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shadmitcorr.html
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shadmitcorr.html
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<h1 id="shadmitcorr">SHAdmitCorr</h1>
<p>Calculate the admittance and correlation spectra of two real functions.</p>
<h1 id="usage">Usage</h1>
<p>call SHAdmitCorr (<code>gilm</code>, <code>tilm</code>, <code>lmax</code>, <code>admit</code>, <code>corr</code>, <code>admit_error</code>)</p>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>gilm</code> : input, real*8, dimension (2, <code>lmaxg</code>+1, <code>lmaxg</code>+1)</dt>
<dd>The real spherical harmonic coefficients of the function <code>G</code>.
</dd>
<dt><code>tilm</code> : input, real*8, dimension (2, <code>lmaxt</code>+1, <code>lmaxt</code>+1)</dt>
<dd>The real spherical harmonic coefficients of the function <code>T</code>.
</dd>
<dt><code>lmax</code> : input, integer</dt>
<dd>The maximum spherical harmonic degree that will be calculated for the admittance and correlation spectra. This must be less than or equal to the minimum of <code>lmaxg</code> and <code>lmaxt</code>.
</dd>
<dt><code>admit</code> : output, real*8, dimension (<code>lmax</code>+1)</dt>
<dd>The admittance function, which is equal to <code>Sgt/Stt</code>.
</dd>
<dt><code>corr</code> : output, real*8, dimension (<code>lmax</code>+1)</dt>
<dd>The degree correlation function, which is equal to <code>Sgt/sqrt(Sgg Stt)</code>.
</dd>
<dt><code>admit_error</code> : output, optional, real*8, dimension (<code>lmax</code>+1)</dt>
<dd>The uncertainty of the admittance function, assuming that <code>gilm</code> and <code>tilm</code> are related by a linear isotropic transfer function, and that the lack of correlation is a result of uncorrelated noise.
</dd>
</dl>
<h1 id="description">Description</h1>
<p><code>SHAdmitCorr</code> will calculate the admittance and correlation spectra associated with two real functions expressed in real spherical harmonics. The admittance is defined as <code>Sgt/Stt</code>, where <code>Sgt</code> is the cross-power spectrum of two functions <code>G</code> and <code>T</code>. The degree-correlation spectrum is defined as <code>Sgt/sqrt(Sgg Stt)</code>, which can possess values between -1 and 1.</p>
<p>If the optional argument <code>admit_error</code> is specified, then the error of the admittance will be calculated by assuming that <code>G</code> and <code>T</code> are related by a linear isotropic transfer function:<code>Gilm = Ql Tilm + Nilm</code>, where <code>N</code> is noise that is uncorrelated with the topography. It is important to note that the relationship between two fields is often not described by such an isotropic expression.</p>
<h1 id="see-also">See also</h1>
<p><a href="shpowerspectrum.html">shpowerspectrum</a>, <a href="shcrosspowerspectrum.html">shcrosspowerspectrum</a></p>
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<td class="c1"><a href="http://www.ipgp.fr/">Institut de Physique du Globe de Paris</a></td>
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