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SeparableBispectrum.f90
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!First version AL October 2010
!Calculates local fnl and CMB lensing bispectra
!CMB lensing bispectra are calculated in the approximation in which the first-order
!result is used replacing the unlensed with the lensing power spectra
!This is non-perturbatively correct to about 1%
!Note the lensing bispectrum only includes the linear potentials, no Rees-Sciama or SZ
!See Lewis, Challinor & Hanson 2010 for details
!Note that the primordial local bispectra are unlensed (see arXiv: 0905.4732)
!Compile with LAPACK and -DFISHER if you want to get the fisher matrix outputs
!This is disabled by default in order not to require LAPACK
!Fisher results are with and without the cosmic variance from low L_1
module Bispectrum
use results
use InitialPower
use SpherBessels
use constants
use MpiUtils
use splines
implicit none
integer, parameter :: max_bispectrum_deltas = 5, max_bispectrum_fields=3
Type TBispectrumParams
logical do_lensing_bispectrum
logical do_primordial_bispectrum
integer nfields
integer Slice_Base_L, ndelta, deltas(max_bispectrum_deltas)
logical do_parity_odd
logical DoFisher
logical export_alpha_beta
real(dl) FisherNoise, FisherNoisePol, FisherNoiseFwhmArcmin
character(LEN=Ini_max_string_len) FullOutputFile
logical SparseFullOutput
end Type
!global parameter for now, only intend for this module to be used interactively for the moment
Type(TBispectrumParams) :: BispectrumParams
Type TBispectrum
real(dl), pointer :: b(:,:)
end Type
Type TCov
real(dl), pointer :: C(:,:)
end type TCov
Type TCov2
real(dl) :: C(2,2)
end type TCov2
Type TCov3
real(dl) :: C(3,3)
end type TCov3
real(dl), allocatable :: dJl(:,:), dddJl(:,:)
real(dl), parameter :: InternalScale = 1d10
character(LEN=1024) :: output_root =''
integer, parameter :: shape_local = 1, shape_warm = 2, shape_warm2 = 3
integer, parameter :: shape = shape_local
real(dl), allocatable :: TransferPolFac(:) !sqrt((l+2)!/(l-2)!)
contains
subroutine InitBesselDerivs(CTrans)
! j_l' array for interpolation if needed; not needed for local fnl
Type(ClTransferData) :: CTrans
integer i,l1,j
real(dl) Jm, Jp
if (allocated(dJl)) then
deallocate(dJL, dddJl)
end if
allocate(dJl(BessRanges%npoints,CTrans%ls%nl),dddJl(BessRanges%npoints,CTrans%ls%nl))
do i=1, CTrans%ls%nl
!Spline agrees well
! call spline_deriv(BessRanges%points,ajl(1,i),ajlpr(1,i),dJl(1,i),BessRanges%npoints)
! call spline_def(BessRanges%points,dJl(1,i),BessRanges%npoints,dddJl(1,i))
l1 = CTrans%ls%l(i)
do j=1, BessRanges%npoints
call BJL(l1-1,BessRanges%points(j),Jm)
call BJL(l1+1,BessRanges%points(j),Jp)
dJl(j,i)= ( l1*Jm - (l1+1)*Jp)/(2*l1+1)
end do
call spline_def(BessRanges%points,dJl(:,i),BessRanges%npoints,dddJl(:,i))
end do
end subroutine InitBesselDerivs
subroutine NonGauss_l_r_localOpt(CP,CTrans, ind, indP, res, resP, nfields, r)
!functions of the form int dk k^2 k^i j_l(kr) Delta_l(k) [P]
!ind and indP are arrays of required k^i powers
!res and resP are the results without and with the power spectrum P in the integrand
Class(CAMBPArams) :: CP
Type(ClTransferData) :: CTrans
integer, intent(in) :: ind(:), indP(:)
integer :: nfields
real(dl) res(CTrans%ls%nl,size(ind),nfields), resP(CTrans%ls%nl,size(indP),nfields)
real(dl), intent(in) :: r
integer q_ix, j, bes_ix
integer n, nP, ellmax
real(dl) xf , J_l, fac, a2, k, dlnk, term, P, kpow, kpowP
n = size(ind)
nP =size(indP)
res=0
resP = 0
do q_ix = 1, CTrans%q%npoints
k = CTrans%q%points(q_ix)
xf = k*r
bes_ix=BessRanges%IndexOf(xf)
fac=BessRanges%points(bes_ix+1)-BessRanges%points(bes_ix)
a2=(BessRanges%points(bes_ix+1)-xf)/fac
fac=fac**2*a2/6
dlnk = CTrans%q%dpoints(q_ix) /k
P = CP%InitPower%ScalarPower(k)*InternalScale !!only first index for now
ellmax = max(xf/(1-xlimfrac), xf + xlimmin) * CP%Accuracy%AccuracyBoost
kpow = k**(ind(1)+3)
kpowP = k**indP(1) * P
do j=1,CTrans%ls%nl
if (CTrans%ls%l(j) <= ellmax) then
J_l=a2*ajl(bes_ix,j)+(1-a2)*(ajl(bes_ix+1,j) - ((a2+1) &
*ajlpr(bes_ix,j)+(2-a2)*ajlpr(bes_ix+1,j))* fac) !cubic spline
term = CTrans%Delta_p_l_k(1,j,q_ix)*J_l*dlnk
res(j,1,1) = res(j,1,1) + term * kpow
resP(j,1,1) = resP(j,1,1) + term * kpowP
if (nfields>1) then
!E pol
term = CTrans%Delta_p_l_k(2,j,q_ix)*J_l*dlnk * TransferPolFac(CTrans%ls%l(j))
res(j,1,2) = res(j,1,2) + term * kpow
resP(j,1,2) = resP(j,1,2) + term * kpowP
if (nfields>2) then
!lensing potential
term = CTrans%Delta_p_l_k(3,j,q_ix)*J_l*dlnk
res(j,1,3) = res(j,1,3) + term * kpow
resP(j,1,3) = resP(j,1,3) + term * kpowP
end if
end if
end if
end do
end do
resP = resP * const_fourpi
res = res * 2/const_pi
end subroutine NonGauss_l_r_localOpt
subroutine NonGauss_l_r(CP,CTrans, ind, indP,res, resP,nfields, r)
!functions of the form int dk k^2 k^i j_l(kr) Delta_l(k) [P]
!ind and indP are arrays of required k^i powers
!res and resP are the results without and with the power spectrum P in the integrand
!Output of P scaled by 1d10 (so bispectrum by 1d20)
Class(CAMBParams) :: CP
Type(ClTransferData) :: CTrans
integer:: nfields
integer, intent(in) :: ind(:), indP(:)
real(dl) res(CTrans%ls%nl,size(ind),nfields), resP(CTrans%ls%nl,size(indP),nfields)
real(dl), intent(in) :: r
integer q_ix, j, bes_ix, i
integer n, nP, ellmax
real(dl) xf , J_l, fac, a2, k, dlnk, term, P, kpow(size(ind)), kpow2(size(indP))
if (shape == shape_local) then
call NonGauss_l_r_localOpt(CP,CTrans, ind, indP,res, resP, nfields, r)
return
end if
n = size(ind)
nP =size(indP)
res=0
resP = 0
do q_ix = 1, CTrans%q%npoints
k = CTrans%q%points(q_ix)
xf = k*r
bes_ix=BessRanges%IndexOf(xf)
fac=BessRanges%points(bes_ix+1)-BessRanges%points(bes_ix)
a2=(BessRanges%points(bes_ix+1)-xf)/fac
fac=fac**2*a2/6
dlnk = CTrans%q%dpoints(q_ix) /k
P = CP%InitPower%ScalarPower(k)*InternalScale !!only first index for now
ellmax = max(xf/(1-xlimfrac), xf + xlimmin) * CP%Accuracy%AccuracyBoost
do i=1,n
kpow(i)=k**(ind(i)+3)
end do
do i=1,nP
kpow2(i)=k**indP(i) * P
end do
do j=1,CTrans%ls%nl
if (CTrans%ls%l(j) <= ellmax) then
J_l=a2*ajl(bes_ix,j)+(1-a2)*(ajl(bes_ix+1,j) - ((a2+1) &
*ajlpr(bes_ix,j)+(2-a2)*ajlpr(bes_ix+1,j))* fac) !cubic spline
!call BJL(CTrans%ls%l(j), xf, J_l)
term = CTrans%Delta_p_l_k(1,j,q_ix)*J_l*dlnk
do i=1,n
res(j,i,1) = res(j,i,1) + term *kpow(i)
end do
do i=1,nP
resP(j,i,1) = resP(j,i,1) + term * kpow2(i)
end do
! if (CTrans%ls%l(j)==8) write (1,'(9D20.7)') &
! k, xf, real(term * k**3/dlnk), real(term * k**indP(1) * P), &
! real(res(j,1)),real(resP(j,1)), J_l, real(term), real(CTrans%Delta_p_l_k(1,j,q_ix))
if (nfields>1) then
!E pol
term = CTrans%Delta_p_l_k(2,j,q_ix)*J_l*dlnk* TransferPolFac(CTrans%ls%l(j))
do i=1,n
res(j,i,2) = res(j,i,2) + term *kpow(i)
end do
do i=1,nP
resP(j,i,2) = resP(j,i,2) + term * kpow2(i)
end do
if (nfields>2) then
!lensing potential
term = CTrans%Delta_p_l_k(3,j,q_ix)*J_l*dlnk
do i=1,n
res(j,i,3) = res(j,i,3) + term *kpow(i)
end do
do i=1,nP
resP(j,i,3) = resP(j,i,3) + term * kpow2(i)
end do
end if
end if
end if
end do
end do
resP = resP * const_fourpi
res = res * 2/const_pi
end subroutine NonGauss_l_r
subroutine GetBispectrum(State,CTrans)
!Note: may need high maxetak to make sure oscillatory k integrals cancel correctly
!for accurate alpha(r), beta(r), e.g. 8000; not so important for bispectrum
!increase accuracy_boost
use lensing
use constants
use RangeUtils
use FileUtils
use ArrayUtils
use MathUtils
#ifdef FISHER
use MatrixUtils
#endif
Class(CAMBdata), target :: State
integer, parameter :: max_bispectra = 2 !fnl, lensing
Type(ClTransferData) :: CTrans
type(TRanges) :: TimeStepsNongauss
integer, allocatable :: ind(:), indP(:), indPd(:)
real(dl), allocatable :: res(:,:,:), resP(:,:,:), resPd(:,:)
real(dl), allocatable :: res_l(:,:,:), resP_l(:,:,:), resPd_l(:,:)
real(dl) r, term
Type(TBispectrum), target,allocatable :: Bispectra(:,:,:,:), OddBispectra (:)
!TTT, TTE, etc; last index is bispectrum kind, default 1=fnl, 2=lensing
!OddBispectra are parity odd terms like TEB (if do_parity_odd requested for lensing)
Type(TBispectrum), pointer :: Bispectrum
!For use in Fisher approximations
real(dl) test(CTrans%ls%lmin:CTrans%ls%l(CTrans%ls%nl))
integer i, j, l1,l2,l3, il1, n,np, npd
integer min_l, max_l, lmin, lmax
real(dl) tmp, tmp1, tmp2, tmp3
real(dl) a3j(0:CTrans%ls%l(CTrans%ls%nl)*2+1)
real(dl) a3j2(0:CTrans%ls%l(CTrans%ls%nl)*2+1,4,2)
real(dl) CLForLensingIn(4,CTrans%ls%lmin:CTrans%ls%l(CTrans%ls%nl))
real(dl) CPhi(3,CTrans%ls%lmin:CTrans%ls%l(CTrans%ls%nl))
Type(lSamples) :: SampleL
integer, allocatable :: ls(:)
real(dl) Bscale
integer field, field1,field2,field3, bi_ix,bix
Type(TCov2), allocatable :: CForLensing(:)
integer nfields, nbispectra, bispectrum_type
integer :: fnl_bispectrum_ix = 1
integer :: lens_bispectrum_ix = 2
character(LEN=256) :: file_tag = ''
integer idelta, fileid
character(LEN=26) :: BispectrumNames(max_bispectra)
integer :: parities(3), oddix
integer, parameter :: lmax_lensing_corrT = 300
!assume C^{T\psi} zero above this for CMB lensing; also neglect lensing contributions to variance
integer, parameter :: lmax_lensing_corrE = 40 !assume C^{E\psi} zero above this for CMB lensing
integer, parameter :: first_order_unlensed = 1, first_order_lensed = 2
integer, parameter :: lens_bispectrum_approx = first_order_lensed
#ifdef FISHER
Type(TBispectrum), pointer :: Bispectrum2
real(dl) Cl(4,lmin:CTrans%ls%l(CTrans%ls%nl))
real(dl) a3j_00(0:CTrans%ls%l(CTrans%ls%nl)*2+1)
integer lstart
real(dl) Noise, NoiseP, bias
real(dl), allocatable:: fish_contribs(:,:,:)
real(dl) fish_contribs_sig(lmin:CTrans%ls%l(CTrans%ls%nl))
real(dl), allocatable :: ifish_contribs(:,:,:,:,:), Fisher(:,:), tmpFisher(:,:),OptimalFisher(:,:)
real(dl), allocatable :: tmpBigFisher(:,:), Fisher_L1(:,:,:),tmpProjFisher(:,:)
real(dl), allocatable :: fish_l1(:,:,:,:), fish_L_ij(:,:), fish_L_noise(:,:)
Type(TBispectrum), target,allocatable :: SqueezedLensingKernel(:,:)
real(dl) sigma2, xlc, tmpf(3)
integer f1,f2,f3, minl2,bigi,bigj, bispectrum_type2, lmaxcuti
integer sz,corrsize
Type(TCov), allocatable :: InvC(:)
integer ix1,ix2
real(dl) tmpArr(lmin:CTrans%ls%l(CTrans%ls%nl))
#endif
type(TTextFile) :: file_alpha, file_beta, file_alpha_beta_r
type(TTextFile), allocatable, dimension(:) :: bispectrum_files
Type(CAMBParams), pointer :: CP
Type(TTimer) :: Timer
CP =>State%CP
parities(1)=1 !T
parities(2)=1 !E
parities(3)=-1 !B
if (BispectrumParams%do_primordial_bispectrum) then
fnl_bispectrum_ix = 1
nbispectra=1
BispectrumNames(fnl_bispectrum_ix)='fnl'
else
fnl_bispectrum_ix = 0
nbispectra=0
end if
if (BispectrumParams%do_lensing_bispectrum) then
lens_bispectrum_ix = fnl_bispectrum_ix+1
nbispectra=nbispectra+1
BispectrumNames(lens_bispectrum_ix)='lensing'
end if
if (nbispectra>max_bispectra) call MpiStop('check max_bispectra')
nfields=BispectrumParams%nfields
if (CP%Accuracy%lSampleBoost <50) call MpiStop('Bispectrum assumes lSampleBoost=50 (all L sampled)')
if (lens_bispectrum_approx == first_order_unlensed) file_tag='_unlens'
lmax = CTrans%ls%l(CTrans%ls%nl)
lmin = CTrans%ls%lmin
if (CP%DoLensing) lmax = State%CLData%lmax_lensed
SampleL%lmin=2
allocate(ls(lmax))
SampleL%nl=0
l1=1
do
if (l1<=lmax_lensing_corrE) then
l1 = l1+1
else if (l1<120) then
l1 =l1+nint(7/CP%Accuracy%AccuracyBoost)
else
l1 =l1+nint(50/CP%Accuracy%AccuracyBoost)
end if
if (l1>lmax) then
l1 =lmax
end if
if (BispectrumParams%Slice_Base_L>0 .and. SampleL%nl>0) then
!Make sure requested slice base is actually calculated
if ( BispectrumParams%Slice_Base_L <l1 .and. BispectrumParams%Slice_Base_L>ls(SampleL%nl)) then
SampleL%nl= SampleL%nl + 1
ls(SampleL%nl) = BispectrumParams%Slice_Base_L
end if
end if
SampleL%nl= SampleL%nl + 1
ls(SampleL%nl) = l1
if (l1 == lmax) exit
end do
allocate(SampleL%l, source=ls(1:SampleL%nl))
allocate(Bispectra(nfields,nfields,nfields,nbispectra))
do field1=1,nfields
do field2=1,nfields
do field3=1,nfields
!Only store l2,l3 that are non-zero, array size is approx
do bispectrum_type=1,nbispectra
allocate(Bispectra(field1,field2,field3,bispectrum_type)%b((lmax*(lmax+1))/4,SampleL%nl))
Bispectra(field1,field2,field3,bispectrum_type)%b=0
end do
end do
end do
end do
if (BispectrumParams%do_lensing_bispectrum) then
if (.not. CP%DoLensing) call MpiStop('Must turn on lensing to get lensing bispectra')
print *,'Getting lensing reduced bispectra'
allocate(CForLensing(lmax))
CPhi=0
do i=lmin,lmax
CPhi(1,i) = State%CLData%Cl_scalar(i,C_Phi)/real(i,dl)**4 * InternalScale
!set correlations to zero where very small to avoid numerical issues
if (i<=lmax_lensing_corrT) then
CPhi(2,i) = State%CLData%Cl_scalar(i,C_PhiTemp) /real(i,dl)**3 * InternalScale
end if
if (i<=lmax_lensing_corrE) then
CPhi(3,i) = State%CLData%Cl_scalar(i,C_PhiE) /real(i,dl)**3 * InternalScale
end if
tmp = i*(i+1)/const_twopi
CLForLensingIn(:,i) = State%CLData%CL_lensed(i,CT_Temp:CT_Cross) * InternalScale/tmp
! CForLensing(i)%C=0
CForLensing(i)%C(1,1)=CLForLensingIn(1,i)
CForLensing(i)%C(1,2)=CLForLensingIn(4,i)
CForLensing(i)%C(2,1)=CLForLensingIn(4,i)
CForLensing(i)%C(2,2)=CLForLensingIn(2,i)
! CForLensing(i)%C(3,3)=CL_lensed(i,1,CT_B) * InternalScale/tmp
end do
#ifdef FISHER
allocate(SqueezedLensingKernel(nfields,nfields))
do field2=1,nfields
do field3=1,nfields
allocate(SqueezedLensingKernel(field2,field3)%b((lmax*(lmax+1))/4,SampleL%nl))
SqueezedLensingKernel(field2,field3)%b=0
end do
end do
#endif
if (DebugMsgs) call Timer%Start()
!$OMP PARALLEL DO DEFAULT(SHARED), SCHEDULE(STATIC,3), &
!$OMP PRIVATE(l1, l2, l3, max_l, min_l, bix, bi_ix, tmp1, tmp2, tmp3), &
!$OMP PRIVATE(field1, field2, field3, Bispectrum, a3j, a3j2)
do il1= 1, SampleL%nl
l1 = SampleL%l(il1)
if (l1 > lmax_lensing_corrT) cycle !no exit in parallel loop
tmp1=l1*(l1+1)
bi_ix=0
do l2= max(lmin,l1), lmax
tmp2= l2*(l2+1)
min_l = max(abs(l1-l2),l2)
if (mod(l1+l2+min_l,2)/=0) then
min_l = min_l+1
end if
max_l = min(lmax,l1+l2)
bix=bi_ix
a3j2(:,:,1)=0.5d0
if (nfields>1) then
call GetThreeJs(a3j(abs(l2-l1)),l1,l2,0,0)
call GetThreeJs(a3j2(max(2,abs(l2-l1)),1,2),l1,l2,2,0)
call GetThreeJs(a3j2(max(2,abs(l2-l1)),2,2),l1,l2,0,2)
call GetThreeJs(a3j2(max(0,abs(l2-l1)),3,2),l1,l2,2,-2)
do l3=min_l,max_l ,2
a3j2(l3,:,2) = a3j2(l3,:,2)/a3j(l3)*0.5d0
end do
end if
do field1=1,nfields
do field2=1,nfields
do field3=1,nfields
Bispectrum=> Bispectra(field1,field2,field3, lens_bispectrum_ix)
bi_ix=bix
do l3=min_l,max_l ,2
bi_ix=bi_ix+1
tmp3=l3*(l3+1)
!bispectrum is the reduced bispectrum
#ifdef FISHER
if (field1==1) then
SqueezedLensingKernel(field2,field3)%b(bi_ix,il1)= &
(-tmp2+tmp3+tmp1)*(a3j2(l3,2,field2)*CForLensing(l3)%C(field2,field3)) + &
(-tmp3+tmp1+tmp2)*(a3j2(l3,2,field3)*CForLensing(l2)%C(field3,field2))
end if
#endif
Bispectrum%b(bi_ix,il1)= &
(-tmp1+tmp2+tmp3) * &
(a3j2(l3,1,field1)*CPhi(1+field2,l2)*CForLensing(l3)%C(field1,field3) + &
a3j2(l3,3,field1)*CPhi(1+field3,l3)*CForLensing(l2)%C(field1,field2) ) + &
(-tmp2+tmp3+tmp1)* &
(a3j2(l3,3,field2)*CPhi(1+field3,l3)*CForLensing(l1)%C(field2,field1) + &
a3j2(l3,2,field2)*CPhi(1+field1,l1)*CForLensing(l3)%C(field2,field3) ) + &
(-tmp3+tmp1+tmp2)* &
(a3j2(l3,2,field3)*CPhi(1+field1,l1)*CForLensing(l2)%C(field3,field2) + &
a3j2(l3,1,field3)*CPhi(1+field2,l2)*CForLensing(l1)%C(field3,field1) )
end do
end do
end do
end do
end do
end do
!$OMP END PARALLEL DO
if (DebugMsgs) call Timer%WriteTime('Time for lensing:')
if (nfields==1) BispectrumParams%do_parity_odd=.false.
if (BispectrumParams%do_parity_odd) then
allocate(OddBispectra(12))
oddix=0
do field1=1,3
do field2=1,3
do field3=1,3
if (parities(field1)+parities(field2)+parities(field3)/=1) cycle
oddix=oddix+1
!Only store l2,l3 that are non-zero, array size is approx
allocate(OddBispectra(oddix)%b((lmax*(lmax+1))/4,SampleL%nl))
OddBispectra(oddix)%b=0
end do
end do
end do
!$OMP PARALLEL DO DEFAULT(SHARED), SCHEDULE(STATIC,3), &
!$OMP PRIVATE(l1, l2, l3, max_l, min_l, bix, bi_ix, tmp1, tmp2, tmp3), &
!$OMP PRIVATE(field1, field2, field3, Bispectrum, a3j2, oddix)
do il1= 1, SampleL%nl
l1 = SampleL%l(il1)
if (l1 > lmax_lensing_corrT) cycle !no exit in parallel loop
tmp1=l1*(l1+1)
bi_ix=0
do l2= max(lmin,l1), lmax
tmp2=l2*(l2+1)
min_l = max(abs(l1-l2),l2)
if (mod(l1+l2+min_l,2)/=1) then
min_l = min_l+1
end if
max_l = min(lmax,l1+l2)
bix=bi_ix
a3j2(:,:,1)=0.5d0
call GetThreeJs(a3j2(max(2,abs(l2-l1)),1,2),l1,l2,2,0)
call GetThreeJs(a3j2(max(2,abs(l2-l1)),2,2),l1,l2,0,2)
call GetThreeJs(a3j2(max(0,abs(l2-l1)),3,2),l1,l2,2,-2)
do l3=min_l,max_l ,2
a3j2(l3,:,2) = a3j2(l3,:,2)*0.5d0*sqrt(real((2*L1+1)*(2*L2+1),dl)*(2*L3+1)/(3.1415926535*4))
end do
oddix=0
do field1=1,3
do field2=1,3
do field3=1,3
!Only calculate terms with one B
if (parities(field1)+parities(field2)+parities(field3)/=1) cycle
oddix=oddix+1
Bispectrum=> OddBispectra(oddix)
bi_ix=bix
do l3=min_l,max_l ,2
bi_ix=bi_ix+1
tmp3=l3*(l3+1)
!bispectrum the non-reduced bispectrum without the i
if (parities(field1)==-1) then
Bispectrum%b(bi_ix,il1)= &
(-tmp1+tmp2+tmp3) * &
(a3j2(l3,1,min(2,field1))*CPhi(1+field2,l2)*CForLensing(l3)%C(2,field3) &
-a3j2(l3,3,min(2,field1))*CPhi(1+field3,l3)*CForLensing(l2)%C(2,field2) )
elseif (parities(field2)==-1) then
Bispectrum%b(bi_ix,il1)= &
(-tmp2+tmp3+tmp1)* &
(-a3j2(l3,3,min(2,field2))*CPhi(1+field3,l3)*CForLensing(l1)%C(2,field1) &
-a3j2(l3,2,min(2,field2))*CPhi(1+field1,l1)*CForLensing(l3)%C(2,field3) )
else if (parities(field3)==-1) then
Bispectrum%b(bi_ix,il1)= &
(-tmp3+tmp1+tmp2)* &
(-a3j2(l3,2,min(2,field3))*CPhi(1+field1,l1)*CForLensing(l2)%C(2,field2) + &
a3j2(l3,1,min(2,field3))*CPhi(1+field2,l2)*CForLensing(l1)%C(2,field1) )
end if
end do
end do
end do
end do
end do
end do
!$OMP END PARALLEL DO
end if
end if
if (BispectrumParams%do_primordial_bispectrum) then
print *,'getting reduced local fnl bispectra'
allocate(TransferPolFac(lmax))
do i=2,lmax
TransferPolFac(i) =sqrt( real((i+1)*i,dl)*(i+2)*(i-1))
end do
if (shape /= shape_local) call MpiStop('Non-local shapes not working')
if (shape == shape_local) then
n=1
np=1
npd=0 !derivatives of function
else if (shape == shape_warm) then
n=2
np=3
npd=0
else if (shape == shape_warm2) then
n=1
np=2
npd=2
else
call MpiStop('unknown shape')
end if
allocate(ind(n))
allocate(indP(np))
if (npd>0) then
call InitBesselDerivs(CTrans)
allocate(indPd(npd))
end if
if (shape==shape_warm) then
!Separable form is very unstable and unworkable probably
ind(1) = 0
ind(2) = 2
indP(1) = 0
indP(2) = 2
indP(3) = -2
else if (shape==shape_warm2) then
ind(1) = 0
indP(1) = 0
indP(2) = -2
indPd(1) = 0
indPd(2) = -2
else
ind(1) = 0
indP(1) = 0
end if
test=0
TimeStepsNongauss = State%TimeSteps
call TimeStepsNongauss%Add_delta(-State%taurst*10*CP%Accuracy%AccuracyBoost, State%taurst, State%dtaurec)
call TimeStepsNongauss%getArray(.true.)
if (BispectrumParams%export_alpha_beta) then
!Note that all the points outside recombination are not really needed
!And these are for curvature perturbation, so do not include 3/5 factor
call file_alpha%CreateFile(trim(output_root)//'_alpha.txt') ! 100
call file_beta%CreateFile(trim(output_root)//'_beta.txt') ! 101
call file_alpha_beta_r%CreateFile(trim(output_root)//'_alpha_beta_r.txt') ! 102
end if
if (DebugMsgs) call Timer%Start()
!When writing to the files is requested, then do not OMP. This is done
!by the IF(.not. ...).
!$OMP PARALLEL DO DEFAUlT(SHARED), SCHEDULE(STATIC,3), &
!$OMP IF(.not. BispectrumParams%export_alpha_beta) &
!$OMP PRIVATE(r, res, resP, resPd, res_l, resP_l, resPd_l, term, j), &
!$OMP PRIVATE(il1, l1, l2, l3, min_l, max_l, tmp, tmp1, tmp2, Bispectrum), &
!$OMP PRIVATE(bi_ix, bix, field1, field2, field3, field)
do i= TimeStepsNongauss%npoints-1, 2,-1
r=(State%tau0-TimeStepsNongauss%points(i))
allocate(res(CTrans%ls%nl,n,nfields))
allocate(resP(CTrans%ls%nl,np,nfields))
allocate(res_l(1:CTrans%ls%l(CTrans%ls%nl),n,nfields))
allocate(resP_l(1:CTrans%ls%l(CTrans%ls%nl),np,nfields))
if (npd>0) then
allocate(resPd(CTrans%ls%nl,npd))
allocate(resPd_l(1:CTrans%ls%l(CTrans%ls%nl),npd))
end if
call NonGauss_l_r(CP,CTrans, ind, indP,res, resP, nfields, r)
if (npd>0) call NonGauss_deriv_l_r(CP,CTrans, indPd,resPd, r, dJl,dddJl)
do field=1,nfields
do j=1,n
call CTrans%ls%InterpolateClArr(res(1,j,field),res_l(lmin,j,field))
end do
do j=1,np
call CTrans%ls%InterpolateClArr(resP(1,j,field),resP_l(lmin,j,field))
end do
end do
deallocate(res,resP)
if (BispectrumParams%export_alpha_beta) then
write(file_alpha%unit, concat('(',lmax-lmin+1 ,'E15.5)')) res_l(lmin:lmax,1,1)
write(file_beta%unit, concat('(',lmax-lmin+1 ,'E15.5)')) resP_l(lmin:lmax,1,1)
write(file_alpha_beta_r%unit, '(1E15.5)') r
end if
if (npd>0) then
do j=1,npd
call InterpolateClArr(CTrans%ls,resPd(1,j),resPd_l(lmin,j))
end do
deallocate(resPd)
end if
term = r**2 * TimeStepsNongauss%dpoints(i) * (3./5)
!Restrict to l1<=l2<=l3
do il1= 1, SampleL%nl
l1 = SampleL%l(il1)
bi_ix=0
do l2= max(lmin,l1), lmax
min_l = max(abs(l1-l2),l2)
if (mod(l1+l2+min_l,2)/=0) then
min_l = min_l+1
end if
max_l = min(lmax,l1+l2)
do field1=1,nfields
do field2=1,nfields
tmp1 = 2*term*(res_l(l1,1,field1)*resP_l(l2,1,field2) + &
res_l(l2,1,field2)*resP_l(l1,1,field1))
tmp2 = 2*term*(resP_l(l1,1,field1)*resP_l(l2,1,field2))
do field3=1,nfields
Bispectrum => Bispectra(field1,field2,field3,fnl_bispectrum_ix)
bix=bi_ix
do l3=min_l,max_l ,2
bix=bix+1
Bispectrum%b(bix,il1) = Bispectrum%b(bix,il1) + &
(tmp1*resP_l(l3,1,field3) + tmp2*res_l(l3,1,field3))
end do
end do
end do
end do
bi_ix=bix
end do !l2
end do !il1
deallocate(res_l,resP_l)
if (npd>0) deallocate(resPd_l)
end do !TimeStepsNongauss
!$OMP END PARALLEL DO
if (BispectrumParams%export_alpha_beta) then
call file_alpha%close()
call file_beta%close()
call file_alpha_beta_r%close()
end if
deallocate(TransferPolFac)
call TimeStepsNongauss%Free()
if (DebugMsgs) call Timer%WriteTime('Time for fnl bispectrum:')
end if !DoPrimordial
if (BispectrumParams%Slice_Base_L>0 .or. BispectrumParams%FullOutputFile/='') then
!write out slice in (muK)^3 units
allocate(bispectrum_files(nbispectra* max(1, BispectrumParams%ndelta)))
Bscale=(COBE_CMBTemp*1d6)**3/InternalScale**2;
do bispectrum_type=1,nbispectra
if (BispectrumParams%Slice_Base_L>0) then
do idelta=1,BispectrumParams%ndelta
if (mod(BispectrumParams%Slice_Base_L + BispectrumParams%deltas(idelta),2)==1 &
.and. bispectrum_type/=lens_bispectrum_ix) cycle
call bispectrum_files(BispectrumParams%ndelta*(bispectrum_type-1)+idelta)% &
CreateFile(concat(trim(output_root)//'bispectrum_'//&
trim(BispectrumNames(bispectrum_type))//'_base_', &
BispectrumParams%Slice_Base_L,'_delta_',BispectrumParams%deltas(idelta), &
trim(file_tag)//'.dat'))
end do
end if
if (BispectrumParams%FullOutputFile/='') then
call bispectrum_files(bispectrum_type)%CreateFile(concat(trim(output_root), &
BispectrumParams%FullOutputFile, '_', BispectrumNames(bispectrum_type), &
file_tag, '.dat'))
end if
end do
do il1= 1, SampleL%nl
l1 = SampleL%l(il1)
bi_ix=0
do l2= max(lmin,l1), lmax
min_l = max(abs(l1-l2),l2)
if (mod(l1+l2+min_l,2)/=0) then
min_l = min_l+1
end if
max_l = min(lmax,l1+l2)
do l3=min_l, max_l ,2
bi_ix=bi_ix+1
if (l1==BispectrumParams%Slice_Base_L &
.and. any(l3-l2==BispectrumParams%deltas(1:BispectrumParams%ndelta))) then
!Particular slice
idelta=IndexOf(l3-l2,BispectrumParams%deltas,BispectrumParams%ndelta)
do bispectrum_type=1,nbispectra
fileid=bispectrum_files(BispectrumParams%ndelta*(bispectrum_type-1)+idelta)%unit
write (fileid,'(1I5)', advance='NO') L2
do field1=1,nfields
do field2=1,nfields
do field3=1,nfields
write(fileid,'(1E15.5)', advance='NO') &
Bispectra(field1,field2,field3,bispectrum_type)%b(bi_ix,il1)*Bscale
end do
end do
end do
write (fileid,'(a)') ''
end do
end if !slice
if (BispectrumParams%FullOutputFile/='') then
if (BispectrumParams%SparseFullOutput .and. .not. any( SampleL%l(1:SampleL%nl)==L2) .or. &
l1 > 30 .and. mod(l3-min_l,10)/=0 .and. l3 /= max_l) cycle
do bispectrum_type=1,nbispectra
if (bispectrum_type==lens_bispectrum_ix .and. L1 > lmax_lensing_corrT) cycle
write(bispectrum_files(bispectrum_type)%unit,'(3I5)', advance='NO') L1, L2, L3
do field1=1,nfields
do field2=1,nfields
do field3=1,nfields
write(bispectrum_files(bispectrum_type)%unit,'(1E14.5)', advance='NO') &
Bispectra(field1,field2,field3,bispectrum_type)%b(bi_ix,il1)*Bscale
end do
end do
end do
write (bispectrum_files(bispectrum_type)%unit,'(a)') ''
end do
end if
end do
end do
end do
if (BispectrumParams%do_parity_odd) then
do il1= 1, SampleL%nl
l1 = SampleL%l(il1)
bi_ix=0
do l2= max(lmin,l1), lmax
min_l = max(abs(l1-l2),l2)
if (mod(l1+l2+min_l,2)/=1) then
min_l = min_l+1
end if
max_l = min(lmax,l1+l2)
do l3=min_l, max_l ,2
bi_ix=bi_ix+1
if (l1==BispectrumParams%Slice_Base_L &
.and. any(l3-l2==BispectrumParams%deltas(1:BispectrumParams%ndelta))) then
!Particular slice
idelta=IndexOf(l3-l2,BispectrumParams%deltas,BispectrumParams%ndelta)
do bispectrum_type=1,nbispectra
if (bispectrum_type/=lens_bispectrum_ix) cycle
fileid=bispectrum_files(BispectrumParams%ndelta*(bispectrum_type-1)+idelta)%unit
write (fileid,'(1I5)', advance='NO') L2
oddix=0
do field1=1,3
do field2=1,3
do field3=1,3
if (parities(field1)+parities(field2)+parities(field3)/=1) cycle
oddix=oddix+1
write(fileid,'(1E15.5)', advance='NO') OddBispectra(oddix)%b(bi_ix,il1)*Bscale
end do
end do
end do
write (fileid,'(a)') ''
end do
end if !slice
end do
end do
end do
end if
! The finalizer closes the files.
deallocate(bispectrum_files)
end if
#ifdef FISHER
if (BispectrumParams%DoFisher) then
!Get stuff for Fisher etc.
print *,'Getting Fisher for lmax = ', lmax
Noise = BispectrumParams%FisherNoise/ (COBE_CMBTemp*1e6)**2 !Planckish, dimensionless units
NoiseP = BispectrumParams%FisherNoisePol/ (COBE_CMBTemp*1e6)**2
do i=lmin,lmax
if (CP%DoLensing) then
cl(:,i) = CL_lensed(i,1,CT_Temp:CT_Cross)
else
cl(1,i) = CL_Scalar(i,1,C_Temp)
cl(2,i) = CL_Scalar(i,1,C_E)
cl(4,i) = CL_Scalar(i,1,C_Cross)
cl(3,i) = 0
end if
if (CP%WantTensors .and. i<= CP%Max_l_tensor .and. i>=2) then
cl(:,i) = cl(:,i) + Cl_tensor(i,1,CT_Temp:CT_Cross)
end if
end do
if (.false.) then
call OpenTxtFile('CAMBdefault_lensedCls.dat',3)
do i=lmin,lmax
!Assume T,E,B,X ordering
read(3,*) j, cl(1:4,i)
if (j<lmin) read(3,*) j, cl(1:4,i)
cl(:,i)=cl(:,i)/(COBE_CMBTemp*1e6)**2
end do
close(3)
end if
if (Noise >0) then
file_tag = concat(file_tag,'_noise')
end if
xlc= 180*sqrt(8.*log(2.))/3.14159
sigma2 = (BispectrumParams%FisherNoiseFwhmArcmin/60/xlc)**2
allocate(InvC(lmax))
do l1= lmin, lmax
tmp = l1*(l1+1)/const_twopi
Cl(1,l1) = Cl(1,l1)/tmp + Noise*exp(l1*(l1+1)*sigma2)
Cl(2:3,l1) = Cl(2:3,l1)/tmp + NoiseP*exp(l1*(l1+1)*sigma2)
Cl(4,l1) = Cl(4,l1)/tmp
allocate(InvC(l1)%C(nfields,nfields))
if (nfields > 2) call MpiStop('Not implemented nfields>2 in detail')
if (nfields==1) then
InvC(l1)%C(1,1)=(2*l1+1)/cl(1,l1)/InternalScale
else
InvC(l1)%C(1,1)=cl(2,l1)
InvC(l1)%C(1,2)=-cl(4,l1)
InvC(l1)%C(2,1)=-cl(4,l1)
InvC(l1)%C(2,2)=cl(1,l1)
InvC(l1)%C= InvC(l1)%C * (2*l1+1)/(cl(1,l1)*cl(2,l1)-cl(4,l1)**2)/InternalScale
end if
end do
if (debugMsgs) call Timer%Start()
allocate(ifish_contribs(SampleL%l0,nbispectra,nbispectra,nfields,nfields) )
!This loop is just in case want to plot out lmax dependence
do lmaxcuti=SampleL%l0, SampleL%l0
! call CreateTxtFile('TE-Planck-LensFish.txt',20)
! do lmaxcuti=1, SampleL%l0
! if (SampleL%l(lmaxcuti) < 425) cycle
lmax= SampleL%l(lmaxcuti)
ifish_contribs=0
lstart = 2 !lmin
!$OMP PARALLEL DO DEFAULT(SHARED), SCHEDULE(STATIC,3), &
!$OMP PRIVATE(il1,l1,l2,l3,fish_l1,bi_ix,min_l,max_l,a3j_00,a3j), &
!$OMP PRIVATE(Bispectrum,Bispectrum2,minl2,bix,tmp,tmp1,tmp2,tmpf), &
!$OMP PRIVATE(field1,field2,field3,f1,f2,f3,bispectrum_type,bispectrum_type2)
do il1= 1, lmaxcuti !!!SampleL%l0
allocate(fish_l1(nbispectra,nbispectra,nfields,nfields)) !last indices are field1,f1
l1 = SampleL%l(il1)
if (l1< lstart) cycle
fish_l1=0
bi_ix=0
do l2 = l1,lmax
if (l2< lstart) cycle
min_l = max(lstart,max(abs(l1-l2),l2))
if (mod(l1+l2+min_l,2)/=0) then
min_l = min_l+1
end if
max_l = min(lmax,l1+l2)
call GetThreeJs(a3j(abs(l2-l1)),l1,l2,0,0)
do l3=min_l,max_l ,2
a3j_00(l3)=a3j(l3)**2
end do
tmp1= 1.d0/const_fourpi !(2l+1) factors included in InvC
minl2=min_l
bix=bi_ix
do field1=1,nfields
do f1=1,nfields
tmpf(1)= InvC(l1)%C(field1,f1)*tmp1
do field2=1,nfields
do f2=1,nfields
tmpf(2)= InvC(l2)%C(field2,f2)*tmpf(1)
do field3=1,nfields
do bispectrum_type=1,nbispectra
if (bispectrum_type==lens_bispectrum_ix) then
Bispectrum=>SqueezedLensingKernel(field2,field3)
else
Bispectrum=>bispectra(field1,field2,field3,bispectrum_type)
end if
do f3=1,nfields
do bispectrum_type2=bispectrum_type,nbispectra
if (bispectrum_type2==lens_bispectrum_ix) then
Bispectrum2=>SqueezedLensingKernel(f2,f3)
else
Bispectrum2=>Bispectra(f1,f2,f3,bispectrum_type2)
end if
min_l=minl2
bi_ix=bix
if (min_l==l2) then
!Symmetry factors
bi_ix=bi_ix+1
l3=l2
if (l2==l1) then
!l1=l2=l3
tmp = Bispectrum%b(bi_ix,il1)*tmpf(2)*Bispectrum2%b(bi_ix,il1) &
*InvC(l3)%C(field3,f3)*a3j_00(l3)/6
else
!l3=l2 (l3=l1<>l2 can't happen because l1<=l2<=l3)
tmp = Bispectrum%b(bi_ix,il1)*tmpf(2)*Bispectrum2%b(bi_ix,il1) &
* InvC(l3)%C(field3,f3)*a3j_00(l3)/2
end if
min_l = min_l+2
else
tmp=0
end if
tmp2=0
do l3=min_l,max_l ,2
bi_ix=bi_ix+1
tmp2 = tmp2 + Bispectrum%b(bi_ix,il1)*Bispectrum2%b(bi_ix,il1) &
* InvC(l3)%C(field3,f3)*a3j_00(l3)