subroutine da_vtovv_spectral(max_wave, sizec, lenr, lenwrk, lensav, inc, & 7,4
alp_size, alp, wsave, power, rcv, field)
!-------------------------------------------------------------------------
! Purpose: Performs spectral to gridpoint transformation on a sphere.
!----------------------------------------------------------------------
implicit none
integer, intent(in) :: max_wave ! Max total wavenumber.
integer, intent(in) :: sizec ! Size of packed spectral array.
integer, intent(in) :: lenr ! FFT info.
integer, intent(in) :: lenwrk ! FFT info.
integer, intent(in) :: lensav ! FFT info.
integer, intent(in) :: inc ! FFT info.
integer, intent(in) :: alp_size ! Size of alp array.
real, intent(in) :: alp(1:alp_size) ! Associated Legendre Polynomials.
real, intent(in) :: wsave(1:lensav) ! Primes for FFT.
real*8, intent(in) :: power(0:max_wave) ! Power spectrum
real, intent(in) :: rcv(1:2*sizec) ! Spectral modes.
real, intent(out) :: field(its:ite,jts:jte) ! Gridpoint field.
integer :: j, l,m, n ! Loop counters.
integer :: index_start ! Position markers in cv.
integer :: index_r, index_c ! Array index for complex v_fou.
real :: r_fou(1:lenr) ! FFT array.
complex :: v_fou(its:ite,0:max_wave)! Intermediate Fourier state.
complex :: ccv(1:sizec) ! Spectral modes.
integer :: index_m, index_j
integer :: jc, js, je, iequator
complex :: sum_legtra ! Summation scalars.
#ifdef FFTPACK
real :: work(1:lenwrk) ! FFT work array.
#endif
if (trace_use) call da_trace_entry
("da_vtovv_spectral")
!----------------------------------------------------------------------------
! [1] Create complex array from read array:
!----------------------------------------------------------------------------
v_fou = 0.0
do n = 1, sizec
ccv(n) = CMPLX(rcv(2*n-1), rcv(2*n))
end do
!----------------------------------------------------------------------------
! [2] Apply power spectrum
!----------------------------------------------------------------------------
if (.not. test_transforms) call da_apply_power
(power, max_wave, ccv, sizec)
!----------------------------------------------------------------------------
! [3] Perform inverse Legendre decomposition in N-S direction:
!----------------------------------------------------------------------------
do m = 0, max_wave
index_start = m * (max_wave + 1 - m) + m * (m + 1) / 2 + 1
index_m = m * (max_wave + 1 - m) + m * (m + 1) / 2 + 1 - m
jc = (jde-jds+1)/2
iequator = mod(jde-jds+1, 2)
je = min(jc+iequator, jte)
do j = jts, je
index_j = (j - 1) * (max_wave + 1) * (max_wave + 2) / 2
v_fou(j,m) = sum(ccv(index_start:index_start-m+max_wave) * &
alp(index_j+index_m+m:index_j+index_m+max_wave))
end do
js = max(jts, jc+iequator+1)
do j = js, jte
index_j = (jds+jde - j - 1) * (max_wave + 1) * (max_wave + 2) / 2
sum_legtra = da_zero_complex
do l = m, max_wave
! Calculate second quadrant values:
if(mod(l+m,2) == 1) then
sum_legtra = sum_legtra - ccv(index_start-m+l) * alp(index_j + index_m + l)
else
sum_legtra = sum_legtra + ccv(index_start-m+l) * alp(index_j + index_m + l)
end if
end do
v_fou(j,m) = sum_legtra
end do
end do
!----------------------------------------------------------------------------
! [4] Perform inverse Fourier decomposition in E-W direction:
!----------------------------------------------------------------------------
do j = jts, jte
r_fou(its) = real(v_fou(j,0)) ! R(m=0) is real.
! r_fou(ite) = aimag(v_fou(j,0)) ! R(m=NI/2) is real, but packed in imag m = 0)
! make r_fou(ide) zero as there is no power computed corresponding to this wavenumber
r_fou(ite) = 0.0
do m = 1, max_wave
index_r = 2 * m
index_c = 2 * m + 1
r_fou(index_r) = real(v_fou(j,m))
r_fou(index_c) = aimag(v_fou(j,m))
end do
#ifdef FFTPACK
call rfft1b(ide, inc, r_fou, lenr, wsave, lensav, work, lenwrk, ierr)
#else
call da_error
(__FILE__,__LINE__,(/"Must compile with FFTPACK"/))
#endif
field(its:ite,j) = r_fou(its:ite)
end do
if (trace_use) call da_trace_exit
("da_vtovv_spectral")
end subroutine da_vtovv_spectral