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<h1 id="shreturntapers">SHReturnTapers</h1>
<p>Calculate the eigenfunctions of the spherical-cap concentration problem.</p>
<h1 id="usage">Usage</h1>
<p>call SHReturnTapers (<code>theta0</code>, <code>lmax</code>, <code>tapers</code>, <code>eigenvalues</code>, <code>taper_order</code>, <code>exitstatus</code>)</p>
<h1 id="parameters">Parameters</h1>
<dl>
<dt><code>theta0</code> : input, real*8</dt>
<dd>The angular radius of the spherical cap in radians.
</dd>
<dt><code>lmax</code> : input, integer</dt>
<dd>The spherical harmonic bandwidth of the localization windows.
</dd>
<dt><code>tapers</code> : output, real*8, dimension (<code>lmax</code>+1, (<code>lmax</code>+1)**2)</dt>
<dd>The spherical harmonic coefficients of the <code>(lmax+1)**2</code> localization windows. Each column contains the coefficients of a single window that possesses non-zero coefficients for the single angular order specified in <code>taper_order</code>. The first and last rows of each column correspond to spherical harmonic degrees 0 and <code>lmax</code>, respectively, and the columns are arranged from best to worst concentrated.
</dd>
<dt><code>eigenvalues</code> : output, real*8, dimension ((<code>lmax</code>+1)**2)</dt>
<dd>The concentration factors of the localization windows.
</dd>
<dt><code>taper_order</code> : output, integer, dimension ((<code>lmax</code>+1)**2)</dt>
<dd>The angular order of the non-zero spherical harmonic coefficients in each column of <code>tapers</code>.
</dd>
<dt><code>exitstatus</code> : output, optional, integer</dt>
<dd>If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.
</dd>
</dl>
<h1 id="description">Description</h1>
<p><code>SHReturnTapers</code> will calculate the eigenfunctions (i.e., localization windows) of the spherical-cap concentration problem. Each column of the matrix <code>tapers</code> contains the spherical harmonic coefficients of a single window and the corresponding concentration factor is given in the array <code>eigenvalues</code>. Each window has non-zero coefficients for only a single angular order that is specified in <code>taper_order</code>: all other spherical harmonic coefficients for a given window are identically zero. The columns of <code>tapers</code> are ordered from best to worst concentrated, and the first and last rows of each column correspond to spherical harmonic degrees 0 and <code>lmax</code>, respectively. The localization windows are normalized such that they have unit power.</p>
<h1 id="references">References</h1>
<p>Wieczorek, M. A. and F. J. Simons, Localized spectral analysis on the sphere, Geophys. J. Int., 162, 655-675, 2005.</p>
<p>Simons, F.J., F.A. Dahlen, and M.A. Wieczorek, Spatiospectral concentration on a sphere, SIAM Review, 48, 504-536, 2006.</p>
<h1 id="see-also">See also</h1>
<p><a href="shreturntapersm.html">shreturntapersm</a>, <a href="computedg82.html">computedg82</a>, <a href="computedm.html">computedm</a></p>
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