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slepiancoeffs.1
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slepiancoeffs.1
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.\" Automatically generated by Pandoc 2.10
.\"
.TH "slepiancoeffs" "1" "2020-09-07" "Fortran 95" "SHTOOLS 4.7"
.hy
.SH SlepianCoeffs
.PP
Determine the expansion coefficients of a function for a given set of
input Slepian functions.
.SH Usage
.PP
call SlepianCoeffs(\f[C]falpha\f[R], \f[C]galpha\f[R], \f[C]film\f[R],
\f[C]lmax\f[R], \f[C]nmax\f[R], \f[C]exitstatus\f[R])
.SH Parameters
.TP
\f[B]\f[CB]falpha\f[B]\f[R] : output, real(dp), dimension (\f[B]\f[CB]nmax\f[B]\f[R])
A vector containing the Slepian coefficients of the input function
\f[C]film\f[R].
.TP
\f[B]\f[CB]galpha\f[B]\f[R] : input, real(dp), dimension ((\f[B]\f[CB]lmax\f[B]\f[R]+1)**2, \f[B]\f[CB]nmax\f[B]\f[R])
An array containing the spherical harmonic coefficients of the Slepian
functions.
Each column corresponds to a single function of which the spherical
harmonic coefficients can be unpacked with \f[C]SHVectorToCilm\f[R].
.TP
\f[B]\f[CB]film\f[B]\f[R] : input, real(dp), dimension (2, \f[B]\f[CB]lmax\f[B]\f[R]+1, \f[B]\f[CB]lmax\f[B]\f[R]+1)
The spherical harmonic coefficients of the global function to be
expanded in Slepian functions.
.TP
\f[B]\f[CB]lmax\f[B]\f[R] : input, integer
The spherical harmonic bandwidth of the Slepian functions.
.TP
\f[B]\f[CB]nmax\f[B]\f[R] : input, integer
The number of expansion coefficients to compute.
This must be less than or equal to (\f[C]lmax\f[R]+1)**2.
.TP
\f[B]\f[CB]exitstatus\f[B]\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]SlepianCoeffs\f[R] will compute the Slepian coefficients of a
global input function \f[C]film\f[R] given the Slepian functions
\f[C]galpha\f[R].
The Slepian functions are determined by a call to either (1)
\f[C]SHReturnTapers\f[R] and then \f[C]SHRotateTapers\f[R], or (2)
\f[C]SHReturnTapersMap\f[R].
Each row of \f[C]galpha\f[R] contains the (\f[C]lmax\f[R]+1)**2
spherical harmonic coefficients of a Slepian function that can be
unpacked using \f[C]SHVectorToCilm\f[R].
The Slepian functions must be normalized to have unit power (that is the
sum of the coefficients squared is 1), and the Slepian coefficients are
calculated as
.PP
\f[C]f_alpha = sum_{ilm}\[ha]{lmax} f_ilm g(alpha)_lm\f[R]
.SH See also
.PP
slepiancoeffstosh, shreturntapers, shslepianvar, shreturntapersmap,
shrotatetapers, shvectortocilm, shscouplingmatrix, shscouplingmatrixcap,
shmtcouplingmatrixcap