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<div class="title">core_smoothers.h</div> </div>
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<a href="algebra__common_2core__smoothers_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * Copyright (c) 2010-2015: G-CSC, Goethe University Frankfurt</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * Author: Martin Rupp</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * This file is part of UG4.</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * UG4 is free software: you can redistribute it and/or modify it under the</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * terms of the GNU Lesser General Public License version 3 (as published by the</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * Free Software Foundation) with the following additional attribution</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * requirements (according to LGPL/GPL v3 §7):</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * (1) The following notice must be displayed in the Appropriate Legal Notices</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * of covered and combined works: "Based on UG4 (www.ug4.org/license)".</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * (2) The following notice must be displayed at a prominent place in the</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> * (3) The following bibliography is recommended for citation and must be</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> * preserved in all covered files:</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"> * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> * parallel geometric multigrid solver on hierarchically distributed grids.</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> * Computing and visualization in science 16, 4 (2013), 151-164"</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> * flexible software system for simulating pde based models on high performance</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> * computers. Computing and visualization in science 16, 4 (2013), 165-179"</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> * This program is distributed in the hope that it will be useful,</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#ifndef __H__UG__CPU_ALGEBRA__CORE_SMOOTHERS__</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#define __H__UG__CPU_ALGEBRA__CORE_SMOOTHERS__</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">namespace </span><a class="code" href="namespaceug.html">ug</a></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// gs_step_LL</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"></span><span class="keyword">template</span><<span class="keyword">typename</span> Matrix_type, <span class="keyword">typename</span> Vector_type></div>
<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="group__lib__algebra.html#ga98970ee004dd8a19da9268ba651ffdce"> 106</a></span> <span class="keywordtype">void</span> <a class="code" href="group__lib__algebra.html#ga98970ee004dd8a19da9268ba651ffdce">gs_step_LL</a>(<span class="keyword">const</span> Matrix_type &A, Vector_type &c, <span class="keyword">const</span> Vector_type &d, <span class="keyword">const</span> <a class="code" href="group__ugbase__common.html#gaf349a0d1e8189254086eb3267fd4f460">number</a> relaxFactor)</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> {</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// gs LL has preconditioning matrix N = (D-L)^{-1}</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="sparsematrix__interface_8h.html#a265a253612b46abed17c61b0a5e5ce30">Matrix_type::value_type</a> matrix_block;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix_type::const_row_iterator const_row_it;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">typename</span> <a class="code" href="sparsematrix__interface_8h.html#a265a253612b46abed17c61b0a5e5ce30">Vector_type::value_type</a> <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keyword">const</span> <span class="keywordtype">size_t</span> sz = c.size();</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < sz; ++i)</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  {</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a> = d[i];</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// loop over all lower left matrix entries.</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// Note: Here the corrections c, which have already been computed in previous loops (wrt. i),</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// are taken to compute the i-th correction. For example the correction of the second row</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">// is computed by s[2] = (d[2] - A[2][1] * c[1]); and c[2] = s[2]/A[2][2];</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keyword">const</span> const_row_it rowEnd = A.end_row(i);</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  const_row_it it = A.begin_row(i);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">for</span>(; it != rowEnd && it.index() < i; ++it)</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">// s -= it.value() * c[it.index()];</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <a class="code" href="namespaceug.html#a6f1addfcc15e261ec19eca7c425d5d79">MatMultAdd</a>(<a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>, 1.0, <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>, -1.0, it.value(), c[it.index()]);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// c[i] = relaxFactor * s/A(i,i)</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">const</span> matrix_block& A_ii = it.index() == i ? it.value() : matrix_block(0);</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="code" href="namespaceug.html#ae3578a2d24573312c4b9c35ebac65494">InverseMatMult</a>(c[i], relaxFactor, A_ii, <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>);</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  }</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> }</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment">// gs_step_UR</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"></span><span class="keyword">template</span><<span class="keyword">typename</span> Matrix_type, <span class="keyword">typename</span> Vector_type></div>
<div class="line"><a name="l00150"></a><span class="lineno"><a class="line" href="group__lib__algebra.html#ga6cec366add5874b559c21b14321e6a25"> 150</a></span> <span class="keywordtype">void</span> <a class="code" href="group__lib__algebra.html#ga6cec366add5874b559c21b14321e6a25">gs_step_UR</a>(<span class="keyword">const</span> Matrix_type &A, Vector_type &c, <span class="keyword">const</span> Vector_type &d, <span class="keyword">const</span> <a class="code" href="group__ugbase__common.html#gaf349a0d1e8189254086eb3267fd4f460">number</a> relaxFactor)</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> {</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="comment">// gs UR has preconditioning matrix N = (D-U)^{-1}</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  </div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keyword">typename</span> <a class="code" href="sparsematrix__interface_8h.html#a265a253612b46abed17c61b0a5e5ce30">Vector_type::value_type</a> <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>;</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">if</span>(c.size() == 0) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordtype">size_t</span> i = c.size()-1;</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">do</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  {</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a> = d[i];</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keyword">typename</span> Matrix_type::const_row_iterator diag = A.get_connection(i, i);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keyword">typename</span> Matrix_type::const_row_iterator it = diag; ++it;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">for</span>(; it != A.end_row(i); ++it)</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// s -= it.value() * x[it.index()];</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <a class="code" href="namespaceug.html#a6f1addfcc15e261ec19eca7c425d5d79">MatMultAdd</a>(<a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>, 1.0, <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>, -1.0, it.value(), c[it.index()]);</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="comment">// c[i] = relaxFactor * s/A(i,i)</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <a class="code" href="namespaceug.html#ae3578a2d24573312c4b9c35ebac65494">InverseMatMult</a>(c[i], relaxFactor, diag.value(), <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>);</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  } <span class="keywordflow">while</span>(i-- != 0);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> }</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// sgs_step</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment"></span><span class="keyword">template</span><<span class="keyword">typename</span> Matrix_type, <span class="keyword">typename</span> Vector_type></div>
<div class="line"><a name="l00189"></a><span class="lineno"><a class="line" href="group__lib__algebra.html#gae550d865ffb7730fde393ab5a1f83a4b"> 189</a></span> <span class="keywordtype">void</span> <a class="code" href="group__lib__algebra.html#gae550d865ffb7730fde393ab5a1f83a4b">sgs_step</a>(<span class="keyword">const</span> Matrix_type &A, Vector_type &c, <span class="keyword">const</span> Vector_type &d, <span class="keyword">const</span> <a class="code" href="group__ugbase__common.html#gaf349a0d1e8189254086eb3267fd4f460">number</a> relaxFactor)</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> {</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="comment">// sgs has preconditioning matrix N = (D-U)^{-1} D (D-L)^{-1}</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="comment">// c1 = (D-L)^{-1} d</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <a class="code" href="group__lib__algebra.html#ga98970ee004dd8a19da9268ba651ffdce">gs_step_LL</a>(A, c, d, relaxFactor);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// c2 = D c1</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keyword">typename</span> <a class="code" href="sparsematrix__interface_8h.html#a265a253612b46abed17c61b0a5e5ce30">Vector_type::value_type</a> <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i<c.size(); i++)</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  {</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>=c[i];</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <a class="code" href="namespaceug.html#ad76b10ff156c4239abd30c333373f71c">MatMult</a>(c[i], 1.0, A(i, i), <a class="codeRef" href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a>);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  }</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="comment">// c3 = (D-U)^{-1} c2</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <a class="code" href="group__lib__algebra.html#ga6cec366add5874b559c21b14321e6a25">gs_step_UR</a>(A, c, c, relaxFactor);</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> }</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// diag_step</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment"></span><span class="keyword">template</span><<span class="keyword">typename</span> Matrix_type, <span class="keyword">typename</span> Vector_type></div>
<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="group__lib__algebra.html#gaa0530b5446400873554834211f173970"> 218</a></span> <span class="keywordtype">void</span> <a class="code" href="group__lib__algebra.html#gaa0530b5446400873554834211f173970">diag_step</a>(<span class="keyword">const</span> Matrix_type& A, Vector_type& c, <span class="keyword">const</span> Vector_type& d, <a class="code" href="group__ugbase__common.html#gaf349a0d1e8189254086eb3267fd4f460">number</a> damp)</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> {</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="comment">//exit(3);</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <a class="code" href="group__ugbase__common.html#ga0b928ef153b78f1b5e025638cf28f841">UG_ASSERT</a>(c.size() == d.size() && c.size() == A.num_rows(), c << <span class="stringliteral">", "</span> << d <<</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="stringliteral">" and "</span> << A << <span class="stringliteral">" need to have same size."</span>);</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  </div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i=0; i < c.size(); i++)</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">// c[i] = damp * d[i]/A(i,i)</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <a class="code" href="namespaceug.html#ae3578a2d24573312c4b9c35ebac65494">InverseMatMult</a>(c[i], damp, A(i,i), d[i]);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> }</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  </div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  </div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> }</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="preprocessor">#endif </span><span class="comment">// __H__UG__CPU_ALGEBRA__CORE_SMOOTHERS__</span></div>
<div class="ttc" id="a_biogas_8lua_html_a9dda901d5ee6289370201a700f88e789"><div class="ttname"><a href="../plugins/_biogas_8lua.html#a9dda901d5ee6289370201a700f88e789">s</a></div><div class="ttdeci">parameterString s</div></div>
<div class="ttc" id="agroup__lib__algebra_html_ga6cec366add5874b559c21b14321e6a25"><div class="ttname"><a href="group__lib__algebra.html#ga6cec366add5874b559c21b14321e6a25">ug::gs_step_UR</a></div><div class="ttdeci">void gs_step_UR(const Matrix_type &A, Vector_type &c, const Vector_type &d, const number relaxFactor)</div><div class="ttdoc">Performs a backward gauss-seidel-step, that is, solve on the upper right of A. Using gs_step_UR withi...</div><div class="ttdef"><b>Definition:</b> core_smoothers.h:150</div></div>
<div class="ttc" id="agroup__lib__algebra_html_ga98970ee004dd8a19da9268ba651ffdce"><div class="ttname"><a href="group__lib__algebra.html#ga98970ee004dd8a19da9268ba651ffdce">ug::gs_step_LL</a></div><div class="ttdeci">void gs_step_LL(const Matrix_type &A, Vector_type &c, const Vector_type &d, const number relaxFactor)</div><div class="ttdoc">Gauss-Seidel-Iterations.</div><div class="ttdef"><b>Definition:</b> core_smoothers.h:106</div></div>
<div class="ttc" id="agroup__lib__algebra_html_gaa0530b5446400873554834211f173970"><div class="ttname"><a href="group__lib__algebra.html#gaa0530b5446400873554834211f173970">ug::diag_step</a></div><div class="ttdeci">void diag_step(const Matrix_type &A, Vector_type &c, const Vector_type &d, number damp)</div><div class="ttdoc">Performs a jacobi-step.</div><div class="ttdef"><b>Definition:</b> core_smoothers.h:218</div></div>
<div class="ttc" id="agroup__lib__algebra_html_gae550d865ffb7730fde393ab5a1f83a4b"><div class="ttname"><a href="group__lib__algebra.html#gae550d865ffb7730fde393ab5a1f83a4b">ug::sgs_step</a></div><div class="ttdeci">void sgs_step(const Matrix_type &A, Vector_type &c, const Vector_type &d, const number relaxFactor)</div><div class="ttdoc">Performs a symmetric gauss-seidel step. Using sgs_step within a preconditioner-scheme leads to the fa...</div><div class="ttdef"><b>Definition:</b> core_smoothers.h:189</div></div>
<div class="ttc" id="agroup__ugbase__common_html_ga0b928ef153b78f1b5e025638cf28f841"><div class="ttname"><a href="group__ugbase__common.html#ga0b928ef153b78f1b5e025638cf28f841">UG_ASSERT</a></div><div class="ttdeci">#define UG_ASSERT(expr, msg)</div><div class="ttdef"><b>Definition:</b> assert.h:70</div></div>
<div class="ttc" id="agroup__ugbase__common_html_gaf349a0d1e8189254086eb3267fd4f460"><div class="ttname"><a href="group__ugbase__common.html#gaf349a0d1e8189254086eb3267fd4f460">number</a></div><div class="ttdeci">double number</div><div class="ttdef"><b>Definition:</b> types.h:124</div></div>
<div class="ttc" id="anamespaceug_html"><div class="ttname"><a href="namespaceug.html">ug</a></div><div class="ttdoc">the ug namespace</div></div>
<div class="ttc" id="anamespaceug_html_a6f1addfcc15e261ec19eca7c425d5d79"><div class="ttname"><a href="namespaceug.html#a6f1addfcc15e261ec19eca7c425d5d79">ug::MatMultAdd</a></div><div class="ttdeci">bool MatMultAdd(vector_t &dest, const number &alpha1, const vector_t &v1, const number &beta1, const matrix_t &A1, const vector_t &w1)</div><div class="ttdoc">calculates dest = alpha1*v1 + beta1 * A1 *w1;</div><div class="ttdef"><b>Definition:</b> operations_mat.h:68</div></div>
<div class="ttc" id="anamespaceug_html_ad76b10ff156c4239abd30c333373f71c"><div class="ttname"><a href="namespaceug.html#ad76b10ff156c4239abd30c333373f71c">ug::MatMult</a></div><div class="ttdeci">bool MatMult(vector_t &dest, const number &beta1, const matrix_t &A1, const vector_t &w1)</div><div class="ttdoc">calculates dest = beta1 * A1;</div><div class="ttdef"><b>Definition:</b> operations_mat.h:59</div></div>
<div class="ttc" id="anamespaceug_html_ae3578a2d24573312c4b9c35ebac65494"><div class="ttname"><a href="namespaceug.html#ae3578a2d24573312c4b9c35ebac65494">ug::InverseMatMult</a></div><div class="ttdeci">bool InverseMatMult(number &dest, const double &beta, const TMat &mat, const TVec &vec)</div><div class="ttdoc">you can implement this function with GetInverse and MatMult</div></div>
<div class="ttc" id="asparsematrix__interface_8h_html_a265a253612b46abed17c61b0a5e5ce30"><div class="ttname"><a href="sparsematrix__interface_8h.html#a265a253612b46abed17c61b0a5e5ce30">value_type</a></div><div class="ttdeci">T value_type</div><div class="ttdef"><b>Definition:</b> sparsematrix_interface.h:2</div></div>
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