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SHMultiTaperSE.f95
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SHMultiTaperSE.f95
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subroutine SHMultiTaperSE(mtse, sd, cilm, lmax, tapers, taper_order, lmaxt, &
K, alpha, lat, lon, taper_wt, norm, csphase, &
exitstatus)
!------------------------------------------------------------------------------
!
! This subroutine will calculate the multitaper spectrum estimate utilizing
! the first K tapers. The standard error is calculated using an unbiased
! estimate of the sample variance.
!
! Calling Parameters
!
! IN
! cilm Input spherical harmonic file.
! lmax Maximum degree of cilm.
! tapers The eigenvector matrix returned from a program
! such as SHReturnTapers, where each column corresponds
! to the coefficients for a window for a single non-zero
! angular order.
! taper_order Angular order of the tapers.
! lmaxt Maximum degree of the eigentapers.
! K Number of tapers to use in the multitaper spectral
! estimation.
!
! OUT
! mtse Multitaper spectrum estimate, valid up to and including
! a maximum degree lmax-lmaxt.
! sd Standard error of the multitaper spectrum estimate.
!
! OPTIONAL (IN)
! alpha Euler angles used to rotate the localizing windows.
! lat Latitude to perform localized analysis (degrees).
! lon Longitude to perform localized analysis (degrees).
! taper_wt Weight to be applied to each direct spectral estimate.
! This should sum to unity.
! csphase: 1: Do not include the phase factor of (-1)^m (default).
! -1: Apply the phase factor of (-1)^m.
! norm: Normalization to be used when calculating Legendre
! functions
! (1) "geodesy" (default)
! (2) Schmidt
! (3) unnormalized
! (4) orthonormalized
!
! OPTIONAL (OUT)
! exitstatus 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.
!
! If the optional parameter alpha (or lat and lon) is input, then the
! spherical harmonic coefficients of the localizing windows will be
! rotated accordingly. To rotate a window originally centered at the
! north pole to (lat, long) given in degrees, use
!
! alpha(1) = 0.0
! alpha(2) = -(90.0_dp - lat)*pi/180.0_dp
! alpha(3) = -lon*pi/180.0_dp
!
! See documentation in file ShRotateRealCoef for further information on
! spherical harmonic rotations.
!
! Copyright (c) 2005-2019, SHTOOLS
! All rights reserved.
!
!------------------------------------------------------------------------------
use SHTOOLS, only: SHPowerSpectrum, SHRotateRealCoef, djpi2, &
SHGLQ, SHExpandGLQ, MakeGridGLQ
use ftypes
implicit none
real(dp), intent(out) :: mtse(:), sd(:)
real(dp), intent(in) :: cilm(:,:,:), tapers(:,:)
integer(int32), intent(in) :: lmax, lmaxt, K, taper_order(:)
real(dp), intent(in), optional :: alpha(:), lat, lon, taper_wt(:)
integer(int32), intent(in), optional :: csphase, norm
integer(int32), intent(out), optional :: exitstatus
integer(int32) :: i, l, phase, mnorm, astat(7), lmaxmul, nlat, nlong
real(dp) :: se(lmax-lmaxt+1, K), x(3), pi, factor
real(dp), allocatable, save :: zero(:), w(:)
integer(int32), save :: first = 1, lmaxmul_last = -1
real(dp), allocatable :: shwin(:,:,:), shloc(:,:,:), dj(:,:,:), &
shwinrot(:,:,:), grid1glq(:,:), gridwinglq(:,:), &
temp(:,:)
!$OMP threadprivate(zero, w, first, lmaxmul_last)
if (present(exitstatus)) exitstatus = 0
pi = acos(-1.0_dp)
if (size(cilm(:,1,1)) < 2 .or. size(cilm(1,:,1)) < lmax+1 .or. &
size(cilm(1,1,:)) < lmax+1) then
print*, "Error --- SHMultiTaperSE"
print*, "CILM must be dimensioned (2,LMAX+1, LMAX+1) where LMAX is ", &
lmax
print*, "Input array is dimensioned ", size(cilm(:,1,1)), &
size(cilm(1,:,1)), size(cilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(tapers(:,1)) < lmaxt+1 .or. size(tapers(1,:)) < K) then
print*, "Error --- SHMultiTaperSE"
print*, "TAPERS must be dimensioned (LMAXT+1, K) where " // &
"LMAXT and K are, ", lmaxt, K
print*, "Input array is dimensioned ", size(tapers(:,1)), &
size(tapers(1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(taper_order) < K) then
print*, "Error --- SHMutltiTaperSE"
print*, "TAPER_ORDER must be dimensioned as (K) where K is ", K
print*, "Input dimension of array is ", size(taper_order)
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(mtse) < lmax-lmaxt+1) then
print*, "Error --- SHMultiTaperSE"
print*, "MTSE must be dimensioned as (LMAX-LMAXT+1) where " // &
"LMAX and LMAXT are ", lmax, lmaxt
print*, "Input dimension of array is ", size(mtse)
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(sd) < lmax-lmaxt+1) then
print*, "Error --- SHMultiTaperSE"
print*, "SD must be dimensioned as (LMAX-LMAXT+1) " // &
"where LMAX and LMAXT are ", lmax, lmaxt
print*, "Input dimension of array is ", size(sd)
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (lmax < lmaxt) then
print*, "Error --- SHMultiTaperSE"
print*, "LMAX must be larger than LMAXT."
print*, "Input valuse of LMAX and LMAXT are ", lmax, lmaxt
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
if (present(taper_wt)) then
if (size(taper_wt) < K) then
print*, "Error --- SHMultiTaperSE"
print*, "TAPER_WT must be dimensioned as (K) where K is ", K
print*, "Input dimension of array is ", size(taper_wt)
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
end if
if (present(norm)) then
if (norm > 4 .or. norm < 1) then
print*, "Error --- SHMultiTaperSE"
print*, "Parameter NORM must be 1 (geodesy), 2 (Schmidt), " // &
"3 (unnormalized), or 4 (orthonormalized)."
print*, "Input value is ", norm
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
mnorm = norm
else
mnorm = 1
end if
if (present(csphase)) then
if (csphase /= -1 .and. csphase /= 1) then
print*, "Error --- SHMultiTaperSE"
print*, "CSPHASE must be 1 (exclude) or -1 (include)."
print*, "Input value if ", csphase
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
else
phase = csphase
end if
else
phase = 1
end if
if (present(lat) .and. .not. present(lon)) then
print*, "Error --- SHMultiTaperSE"
print*, "Both the optional parameters LAT and LON must be present."
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
end if
if (present(lon) .and. .not. present(lat)) then
print*, "Error --- SHMultiTaperSE"
print*, "Both the optional parameters LAT and LON must be present."
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
end if
if (present(alpha) .and. present(lat) .and. present(lon)) then
print*, "Error --- SHMultiTaperSE"
print*, "Only ALPHA or LAT and LON can be present, but not both"
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
end if
if (present(lat) .and. present(lon)) then
x(1) = 0.0_dp
x(2) = -(90.0_dp - lat) * pi / 180.0_dp
x(3) = -lon * pi / 180.0_dp
else if (present(alpha)) then
if (size(alpha) < 3) then
print*, "Error --- SHMultiTaperSE"
print*, "ALPHA must be dimensioned as (3)."
print*, "Input array is dimensioned as ", size(alpha)
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
x = alpha
end if
lmaxmul = lmax + lmaxt
nlat = lmax + lmaxt + 1
nlong = 2 * (lmax + lmaxt) + 1
allocate (shwin(2,lmaxt+1,lmaxt+1), stat = astat(1))
allocate (shloc(2, lmax+lmaxt+1, lmax+lmaxt+1), stat = astat(2))
allocate (dj(lmaxt+1,lmaxt+1,lmaxt+1), stat = astat(3))
allocate (shwinrot(2,lmaxt+1,lmaxt+1), stat = astat(4))
allocate (grid1glq(nlat,nlong), stat = astat(5))
allocate (gridwinglq(nlat,nlong), stat = astat(6))
allocate (temp(nlat,nlong), stat = astat(7))
if (sum(astat(1:7)) /= 0) then
print*, "Error --- SHMultiTaperSE"
print*, "Problem allocating arrays SHWIN, SHLOC, DJ, " // &
"SHWINROT, GRID1GLQ, GRIDWINGLQ and TEMP", &
astat(1), astat(2), astat(3), astat(4), astat(5), &
astat(6), astat(7)
if (present(exitstatus)) then
exitstatus = 3
return
else
stop
end if
end if
if (first == 1) then
first = 0
lmaxmul_last = lmaxmul
allocate (zero(lmaxmul+1), stat = astat(1))
allocate (w(lmaxmul+1), stat = astat(2))
if (sum(astat(1:2)) /= 0) then
print*, "Error --- SHMultiTaperSE"
print*, "Problem allocating arrays ZERO and W", astat(1), astat(2)
if (present(exitstatus)) then
exitstatus = 3
return
else
stop
end if
end if
if (present(exitstatus)) then
call SHGLQ(lmaxmul, zero, w, csphase = phase, norm = mnorm, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHGLQ(lmaxmul, zero, w, csphase = phase, norm = mnorm)
end if
end if
if (lmaxmul /= lmaxmul_last) then
lmaxmul_last = lmaxmul
deallocate (zero)
deallocate (w)
allocate (zero(lmaxmul+1), stat = astat(1))
allocate (w(lmaxmul+1), stat = astat(2))
if (sum(astat(1:2)) /= 0) then
print*, "Error --- SHMultiTaperSE"
print*, "Problem allocating arrays ZERO and W", astat(1), astat(2)
if (present(exitstatus)) then
exitstatus = 3
return
else
stop
end if
end if
if (present(exitstatus)) then
call SHGLQ(lmaxmul, zero, w, csphase = phase, norm = mnorm, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHGLQ(lmaxmul, zero, w, csphase = phase, norm = mnorm)
end if
end if
mtse = 0.0_dp
sd = 0.0_dp
!--------------------------------------------------------------------------
!
! Calculate localized power spectra
!
!--------------------------------------------------------------------------
if (present(alpha) .or. (present(lat) .and. present(lon)) ) then
! Create rotation matrix used in the rotation routine.
if (present(exitstatus)) then
call djpi2(dj, lmaxt, exitstatus=exitstatus)
if (exitstatus /= 0) return
else
call djpi2(dj, lmaxt)
end if
end if
if (present(exitstatus)) then
call MakeGridGLQ(grid1glq, cilm(1:2,1:lmax+1, 1:lmax+1), &
lmaxmul, zero = zero, csphase = phase, norm = mnorm, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call MakeGridGLQ(grid1glq, cilm(1:2,1:lmax+1, 1:lmax+1), &
lmaxmul, zero = zero, csphase = phase, norm = mnorm)
end if
do i = 1, K
shwin = 0.0_dp
if (taper_order(i) < 0) then
shwin(2,1:lmaxt+1,abs(taper_order(i))+1) = tapers(1:lmaxt+1,i)
else
shwin(1,1:lmaxt+1,taper_order(i)+1) = tapers(1:lmaxt+1,i)
end if
if (present(alpha) .or. (present(lat) .and. present(lon)) ) then
if (present(exitstatus)) then
call SHRotateRealCoef(shwinrot, shwin, lmaxt, x, dj, &
exitstatus=exitstatus)
if (exitstatus /= 0) return
else
call SHRotateRealCoef(shwinrot, shwin, lmaxt, x, dj)
end if
shwin(1:2,1:lmaxt+1,1:lmaxt+1) = shwinrot(1:2,1:lmaxt+1,1:lmaxt+1)
end if
if (present(exitstatus)) then
call MakeGridGLQ(gridwinglq, shwin(1:2,1:lmaxt+1, 1:lmaxt+1), &
lmaxmul, zero = zero, csphase = phase, &
norm = mnorm, exitstatus = exitstatus)
if (exitstatus /= 0) return
temp(1:nlat,1:nlong) = grid1glq(1:nlat,1:nlong) &
* gridwinglq(1:nlat,1:nlong)
call SHExpandGLQ(shloc, lmaxmul, temp, w, zero = zero, &
csphase = phase, norm = mnorm, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
call SHPowerSpectrum(shloc, lmax-lmaxt, se(:,i), &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call MakeGridGLQ(gridwinglq, shwin(1:2,1:lmaxt+1, 1:lmaxt+1), &
lmaxmul, zero = zero, csphase = phase, &
norm = mnorm)
temp(1:nlat,1:nlong) = grid1glq(1:nlat,1:nlong) &
* gridwinglq(1:nlat,1:nlong)
call SHExpandGLQ(shloc, lmaxmul, temp, w, zero = zero, &
csphase = phase, norm = mnorm)
call SHPowerSpectrum(shloc, lmax-lmaxt, se(:,i))
end if
end do
if (present(taper_wt)) then
factor = sum(taper_wt(1:K))**2 - sum(taper_wt(1:K)**2)
factor = factor * sum(taper_wt(1:K))
factor = sum(taper_wt(1:K)**2) / factor
do l = 0, lmax-lmaxt, 1
mtse(l+1) = dot_product(se(l+1,1:K), taper_wt(1:K)) / &
sum(taper_wt(1:K))
if (K > 1) then
sd(l+1) = dot_product( (se(l+1,1:K) - mtse(l+1) )**2, &
taper_wt(1:K) ) * factor
end if
end do
else
do l = 0, lmax-lmaxt, 1
mtse(l+1) = sum(se(l+1,1:K)) / dble(K)
if (K > 1) then
sd(l+1) = sum( ( se(l+1,1:K) - mtse(l+1) )**2 ) / dble(K-1) &
/ dble(K) ! standard error!
end if
end do
end if
if (K > 1) sd(1:lmax-lmaxt+1) = sqrt(sd(1:lmax-lmaxt+1))
deallocate (shwin)
deallocate (shloc)
deallocate (dj)
deallocate (shwinrot)
deallocate (grid1glq)
deallocate (gridwinglq)
deallocate (temp)
end subroutine SHMultiTaperSE