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pyeigvalvecsym.html
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pyeigvalvecsym.html
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<h1 id="eigvalvecsym">EigValVecSym</h1>
<p>Compute the eigenvalues and eigenvectors of a real symmetric matrix.</p>
<h1 id="usage">Usage</h1>
<p><code>eval</code>, <code>evec</code> = pyshtools.EigValVecSym (<code>ain</code>, [<code>n</code>, <code>ul</code>, <code>k</code>])</p>
<h1 id="returns">Returns</h1>
<dl>
<dt><code>eval</code> : float, dimension (<code>k</code>)</dt>
<dd>The eigenvalues of <code>ain</code>, sorted from largest to smallest.
</dd>
<dt><code>evec</code> : float, dimension (<code>n</code>, <code>k</code>)</dt>
<dd>The eigenvectors of <code>ain</code>, sorted from largest to smallest eigenvalues. The sign of the first element of each eigenvector is chosen to be positive.
</dd>
</dl>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>ain</code> : float, dimension (<code>nin</code>, <code>nin</code>)</dt>
<dd>The input real symmetric matrix. By default, only the upper portion of the matrix is used.
</dd>
<dt><code>n</code> : optional, integer, default = <code>nin</code></dt>
<dd>The rank of the matrix <code>ain</code>.
</dd>
<dt><code>ul</code> : optional, character, default = <code>U</code></dt>
<dd>If <code>U</code> then the upper portion of the matrix <code>ain</code> will be used (default). If <code>L</code> then the lower portion of the matrix <code>ain</code> will be used.
</dd>
<dt><code>k</code> : optional, optional, integer, default = <code>nin</code></dt>
<dd>The number of largest eigenvalues and corresponding eigenvectors to be output.
</dd>
</dl>
<h1 id="description">Description</h1>
<p><code>EigValVecSym</code> will calculate the eigenvalues and eigenvectors of a real symmetric matrix. By default, only the upper portion of the matrix is used, but this can be changed by the optional argument <code>ul</code>. The eigenvalues and eigenvectors are sorted from largest to smallest eigenvalues. If the optional parameter <code>k</code> is specified, then only the <code>k</code> largest eigenvalues and their corresponding eigenvectors will be output.</p>
<p>The matrix <code>ain</code> is first factorized into a tridiagonal matrix using the LAPACK routine <code>DSYTRD</code>, and then the eigenvalues are calculated by calls to <code>DSTEGR</code> and <code>DORMTR</code>.</p>
<h1 id="see-also">See also</h1>
<p><a href="pyeigvalsym.html">eigvalsym</a>, <a href="pyeigvalvecsymtri.html">eigvalvecsymtri</a></p>
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