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computedm.3
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computedm.3
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.\" Automatically generated by Pandoc 3.1.3
.\"
.\" Define V font for inline verbatim, using C font in formats
.\" that render this, and otherwise B font.
.ie "\f[CB]x\f[]"x" \{\
. ftr V B
. ftr VI BI
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.el \{\
. ftr V CR
. ftr VI CI
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. ftr VBI CBI
.\}
.TH "computedm" "1" "2021-02-15" "Fortran 95" "SHTOOLS 4.11"
.hy
.SH ComputeDM
.PP
Compute the space-concentration kernel of a spherical cap.
.SH Usage
.PP
call ComputeDM (\f[V]dm\f[R], \f[V]lmax\f[R], \f[V]m\f[R],
\f[V]theta0\f[R], \f[V]degrees\f[R], \f[V]exitstatus\f[R])
.SH Parameters
.TP
\f[V]dm\f[R] : output, real(dp), dimension (\f[V]lmax\f[R]+1, \f[V]lmax\f[R]+1)
The space-concentration kernel of angular order \f[V]m\f[R].
.TP
\f[V]lmax\f[R] : input, integer(int32)
The spherical harmonic bandwidth of the windows.
.TP
\f[V]m\f[R] : input, integer(int32)
The angular order of the concentration problem.
.TP
\f[V]theta0\f[R] : input, real(dp)
The angular radius of the spherical cap in radians.
.TP
\f[V]degrees\f[R] : input, integer(int32), optional, dimension (\f[V]lmax\f[R]+1)
List of degrees to compute.
If degrees(l+1) is 0, do not compute degree l of the kernel.
.TP
\f[V]exitstatus\f[R] : output, optional, integer(int32)
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[V]ComputeDM\f[R] will calculate the space-concentration kernel of
angular order \f[V]m\f[R] for the spherical-cap concentration problem.
The eigenfunctions of this matrix correspond to a family of orthogonal
windowing functions, and the eigenvalues correspond to the window\[cq]s
concentration factor (i.e., the power of the window within
\f[V]theta0\f[R] divided by the total power of the function).
It is assumed that the employed spherical harmonic functions are
normalized to the same value for all degrees and angular orders, which
is the case for both the geodesy 4-pi and orthonormalized harmonics.
This kernel is symmetric and is computed exactly by Gauss-Legendre
quadrature.
If the optional vector \f[V]degrees\f[R] is specified, then the matrix
will be computed only for elements where \f[V]degrees(l+1)\f[R] is not
zero.
.SH References
.PP
Simons, F.J., F.A.
Dahlen, and M.A.\ Wieczorek, Spatiospectral concentration on a sphere,
SIAM Review, 48, 504-536, 2006.
.SH See also
.PP
computedg82, shreturntapers, shreturntapersm