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pyshmultiply.html
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pyshmultiply.html
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
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<title>SHTOOLS - Spherical harmonic transformations</title>
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<h1 id="shmultiply">SHMultiply</h1>
<p>Multiply two functions and determine the spherical harmonic coefficients of the resulting function.</p>
<h1 id="usage">Usage</h1>
<p><code>shout</code> = pyshtools.SHMultiply (<code>sh1</code>, <code>lmax1</code>, <code>sh2</code>, <code>lmax2</code>, [<code>norm</code>, <code>csphase</code>])</p>
<h1 id="returns">Returns</h1>
<dl>
<dt><code>shout</code> : float, dimension (2, <code>lmax1</code>+<code>lmax2</code>+1, <code>lmax1</code>+<code>lmax2</code>+1)</dt>
<dd>The real spherical harmonic coefficients corresponding to the multiplication of <code>sh1</code> and <code>sh2</code> in the space domain.
</dd>
</dl>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>sh1</code> : float, dimension (2, <code>lmax1in</code>+1, <code>lmax1in</code>+1)</dt>
<dd>The spherical harmonic coefficients of the first function.
</dd>
<dt><code>lmax1</code> : integer</dt>
<dd>The maximum spherical harmonic degree used in evaluting <code>sh1</code>.
</dd>
<dt><code>sh2</code> : float, dimension (2, <code>lmax2in</code>+1, <code>lmax2in</code>+1)</dt>
<dd>The spherical harmonic coefficients of the second function.
</dd>
<dt><code>lmax2</code> : integer</dt>
<dd>The maximum spherical harmonic degree used in evaluting <code>sh2</code>.
</dd>
<dt><code>norm</code> : optional, integer, default = 1</dt>
<dd>1 (default) = Geodesy 4-pi normalized harmonics; 2 = Schmidt semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal harmonics.
</dd>
<dt><code>csphase</code> : optional, integer, default = 1</dt>
<dd>1 (default) = do not apply the Condon-Shortley phase factor to the associated Legendre functions; -1 = append the Condon-Shortley phase factor of (-1)^m to the associated Legendre functions.
</dd>
</dl>
<h1 id="description">Description</h1>
<p><code>SHMultiply</code> will take two sets of spherical harmonic coefficients, multiply the functions in the space domain, and expand the resulting field in spherical harmonics using <code>SHExpandGLQ</code>. The spherical harmonic bandwidth of the resulting field is <code>lmax1+lmax2</code>, where <code>lmax1</code> and <code>lmax2</code> are the bandwidths of the input fields.</p>
<p>The employed spherical harmonic normalization and Condon-Shortley phase convention can be set by the optional arguments <code>norm</code> and <code>csphase</code>; if not set, the default is to use geodesy 4-pi normalized harmonics that exclude the Condon-Shortley phase of (-1)^m.</p>
<h1 id="see-also">See also</h1>
<p><a href="pyshexpandglq.html">shexpandglq</a>, <a href="pymakegridglq.html">makegridglq</a>, <a href="pyshglq.html">shglq</a></p>
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> <a href="../../../index.html" class="dir">Home</a> > <a href="../../documentation.html" class="dir">Documentation</a> > <a href="../../python-routines.html" class="dir">Python</a> > <a href="../../pytransformations.html" class="dir">Spherical Harmonic Transformations</a></p>
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<td class="c1"><a href="http://www.ipgp.fr/">Institut de Physique du Globe de Paris</a></td>
<td class="c2"><a href="http://www.sorbonne-paris-cite.fr/index.php/en">University of Sorbonne Paris Cité</a></td>
<td class="c3">© 2016 <a href="https://github.com/SHTOOLS">SHTOOLS</a></td>
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