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<div class="title">Solving linear least squares problems</div> </div>
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<p>lede</p>
<h1><a class="anchor" id="LinearLeastSquaresCopied"></a>
Copied</h1>
<p>The best way to do least squares solving is with a SVD decomposition. <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library. ">Eigen</a> provides one as the <a class="el" href="classEigen_1_1JacobiSVD.html" title="Two-sided Jacobi SVD decomposition of a rectangular matrix. ">JacobiSVD</a> class, and its solve() is doing least-squares solving.</p>
<p>Here is an example: </p>
<table class="example">
<tr>
<th>Example:</th><th>Output: </th></tr>
<tr>
<td><div class="fragment"><div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"><span class="preprocessor">#include <Eigen/Dense></span></div>
<div class="line"></div>
<div class="line"><span class="keyword">using namespace </span>std;</div>
<div class="line"><span class="keyword">using namespace </span>Eigen;</div>
<div class="line"></div>
<div class="line"><span class="keywordtype">int</span> main()</div>
<div class="line">{</div>
<div class="line"> <a class="code" href="classEigen_1_1Matrix.html">MatrixXf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">MatrixXf::Random</a>(3, 2);</div>
<div class="line"> cout << <span class="stringliteral">"Here is the matrix A:\n"</span> << A << endl;</div>
<div class="line"> VectorXf b = <a class="code" href="classEigen_1_1DenseBase.html#a8e759dafdd9ecc446d397b7f5435f60a">VectorXf::Random</a>(3);</div>
<div class="line"> cout << <span class="stringliteral">"Here is the right hand side b:\n"</span> << b << endl;</div>
<div class="line"> cout << <span class="stringliteral">"The least-squares solution is:\n"</span></div>
<div class="line"> << A.<a class="code" href="classEigen_1_1MatrixBase.html#a27a6a2e9d8839662a29cc8294398ff97">jacobiSvd</a>(<a class="code" href="group__enums.html#gga2d78499b99ddc29b9494f7ea33864d52aa1954d61a33cbb0e9960ca88085ec487">ComputeThinU</a> | <a class="code" href="group__enums.html#gga2d78499b99ddc29b9494f7ea33864d52aa0bec1072bc1ecbbaaa436f96fe02e78">ComputeThinV</a>).solve(b) << endl;</div>
<div class="line">}</div>
</div><!-- fragment --> </td><td><pre class="fragment">Here is the matrix A:
0.68 0.597
-0.211 0.823
0.566 -0.605
Here is the right hand side b:
-0.33
0.536
-0.444
The least-squares solution is:
-0.67
0.314
</pre> </td></tr>
</table>
<p>For more information, including faster but less reliable methods, read our page concentrating on <a class="el" href="group__LinearLeastSquares.html">linear least squares problems</a>. </p>
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