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SHConvertCoef.f95
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SHConvertCoef.f95
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subroutine SHrtoc(rcilm, ccilm, degmax, convention, switchcs, exitstatus)
!------------------------------------------------------------------------------
!
! This subroutine will convert the real "geodesy 4-pi" spherical harmonic
! coefficients into complex form with either a 4 pi or unit normalization.
! The complex coefficients are only calculated for positive m's (the negative
! m's are given by
!
! c_l,m* = (-1)^m c_l,-m
!
! If degmax is not specified, then the maximum degree of the conversion is
! taken from the size of the input arrays.
!
! Calling Parameters
!
! IN
! rcilm Real "geodesy" spherical harmonic coefficients with
! dimensions (2, lmax+1, lmax+1).
!
! OUT
! ccilm Complex unity-normalized spherical harmonic
! coefficients, dimensioned as (2, lmax+1, lmax+1). The
! first index corresponds to the real and complex
! coefficients, respectively.
!
! OPTIONAL
! degmax Maximum degree of conversion to be performed.
! convention 1=output 4-pi normalized coefficients
! 2=output Varshalovich et al. normalized coefficients
! switchcs If 1, Change between different Condon-Shortley phase
! conventions. If 0, use consistent phase convention.
! 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.
!
! Copyright (c) 2005-2019, SHTOOLS
! All rights reserved.
!
!------------------------------------------------------------------------------
use ftypes
implicit none
real(dp), intent(in) :: rcilm(:,:,:)
real(dp), intent(out) :: ccilm(:,:,:)
integer(int32), intent(in), optional :: degmax, convention, switchcs
integer(int32), intent(out), optional :: exitstatus
integer(int32) :: lmax, l, m, convention_flag, switchcs_flag
real(dp) :: pi
if (present(exitstatus)) exitstatus = 0
switchcs_flag = 0
if (present(switchcs)) then
if (switchcs /= 1 .and. switchcs /= 0) then
print*, "Error --- SHrtoc"
print*, "switchcs must be equal to either 0 (keep same " // &
"convention) of 1 (change Condon-Shortley phase)"
print*, "Input value is ", switchcs
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
switchcs_flag = switchcs
end if
convention_flag = 1
if (present(convention) ) then
if (convention /= 1 .and. convention /= 2) then
print*, "Error --- SHrtoc"
print*, "CONVENTION must be 1 or 2."
print*, "Input valuse is ", convention
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
convention_flag = convention
end if
if (present(degmax)) then
lmax = degmax
if (size(rcilm(:,1,1)) < 2 .or. size(rcilm(1,:,1)) < lmax +1 &
.or. size(rcilm(1,1,:)) < lmax +1) then
print*, "Error --- SHrtoc"
print*, "RCILM must be dimensioned as (2, DEGMAX+1, DEGMAX+1) " // &
"where DEGMAX is ", degmax
print*, "Input array is dimensioned as ", size(rcilm(:,1,1)), &
size(rcilm(1,:,1)), size(rcilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(ccilm(:,1,1)) < 2 .or. size(ccilm(1,:,1)) < lmax +1 &
.or. size(ccilm(1,1,:)) < lmax +1) then
print*, "Error --- SHrtoc"
print*, "CCILM must be dimensioned as (2, DEGMAX+1, DEGMAX+1) " // &
"where DEGMAX is ", degmax
print*, "Input array is dimensioned as ", size(ccilm(:,1,1)), &
size(ccilm(1,:,1)), size(ccilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
else
if (size(rcilm(:,1,1)) < 2) then
print*, "Error --- SHrtoc"
print*, "RCILM must be dimensioned as (2,*,*)."
print*, "Input array is dimensioned as ", size(rcilm(:,1,1)), &
size(rcilm(1,:,1)), size(rcilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(ccilm(:,1,1)) < 2) then
print*, "Error --- SHrtoc"
print*, "CCILM must be dimensioned as (2,*,*)."
print*, "Input array is dimensioned as ", size(ccilm(:,1,1)), &
size(ccilm(1,:,1)), size(ccilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
lmax = min(size(rcilm(1,1,:)) -1, size(ccilm(1,1,:)) -1, &
size(rcilm(1,:,1)) -1, size(ccilm(1,:,1)) -1)
end if
pi = acos(-1.0_dp)
ccilm = 0.0_dp
do l = 0, lmax, 1
if (convention_flag == 2) then
ccilm(1,l+1, 1) = sqrt(4.0_dp*pi) * rcilm(1,l+1,1)
ccilm(2,l+1, 1) = 0.0_dp
do m = 1, l, 1
if (switchcs_flag == 1) then
ccilm(1, l+1, m+1) = sqrt(2.0_dp*pi) * rcilm(1,l+1,m+1) &
* (-1)**m
ccilm(2, l+1, m+1) = -sqrt(2.0_dp*pi) * rcilm(2,l+1,m+1) &
* (-1)**m
else
ccilm(1, l+1, m+1) = sqrt(2.0_dp*pi) * rcilm(1,l+1,m+1)
ccilm(2, l+1, m+1) = -sqrt(2.0_dp*pi) * rcilm(2,l+1,m+1)
end if
end do
else
ccilm(1,l+1, 1) = rcilm(1,l+1,1)
ccilm(2,l+1, 1) = 0.0_dp
do m = 1, l, 1
if (switchcs_flag == 1) then
ccilm(1, l+1, m+1) = rcilm(1,l+1,m+1) / sqrt(2.0_dp) &
* (-1)**m
ccilm(2, l+1, m+1) = -rcilm(2,l+1,m+1) / sqrt(2.0_dp) &
* (-1)**m
else
ccilm(1, l+1, m+1) = rcilm(1,l+1,m+1) / sqrt(2.0_dp)
ccilm(2, l+1, m+1) = -rcilm(2,l+1,m+1) / sqrt(2.0_dp)
end if
end do
end if
end do
end subroutine SHrtoc
subroutine SHctor(ccilm, rcilm, degmax, convention, switchcs, exitstatus)
!-------------------------------------------------------------------------------
!
! This subroutine will convert either "geodesy 4-pi" or "Varshalovich et al."
! complex spherical harmonic coefficients into real "geodesy 4-pi" spherical
! harmonic coefficients.
!
! If degmax is not specified, then the maximum degree of the
! conversion is taken from the size of the input arrays.
!
! Calling Parameters
!
! IN
! ccilm Complex unity-normalized spherical harmonic
! coefficients, dimensioned as (2, lmax+1, lmax+1). The
! first index corresponds to the real and complex
! coefficients, respectively.
! OUT
! rcilm Real "geodesy" spherical harmonic coefficients with
! dimensions (2, lmax+1, lmax+1).
!
! OPTIONAL
! degmax Maximum degree of conversion to be performed.
! convention 1=input coefficients are 4-pi normalized
! 2=input coefficients are Varshalovich et al. normalized.
! switchcs If 1, Change between different Condon-Shortley phase
! conventions. If 0, use consistent phase convention.
! 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.
!
! Copyright (c) 2016, SHTOOLS
! All rights reserved.
!
!-------------------------------------------------------------------------------
use ftypes
implicit none
real(dp), intent(in) :: ccilm(:,:,:)
real(dp), intent(out) :: rcilm(:,:,:)
integer(int32), intent(in), optional :: degmax, convention, switchcs
integer(int32), intent(out), optional :: exitstatus
integer(int32) :: lmax, l, m, convention_flag, switchcs_flag
real(dp) :: pi
if (present(exitstatus)) exitstatus = 0
switchcs_flag = 0
if (present(switchcs)) then
if (switchcs /= 1 .and. switchcs /= 0) then
print*, "Error --- SHrtoc"
print*, "switchcs must be equal to either 0 (keep same " // &
"convention) of 1 (change Condon-Shortley phase)"
print*, "Input value is ", switchcs
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
switchcs_flag = switchcs
end if
convention_flag = 1
if (present(convention) ) then
if (convention /= 1 .and. convention /= 2) then
print*, "Error --- SHrtoc"
print*, "CONVENTION must be 1 or 2."
print*, "Input valuse is ", convention
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
convention_flag = convention
end if
if (present(degmax)) then
lmax = degmax
if (size(rcilm(:,1,1)) < 2 .or. size(rcilm(1,:,1)) < lmax +1 .or. &
size(rcilm(1,1,:)) < lmax +1) then
print*, "Error --- SHrtoc"
print*, "RCILM must be dimensioned as (2, DEGMAX+1, DEGMAX+1) " // &
"where DEGMAX is ", degmax
print*, "Input array is dimensioned as ", size(rcilm(:,1,1)), &
size(rcilm(1,:,1)), size(rcilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(ccilm(:,1,1)) < 2 .or. size(ccilm(1,:,1)) < lmax +1 &
.or. size(ccilm(1,1,:)) < lmax +1) then
print*, "Error --- SHrtoc"
print*, "CCILM must be dimensioned as (2, DEGMAX+1, DEGMAX+1) " // &
"where DEGMAX is ", degmax
print*, "Input array is dimensioned as ", size(ccilm(:,1,1)), &
size(ccilm(1,:,1)), size(ccilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
else
if (size(rcilm(:,1,1)) < 2) then
print*, "Error --- SHrtoc"
print*, "RCILM must be dimensioned as (2,*,*)."
print*, "Input array is dimensioned as ", size(rcilm(:,1,1)), &
size(rcilm(1,:,1)), size(rcilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(ccilm(:,1,1)) < 2) then
print*, "Error --- SHrtoc"
print*, "CCILM must be dimensioned as (2,*,*)."
print*, "Input array is dimensioned as ", size(ccilm(:,1,1)), &
size(ccilm(1,:,1)), size(ccilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
lmax = min(size(rcilm(1,1,:)) -1, size(ccilm(1,1,:)) -1, &
size(rcilm(1,:,1)) -1, size(ccilm(1,:,1)) -1)
end if
pi = acos(-1.0_dp)
rcilm = 0.0_dp
do l = 0, lmax, 1
if (convention == 2) then
rcilm(1,l+1,1) = ccilm(1,l+1,1) / sqrt(4.0_dp*pi)
rcilm(2, l+1, 1) = 0.0_dp
do m = 1, l, 1
if (switchcs == 1) then
rcilm(1,l+1, m+1) = ccilm(1, l+1, m+1) / sqrt(2.0_dp*pi) &
* (-1)**m
rcilm(2,l+1, m+1) = - ccilm(2,l+1,m+1) / sqrt(2.0_dp*pi) &
* (-1)**m
else
rcilm(1,l+1, m+1) = ccilm(1, l+1, m+1) / sqrt(2.0_dp*pi)
rcilm(2,l+1, m+1) = - ccilm(2,l+1,m+1) / sqrt(2.0_dp*pi)
end if
end do
else
rcilm(1,l+1,1) = ccilm(1,l+1,1)
rcilm(2, l+1, 1) = 0.0_dp
do m = 1, l, 1
if(switchcs == 1) then
rcilm(1,l+1, m+1) = sqrt(2.0_dp) * ccilm(1, l+1, m+1) &
* (-1)**m
rcilm(2,l+1, m+1) = -sqrt(2.0_dp) * ccilm(2, l+1, m+1) &
* (-1)**m
else
rcilm(1,l+1, m+1) = sqrt(2.0_dp) * ccilm(1, l+1, m+1)
rcilm(2,l+1, m+1) = -sqrt(2.0_dp) * ccilm(2, l+1, m+1)
end if
end do
end if
end do
end subroutine SHctor
subroutine SHCilmToCindex(cilm, cindex, degmax, exitstatus)
!------------------------------------------------------------------------------
!
! This routine will convert a 3D matrix of spherical harmonics indexed as
! (i, l+1, m+1) into a 2D matrix that is indexed as (i, index) where
! index = l(l+1)/2+m+1.
!
! Calling Parameters
!
! IN
! cilm Array of spherical harmonic coefficients with dimensions
! (2, lmax+1, lmax+1).
! OUT
! cindex Array of indexed spherical harmonic coefficnets with
! dimensions (2, (lmax+1)*(lmax+2)/2).
! 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.
!
! Copyright (c) 2016, SHTOOLS
! All rights reserved.
!
!------------------------------------------------------------------------------
use ftypes
implicit none
real(dp), intent(in) :: cilm(:,:,:)
real(dp), intent(out) :: cindex(:,:)
integer(int32), intent(in), optional :: degmax
integer(int32), intent(out), optional :: exitstatus
integer(int32) :: lmax, l, m, index
if (present(exitstatus)) exitstatus = 0
if (present(degmax)) then
lmax = degmax
if (size(cilm(:,1,1)) < 2 .or. size(cilm(1,:,1)) < lmax + 1 .or. &
size(cilm(1,1,:)) < lmax+1 ) then
print*, "Error --- SHcilmtocindex"
print*, "CILM must be dimensioned as (2, DEGMAX+1, DEGMAX+1) " // &
"where DEGMAX is ", degmax
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(cindex(:,1)) < 2 .or. size(cindex(1,:)) &
< ((lmax+1)*(lmax+2))/2) then
print*, "Error --- SHcilmtocindex"
print*, "CINDEX must be dimensioned as " // &
"(2, (DEGMAX+1)*(DEGMAX+2)/2) where DEGMAX is ", degmax
print*, "Input array is dimensioned ", size(cindex(:,1)), &
size(cindex(1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
else
lmax = min(size(cilm(1,1,:)) - 1, size(cilm(1,:,1)) - 1)
if (size(cilm(:,1,1)) < 2) then
print*, "Error --- SHcilmtocindex"
print*, "CILM must be dimensioned as (2, *, *)."
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(cindex(:,1)) < 2 .or. size(cindex(1,:)) &
< ((lmax+1)*(lmax+2))/2) then
print*, "Error --- SHcilmtocindex"
print*, "CINDEX must be dimensioned as " // &
"(2, (LMAX+1)*(LMAX+2)/2) where LMAX is ", lmax
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
end if
cindex = 0.0_dp
do l = 0, lmax
do m = 0, l
index = (l*(l+1))/2+m+1
cindex(1, index) = cilm(1,l+1,m+1)
cindex(2, index) = cilm(2,l+1,m+1)
end do
end do
end subroutine SHCilmToCindex
subroutine SHCindexToCilm(cindex, cilm, degmax, exitstatus)
!------------------------------------------------------------------------------
!
! This subroutine will convert a 2D matrix of spherical harmonics indexed as
! (i, index) into a 2D matrix that is index as (i, l+1, m+1) where
! index = l(l+1)/2+m+1.
!
! Calling Parameters
!
! IN
! cindex Array of indexed spherical harmonic coefficnets with
! dimensions (2, (lmax+1)*(lmax+2)/2).
! OUT
! cilm Array of spherical harmonic coefficients with dimensions
! (2, lmax+1, lmax+1).
! 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.
!
! Copyright (c) 2016, SHTOOLS
! All rights reserved.
!
!-------------------------------------------------------------------------------
use ftypes
implicit none
real(dp), intent(out) :: cilm(:,:,:)
real(dp), intent(in) :: cindex(:,:)
integer(int32), intent(in), optional :: degmax
integer(int32), intent(out), optional :: exitstatus
integer(int32) :: lmax, l, m, index, n
if (present(exitstatus)) exitstatus = 0
n = size(cindex(1,:))
if (present(degmax)) then
lmax = degmax
if (lmax > nint((-3.0_dp + sqrt(1.0_dp + 8.0_dp*n) ) / 2.0_dp) ) then
print*, "Error - SHCindextocilm"
print*, "The output spherical harmonic degree DEGMAX is larger " // &
"than the input coefficients."
print*, "Input value of DEGMAX ", degmax
print*, "Maximum spherical harmonic degree of CINDEX ", &
nint((-3.0_dp + sqrt(1.0_dp + 8.0_dp*n) )/2.0_dp)
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
else if (size(cilm(:,1,1)) < 2 .or. size(cilm(1,:,1)) < lmax + 1 &
.or. size(cilm(1,1,:)) < lmax+1 ) then
print*, "Error --- SHCindextocilm"
print*, "CILM must be dimensioned as (2, DEGMAX+1, DEGMAX+1) " // &
"where DEGMAX is ", degmax
print*, "Input array is dimensioned ", size(cilm(:,1,1)), &
size(cilm(1,:,1)), size(cilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
else
lmax = nint((-3.0_dp + sqrt(1.0_dp + 8.0_dp*n) )/2.0_dp)
if (size(cilm(:,1,1)) < 2 .or. size(cilm(1,:,1)) < lmax + 1 .or. &
size(cilm(1,1,:)) < lmax+1 ) then
print*, "Error --- SHcindextocilm"
print*, "CILM must be dimensioned as (2, DEGMAX+1, DEGMAX+1) " // &
"where DEGMAX is ", degmax
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
end if
end if
cilm = 0.0_dp
do l = 0, lmax
do m = 0, l
index = (l * (l + 1)) / 2 + m + 1
cilm(1,l+1,m+1) = cindex(1, index)
cilm(2,l+1,m+1) = cindex(2, index)
end do
end do
end subroutine SHCindexToCilm