Unverified Commit 1e19a60a authored by mrk-w's avatar mrk-w Committed by GitHub

Merge pull request #250 from MarkWieczorek/develop

Fix minor consistency issues in web documentation and shtools interface block
parents bf88a99e aed3d1cd
......@@ -13,7 +13,7 @@ Perform a localized multitaper cross-spectral analysis using spherical cap windo
## Usage
call SHMultiTaperCSE (`mtse`, `sd`, `sh1`, `lmax1`, `sh2`, `lmax2`, `tapers`, `taper_order`, `lmaxt`, `k`, `alpha`, `lat`, `lon`, `taper_wt`, `norm`, `csphase`, `exitstatus`)
call SHMultiTaperCSE (`mtse`, `sd`, `cilm1`, `lmax1`, `cilm2`, `lmax2`, `tapers`, `taper_order`, `lmaxt`, `k`, `alpha`, `lat`, `lon`, `taper_wt`, `norm`, `csphase`, `exitstatus`)
## Parameters
......@@ -23,17 +23,17 @@ call SHMultiTaperCSE (`mtse`, `sd`, `sh1`, `lmax1`, `sh2`, `lmax2`, `tapers`, `t
`sd` : output, real(dp), dimension (`lmax`-`lmaxt`+1)
: The standard error of the localized multitaper cross-power spectral estimates. `lmax` is the smaller of `lmax1` and `lmax2`.
`sh1` : input, real(dp), dimension (2, `lmax1`+1, `lmax1`+1)
`cilm1` : input, real(dp), dimension (2, `lmax1`+1, `lmax1`+1)
: The spherical harmonic coefficients of the first function.
`lmax1` : input, integer
: The spherical harmonic bandwidth of `sh1`.
: The spherical harmonic bandwidth of `cilm1`.
`sh2` : input, real(dp), dimension (2, `lmax2`+1, `lmax2`+1)
`cilm2` : input, real(dp), dimension (2, `lmax2`+1, `lmax2`+1)
: The spherical harmonic coefficients of the second function.
`lmax2` : input, integer
: The spherical harmonic bandwidth of `sh2`.
: The spherical harmonic bandwidth of `cilm2`.
`tapers` : input, real(dp), dimension (`lmaxt`+1, `k`)
: An array of the `k` windowing functions, arranged in columns, obtained from a call to `SHReturnTapers`. Each window has non-zero coefficients for a single angular order that is specified in the array `taper_order`.
......@@ -70,7 +70,7 @@ call SHMultiTaperCSE (`mtse`, `sd`, `sh1`, `lmax1`, `sh2`, `lmax2`, `tapers`, `t
## Description
`SHMultiTaperCSE` will perform a localized multitaper cross-spectral analysis of two input functions expressed in spherical harmonics, `SH1` and `SH2`. The maximum degree of the localized multitaper power spectrum estimate is `lmax-lmaxt`, where `lmax` is the smaller of `lmax1` and `lmax2`. The coefficients and angular orders of the windowing coefficients (`tapers` and `taper_order`) are obtained by a call to `SHReturnTapers`. If `lat` and `lon` or `alpha` is specified, then the symmetry axis of the localizing windows will be rotated to these coordinates. Otherwise, the localized spectral analysis will be centered over the north pole.
`SHMultiTaperCSE` will perform a localized multitaper cross-spectral analysis of two input functions expressed in spherical harmonics, `CILM1` and `CILM2`. The maximum degree of the localized multitaper power spectrum estimate is `lmax-lmaxt`, where `lmax` is the smaller of `lmax1` and `lmax2`. The coefficients and angular orders of the windowing coefficients (`tapers` and `taper_order`) are obtained by a call to `SHReturnTapers`. If `lat` and `lon` or `alpha` is specified, then the symmetry axis of the localizing windows will be rotated to these coordinates. Otherwise, the localized spectral analysis will be centered over the north pole.
If the optional array `taper_wt` is specified, then these weights will be used in calculating a weighted average of the individual `k` tapered estimates (`mtse`) and the corresponding standard error of the estimates (`sd`). If not present, the weights will all be assumed to be equal. When `taper_wt` is not specified, the mutltitaper spectral estimate for a given degree will be calculated as the average obtained from the `k` individual tapered estimates. The standard error of the multitaper estimate at degree l is simply the population standard deviation, `S = sqrt(sum (Si - mtse)^2 / (k-1))`, divided by sqrt(`k`). See Wieczorek and Simons (2007) for the relevant expressions when weighted estimates are used.
......
.\" Automatically generated by Pandoc 2.10
.\"
.TH "shmultitapercse" "1" "2020-04-07" "Fortran 95" "SHTOOLS 4.7"
.TH "shmultitapercse" "1" "2020-09-13" "Fortran 95" "SHTOOLS 4.7"
.hy
.SH SHMultiTaperCSE
.PP
......@@ -8,8 +8,8 @@ Perform a localized multitaper cross-spectral analysis using spherical
cap windows.
.SH Usage
.PP
call SHMultiTaperCSE (\f[C]mtse\f[R], \f[C]sd\f[R], \f[C]sh1\f[R],
\f[C]lmax1\f[R], \f[C]sh2\f[R], \f[C]lmax2\f[R], \f[C]tapers\f[R],
call SHMultiTaperCSE (\f[C]mtse\f[R], \f[C]sd\f[R], \f[C]cilm1\f[R],
\f[C]lmax1\f[R], \f[C]cilm2\f[R], \f[C]lmax2\f[R], \f[C]tapers\f[R],
\f[C]taper_order\f[R], \f[C]lmaxt\f[R], \f[C]k\f[R], \f[C]alpha\f[R],
\f[C]lat\f[R], \f[C]lon\f[R], \f[C]taper_wt\f[R], \f[C]norm\f[R],
\f[C]csphase\f[R], \f[C]exitstatus\f[R])
......@@ -24,17 +24,17 @@ The standard error of the localized multitaper cross-power spectral
estimates.
\f[C]lmax\f[R] is the smaller of \f[C]lmax1\f[R] and \f[C]lmax2\f[R].
.TP
\f[B]\f[CB]sh1\f[B]\f[R] : input, real(dp), dimension (2, \f[B]\f[CB]lmax1\f[B]\f[R]+1, \f[B]\f[CB]lmax1\f[B]\f[R]+1)
\f[B]\f[CB]cilm1\f[B]\f[R] : input, real(dp), dimension (2, \f[B]\f[CB]lmax1\f[B]\f[R]+1, \f[B]\f[CB]lmax1\f[B]\f[R]+1)
The spherical harmonic coefficients of the first function.
.TP
\f[B]\f[CB]lmax1\f[B]\f[R] : input, integer
The spherical harmonic bandwidth of \f[C]sh1\f[R].
The spherical harmonic bandwidth of \f[C]cilm1\f[R].
.TP
\f[B]\f[CB]sh2\f[B]\f[R] : input, real(dp), dimension (2, \f[B]\f[CB]lmax2\f[B]\f[R]+1, \f[B]\f[CB]lmax2\f[B]\f[R]+1)
\f[B]\f[CB]cilm2\f[B]\f[R] : input, real(dp), dimension (2, \f[B]\f[CB]lmax2\f[B]\f[R]+1, \f[B]\f[CB]lmax2\f[B]\f[R]+1)
The spherical harmonic coefficients of the second function.
.TP
\f[B]\f[CB]lmax2\f[B]\f[R] : input, integer
The spherical harmonic bandwidth of \f[C]sh2\f[R].
The spherical harmonic bandwidth of \f[C]cilm2\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, \f[B]\f[CB]k\f[B]\f[R])
An array of the \f[C]k\f[R] windowing functions, arranged in columns,
......@@ -103,7 +103,7 @@ error.
.PP
\f[C]SHMultiTaperCSE\f[R] will perform a localized multitaper
cross-spectral analysis of two input functions expressed in spherical
harmonics, \f[C]SH1\f[R] and \f[C]SH2\f[R].
harmonics, \f[C]CILM1\f[R] and \f[C]CILM2\f[R].
The maximum degree of the localized multitaper power spectrum estimate
is \f[C]lmax-lmaxt\f[R], where \f[C]lmax\f[R] is the smaller of
\f[C]lmax1\f[R] and \f[C]lmax2\f[R].
......
......@@ -241,7 +241,7 @@ SHRead2.o : ftypes.mod
SHReadJPL.o : ftypes.mod
SHReturnTapers.o : ftypes.mod SHTOOLS.mod
SHReturnTapersM.o : ftypes.mod SHTOOLS.mod
SHReturnTapersMap.o : SHTOOLS.mod
SHReturnTapersMap.o : ftypes.mod SHTOOLS.mod
SHRotateCoef.o : ftypes.mod
SHRotateRealCoef.o : ftypes.mod SHTOOLS.mod
SHRotateTapers.o : ftypes.mod SHTOOLS.mod
......
......@@ -4,7 +4,7 @@ Perform a localized multitaper cross-spectral analysis using spherical cap windo
# Usage
call SHMultiTaperCSE (`mtse`, `sd`, `sh1`, `lmax1`, `sh2`, `lmax2`, `tapers`, `taper_order`, `lmaxt`, `k`, `alpha`, `lat`, `lon`, `taper_wt`, `norm`, `csphase`, `exitstatus`)
call SHMultiTaperCSE (`mtse`, `sd`, `cilm1`, `lmax1`, `cilm2`, `lmax2`, `tapers`, `taper_order`, `lmaxt`, `k`, `alpha`, `lat`, `lon`, `taper_wt`, `norm`, `csphase`, `exitstatus`)
# Parameters
......@@ -14,17 +14,17 @@ call SHMultiTaperCSE (`mtse`, `sd`, `sh1`, `lmax1`, `sh2`, `lmax2`, `tapers`, `t
`sd` : output, real(dp), dimension (`lmax`-`lmaxt`+1)
: The standard error of the localized multitaper cross-power spectral estimates. `lmax` is the smaller of `lmax1` and `lmax2`.
`sh1` : input, real(dp), dimension (2, `lmax1`+1, `lmax1`+1)
`cilm1` : input, real(dp), dimension (2, `lmax1`+1, `lmax1`+1)
: The spherical harmonic coefficients of the first function.
`lmax1` : input, integer
: The spherical harmonic bandwidth of `sh1`.
: The spherical harmonic bandwidth of `cilm1`.
`sh2` : input, real(dp), dimension (2, `lmax2`+1, `lmax2`+1)
`cilm2` : input, real(dp), dimension (2, `lmax2`+1, `lmax2`+1)
: The spherical harmonic coefficients of the second function.
`lmax2` : input, integer
: The spherical harmonic bandwidth of `sh2`.
: The spherical harmonic bandwidth of `cilm2`.
`tapers` : input, real(dp), dimension (`lmaxt`+1, `k`)
: An array of the `k` windowing functions, arranged in columns, obtained from a call to `SHReturnTapers`. Each window has non-zero coefficients for a single angular order that is specified in the array `taper_order`.
......@@ -61,7 +61,7 @@ call SHMultiTaperCSE (`mtse`, `sd`, `sh1`, `lmax1`, `sh2`, `lmax2`, `tapers`, `t
# Description
`SHMultiTaperCSE` will perform a localized multitaper cross-spectral analysis of two input functions expressed in spherical harmonics, `SH1` and `SH2`. The maximum degree of the localized multitaper power spectrum estimate is `lmax-lmaxt`, where `lmax` is the smaller of `lmax1` and `lmax2`. The coefficients and angular orders of the windowing coefficients (`tapers` and `taper_order`) are obtained by a call to `SHReturnTapers`. If `lat` and `lon` or `alpha` is specified, then the symmetry axis of the localizing windows will be rotated to these coordinates. Otherwise, the localized spectral analysis will be centered over the north pole.
`SHMultiTaperCSE` will perform a localized multitaper cross-spectral analysis of two input functions expressed in spherical harmonics, `CILM1` and `CILM2`. The maximum degree of the localized multitaper power spectrum estimate is `lmax-lmaxt`, where `lmax` is the smaller of `lmax1` and `lmax2`. The coefficients and angular orders of the windowing coefficients (`tapers` and `taper_order`) are obtained by a call to `SHReturnTapers`. If `lat` and `lon` or `alpha` is specified, then the symmetry axis of the localizing windows will be rotated to these coordinates. Otherwise, the localized spectral analysis will be centered over the north pole.
If the optional array `taper_wt` is specified, then these weights will be used in calculating a weighted average of the individual `k` tapered estimates (`mtse`) and the corresponding standard error of the estimates (`sd`). If not present, the weights will all be assumed to be equal. When `taper_wt` is not specified, the mutltitaper spectral estimate for a given degree will be calculated as the average obtained from the `k` individual tapered estimates. The standard error of the multitaper estimate at degree l is simply the population standard deviation, `S = sqrt(sum (Si - mtse)^2 / (k-1))`, divided by sqrt(`k`). See Wieczorek and Simons (2007) for the relevant expressions when weighted estimates are used.
......
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