment">// m[i][j] = value at row i and column j</span></div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span>&#160; <span class="comment">// 0 &lt;= i &lt; RowCount()</span></div><div class="line"><a name="l00410"></a><span class="lineno"><a class="line" href="../../d7/d20/class_o_n___matrix.html#a83af73f8033024e23fdae01d2b9d340b"> 410</a></span>&#160; <span class="comment">// 0 &lt;= j &lt; ColCount()</span></div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span>&#160;<span class="keyword">private</span>:</div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>&#160; <span class="keywordtype">int</span> m_row_count = 0;</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>&#160; <span class="keywordtype">int</span> m_col_count = 0;</div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>&#160; <span class="comment">// m_rowmem[i][j] = row i+m_row_offset and column j+m_col_offset.</span></div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>&#160; <a class="code" href="../../dc/dfe/class_o_n___simple_array.html">ON_SimpleArray&lt;double*&gt;</a> m_rowmem; </div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>&#160; <span class="keywordtype">double</span>** m_Mmem = <span class="keyword">nullptr</span>; <span class="comment">// used by Create(row_count,col_count,user_memory,true);</span></div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>&#160; <span class="keywordtype">int</span> m_row_offset = 0; <span class="comment">// = ri0 when sub-matrix constructor is used</span></div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>&#160; <span class="keywordtype">int</span> m_col_offset = 0; <span class="comment">// = ci0 when sub-matrix constructor is used</span></div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span>&#160; <span class="keywordtype">void</span>* m_cmem = <span class="keyword">nullptr</span>;</div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span>&#160; <span class="comment">// returns 0 based arrays, even in submatrix case.</span></div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span>&#160; <span class="keywordtype">double</span> <span class="keyword">const</span> * <span class="keyword">const</span> * ThisM() <span class="keyword">const</span>;</div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span>&#160; <span class="keywordtype">double</span> * * ThisM();</div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>&#160;};</div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span>&#160;</div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span>&#160;</div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>&#160;<span class="comment"> Perform simple row reduction on a matrix. If A is square, positive</span></div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span>&#160;<span class="comment"> definite, and really really nice, then the returned B is the inverse</span></div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span>&#160;<span class="comment"> of A. If A is not positive definite and really really nice, then it</span></div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span>&#160;<span class="comment"> is probably a waste of time to call this function.</span></div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span>&#160;<span class="comment"> row_count - [in]</span></div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span>&#160;<span class="comment"> col_count - [in]</span></div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span>&#160;<span class="comment"> zero_pivot - [in]</span></div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span>&#160;<span class="comment"> absolute values &lt;= zero_pivot are considered to be zero</span></div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span>&#160;<span class="comment"> A - [in/out]</span></div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span>&#160;<span class="comment"> A row_count X col_count matrix. Input is the matrix to be</span></div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span>&#160;<span class="comment"> row reduced. The calculation destroys A, so output A is garbage.</span></div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span>&#160;<span class="comment"> B - [out]</span></div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span>&#160;<span class="comment"> A a row_count X row_count matrix. That records the row reduction.</span></div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span>&#160;<span class="comment"> pivots - [out]</span></div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span>&#160;<span class="comment"> minimum and maximum absolute values of pivots.</span></div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>&#160;<span class="comment"> Rank of A. If the returned value &lt; min(row_count,col_count),</span></div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span>&#160;<span class="comment"> then a zero pivot was encountered.</span></div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span>&#160;<span class="comment"> If C = input value of A, then B*C = (I,*)</span></div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span>&#160;ON_DECL</div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span>&#160;<span class="keywordtype">int</span> ON_RowReduce( </div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span>&#160; <span class="keywordtype">int</span> row_count, </div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span>&#160; <span class="keywordtype">int</span> col_count,</div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span>&#160; <span class="keywordtype">double</span> zero_pivot,</div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>&#160; <span class="keywordtype">double</span>** A, </div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>&#160; <span class="keywordtype">double</span>** B, </div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span>&#160; <span class="keywordtype">double</span> pivots[2] </div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span>&#160; );</div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>&#160;</div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>&#160;</div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span>&#160;<span class="comment"> Calculate a row reduction matrix so that R*M = upper triangular matrixPerform simple row reduction on a matrix. If A is square, positive</span></div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span>&#160;<span class="comment"> definite, and really really nice, then the returned B is the inverse</span></div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>&#160;<span class="comment"> of A. If A is not positive definite and really really nice, then it</span></div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span>&#160;<span class="comment"> is probably a waste of time to call this function.</span></div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>&#160;<span class="comment"> row_count - [in]</span></div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span>&#160;<span class="comment"> col_count - [in]</span></div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span>&#160;<span class="comment"> zero_pivot - [in]</span></div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span>&#160;<span class="comment"> absolute values &lt;= zero_pivot_tolerance are considered to be zero</span></div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span>&#160;<span class="comment"> constA - [in]</span></div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span>&#160;<span class="comment"> nullptr or a row_count x col_count matrix.</span></div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span>&#160;<span class="comment"> bInitializeB - [in]</span></div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span>&#160;<span class="comment"> If true, then B is set to the rox_count x row_count identity</span></div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span>&#160;<span class="comment"> before the calculation begins.</span></div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>&#160;<span class="comment"> bInitializeColumnPermutation - [in]</span></div><div class="line"><a name="l00477"></a><span class="lineno"> 477</span>&#160;<span class="comment"> If true and nullptr != column_permutation, then</span></div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span>&#160;<span class="comment"> column_permutation[] is initialized to (0, 1, ..., col_count-1)</span></div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span>&#160;<span class="comment"> before the calculation begins.</span></div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span>&#160;<span class="comment"> A - [in/out]</span></div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span>&#160;<span class="comment"> A row_count X col_count matrix. </span></div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span>&#160;<span class="comment"> If constA is not null, then A can be null or is the workspace used</span></div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span>&#160;<span class="comment"> to row reduce.</span></div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span>&#160;<span class="comment"> If constA is null, then the input A must not be null and must be initialized.</span></div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span>&#160;<span class="comment"> In all cases, the calculation destroys the contents of A and</span></div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span>&#160;<span class="comment"> output A contains garbage.</span></div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>&#160;<span class="comment"> B - [in/out]</span></div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span>&#160;<span class="comment"> A a row_count X row_count matrix</span></div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span>&#160;<span class="comment"> The row operations applied to A are also applied to B. </span></div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span>&#160;<span class="comment"> If the input B is the identity, then R*(input A) would have zeros below the diagonal.</span></div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span>&#160;<span class="comment"> column_permutation - [in/out]</span></div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span>&#160;<span class="comment"> The permutation applied to the columns of A is also applied to</span></div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span>&#160;<span class="comment"> the column_permutation[] array.</span></div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span>&#160;<span class="comment"> pivots - [out]</span></div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span>&#160;<span class="comment"> pivots[0] = maximum nonzero pivot</span></div><div class="line"><a name="l00496"></a><span class="lineno"> 496</span>&#160;<span class="comment"> pivots[1] = minimum nonzero pivot</span></div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span>&#160;<span class="comment"> pivots[2] = largest pivot that was treated as zero</span></div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span>&#160;<span class="comment"> Rank of A. If the returned value &lt; min(row_count,col_count),</span></div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span>&#160;<span class="comment"> then a zero pivot was encountered.</span></div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span>&#160;<span class="comment"> If C = input value of A, then B*C = (I,*)</span></div><div class="line"><a name="l00502"></a><span class="lineno"> 502</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span>&#160;ON_DECL</div><div class="line"><a name="l00504"></a><span class="lineno"> 504</span>&#160;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ON_RowReduce(</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> row_count,</div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span>&#160; <span class="keywordtype">unsigned</span> col_count,</div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span>&#160; <span class="keywordtype">double</span> zero_pivot_tolerance,</div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*<span class="keyword">const</span>* constA,</div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span>&#160; <span class="keywordtype">bool</span> bInitializeB,</div><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>&#160; <span class="keywordtype">bool</span> bInitializeColumnPermutation,</div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span>&#160; <span class="keywordtype">double</span>** A,</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span>&#160; <span class="keywordtype">double</span>** B,</div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* column_permutation,</div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span>&#160; <span class="keywordtype">double</span> pivots[3]</div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span>&#160; );</div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>&#160;</div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span>&#160;<span class="comment"> N - [in] &gt;= 1</span></div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span>&#160;<span class="comment"> M - [in]</span></div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span>&#160;<span class="comment"> M is an NxN matrix</span></div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span>&#160;<span class="comment"> bTransposeM - [in]</span></div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>&#160;<span class="comment"> If true, the eigenvectors of the transpose of M are calculated.</span></div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span>&#160;<span class="comment"> Put another way, if bTransposeM is false, then the &quot;right&quot;</span></div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span>&#160;<span class="comment"> eigenvectors are calculated; if bTransposeM is true, then the &quot;left&quot;</span></div><div class="line"><a name="l00527"></a><span class="lineno"> 527</span>&#160;<span class="comment"> eigenvectors are calculated.</span></div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span>&#160;<span class="comment"> lambda - [in]</span></div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span>&#160;<span class="comment"> known eigenvalue of M</span></div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span>&#160;<span class="comment"> lambda_multiplicity - [in]</span></div><div class="line"><a name="l00533"></a><span class="lineno"> 533</span>&#160;<span class="comment"> &gt; 0: known algebraic multiplicity of lambda</span></div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span>&#160;<span class="comment"> 0: algebraic multiplicity is unknown.</span></div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span>&#160;<span class="comment"> termination_tolerances - [in]</span></div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span>&#160;<span class="comment"> An array of three tolerances that control when the calculation</span></div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span>&#160;<span class="comment"> will stop searching for eigenvectors.</span></div><div class="line"><a name="l00539"></a><span class="lineno"> 539</span>&#160;<span class="comment"> If you do not understand what pivot values are, then pass nullptr</span></div><div class="line"><a name="l00540"></a><span class="lineno"> 540</span>&#160;<span class="comment"> and the values (1.0e-12, 1.0e-3, 1.0e4) will be used.</span></div><div class="line"><a name="l00541"></a><span class="lineno"> 541</span>&#160;<span class="comment"> If termination_tolerances[0] is not strictly positive, then 1.0e-12 is used.</span></div><div class="line"><a name="l00542"></a><span class="lineno"> 542</span>&#160;<span class="comment"> If termination_tolerances[1] is not strictly positive, then 1.0e-3 is used.</span></div><div class="line"><a name="l00543"></a><span class="lineno"> 543</span>&#160;<span class="comment"> If termination_tolerances[2] is not strictly positive, then 1.0e4 is used.</span></div><div class="line"><a name="l00544"></a><span class="lineno"> 544</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00545"></a><span class="lineno"> 545</span>&#160;<span class="comment"> The search for eigenvectors will continue if condition 1, </span></div><div class="line"><a name="l00546"></a><span class="lineno"> 546</span>&#160;<span class="comment"> and condition 2, and condition 3a or 3b is true.</span></div><div class="line"><a name="l00547"></a><span class="lineno"> 547</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00548"></a><span class="lineno"> 548</span>&#160;<span class="comment"> 1) The number of found eigenvectors is &lt; lambda_multiplicity.</span></div><div class="line"><a name="l00549"></a><span class="lineno"> 549</span>&#160;<span class="comment"> 2) eigenpivots[0] &gt;= eigenpivots[1] &gt; eigenpivots[2] &gt;= 0.</span></div><div class="line"><a name="l00550"></a><span class="lineno"> 550</span>&#160;<span class="comment"> 3a) eigenpivots[1]/eigenpivots[0] &lt; termination_tolerance[0].</span></div><div class="line"><a name="l00551"></a><span class="lineno"> 551</span>&#160;<span class="comment"> 3b) eigenpivots[1]/eigenpivots[0] &gt; termination_tolerance[1]</span></div><div class="line"><a name="l00552"></a><span class="lineno"> 552</span>&#160;<span class="comment"> or</span></div><div class="line"><a name="l00553"></a><span class="lineno"> 553</span>&#160;<span class="comment"> eigenpivots[0] - eigenpivots[1] &lt;= termination_tolerance[2]*eigenpivots[1].</span></div><div class="line"><a name="l00554"></a><span class="lineno"> 554</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00555"></a><span class="lineno"> 555</span>&#160;<span class="comment"> eigenvectors - [out]</span></div><div class="line"><a name="l00556"></a><span class="lineno"> 556</span>&#160;<span class="comment"> eigenvectors[0,...,eigendim-1][0,...,N-1]</span></div><div class="line"><a name="l00557"></a><span class="lineno"> 557</span>&#160;<span class="comment"> a basis for the lambda eigenspace. The eigenvectors are generally</span></div><div class="line"><a name="l00558"></a><span class="lineno"> 558</span>&#160;<span class="comment"> neither normalized nor orthoganal. </span></div><div class="line"><a name="l00559"></a><span class="lineno"> 559</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00560"></a><span class="lineno"> 560</span>&#160;<span class="comment"> eigenprecision - [out]</span></div><div class="line"><a name="l00561"></a><span class="lineno"> 561</span>&#160;<span class="comment"> eigenprecision[i] = maximum value of fabs(lambda*E[j] = E[j])/length(E) 0 &lt;= j &lt; N,</span></div><div class="line"><a name="l00562"></a><span class="lineno"> 562</span>&#160;<span class="comment"> where E = eigenvectors[i].</span></div><div class="line"><a name="l00563"></a><span class="lineno"> 563</span>&#160;<span class="comment"> If eigenprecision[i] is not &quot;small&quot; compared to nonzero coefficients in M and E,</span></div><div class="line"><a name="l00564"></a><span class="lineno"> 564</span>&#160;<span class="comment"> then E is not precise.</span></div><div class="line"><a name="l00565"></a><span class="lineno"> 565</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00566"></a><span class="lineno"> 566</span>&#160;<span class="comment"> eigenpivots - [out]</span></div><div class="line"><a name="l00567"></a><span class="lineno"> 567</span>&#160;<span class="comment"> eigenpivots[0] = maximum nonzero pivot</span></div><div class="line"><a name="l00568"></a><span class="lineno"> 568</span>&#160;<span class="comment"> eigenpivots[1] = minimum nonzero pivot</span></div><div class="line"><a name="l00569"></a><span class="lineno"> 569</span>&#160;<span class="comment"> eigenpivots[2] = maximum &quot;zero&quot; pivot</span></div><div class="line"><a name="l00570"></a><span class="lineno"> 570</span>&#160;<span class="comment"> When eigenpivots[2] s not &quot;small&quot; compared to eigenpivots[1],</span></div><div class="line"><a name="l00571"></a><span class="lineno"> 571</span>&#160;<span class="comment"> the answer is suspect.</span></div><div class="line"><a name="l00572"></a><span class="lineno"> 572</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00573"></a><span class="lineno"> 573</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00574"></a><span class="lineno"> 574</span>&#160;<span class="comment"> Number of eigenvectors found. In stable cases, this is the geometric</span></div><div class="line"><a name="l00575"></a><span class="lineno"> 575</span>&#160;<span class="comment"> multiplicity of the eigenvalue.</span></div><div class="line"><a name="l00576"></a><span class="lineno"> 576</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00577"></a><span class="lineno"> 577</span>&#160;ON_DECL</div><div class="line"><a name="l00578"></a><span class="lineno"> 578</span>&#160;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ON_GetEigenvectors(</div><div class="line"><a name="l00579"></a><span class="lineno"> 579</span>&#160; <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> N,</div><div class="line"><a name="l00580"></a><span class="lineno"> 580</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*<span class="keyword">const</span>* M,</div><div class="line"><a name="l00581"></a><span class="lineno"> 581</span>&#160; <span class="keywordtype">bool</span> bTransposeM,</div><div class="line"><a name="l00582"></a><span class="lineno"> 582</span>&#160; <span class="keywordtype">double</span> lambda,</div><div class="line"><a name="l00583"></a><span class="lineno"> 583</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> lambda_multiplicity,</div><div class="line"><a name="l00584"></a><span class="lineno"> 584</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* termination_tolerances,</div><div class="line"><a name="l00585"></a><span class="lineno"> 585</span>&#160; <span class="keywordtype">double</span>** eigenvectors,</div><div class="line"><a name="l00586"></a><span class="lineno"> 586</span>&#160; <span class="keywordtype">double</span>* eigenprecision,</div><div class="line"><a name="l00587"></a><span class="lineno"> 587</span>&#160; <span class="keywordtype">double</span>* eigenpivots</div><div class="line"><a name="l00588"></a><span class="lineno"> 588</span>&#160; );</div><div class="line"><a name="l00589"></a><span class="lineno"> 589</span>&#160;</div><div class="line"><a name="l00590"></a><span class="lineno"> 590</span>&#160;ON_DECL</div><div class="line"><a name="l00591"></a><span class="lineno"> 591</span>&#160;<span class="keywordtype">double</span> ON_EigenvectorPrecision(</div><div class="line"><a name="l00592"></a><span class="lineno"> 592</span>&#160; <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> N,</div><div class="line"><a name="l00593"></a><span class="lineno"> 593</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*<span class="keyword">const</span>* M,</div><div class="line"><a name="l00594"></a><span class="lineno"> 594</span>&#160; <span class="keywordtype">bool</span> bTransposeM,</div><div class="line"><a name="l00595"></a><span class="lineno"> 595</span>&#160; <span class="keywordtype">double</span> lambda,</div><div class="line"><a name="l00596"></a><span class="lineno"> 596</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* eigenvector</div><div class="line"><a name="l00597"></a><span class="lineno"> 597</span>&#160; );</div><div class="line"><a name="l00598"></a><span class="lineno"> 598</span>&#160;</div><div class="line"><a name="l00599"></a><span class="lineno"> 599</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00600"></a><span class="lineno"> 600</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00601"></a><span class="lineno"> 601</span>&#160;<span class="comment"> Maximum of fabs( ((M-lambda*I)*X)[i] - B[i] ) for 0 &lt;= i &lt; N</span></div><div class="line"><a name="l00602"></a><span class="lineno"> 602</span>&#160;<span class="comment"> Pass lambda = 0.0 if you&#39;re not testing some type of generalized eigenvalue.</span></div><div class="line"><a name="l00603"></a><span class="lineno"> 603</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00604"></a><span class="lineno"> 604</span>&#160;ON_DECL</div><div class="line"><a name="l00605"></a><span class="lineno"> 605</span>&#160;<span class="keywordtype">double</span> ON_MatrixSolutionPrecision(</div><div class="line"><a name="l00606"></a><span class="lineno"> 606</span>&#160; <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> N,</div><div class="line"><a name="l00607"></a><span class="lineno"> 607</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*<span class="keyword">const</span>* M,</div><div class="line"><a name="l00608"></a><span class="lineno"> 608</span>&#160; <span class="keywordtype">bool</span> bTransposeM,</div><div class="line"><a name="l00609"></a><span class="lineno"> 609</span>&#160; <span class="keywordtype">double</span> lambda,</div><div class="line"><a name="l00610"></a><span class="lineno"> 610</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* X,</div><div class="line"><a name="l00611"></a><span class="lineno"> 611</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* B</div><div class="line"><a name="l00612"></a><span class="lineno"> 612</span>&#160; );</div><div class="line"><a name="l00613"></a><span class="lineno"> 613</span>&#160;</div><div class="line"><a name="l00614"></a><span class="lineno"> 614</span>&#160;<span class="preprocessor">#endif</span></div><div class="ttc" id="class_o_n___simple_array_html"><div class="ttname"><a href="../../dc/dfe/class_o_n___simple_array.html">ON_SimpleArray&lt; double &gt;</a></div></div>
<div class="ttc" id="class_o_n___xform_html"><div class="ttname"><a href="../../d3/d13/class_o_n___xform.html">ON_Xform</a></div><div class="ttdef"><b>Definition:</b> opennurbs_xform.h:28</div></div>
<div class="ttc" id="class_o_n___matrix_html"><div class="ttname"><a href="../../d7/d20/class_o_n___matrix.html">ON_Matrix</a></div><div class="ttdef"><b>Definition:</b> opennurbs_matrix.h:22</div></div>
<div class="ttc" id="class_o_n__3d_point_html"><div class="ttname"><a href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:460</div></div>
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