-
Notifications
You must be signed in to change notification settings - Fork 106
/
shmultitapermaskse.1
110 lines (110 loc) · 4.69 KB
/
shmultitapermaskse.1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
.\" Automatically generated by Pandoc 2.9.2
.\"
.TH "shmultitapermaskse" "1" "2019-09-23" "Fortran 95" "SHTOOLS 4.6"
.hy
.SH SHMultiTaperMaskSE
.PP
Perform a localized multitaper spectral analysis using arbitrary windows
derived from a mask.
.SH Usage
.PP
call SHMultiTaperMaskSE (\f[C]mtse\f[R], \f[C]sd\f[R], \f[C]sh\f[R],
\f[C]lmax\f[R], \f[C]tapers\f[R], \f[C]lmaxt\f[R], \f[C]k\f[R],
\f[C]taper_wt\f[R], \f[C]norm\f[R], \f[C]csphase\f[R],
\f[C]exitstatus\f[R])
.SH Parameters
.TP
\f[B]\f[CB]mtse\f[B]\f[R] : output, real(dp), dimension (\f[B]\f[CB]lmax\f[B]\f[R]-\f[B]\f[CB]lmaxt\f[B]\f[R]+1)
The localized multitaper power spectrum estimate.
.TP
\f[B]\f[CB]sd\f[B]\f[R] : output, real(dp), dimension (\f[B]\f[CB]lmax\f[B]\f[R]-\f[B]\f[CB]lmaxt\f[B]\f[R]+1)
The standard error of the localized multitaper power spectral estimates.
.TP
\f[B]\f[CB]sh\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 function to be localized.
.TP
\f[B]\f[CB]lmax\f[B]\f[R] : input, integer
The spherical harmonic bandwidth of \f[C]sh\f[R].
.TP
\f[B]\f[CB]tapers\f[B]\f[R] : input, real(dp), dimension ((\f[B]\f[CB]lmaxt\f[B]\f[R]+1)**2, \f[B]\f[CB]k\f[B]\f[R])
An array of the \f[C]k\f[R] windowing functions, arranged in columns,
obtained from a call to \f[C]SHReturnTapersMap\f[R].
The spherical harmonic coefficients are packed according to the
conventions in \f[C]SHCilmToVector\f[R].
.TP
\f[B]\f[CB]lmaxt\f[B]\f[R] : input, integer
The spherical harmonic bandwidth of the windowing functions in the array
\f[C]tapers\f[R].
.TP
\f[B]\f[CB]k\f[B]\f[R] : input, integer
The number of tapers to be utilized in performing the multitaper
spectral analysis.
.TP
\f[B]\f[CB]taper_wt\f[B]\f[R] : input, optional, real(dp), dimension (\f[B]\f[CB]k\f[B]\f[R])
The weights used in calculating the multitaper spectral estimates and
standard error.
Optimal values of the weights (for a known global power spectrum) can be
obtained from the routine \f[C]SHMTVarOpt\f[R].
.TP
\f[B]\f[CB]norm\f[B]\f[R] : input, optional, integer, default = 1
1 (default) = 4-pi (geodesy) normalized harmonics; 2 = Schmidt
semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal
harmonics.
.TP
\f[B]\f[CB]csphase\f[B]\f[R] : input, optional, integer, default = 1
1 (default) = do not apply the Condon-Shortley phase factor to the
associated Legendre functions; -1 = append the Condon-Shortley phase
factor of (-1)\[ha]m to the associated Legendre functions.
.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]SHMultiTaperMaskSE\f[R] will perform a localized multitaper
spectral analysis of an input function expressed in spherical harmonics
using an arbitrary set of windows derived from a mask.
The maximum degree of the localized multitaper cross-power spectrum
estimate is \f[C]lmax-lmaxt\f[R].
The matrix \f[C]tapers\f[R] contains the spherical harmonic coefficients
of the windows and can be obtained by a call to
\f[C]SHReturnTapersMap\f[R].
The coefficients of each window are stored in a single column, ordered
according to the conventions used in \f[C]SHCilmToVector\f[R].
.PP
If the optional array \f[C]taper_wt\f[R] is specified, these weights
will be used in calculating a weighted average of the individual
\f[C]k\f[R] tapered estimates \f[C]mtse\f[R] and the corresponding
standard error of the estimates \f[C]sd\f[R].
If not present, the weights will all be assumed to be equal.
When \f[C]taper_wt\f[R] is not specified, the mutltitaper spectral
estimate for a given degree will be calculated as the average obtained
from the \f[C]k\f[R] individual tapered estimates.
The standard error of the multitaper estimate at degree \f[C]l\f[R] is
simply the population standard deviation,
\f[C]S = sqrt(sum (Si - mtse)\[ha]2 / (k-1))\f[R], divided by
\f[C]sqrt(k)\f[R].
See Wieczorek and Simons (2007) for the relevant expressions when
weighted estimates are used.
.PP
The employed spherical harmonic normalization and Condon-Shortley phase
convention can be set by the optional arguments \f[C]norm\f[R] and
\f[C]csphase\f[R]; if not set, the default is to use geodesy 4-pi
normalized harmonics that exclude the Condon-Shortley phase of
(-1)\[ha]m.
.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
shmultitapermaskcse, shreturntapersmap, shcilmtovector