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<div id="projectname">Eigenvalues problems
&#160;<span id="projectnumber">0.3</span>
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<div id="projectbrief">The final aim of our program is to implement numerical methods for the calculation of the eigenvalues and eigenvectors ​​of a matrix.</div>
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<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="class_matrix-members.html">List of all members</a> </div>
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<div class="title">Matrix Class Reference</div> </div>
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<p>The <a class="el" href="class_matrix.html" title="The Matrix class. ">Matrix</a> class.
<a href="class_matrix.html#details">More...</a></p>
<p><code>#include &lt;<a class="el" href="_matrix_8h_source.html">Matrix.h</a>&gt;</code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a93858ae6bf7a97e68dbf67dd45169ed9"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a93858ae6bf7a97e68dbf67dd45169ed9">Matrix</a> (string filename)</td></tr>
<tr class="memdesc:a93858ae6bf7a97e68dbf67dd45169ed9"><td class="mdescLeft">&#160;</td><td class="mdescRight">A constructor. <a href="#a93858ae6bf7a97e68dbf67dd45169ed9">More...</a><br /></td></tr>
<tr class="separator:a93858ae6bf7a97e68dbf67dd45169ed9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9b1c3627f573d78a2f08623fdfef990f"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a9b1c3627f573d78a2f08623fdfef990f">~Matrix</a> ()</td></tr>
<tr class="memdesc:a9b1c3627f573d78a2f08623fdfef990f"><td class="mdescLeft">&#160;</td><td class="mdescRight">A destructor. <a href="#a9b1c3627f573d78a2f08623fdfef990f">More...</a><br /></td></tr>
<tr class="separator:a9b1c3627f573d78a2f08623fdfef990f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5ecdee507bf406c65889542907874eee"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a5ecdee507bf406c65889542907874eee">printMatrix</a> (double **matrix, int size)</td></tr>
<tr class="memdesc:a5ecdee507bf406c65889542907874eee"><td class="mdescLeft">&#160;</td><td class="mdescRight">A public member printing the content of the square matrix. <a href="#a5ecdee507bf406c65889542907874eee">More...</a><br /></td></tr>
<tr class="separator:a5ecdee507bf406c65889542907874eee"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1de096de305701dc6eb63c56eed18cfb"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a1de096de305701dc6eb63c56eed18cfb">powerMethod</a> (double **m, int size, double tol, double shift_amount)</td></tr>
<tr class="memdesc:a1de096de305701dc6eb63c56eed18cfb"><td class="mdescLeft">&#160;</td><td class="mdescRight">A public member for eigenvalue computation based either on the Power method or on the Power method with shift (if shift is provided in the input file) <a href="#a1de096de305701dc6eb63c56eed18cfb">More...</a><br /></td></tr>
<tr class="separator:a1de096de305701dc6eb63c56eed18cfb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae0bb7d862099f287b92e91aca8048671"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#ae0bb7d862099f287b92e91aca8048671">inversePowerMethod</a> (double **matrix, int size, double tol, double shift_amount)</td></tr>
<tr class="memdesc:ae0bb7d862099f287b92e91aca8048671"><td class="mdescLeft">&#160;</td><td class="mdescRight">A public member for eigenvalue computation based either on the Inverse Power method or on the Inverse Power method with shift (if shift is provided) <a href="#ae0bb7d862099f287b92e91aca8048671">More...</a><br /></td></tr>
<tr class="separator:ae0bb7d862099f287b92e91aca8048671"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aacd7d0703d317afb759fd9789467e5a3"><td class="memItemLeft" align="right" valign="top"><a id="aacd7d0703d317afb759fd9789467e5a3"></a>
double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#aacd7d0703d317afb759fd9789467e5a3">get_shift_amount</a> ()</td></tr>
<tr class="memdesc:aacd7d0703d317afb759fd9789467e5a3"><td class="mdescLeft">&#160;</td><td class="mdescRight">A getter method that returns the shift_amount variable. <br /></td></tr>
<tr class="separator:aacd7d0703d317afb759fd9789467e5a3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a20dfc0664e471990cf08a1e854a0a87f"><td class="memItemLeft" align="right" valign="top"><a id="a20dfc0664e471990cf08a1e854a0a87f"></a>
double **&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a20dfc0664e471990cf08a1e854a0a87f">get_matrix</a> ()</td></tr>
<tr class="memdesc:a20dfc0664e471990cf08a1e854a0a87f"><td class="mdescLeft">&#160;</td><td class="mdescRight">A getter method that returns the matrix variable. <br /></td></tr>
<tr class="separator:a20dfc0664e471990cf08a1e854a0a87f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0dfe20b13369ad36449d086b46252494"><td class="memItemLeft" align="right" valign="top"><a id="a0dfe20b13369ad36449d086b46252494"></a>
int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a0dfe20b13369ad36449d086b46252494">get_size</a> ()</td></tr>
<tr class="memdesc:a0dfe20b13369ad36449d086b46252494"><td class="mdescLeft">&#160;</td><td class="mdescRight">A getter method that returns the size variable. <br /></td></tr>
<tr class="separator:a0dfe20b13369ad36449d086b46252494"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac867d86cbc3be78de23405d705f148a6"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#ac867d86cbc3be78de23405d705f148a6">LUPDecompose</a> (double **A, int N, double Tol, int *P)</td></tr>
<tr class="memdesc:ac867d86cbc3be78de23405d705f148a6"><td class="mdescLeft">&#160;</td><td class="mdescRight">A public member that computes the PA=LU decomposition. <a href="#ac867d86cbc3be78de23405d705f148a6">More...</a><br /></td></tr>
<tr class="separator:ac867d86cbc3be78de23405d705f148a6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a49cbcea74e3453738df7127817ae4dd7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a49cbcea74e3453738df7127817ae4dd7">LUPSolve</a> (double **A, int *P, double *b, int N, double *x)</td></tr>
<tr class="memdesc:a49cbcea74e3453738df7127817ae4dd7"><td class="mdescLeft">&#160;</td><td class="mdescRight">A public member that solves the equation A*x=b. <a href="#a49cbcea74e3453738df7127817ae4dd7">More...</a><br /></td></tr>
<tr class="separator:a49cbcea74e3453738df7127817ae4dd7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a568fbdaf8c09b0d2584328b5940affe2"><td class="memItemLeft" align="right" valign="top">double **&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#a568fbdaf8c09b0d2584328b5940affe2">shift</a> (double **A, int size, double shift)</td></tr>
<tr class="memdesc:a568fbdaf8c09b0d2584328b5940affe2"><td class="mdescLeft">&#160;</td><td class="mdescRight">A public member that computes the A-shift_amount*I matrix. <a href="#a568fbdaf8c09b0d2584328b5940affe2">More...</a><br /></td></tr>
<tr class="separator:a568fbdaf8c09b0d2584328b5940affe2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab6595c99011b24abc53a11fab652a68f"><td class="memItemLeft" align="right" valign="top"><a id="ab6595c99011b24abc53a11fab652a68f"></a>
int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="class_matrix.html#ab6595c99011b24abc53a11fab652a68f">test</a> (int i)</td></tr>
<tr class="memdesc:ab6595c99011b24abc53a11fab652a68f"><td class="mdescLeft">&#160;</td><td class="mdescRight">A public member that runs the tests. <br /></td></tr>
<tr class="separator:ab6595c99011b24abc53a11fab652a68f"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>The <a class="el" href="class_matrix.html" title="The Matrix class. ">Matrix</a> class. </p>
<p>The "Matrix" class is meant to perform different kinds of operations on a data structure representing a square matrix. Specifically, it provides the following implementations of numerical methods for eigenvalue computation:</p><ul>
<li>Power and Inverse power method;</li>
<li>Implementation of Power and Inverse power methods with shift. </li>
</ul>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a93858ae6bf7a97e68dbf67dd45169ed9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a93858ae6bf7a97e68dbf67dd45169ed9">&#9670;&nbsp;</a></span>Matrix()</h2>
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<div class="memproto">
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<td class="memname">Matrix::Matrix </td>
<td>(</td>
<td class="paramtype">string&#160;</td>
<td class="paramname"><em>filename</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A constructor. </p>
<p>The constructor initializes the content of the square matrix by reading size*size values from a text file </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">filename</td><td>a string representing the name of the input text file </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a id="a9b1c3627f573d78a2f08623fdfef990f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9b1c3627f573d78a2f08623fdfef990f">&#9670;&nbsp;</a></span>~Matrix()</h2>
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<td class="memname">Matrix::~Matrix </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A destructor. </p>
<p>The destructor deletes the square matrix </p>
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a id="ae0bb7d862099f287b92e91aca8048671"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae0bb7d862099f287b92e91aca8048671">&#9670;&nbsp;</a></span>inversePowerMethod()</h2>
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<td class="memname">double Matrix::inversePowerMethod </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>matrix</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>size</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>tol</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>shift_amount</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A public member for eigenvalue computation based either on the Inverse Power method or on the Inverse Power method with shift (if shift is provided) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">matrix</td><td>the square matrix </td></tr>
<tr><td class="paramname">size</td><td>the row and the column dimension of the square matrix </td></tr>
<tr><td class="paramname">tol</td><td>the accepted tolerance adopted in the eigenvalue computation </td></tr>
<tr><td class="paramname">shift_amount</td><td>the shift amount adopted in the Power method with shift </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>a double value representing the eigenvalue </dd></dl>
</div>
</div>
<a id="ac867d86cbc3be78de23405d705f148a6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac867d86cbc3be78de23405d705f148a6">&#9670;&nbsp;</a></span>LUPDecompose()</h2>
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<td class="memname">int Matrix::LUPDecompose </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>N</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>Tol</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int *&#160;</td>
<td class="paramname"><em>P</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A public member that computes the PA=LU decomposition. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>the square matrix with size N; <a class="el" href="class_matrix.html" title="The Matrix class. ">Matrix</a> A is modified, containing both matrices L-E and U as A=(L-E)+U such that P*A=L*U </td></tr>
<tr><td class="paramname">Tol</td><td>a small tolerance number to detect failure when the matrix is near degenerate </td></tr>
<tr><td class="paramname">N</td><td>the size of the square matrix </td></tr>
<tr><td class="paramname">P</td><td>an integer vector P of size N+1 </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 if the method failed, 1 if the method succeeded </dd></dl>
</div>
</div>
<a id="a49cbcea74e3453738df7127817ae4dd7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a49cbcea74e3453738df7127817ae4dd7">&#9670;&nbsp;</a></span>LUPSolve()</h2>
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<td class="memname">void Matrix::LUPSolve </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int *&#160;</td>
<td class="paramname"><em>P</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double *&#160;</td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>N</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double *&#160;</td>
<td class="paramname"><em>x</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A public member that solves the equation A*x=b. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>the matrix filled in LUPDecompose </td></tr>
<tr><td class="paramname">P</td><td>the array filled in LUPDecompose </td></tr>
<tr><td class="paramname">b</td><td>a known array of double values </td></tr>
<tr><td class="paramname">N</td><td>the size of the square matrix </td></tr>
<tr><td class="paramname">x</td><td>the solution vector of A*x=b </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
</div>
</div>
<a id="a1de096de305701dc6eb63c56eed18cfb"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a1de096de305701dc6eb63c56eed18cfb">&#9670;&nbsp;</a></span>powerMethod()</h2>
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<td class="memname">double Matrix::powerMethod </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>size</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>tol</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>shift_amount</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A public member for eigenvalue computation based either on the Power method or on the Power method with shift (if shift is provided in the input file) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">m</td><td>the square matrix </td></tr>
<tr><td class="paramname">size</td><td>the row and the column dimension of the square matrix </td></tr>
<tr><td class="paramname">tol</td><td>the accepted tolerance adopted in the eigenvalue computation </td></tr>
<tr><td class="paramname">shift_amount</td><td>the shift amount adopted in the Power method with shift </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>a double value representing the eigenvalue </dd></dl>
</div>
</div>
<a id="a5ecdee507bf406c65889542907874eee"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a5ecdee507bf406c65889542907874eee">&#9670;&nbsp;</a></span>printMatrix()</h2>
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<td class="memname">void Matrix::printMatrix </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>matrix</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>size</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A public member printing the content of the square matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">matrix</td><td>the square matrix </td></tr>
<tr><td class="paramname">size</td><td>the row and the column dimension of the square matrix </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
</div>
</div>
<a id="a568fbdaf8c09b0d2584328b5940affe2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a568fbdaf8c09b0d2584328b5940affe2">&#9670;&nbsp;</a></span>shift()</h2>
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<td class="memname">double ** Matrix::shift </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>A</em>, </td>
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<td class="paramtype">int&#160;</td>
<td class="paramname"><em>size</em>, </td>
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<td class="paramtype">double&#160;</td>
<td class="paramname"><em>shift</em>&#160;</td>
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<p>A public member that computes the A-shift_amount*I matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">A</td><td>a matrix filled in LUPDecompose </td></tr>
<tr><td class="paramname">size</td><td>the size of the square matrix </td></tr>
<tr><td class="paramname">shift</td><td>the shift amount </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the output matrix (A-shift_amount*I) </dd></dl>
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<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="_matrix_8h_source.html">Matrix.h</a></li>
<li>Matrix.cpp</li>
</ul>
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