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pyshsjkpg.1
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pyshsjkpg.1
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.\" Automatically generated by Pandoc 2.1.3
.\"
.TH "pyshsjkpg" "1" "2017\-11\-28" "Python" "SHTOOLS 4.2"
.hy
.SH SHSjkPG
.PP
Calculate the expectation of the product of two functions, each
multiplied by a different data taper, for a given spherical harmonic
degree and two different angular orders.
.SH Usage
.PP
\f[C]value\f[] = SHSjkPG (\f[C]incspectra\f[], \f[C]l\f[], \f[C]m\f[],
\f[C]mprime\f[], \f[C]hj_real\f[], \f[C]hk_real\f[], \f[C]mj\f[],
\f[C]mk\f[], \f[C]lwin\f[], \f[C]hkcc\f[])
.SH Returns
.TP
.B \f[C]value\f[] : complex
The expectation of the product of two functions, each multiplied by a
different data taper, for a given spherical harmonic degree and two
different angular orders.
.RS
.RE
.SH Parameters
.TP
.B \f[C]incspectra\f[] : float, dimension (\f[C]l\f[]+\f[C]lwin\f[]+1)
The global cross\-power spectrum of \f[C]f\f[] and \f[C]g\f[].
.RS
.RE
.TP
.B \f[C]l\f[] : integer
The spherical harmonic degree for which to calculate the expectation.
.RS
.RE
.TP
.B \f[C]m\f[] : integer
The angular order of the first localized function, \f[C]Phi\f[].
.RS
.RE
.TP
.B \f[C]mprime\f[] : integer
The angular order of the second localized function, \f[C]Gamma\f[].
.RS
.RE
.TP
.B \f[C]hj_real\f[] : float, dimension (\f[C]lwin\f[]+1)
The real spherical harmonic coefficients of angular order \f[C]mj\f[]
used to localize the first function \f[C]f\f[].
These are obtained by a call to \f[C]SHReturnTapers\f[].
.RS
.RE
.TP
.B \f[C]hk_real\f[] : float, dimension (\f[C]lwin\f[]+1)
The real spherical harmonic coefficients of angular order \f[C]mk\f[]
used to localize the second function \f[C]g\f[].
These are obtained by a call to \f[C]SHReturnTapers\f[].
.RS
.RE
.TP
.B \f[C]mj\f[] : integer
The angular order of the window coefficients \f[C]hj_real\f[].
.RS
.RE
.TP
.B \f[C]mk\f[] : integer
The angular order of the window coefficients \f[C]hk_real\f[].
.RS
.RE
.TP
.B \f[C]lwin\f[] : integer
the spherical harmonic bandwidth of the localizing windows
\f[C]hj_real\f[] and \f[C]hk_real\f[].
.RS
.RE
.TP
.B \f[C]hkcc\f[] : integer
If 1, the function described in the \f[C]description\f[] will be
calculated as is.
If 2, the second localized function \f[C]Gamma\f[] will not have its
complex conjugate taken.
.RS
.RE
.SH Description
.PP
\f[C]SHSjkPG\f[] will calculate the expectation of two functions
(\f[C]f\f[] and \f[C]g\f[]), each localized by a different data taper
that is a solution of the spherical cap concentration problem, for a
given spherical harmonic degree and two different angular orders.
As described in Wieczorek and Simons (2007), this is the function
.IP
.nf
\f[C]
\ \ /\ \ \ \ m(j)\ \ \ \ \ \ \ mprime(k)*\ \\
\ |\ \ Phi\ \ \ \ \ \ Gamma\ \ \ \ \ \ \ \ \ \ \ \ |
\ \ \\\ \ \ \ l\ \ \ \ \ \ \ \ \ \ l\ \ \ \ \ \ \ \ \ \ /
\f[]
.fi
.PP
The global cross\-power spectrum of \f[C]f\f[] and \f[C]g\f[] is input
as \f[C]incspectra\f[], and the real coefficients of the two data tapers
of angular order \f[C]mj\f[] and \f[C]mk\f[] (obtained by a call to
\f[C]SHReturnTapers\f[]) are specified by \f[C]hj_real\f[] and
\f[C]hk_real\f[].
If \f[C]hkcc\f[] is set to 1, then the above function is calculated as
is.
However, if this is set to 2, then the complex conjugate of the second
localized function is not taken.
.SH References
.PP
Wieczorek, M.
A.
and F.
J.
Simons, Minimum\-variance multitaper spectral estimation on the sphere,
J.
Fourier Anal.
Appl., 13, doi:10.1007/s00041\-006\-6904\-1, 665\-692, 2007.
.SH See also
.PP
shreturntapers, shmtvaropt