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shsjkpg0.html
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
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<title>SHTOOLS - Localized spectral analysis</title>
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<p class="centeredimage"><img src="../../images/logo.jpg" width=894 height=135 alt="SHTOOLS --- Tools for working with spherical harmonics"></p>
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<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
<B>SHSJKPG0(1)</B> SHTOOLS 3.0 <B>SHSJKPG0(1)</B>
</PRE>
<H2 class="man">SHSjkPG0</H2 class="man"><PRE>
SHSjkPG0 - Calculate the expectation of the product of two functions,
each multiplied by a different zonal data taper, for a given
spherical harmonic degree and angular order.
</PRE>
<H2 class="man">SYNOPSIS</H2 class="man"><PRE>
REAL*8 SHSjkPG0 ( INCSPECTRA, J, K, L, M, EVEC, LWIN )
REAL*8 INCPECTRA(L+LWIN+1), EVEC(LWIN+1, LWIN+1)
INTEGER J, K, L, M, LWIN
</PRE>
<H2 class="man">DESCRIPTION</H2 class="man"><PRE>
<B>SHSjkPG0</B> will calculate the expectation of two functions (f and g),
each localized by a different zonal data taper that is a solution of
the spherical cap concentration problem, for a given spherical harmonic
degree and angular order. As described in Wieczorek and Simons (2005,
eq. D8), this is the function
/ (j) (k) \
| Phi Gamma |
\ lm lm /
The global cross-power spectrum of f and g is input as INCSPECTRA, and
the real coefficients of the data tapers (obtained by a call to
<B>SHReturnTapersM</B>) is input as the matrix EVEC.
</PRE>
<H2 class="man">ARGUMENTS</H2 class="man"><PRE>
INCSPECTRA (input) REAL*8, DIMENSION (L+LWIN+1)
The global cross-power spectrum of f and g.
J (input) INTEGER
The taper number (corresponding to the column of EVEC)
that is used to localize the first function f.
K (input) INTEGER
The taper number (corresponding to the column of EVEC)
that is used to localize the second function g.
L (input) INTEGER
The spherical harmonic degree for which to calculate the
expectation.
M (input) INTEGER
The angular order for which to calculated the
expectation.
EVEC (input) REAL*8, DIMENSION (LWIN+1, LWIN+1)
The spherical harmonic coefficients that are the
solutions to the zonal spherical-cap concentration
problem. These are arranged in columns, and are obtained
by a call to <B>SHReturnTapersM</B>.
LWIN (input) INTEGER
The spherical harmonic bandwidth of the localizing
windows.
</PRE>
<H2 class="man">SEE ALSO</H2 class="man"><PRE>
<B>shreturntaper0(1)</B>, <B>shmtvaropt0(1)</B>, <B>shmtvaropt(1)</B>, <B>shsjkpg(1)</B>
<http://shtools.ipgp.fr/>
</PRE>
<H2 class="man">REFERENCES</H2 class="man"><PRE>
Wieczorek, M. A. and F. J. Simons, Localized spectral analysis on the
sphere, <B>Geophys.</B> <B>J.</B> <B>Int.</B>, 162, 655-675.
</PRE>
<H2 class="man">COPYRIGHT AND LICENSE</H2 class="man"><PRE>
Copyright 2012 by Mark Wieczorek <wieczor@ipgp.fr>.
This is free software; you can distribute and modify it under the terms
of the revised BSD license.
SHTOOLS 3.0 2014-09-12 <B>SHSJKPG0(1)</B>
</PRE>
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<table class="footer2" summary = "SHTOOLS; Fortran and Python spherical harmonic transform software package">
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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">© 2015 <a href="http://www.ipgp.fr/~wieczor">Mark Wieczorek</a></td>
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