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plmbar.html
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
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<title>SHTOOLS - Legendre functions</title>
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<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
<B>PLMBAR(1)</B> SHTOOLS 3.0 <B>PLMBAR(1)</B>
</PRE>
<H2 class="man">PlmBar</H2 class="man"><PRE>
PlmBar - Compute all the geodesy-normalized associated Legendre
functions.
</PRE>
<H2 class="man">SYNOPSIS</H2 class="man"><PRE>
SUBROUTINE PlmBar ( P, LMAX, Z, CSPHASE, CNORM )
REAL*8 P((LMAX+1)*(LMAX+2)/2), Z
INTEGER LMAX
INTEGER, OPTIONAL CSPHASE, CNORM
</PRE>
<H2 class="man">DESCRIPTION</H2 class="man"><PRE>
<B>PlmBar</B> will calculate all of the geodesy-normalized associated Legendre
functions up to degree LMAX for a given argument. These are calculated
using a standard three-term recursion formula, and in order to prevent
overflows, the scaling approach of Holmes and Featherstone (2002) is
utilized. These functions are accurate to about degree 2800. The index
of the array corresponding to a given degree L and angular order M can
be computed by a call to <B>PlmIndex</B>.
The integral of the squared Legendre functions over the interval [-1,
1] is 2 * (2 - delta(0,m)), where delta is the Kronecker delta
function. If the optional parameter CNORM is set equal to 1, the
complex normalization will be used where the integral of the squared
Legendre functions over the interval [-1, 1] is 2. The default is to
exclude the Condon-Shortley phase, but this can be modified by setting
the optional argument CSPHASE to -1.
</PRE>
<H2 class="man">ARGUMENTS</H2 class="man"><PRE>
P (output) REAL*8, DIMENSION ((LMAX+1)*(LMAX+2)/2)
An array of geodesy-normalized associated Legendre functions
up to degree LMAX. The index corresponds to L*(L+1)/2 + M +
1, which can be calculated by a call to <B>PlmIndex</B>.
LMAX (input) INTEGER
The maximum degree of the associated Legendre functions to be
computed. If LMAX is -1, allocated memory will be deallocated
(see notes below).
Z (input) REAL*8
The argument of the associated Legendre functions.
CSPHASE (input) INTEGER, OPTIONAL
If 1 (default), the Condon-Shortley phase will be excluded.
If -1, the Condon-Shortley phase of (-1)^m will be appended
to the associated Legendre functions.
CNORM (input) INTEGER, OPTIONAL
If 1, the complex normalization of the associated Legendre
functions will be used. The default is to use the real
normalization.
</PRE>
<H2 class="man">NOTES</H2 class="man"><PRE>
This routine saves the three-term recursion factors and square roots of
the integers the first time being called. If subsequent calls possess
the same value of LMAX, these will not be recomputed. If you wish to
deallocate this memory, which is an array of length (LMAX+1)*(LMAX+2),
recall this routine with LMAX=-1.
</PRE>
<H2 class="man">REFERENCES</H2 class="man"><PRE>
Holmes, S. A., and W. E. Featherstone, A unified approach to the
Clenshaw summation and the recursive computation of very high degree
and order normalised associated Legendre functions, <B>J.</B> <B>Geodesy</B>, 76,
279- 299, 2002.
</PRE>
<H2 class="man">SEE ALSO</H2 class="man"><PRE>
<B>plbar(1)</B>, <B>plbar_d1(1)</B>, <B>plmbar_d1(1)</B>, <B>plon(1)</B>, <B>plon_d1(1)</B>, <B>plmon(1)</B>,
<B>plmon_d1(1)</B>, <B>plschmidt(1)</B>, <B>plschmidt_d1(1)</B>, <B>plmschmidt(1)</B>,
<B>plmschmidt_d1(1)</B>, <B>plegendre(1)</B>, <B>plegendre_d1(1)</B>, <B>plegendrea(1)</B>,
<B>plegendrea_d1(1)</B>, <B>plmindex(1)</B>
<http://shtools.ipgp.fr/>
</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>PLMBAR(1)</B>
</PRE>
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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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