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shslepianvar.1
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shslepianvar.1
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.\" Automatically generated by Pandoc 2.7.3
.\"
.TH "shslepianvar" "1" "2019-09-17" "Fortran 95" "SHTOOLS 4.5"
.hy
.SH SHSlepianVar
.PP
Calculate the theoretical variance of the power of a function expanded
in spherical-cap Slepian functions for a given spherical harmonic
degree.
.SH Usage
.PP
call SHSlepianVar (\f[C]l\f[R], \f[C]galpha\f[R],
\f[C]galpha_order\f[R], \f[C]lmax\f[R], \f[C]kmax\f[R], \f[C]sff\f[R],
\f[C]variance\f[R], \f[C]exitstatus\f[R])
.SH Parameters
.TP
.B \f[C]l\f[R] : input, integer
The spherical harmonic degree used to calculate the theoretical
variance.
.TP
.B \f[C]galpha\f[R] : input, real(dp), dimension (\f[C]lmax\f[R]+1, \f[C]kmax\f[R])
A matrix of spherical-cap Slepian functions obtained from
\f[C]SHReturnTapers\f[R] or \f[C]SHReturnTapersM\f[R].
.TP
.B \f[C]galpha_order\f[R] : input, integer, dimension (\f[C]kmax\f[R])
The angular orders of the spherical-cap Slepian functions in
\f[C]galpha\f[R].
.TP
.B \f[C]lmax\f[R] : input, integer
The spherical harmonic bandwidth of the Slepian functions.
.TP
.B \f[C]kmax\f[R] : input, integer
The maximum number of Slepian functions to use when calculating the
variance.
.TP
.B \f[C]sff\f[R] : input, real(dp), dimension (\f[C]lmax\f[R]+1)
The global power spectrum of the function.
.TP
.B \f[C]variance\f[R] : output, real(dp)
The theoretical variance of the spectral estimate for degree
\f[C]l\f[R].
.TP
.B \f[C]exitstatus\f[R] : output, optional, integer
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.
.SH Description
.PP
\f[C]SHSlepianVar\f[R] will compute the theoretical variance of the
power of a function expanded in spherical-cap Slepian functions for a
given spherical harmonic degree.
This routine takes as input the spherical harmonic coefficients of the
spherical-cap Slepian functions as obtained by a call to
\f[C]SHReturnTapers\f[R], and only the first \f[C]KMAX\f[R] Slepian
functions in the matrix \f[C]GALPHA\f[R] are used to compute the
variance.
.SH See also
.PP
shreturntapers, shreturntapersm, slepiancoeffs, slepiancoeffstosh,
shscouplingmatrixcap