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TimingAccuracyGLQC.f95
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TimingAccuracyGLQC.f95
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Program TimingAccuracyGLQC
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! This program will test the accuracy of the spherical harmonic GLQ tranformation
! routines by expanding a field in the space domain, transforming this
! to spherical harmonics, and comparing the relative error of the coefficients
!
!
! Written by Mark Wieczorek (July 2006)
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
use SHTOOLS
implicit none
integer, parameter :: maxdeg = 2800
character*200 :: outfile1, outfile2, outfile3, outfile4, outfile
complex*16, allocatable :: cilm(:,:,:), cilm2(:,:,:), gridglq(:,:)
real*8, allocatable :: zero(:), w(:)
real*8 :: huge8, maxerror, err1, err2, beta, rms, timein(3), timeout(3)
integer :: lmax, l, m, seed, astat(5)
allocate(cilm(2,maxdeg+1,maxdeg+1), stat=astat(1))
allocate(cilm2(2,maxdeg+1,maxdeg+1), stat=astat(2))
allocate(zero(maxdeg+1), stat=astat(3))
allocate(gridglq(maxdeg+1,2*maxdeg+1), stat=astat(4))
allocate(w(maxdeg+1), stat=astat(5))
if (sum(astat(1:5)) /= 0) then
print*, "Error --- TimingAccuracyGLQ"
print*, "Problem allocating arrays CILM, CILM2, ZERO, GRIDGLQ, W"
stop
endif
print*, "Value of beta for power law Sff = l^(-beta) > "
read(*,*) beta
print*, "output file name > "
read(*,*) outfile
outfile1 = trim(outfile) // ".timef"
outfile2 = trim(outfile) // ".timei"
outfile3 = trim(outfile) // ".maxerror"
outfile4 = trim(outfile) // ".rmserror"
huge8 = huge(maxerror)
seed = -1053253
cilm = 0.0d0
do l=1, maxdeg
do m=0, l
if (m==0) then
cilm(1,l+1,m+1) = dcmplx(RandomGaussian(seed),RandomGaussian(seed))
else
cilm(1,l+1,m+1) = dcmplx(RandomGaussian(seed),RandomGaussian(seed))
cilm(2,l+1,m+1) = dcmplx(RandomGaussian(seed),RandomGaussian(seed))
endif
enddo
cilm(1:2, l+1, 1:l+1) = cilm(1:2, l+1, 1:l+1)*sqrt(dble(l)**beta)/sqrt(2.0d0*l+1)
enddo
print*, "Lmax, Maximum rel. error of Cilm, RMS relative error, Precompute time (sec), Time inverse (sec), Time forward (sec)"
lmax = 1
do
lmax = lmax*2
if (lmax > maxdeg) lmax = maxdeg
if (lmax==2) then
open(12,file=outfile1, status="replace")
open(13,file=outfile2, status="replace")
open(14,file=outfile3, status="replace")
open(15,file=outfile4, status="replace")
else
open(12,file=outfile1, position="append")
open(13,file=outfile2, position="append")
open(14,file=outfile3, position="append")
open(15,file=outfile4, position="append")
endif
call cpu_time(timein(1))
call PreCompute(lmax, zero(1:lmax+1), w(1:lmax+1))
call cpu_time(timeout(1))
call cpu_time(timein(2))
call MakeGridGLQC(gridglq(1:lmax+1, 1:2*lmax+1), cilm(1:2,1:lmax+1, 1:lmax+1), lmax, zero=zero(1:lmax+1), norm=1)
call cpu_time(timeout(2))
call cpu_time(timein(3))
call SHExpandGLQC(cilm2(1:2, 1:lmax+1, 1:lmax+1), lmax, gridglq(1:lmax+1, 1:2*lmax+1), w, zero=zero(1:lmax+1), norm=1)
call cpu_time(timeout(3))
maxerror = 0.0d0
rms = 0.0d0
do l=1, lmax
do m=0, l
if (m==0) then
err1 = abs( (cilm(1,l+1,m+1)-cilm2(1,l+1,m+1)) ) / abs( cilm(1,l+1,m+1) )
if (err1 >= maxerror) maxerror = err1
rms = rms + err1**2
else
err1 = abs( (cilm(1,l+1,m+1)-cilm2(1,l+1,m+1)) ) / abs( cilm(1,l+1,m+1) )
err2 = abs( (cilm(2,l+1,m+1)-cilm2(2,l+1,m+1)) ) / abs( cilm(2,l+1,m+1) )
if (err1 >= maxerror) maxerror = err1
if (err2 >= maxerror) maxerror = err2
rms = rms + err1**2 + err2**2
endif
enddo
enddo
rms = sqrt(rms/dble(l+1)**2)
! elasped time in seconds!
print*, lmax, maxerror, rms, timeout(1)-timein(1), timeout(2)-timein(2), timeout(3)-timein(3)
write(12,*) lmax, timeout(2)-timein(2)
write(13,*) lmax, timeout(3)-timein(3)
write(14,*) lmax, maxerror
write(15,*) lmax, rms
if (maxerror > huge8) then
print*, "Overflow problems"
print*, "Overflow problems"
close(12)
close(13)
close(14)
close(15)
stop
endif
if (maxerror > 10.0d0) then
close(12)
close(13)
close(14)
close(15)
stop
endif
close(12)
close(13)
close(14)
close(15)
if (lmax == maxdeg) exit
enddo
end program TimingAccuracyGLQC