forked from cmbant/CAMB
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathlensing.f90
1092 lines (884 loc) · 36.4 KB
/
lensing.f90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
!Lensing the C_l using the deflection angle from the computed lensing potential
!power spectrum.
!lensing_method=1: using an accurate curved-sky correlation function method
!lensing_method=2: using the flat-sky lower order result of astro-ph/9505109
! and astro-ph/9803150 as in CMBFAST
!lensing_method=3: using inaccurate full sky harmonic method of astro-ph/0001303
!The flat sky result is accurate to about 0.1% in TT, and 0.4% in EE and is
!about a factor of two faster than lensing_method=1.
!lensing_method=3 is only present for comparison and is not recommended in any regime
!Set accurate_BB=T if you want BB accurately by integrating the full angular range
!otherwise it saves a large amount of time by only integrating the small scales
!accute_BB only does *not* include any non-linear corrections or ensure you have
!chosen sufficiently high l_max and k_max, so does not neccessarily give an accurate
!result
!Uses the un-lensed Cls and the computed lensing potential power spectrum.
!Usual values of k_max are fine for all but the lensed BB Cls
!To get the lensed BB accurate around l=1000 you need to go to l_max >2000, and
!higher for higher l. Since this probes small scales in the lensing power spectrum you
!also need to go to higher k_max - for concordance models something like
!k_eta_max_scalar=10000. At l>1000 you can expect to need higher k_max, and for
!non-linear evolution to cause a significant error.
!Correlation function routines by AL+AC Nov 2004 with flat-sky borrowings from CMBFAST
!Curved sky results use the method of astro-ph/xxx.
!Full sky harmonic lensing routines by Gayoung Chon and AC.
!Ref: astro-ph/0001303 by W. Hu.
!For better derivations see also astro-ph/0301064 and astro-ph/0301031
!Adapted for CAMB and optimized by AL.
!Uses f90 version of "J1-RECURSION OF 3J-COEFFICIENTS" by K. Schulten and R.G. Gordon
!obtainable from the CPC program library (www.cpc.cs.qub.ac.uk).
!March 2006: fixed problem with l_max when generating with tensors (thanks Chad Fendt)
module lensing
use Precision
use ModelParams
use AmlUtils
implicit none
integer, parameter :: lensing_method_curv_corr=1,lensing_method_flat_corr=2, &
lensing_method_harmonic=3
integer :: lensing_method = lensing_method_curv_corr
real(dl) :: lensing_sanity_check_amplitude = 1e-7
real(dl) :: ALens_Fiducial = 0._dl
!Change from zero to set lensing smoothing by scaling amplitude of fiducial template
private
logical :: lensing_includes_tensors = .false.
!flat method stores
real(dl), parameter :: dbessel = 0.05_dl
real(dl), dimension(:), allocatable :: Bess0, ddBess0
real(dl), dimension(:), allocatable :: Bess2, ddBess2
real(dl), dimension(:), allocatable :: Bess4, ddBess4
real(dl), dimension(:), allocatable :: Bess6, ddBess6
integer, parameter :: lensed_convolution_margin = 100
!Number of L less than L max at which the lensed power spectrum is calculated
!Harmonic method stores
integer :: lmax_donelnfa = 0
real(dl), dimension(:), allocatable :: lnfa
public lens_Cls, lensing_includes_tensors, lensing_method, lensing_method_flat_corr,&
lensing_method_curv_corr,lensing_method_harmonic, BessI, bessj0, ALens_Fiducial, &
lensing_sanity_check_amplitude
contains
subroutine lens_Cls
use lvalues
!Must set l again in case computed tessors (thanks to Chad)
call initlval(lSamp,CP%Max_l)
if (lensing_method == lensing_method_curv_corr) then
call CorrFuncFullSky()
elseif (lensing_method == lensing_method_flat_corr) then
call CorrFuncFlatSky()
elseif (lensing_method == lensing_method_harmonic) then
call BadHarmonic
else
error stop 'Unknown lensing method'
end if
end subroutine lens_Cls
subroutine CorrFuncFullSky
integer :: lmax_extrap
lmax_extrap = CP%Max_l - lensed_convolution_margin + 450
if (HighAccuracyDefault) lmax_extrap=lmax_extrap+300
lmax_extrap = min(lmax_extrap_highl,lmax_extrap)
call CorrFuncFullSkyImpl(max(lmax_extrap,CP%max_l))
end subroutine CorrFuncFullSky
subroutine CorrFuncFullSkyImpl(lmax)
!Accurate curved sky correlation function method
!Uses non-perturbative isotropic term with 2nd order expansion in C_{gl,2}
!Neglects C_{gl}(theta) terms (very good approx)
use ModelParams
use ModelData
use lvalues
implicit none
integer, intent(in) :: lmax
integer l, i, in
integer :: npoints
real(dl) corr(4), Cg2, sigmasq, theta
real(dl) dtheta
real(dl) llp1,fac, fac1,fac2,fac3, rootllp1, rootfac1, rootfac2, rootfac3
integer max_lensed_ix
real(dl) P(lmax),dP(lmax)
real(dl) sinth,halfsinth, x, T2,T4
real(dl) roots(-1:lmax+4), lfacs(lmax), lfacs2(lmax), lrootfacs(lmax)
real(dl) d_11(lmax),d_m11(lmax)
real(dl) d_22(lmax),d_2m2(lmax),d_20(lmax)
real(dl) Cphil3(lmin:lmax), CTT(lmin:lmax), CTE(lmin:lmax),CEE(lmin:lmax)
real(dl) ls(lmax)
real(dl) xl(lmax)
real(dl), allocatable :: ddcontribs(:,:),corrcontribs(:,:)
real(dl), allocatable :: lens_contrib(:,:,:)
integer thread_ix
real(dl) pmm, pmmp1
real(dl) d4m4,d11,dm11,d2m2,d22,d20,d23,d2m3,d33,d3m3,d04,d1m2,d12,d13,d1m3,d2m4
real(dl) sinfac, Cg2sq
real(dl) X000,X022,X220,X121,X132,X242
real(dl) dX000,dX022
real(sp) timeprev
integer interp_fac
integer j,jmax
integer llo, lhi
real(dl) a0,b0,ho, sc
integer apodize_point_width
logical :: short_integral_range
real(dl) range_fac
logical, parameter :: approx = .false.
real(dl) theta_cut(lmax)
!$ integer OMP_GET_THREAD_NUM, OMP_GET_MAX_THREADS
!$ external OMP_GET_THREAD_NUM, OMP_GET_MAX_THREADS
if (lensing_includes_tensors) call MpiStop('Haven''t implemented tensor lensing')
max_lensed_ix = lSamp%l0-1
do while(lSamp%l(max_lensed_ix) > CP%Max_l - lensed_convolution_margin)
max_lensed_ix = max_lensed_ix -1
end do
lmax_lensed = lSamp%l(max_lensed_ix)
if (allocated(Cl_lensed)) deallocate(Cl_lensed)
allocate(Cl_lensed(lmin:lmax_lensed,CP%InitPower%nn,1:4))
Cl_Lensed = 0
npoints = CP%Max_l * 2 *AccuracyBoost
short_integral_range = .not. CP%AccurateBB
dtheta = pi / npoints
if (CP%Max_l > 3500) dtheta=dtheta/1.3
apodize_point_width = nint(0.003 / dtheta)
npoints = int(pi/dtheta)
if (short_integral_range) then
range_fac= max(1._dl,32/AccuracyBoost) !fraction of range to integrate
npoints = int(npoints /range_fac)
!OK for TT, EE, TE but inaccurate for low l BB
!this induces high frequency ringing on very small scales
!which is then mitigated by the apodization below
else
range_fac=1
end if
if (DebugMsgs) timeprev=GetTestTime()
interp_fac = max(1,min(nint(10/AccuracyBoost),int(range_fac*2)-1))
jmax = 0
do l=lmin,lmax
if (l<=15 .or. mod(l-15,interp_fac)==interp_fac/2) then
jmax =jmax+1
ls(jmax)=l
xl(jmax)=l
end if
lfacs(l) = real(l*(l+1),dl)
lfacs2(l) = real((l+2)*(l-1),dl)
lrootfacs(l) = sqrt(lfacs(l)*lfacs2(l))
end do
do l=2,lmax
theta_cut(l) = 0.244949_dl/sqrt(3._dl*lfacs(l) - 8._dl)
end do
roots(-1)=0 !just so dipole doesn't screw up
do l=0,lmax+4
roots(l) = sqrt(real(l,dl))
end do
thread_ix = 1
!$ thread_ix = OMP_GET_MAX_THREADS()
allocate(lens_contrib(4,lmax_lensed,thread_ix))
allocate(ddcontribs(lmax,4),corrcontribs(lmax,4))
do in = 1, CP%InitPower%nn
do l=lmin,CP%Max_l
! (2*l+1)l(l+1)/4pi C_phi_phi: Cl_scalar(l,1,C_Phi) is l^4 C_phi_phi
Cphil3(l) = Cl_scalar(l,in,C_Phi)*(2*l+1)*(l+1)/real(l,dl)**3/(4*pi)
fac = (2*l+1)/(4*pi) * 2*pi/(l*(l+1))
CTT(l) = Cl_scalar(l,in,C_Temp)*fac
CEE(l) = Cl_scalar(l,in,C_E)*fac
CTE(l) = Cl_scalar(l,in,C_Cross)*fac
end do
if (Cphil3(10) > lensing_sanity_check_amplitude) then
write (*,*) 'You need to normalize realistically to use lensing.'
write (*,*) 'see http://cosmocoffee.info/viewtopic.php?t=94'
call MpiStop()
end if
if (lmax > CP%Max_l) then
l=CP%Max_l
sc = (2*l+1)/(4*pi) * 2*pi/(l*(l+1))
fac2=CTT(CP%Max_l)/(sc*highL_CL_template(CP%Max_l, C_Temp))
fac=Cphil3(CP%Max_l)/(sc*highL_CL_template(CP%Max_l, C_Phi))
do l=CP%Max_l+1, lmax
!Fill in tail from template
sc = (2*l+1)/(4*pi) * 2*pi/(l*(l+1))
Cphil3(l) = highL_CL_template(l, C_Phi)*fac*sc
CTT(l) = highL_CL_template(l, C_Temp)*fac2*sc
CEE(l) = highL_CL_template(l, C_E)*fac2 *sc
CTE(l) = highL_CL_template(l, C_Cross)*fac2*sc
if (Cphil3(CP%Max_l+1) > 1e-7) then
call MpiStop('You need to normalize the high-L template so it is dimensionless')
end if
end do
end if
if (ALens_Fiducial > 0) then
do l=2, lmax
sc = (2*l+1)/(4*pi) * 2*pi/(l*(l+1))
Cphil3(l) = sc * highL_CL_template(l, C_Phi) * ALens_Fiducial
end do
end if
lens_contrib=0
!uncomment second line for PGF90 workaround
!$OMP PARALLEL DO DEFAULT(PRIVATE), &
!OMP PRIVATE(P,dP,d11,dm11,d22,d2m2,d20,corrcontribs,ddcontribs),&
!$OMP SHARED(lfacs,lfacs2,lrootfacs,Cphil3,CTT,CTE,CEE,lens_contrib, lmax, theta_cut), &
!$OMP SHARED(dtheta,CP,lmax_lensed,roots, npoints,interp_fac,jmax,ls,xl,short_integral_range,apodize_point_width)
do i=1,npoints-1
theta = i * dtheta
x = cos(theta)
sinth = sin(theta)
halfsinth = sinth/2
pmm=1
pmmp1=x
Cg2=0
sigmasq=0
if (lmin==1) then
d_11(1) = cos(theta/2)**2
d_m11(1) = sin(theta/2)**2
sigmasq = sigmasq + (1-d_11(1))*Cphil3(lmin)
Cg2 = Cg2 + d_m11(1)*Cphil3(lmin)
P(1) = x
d_22(1)=0
d_2m2(1)=0
d_20(1)=0
end if
do l=2,lmax
P(l)= ((2*l-1)* x *pmmp1 - (l-1)*Pmm)/ l
dP(l) = l*(pmmp1-x*P(l))/sinth**2
Pmm=pmmp1
pmmp1=P(l)
llp1 = lfacs(l)
fac1 = (1-x)
fac2 = (1+x)
fac = fac1/fac2
d_11(l) = fac1*dP(l)/llp1 + P(l)
d_m11(l) = fac2*dP(l)/llp1 - P(l)
sigmasq = sigmasq + (1-d_11(l))*Cphil3(l)
Cg2 = Cg2 + d_m11(l)*Cphil3(l)
d_22(l) = ( ((4*x-8)/fac2 + llp1)*P(l) &
+ 4*fac*( fac2 + (x - 2)/llp1)*dP(l) )/ lfacs2(l)
!For small theta use Taylor expansion for better stability (thanks Pavel Motloch)
if (theta > theta_cut(l)) then
d_2m2(l) = ( (llp1- (4*x+8)/fac1) *P(l) &
+4/fac*( -fac1 + (x+2)/llp1) *dP(l) )/lfacs2(l)
else
d_2m2(l) = lfacs(l)*lfacs2(l)*theta**4*(1._dl/384._dl &
- (3._dl*lfacs(l) - 8._dl)/23040._dl*theta**2)
endif
d_20(l) = (2*x*dP(l) - llp1*P(l) ) / lrootfacs(l)
end do
do j=1,jmax
l =ls(j)
fac1 = (1-x)
fac2 = (1+x)
llp1 = lfacs(l)
rootllp1 = roots(l)*roots(l+1)
rootfac1 = roots(l+2)*roots(l-1)
rootfac2 = roots(l+3)*roots(l-2)
llp1=lfacs(l)
dm11=d_m11(l)
d11=d_11(l)
if (l<2) then
d2m2=0
d22=0
d20=0
d1m2 = 0
d12 = 0
else
d2m2=d_2m2(l)
d22=d_22(l)
d20=d_20(l)
d1m2 = sinth/rootfac1*(dP(l) -2/fac1*dm11)
d12 = sinth/rootfac1*(dP(l) -2/fac2*d11)
end if
if (l<3) then
d1m3=0
d2m3=0
d3m3=0
d13 =0
d23 =0
d33 =0
else
sinfac=4/sinth
d1m3 = (-(x+0.5_dl)*d1m2*sinfac - lfacs2(l)*dm11/rootfac1 )/rootfac2
d2m3 = (-fac2*d2m2*sinfac - rootfac1*d1m2)/rootfac2
d3m3 = (-(x+1.5_dl)*d2m3*sinfac - rootfac1*d1m3)/rootfac2
d13 = ((x-0.5_dl)*d12*sinfac - lfacs2(l)*d11/rootfac1 ) /rootfac2
d23 = (-fac1*d22*sinfac + rootfac1*d12 ) / rootfac2
d33 = (-(x-1.5_dl)*d23*sinfac - rootfac1*d13)/rootfac2
end if
if (l<4) then
d04=0
d2m4=0
d4m4=0
rootfac3=0
else
rootfac3=roots(l-3)*roots(l+4)
d04=( (-llp1 + (18*x**2 + 6)/sinth**2 )*d20 -&
6*x*lfacs2(l)*dP(l)/lrootfacs(l) ) / (rootfac2*rootfac3)
d2m4= (-(6*x+4)*d2m3/sinth - rootfac2*d2m2 ) / rootfac3
d4m4 = (-7/5._dl*(llp1-6)*d2m2 + &
12/5._dl*( -llp1+(9*x+26)/fac1)*d3m3 ) / (llp1-12)
end if
!Non perturbative isotropic integrals
!these are approx, but extremely good approximations
X000 = exp(-llp1*sigmasq/4)
if (approx) then
X022 = X000
X220 = rootllp1**2/4*X000
X121 = -0.5_dl*rootllp1*X000
X132 = -0.5_dl*rootllp1*X000
X242 = 0.25_dl*rootllp1**2*X022
dX000 = -llp1/4*X000
dX022 = -llp1/4*X022
else
X022 = X000*(1+sigmasq) !exp(-(llp1-4)*sigmasq/4)
X220 = lrootfacs(l)/4*X000
X121 = -0.5_dl*rootfac1*X000
X132 = -0.5_dl*rootfac2*X000
X242 = 0.25_dl*rootfac2*rootfac3*X022
dX000 = -llp1/4*X000
dX022 = (1-llp1/4)*X022
end if
!second order
!TT
fac1 = dX000**2
fac3 = X220**2
Cg2sq = Cg2**2
!Here we drop terms in Cgt which are down by powers of l
!Approx good to 1e-4 level
fac = ( (X000**2-1) + Cg2sq*fac1)*P(l)+ Cg2sq*fac3*d2m2 &
+ 8/llp1* fac1*Cg2*dm11
corrcontribs(j,1)= CTT(l) * fac
fac2=(Cg2*dX022)**2+(X022**2-1)
!Q+U
fac = 2*Cg2*X121*X132*d13 + fac2*d22 +Cg2sq*X242*X220*d04
corrcontribs(j,2)= CEE(l) * fac
!Q-U
fac = ( fac3*P(l) + X242**2*d4m4)*Cg2sq/2 &
+ Cg2*(X121**2*dm11+ X132**2*d3m3) + fac2*d2m2
corrcontribs(j,3)= CEE(l) * fac
!TE
fac = (X000*X022-1)*d20+ &
2*dX000*Cg2*(X121*d11 + X132*d1m3)/rootllp1 &
+ Cg2sq*(X220/2*d2m4*X242 +( fac3/2 + dX022*dX000)*d20)
corrcontribs(j,4)= CTE(l) * fac
end do
do j=1,4
corr(j) = sum(corrcontribs(1:14,j))+interp_fac*sum(corrcontribs(15:jmax,j))
end do
!if (short_integral_range .and. i>npoints-20) &
! corr=corr*exp(-(i-npoints+20)**2/150.0) !taper the end to help prevent ringing
if (short_integral_range .and. i>npoints-apodize_point_width*3) &
corr=corr*exp(-(i-npoints+apodize_point_width*3)**2/real(2*apodize_point_width**2))
!taper the end to help prevent ringing
!Interpolate contributions
!Increasing interp_fac and using this seems to be slower than above
if (.false.) then
if (abs(sum(corrcontribs(1:jmax,1)))>1e-11) print *,i,sum(corrcontribs(1:jmax,1))
do j=1,4
call spline(xl,corrcontribs(1,j),jmax,1d30,1d30,ddcontribs(1,j))
end do
corr=0
llo=1
do l=lmin,lmax
if ((l > ls(llo+1)).and.(llo < jmax)) then
llo=llo+1
end if
lhi=llo+1
ho=ls(lhi)-ls(llo)
a0=(ls(lhi)-l)/ho
b0=(l-ls(llo))/ho
fac1 = ho**2/6
fac2 = (b0**3-b0)*fac1
fac1 = (a0**3-a0)*fac1
corr(1) = Corr(1)+ a0*corrcontribs(llo,1)+ b0*corrcontribs(lhi,1)+ &
fac1* ddcontribs(llo,1) +fac2*ddcontribs(lhi,1)
corr(2) = Corr(2)+ a0*corrcontribs(llo,2)+ b0*corrcontribs(lhi,2)+ &
fac1* ddcontribs(llo,2) +fac2*ddcontribs(lhi,2)
corr(3) = Corr(3)+ a0*corrcontribs(llo,3)+ b0*corrcontribs(lhi,3)+ &
fac1* ddcontribs(llo,3) +fac2*ddcontribs(lhi,3)
corr(4) = Corr(4)+ a0*corrcontribs(llo,4)+ b0*corrcontribs(lhi,4)+ &
fac1* ddcontribs(llo,4) +fac2*ddcontribs(lhi,4)
end do
end if
!$ thread_ix = OMP_GET_THREAD_NUM()+1
do l=lmin, lmax_lensed
!theta factors were put in earlier (already in corr)
lens_contrib(C_Temp, l, thread_ix)= lens_contrib(C_Temp,l, thread_ix) + &
corr(1)*P(l)*sinth
T2 = corr(2)* d_22(l)
T4 = corr(3)* d_2m2(l)
lens_contrib(CT_E, l, thread_ix)= lens_contrib(CT_E,l, thread_ix) + &
(T2+T4)*halfsinth
lens_contrib(CT_B, l, thread_ix)= lens_contrib(CT_B,l, thread_ix) + &
(T2-T4)*halfsinth
lens_contrib(CT_Cross, l, thread_ix)= lens_contrib(CT_Cross,l, thread_ix) + &
corr(4)*d_20(l)*sinth
end do
end do
!$OMP END PARALLEL DO
do l=lmin, lmax_lensed
!sign from d(cos theta) = -sin theta dtheta
fac = l*(l+1)/OutputDenominator*dtheta *2*pi
Cl_lensed(l,in,CT_Temp) = sum(lens_contrib(CT_Temp,l,:))*fac &
+ Cl_scalar(l,in,C_Temp)
Cl_lensed(l,in,CT_E) = sum(lens_contrib(CT_E,l,:))*fac &
+ Cl_scalar(l,in,C_E)
Cl_lensed(l,in,CT_B) = sum(lens_contrib(CT_B,l,:))*fac
Cl_lensed(l,in,CT_Cross) = sum(lens_contrib(CT_Cross,l,:))*fac &
+ Cl_scalar(l,in,C_Cross)
end do
end do !loop over different initial power spectra
deallocate(ddcontribs,corrcontribs)
deallocate(lens_contrib)
if (DebugMsgs) write(*,*) GetTestTime()-timeprev, 'Time for corr lensing'
end subroutine CorrFuncFullSkyImpl
subroutine CorrFuncFlatSky
!Do flat sky approx partially non-perturbative lensing, lensing_method=2
use ModelParams
use ModelData
use lvalues
integer l, i
integer :: npoints
real(dl) Cgl2, sigmasq, theta
real(dl) dtheta
real(dl) dbessfac, fac, fac1,fac2, C2term, expsig, corr(4)
real(sp) timeprev
real(dl) Bessel0(lmin:CP%Max_l),Bessel2(lmin:CP%Max_l)
real(dl) Bessel4(lmin:CP%Max_l),Bessel6(lmin:CP%Max_l)
real(dl) Cphil3(lmin:CP%Max_l), CTT(lmin:CP%Max_l), CTE(lmin:CP%Max_l),CEE(lmin:CP%Max_l)
integer max_lensed_ix
integer b_lo
integer in
real(dl) T2,T4,a0, b0
real(dl) lfacs(CP%Max_l)
real(dl), allocatable, dimension(:,:,:) :: lens_contrib(:,:,:)
integer thread_ix
!$ integer OMP_GET_THREAD_NUM, OMP_GET_MAX_THREADS
!$ external OMP_GET_THREAD_NUM, OMP_GET_MAX_THREADS
if (lensing_includes_tensors) stop 'Haven''t implemented tensor lensing'
max_lensed_ix = lSamp%l0-1
do while(lSamp%l(max_lensed_ix) > CP%Max_l -250)
max_lensed_ix = max_lensed_ix -1
end do
lmax_lensed = lSamp%l(max_lensed_ix)
if (allocated(Cl_lensed)) deallocate(Cl_lensed)
allocate(Cl_lensed(lmin:lmax_lensed,CP%InitPower%nn,1:4))
Cl_Lensed = 0
npoints = CP%Max_l * 2
if (CP%AccurateBB) npoints = npoints * 2
dtheta = pi / npoints
if (.not. CP%AccurateBB) then
npoints = int(npoints /32 *min(32._dl,AccuracyBoost))
!OK for TT, EE, TE but inaccurate for low l BB
!this induces high frequency ringing on very small scales
end if
call GetBessels(npoints*dtheta*CP%Max_l)
if (DebugMsgs) timeprev=GetTestTime()
dbessfac = dbessel**2/6
thread_ix = 1
!$ thread_ix = OMP_GET_MAX_THREADS()
allocate(lens_contrib(4,lmax_lensed,thread_ix))
do in = 1, CP%InitPower%nn
do l=lmin,CP%Max_l
! l^3 C_phi_phi/2/pi: Cl_scalar(l,1,C_Phi) is l^4 C_phi_phi
Cphil3(l) = Cl_scalar(l,in,C_Phi)/l /(2*pi)
fac = l/(2*pi)*2*pi/(l*(l+1))
CTT(l) = Cl_scalar(l,in,C_Temp)*fac
CEE(l) = Cl_scalar(l,in,C_E)*fac
CTE(l) = Cl_scalar(l,in,C_Cross)*fac
lfacs(l) = l**2*0.5_dl
end do
if (Cphil3(10) > 1e-7) then
write (*,*) 'You need to normalize realistically to use lensing.'
write (*,*) 'see http://cosmocoffee.info/viewtopic.php?t=94'
stop
end if
lens_contrib=0
!$OMP PARALLEL DO DEFAULT(SHARED), &
!$OMP PRIVATE(theta, sigmasq,cgl2,b_lo,a0,b0,fac,fac1,fac2), &
!$OMP PRIVATE(Bessel0,Bessel2,Bessel4,Bessel6), &
!$OMP PRIVATE(corr,expsig,C2term,T2,T4,i,l, thread_ix)
do i=1,npoints-1
theta = i * dtheta
sigmasq =0
Cgl2=0
fac = theta /dbessel
do l=lmin,CP%Max_l
!Interpolate the Bessel functions, and compute sigma^2 and C_{gl,2}
b0 = l*fac
b_lo = int(b0) +1
a0= b_lo - b0
b0= 1._dl - a0
fac1 = a0*b0*dbessfac
fac2 = fac1*(a0-2)
fac1 = fac1*(b0-2)
Bessel0(l) = a0*Bess0(b_lo)+ b0*Bess0(b_lo+1) +fac1*ddBess0(b_lo) &
+fac2*ddBess0(b_lo+1)
sigmasq = sigmasq + (1-Bessel0(l))*Cphil3(l)
Bessel2(l) = a0*Bess2(b_lo)+ b0*Bess2(b_lo+1) +fac1*ddBess2(b_lo) &
+fac2*ddBess2(b_lo+1)
Cgl2 = Cgl2 + Bessel2(l)*Cphil3(l)
Bessel4(l) = a0*Bess4(b_lo)+ b0*Bess4(b_lo+1) +fac1*ddBess4(b_lo) &
+fac2*ddBess4(b_lo+1)
Bessel6(l) = a0*Bess6(b_lo)+ b0*Bess6(b_lo+1) +fac1*ddBess6(b_lo) &
+fac2*ddBess6(b_lo+1)
end do
!Get difference between lensed and unlensed correlation function
corr = 0
do l=lmin,CP%Max_l
!For 2nd order perturbative result use
! expsig = 1 -sigmasq*l**2/2._dl
! C2term = l**2*Cgl2/2._dl
fac = sigmasq*lfacs(l)
expsig = exp(-fac)
C2term = Cgl2*lfacs(l)
!Put theta factor later in here
fac1 = expsig*theta
fac2 = C2term*fac1
fac1 = fac1 - theta !we want expsig-1 to get lensing difference
fac = fac1*Bessel0(l) + fac2*Bessel2(l)
!TT
corr(1) = corr(1) + CTT(l) * fac
!Q + U
corr(2) = corr(2) + CEE(l) * fac
fac2 = fac2*0.5_dl
!Q-U
corr(3) = corr(3) + CEE(l) * &
(fac1*Bessel4(l) + fac2*(Bessel2(l)+Bessel6(l)))
!Cross
corr(4) = corr(4) + CTE(l) * &
(fac1*Bessel2(l) + fac2*(Bessel0(l)+Bessel4(l)))
end do
!$ thread_ix = OMP_GET_THREAD_NUM()+1
do l=lmin, lmax_lensed
!theta factors were put in earlier (already in corr)
lens_contrib(C_Temp, l, thread_ix)= lens_contrib(C_Temp,l, thread_ix) + &
corr(1)*Bessel0(l)
T2 = corr(2)*Bessel0(l)
T4 = corr(3)*Bessel4(l)
lens_contrib(CT_E,l,thread_ix) = lens_contrib(CT_E,l, thread_ix) + T2+T4
lens_contrib(CT_B,l,thread_ix) = lens_contrib(CT_B,l, thread_ix) + T2-T4
lens_contrib(CT_Cross,l, thread_ix) = lens_contrib(CT_Cross,l, thread_ix) + &
corr(4)*Bessel2(l)
end do
end do
!$OMP END PARALLEL DO
do l=lmin, lmax_lensed
fac = l*(l+1)* 2*pi/OutputDenominator*dtheta
Cl_lensed(l,in,CT_Temp) = sum(lens_contrib(CT_Temp,l,:))*fac &
+ Cl_scalar(l,in,CT_Temp)
Cl_lensed(l,in,CT_Cross) = sum(lens_contrib(CT_Cross,l,:))*fac &
+Cl_scalar(l,in,C_Cross)
fac = fac /2 !(factor of 1/2 should have been in T2+/-T4 above
Cl_lensed(l,in,CT_E) = sum(lens_contrib(CT_E,l,:))*fac &
+ Cl_scalar(l,in,CT_E)
Cl_lensed(l,in,CT_B) = sum(lens_contrib(CT_B,l,:))*fac
end do
end do !loop over different initial power spectra
deallocate(lens_contrib)
if (DebugMsgs) write(*,*) GetTestTime()-timeprev, 'Time for corr lensing'
end subroutine CorrFuncFlatSky
subroutine BadHarmonic
use ModelParams
use ModelData
use lvalues
use InitialPower
integer maxl, i, in, almin, max_lensed_ix, maxl_phi
real(dl) , dimension (:,:,:), allocatable :: bare_cls
real(dl) pp(CP%InitPower%nn,CP%Max_l)
real(dl) asum(CP%InitPower%nn), RR(CP%InitPower%nn), roots(CP%Max_l)
real(dl) asum_TE(CP%InitPower%nn), asum_EE(CP%InitPower%nn), asum_BB(CP%InitPower%nn)
integer l1,l2,al,j, j1, k, hk, llp_1, llp_al, g1
real(dl) F, fct
real(dl) g2l,g2l1, norm
real(dl) a3j(CP%Max_l*2+1), tF, expF
logical DoPol
real(dl) iContribs(lSamp%l0,CP%InitPower%nn, 1:4), intcontrib(lmin:lSamp%l(lSamp%l0))
real(dl) , dimension (:,:,:), allocatable :: iCl_lensed
integer max_j_contribs
real(sp) timeprev
!Otherwise use second order perturbative harmonic method
if (DebugMsgs) timeprev=GetTestTime()
DoPol = CP%AccuratePolarization
maxl = CP%Max_l
if (allocated(Cl_lensed)) deallocate(Cl_lensed)
allocate(bare_cls(CP%InitPower%nn,maxl,1:4))
RR = 0
do j=lmin,maxl
norm = OutputDenominator/(j*(j+1))
if (lensing_includes_tensors .and. CP%WantTensors .and. j<= CP%Max_l_tensor) then !Use total Cls
bare_cls(:,j,CT_Temp:CT_E) = (Cl_scalar(j,:,C_Temp:C_E) + &
Cl_tensor(j,:,CT_Temp:CT_E))*norm
bare_cls(:,j,CT_B) = Cl_tensor(j,:,CT_B)*norm
bare_cls(:,j,CT_Cross) = (Cl_scalar(j,:,C_Cross) + &
Cl_tensor(j,:,CT_Cross))*norm
else
bare_cls(:,j,CT_Temp:CT_E) = Cl_scalar(j,:,C_Temp:C_E)*norm
bare_cls(:,j,CT_B) = 0
bare_cls(:,j,CT_Cross) = Cl_scalar(j,:,C_Cross)*norm
end if
pp(:,j) = Cl_scalar(j,:,C_Phi)/real(j**2,dl)**2
RR = RR + j*(j+1)*real(2*j+1,dl)*pp(:,j)
roots(j) = sqrt(real(2*j+1,dl))
end do
RR = RR/2/fourpi
if (RR(1) > 1e-5) then
write (*,*) 'You need to normalize realistically to use lensing.'
write (*,*) 'see http://cosmocoffee.info/viewtopic.php?t=94'
call MpiStop()
end if
if (maxl > lmax_donelnfa) then
!Get ln factorials
if (allocated(lnfa)) deallocate(lnfa)
allocate(lnfa(0:maxl*3+1))
lmax_donelnfa = maxl
lnfa(0) = 0
do i=1,CP%Max_l*3+1
lnfa(i)=lnfa(i-1) + log(real(i,dl))
end do
end if
max_lensed_ix = lSamp%l0-1
do while(lSamp%l(max_lensed_ix) > maxl -250)
max_lensed_ix = max_lensed_ix -1
end do
lmax_lensed = lSamp%l(max_lensed_ix)
allocate(iCl_lensed(max_lensed_ix, CP%InitPower%nn, 1:4))
max_j_contribs = lSamp%l0-1
if (.not. DoPol) then
maxl_phi = min(maxl,nint(max(600,(maxl*2)/5)*scale*AccuracyBoost))
do while (lSamp%l(max_j_contribs) > maxl_phi)
max_j_contribs=max_j_contribs-1
end do
end if
!$OMP PARALLEL DO DEFAULT(SHARED), SCHEDULE(DYNAMIC), SHARED(max_j_contribs) &
!$OMP PRIVATE(al,g1,llp_al,llp_1,g2l,asum,l1,g2l1,l2,k,hk,F,fct,almin), &
!$OMP PRIVATE(asum_EE,asum_BB,asum_TE,expF,tF, a3j, iContribs,in,intcontrib)
do j=max_lensed_ix,1,-1
!Only compute lensed spectra at lSamp%l(j). Start with slow ones.
al=lSamp%l(j)
llp_al = al*(al+1)
g2l=sqrt((2*al+1)/fourpi)
asum = 0
asum_EE = 0
asum_BB = 0
asum_TE = 0
do j1 = 1, max_j_contribs
! Contributions to C_al are a smooth function of l_1 - so interpolate
l1=lSamp%l(j1)
llp_1 = l1*(l1+1)
g2l1=roots(l1)
almin = max(abs(al-l1),2)
if (DoPol) then
call GetThreeJs(a3j(almin),l1,al,0,2)
do l2= almin, min(maxl,al+l1)
g1 = llp_1+l2*(l2+1)-llp_al
if (g1 == 0 ) cycle
k=al+l1+l2
fct=g1*g2l*g2l1*roots(l2)/2
tF = fct*a3j(l2)
if (mod(k,2)==0) then
hk = k/2
F = lnfa(hk)-lnfa(hk-al)-lnfa(hk-l1)-lnfa(hk-l2)+(lnfa(k-2*al)+lnfa(k-2*l1)&
& +lnfa(k-2*l2)-lnfa(k+1))/2
expF = exp(F)
asum=asum + bare_cls(:,l2,C_Temp)*(expF*fct)**2
asum_EE = asum_EE + bare_cls(:,l2,CT_E)*tF**2
asum_BB = asum_BB + bare_cls(:,l2,CT_B)*tF**2
if (mod(hk,2)/=0) tF=-tF
asum_TE = asum_TE + bare_cls(:,l2,CT_Cross)*expF*fct*tF
else
asum_BB = asum_BB + bare_cls(:,l2,CT_E)*tF**2
asum_EE = asum_EE +bare_cls(:,l2,CT_B)*tF**2
end if
end do
else !No polarization
do l2= almin +mod(al+l1+almin,2),min(maxl,al+l1), 2
!Only do lSamp%l's where al + l1 + l2 is even
g1 = llp_1+l2*(l2+1)-llp_al
if (g1 == 0 ) cycle !Contribution is zero
k=al+l1+l2
hk=k/2
fct=g1*g2l*g2l1*roots(l2)/2
expF = exp(2*(lnfa(hk)-lnfa(hk-al)-lnfa(hk-l1)-lnfa(hk-l2))+lnfa(k-2*al)+lnfa(k-2*l1)&
& +lnfa(k-2*l2)-lnfa(k+1))
asum=asum + bare_cls(:,l2,CT_Temp)*expF *fct**2
end do
end if !No polarization
iContribs(j1,:,CT_Temp) = asum*pp(:,l1)
if (DoPol) then
iContribs(j1,:,CT_E) = asum_EE*pp(:,l1)
iContribs(j1,:,CT_B) = asum_BB*pp(:,l1)
iContribs(j1,:,CT_Cross) = asum_TE*pp(:,l1)
end if
asum = 0
asum_EE = 0
asum_BB = 0
asum_TE = 0
end do
!Interpolate contributions to sum and add up
do in=1, CP%InitPower%nn
call InterpolateClArr(lSamp,iContribs(1,in,CT_Temp),intcontrib,max_j_contribs)
asum(in) = sum(intcontrib(lmin:lSamp%l(max_j_contribs)))
if (DoPol) then
call InterpolateClArr(lSamp,iContribs(1,in,CT_E),intcontrib,max_j_contribs)
asum_EE(in) = sum(intcontrib(lmin:lSamp%l(max_j_contribs)))
call InterpolateClArr(lSamp,iContribs(1,in,CT_B),intcontrib,max_j_contribs)
asum_BB(in) = sum(intcontrib(lmin:lSamp%l(max_j_contribs)))
call InterpolateClArr(lSamp,iContribs(1,in,CT_Cross),intcontrib,max_j_contribs)
asum_TE(in) = sum(intcontrib(lmin:lSamp%l(max_j_contribs)))
end if
end do
iCl_lensed(j,:,CT_Temp) = ((1-al*(al+1)*RR)*bare_cls(:,al,CT_Temp) & !Linear part
+ asum/(2*al+1))*llp_al/OutputDenominator !add quadratic part and *l(l+1)/2pi
if (DoPol) then
iCl_lensed(j,:,CT_E) = ((1-(al**2+al-4)*RR)*bare_cls(:,al,CT_E) &
+ asum_EE/(2*al+1))*llp_al/OutputDenominator
iCl_lensed(j,:,CT_B) = ((1-(al**2+al-4)*RR)*bare_cls(:,al,CT_B) &
+ asum_BB/(2*al+1))*llp_al/OutputDenominator
iCl_lensed(j,:,CT_Cross) = ((1-(al**2+al-2)*RR)*bare_cls(:,al,CT_Cross) &
+ asum_TE/(2*al+1))*llp_al/OutputDenominator
else
iCl_lensed(j,:,CT_E:CT_Cross) = bare_cls(:,al,CT_E:CT_Cross)
end if
end do
!$OMP END PARALLEL DO
deallocate(bare_cls)
allocate(Cl_lensed(lmin:lmax_lensed,CP%InitPower%nn,1:4))
!Interpolate to get final spectrum
do in=1, CP%InitPower%nn
do j = CT_Temp, CT_Cross
call InterpolateClArr(lSamp,iCl_lensed(1,in,j),Cl_lensed(lmin, in, j),max_lensed_ix)
end do
end do
deallocate(iCl_lensed)
if (DebugMsgs) then
if (FeedbackLevel>0) write(*,*) GetTestTime()-timeprev,' Timing for lensing'
end if
end subroutine BadHarmonic
subroutine GetBessels(MaxArg)
real(dl), intent(in):: MaxArg
integer i
real(dl), allocatable, dimension(:) :: x
integer max_bes_ix
integer, save :: last_max = 0
max_bes_ix = nint(MaxArg / dbessel) + 3
if (max_bes_ix > last_max) then
last_max = max_bes_ix
if (allocated(Bess0)) then
deallocate(Bess0,ddBess0)
deallocate(Bess2,ddBess2)
deallocate(Bess4,ddBess4)
deallocate(Bess6,ddBess6)
end if
allocate(Bess0(max_bes_ix),ddBess0(max_bes_ix))
allocate(Bess2(max_bes_ix),ddBess2(max_bes_ix))
allocate(Bess4(max_bes_ix),ddBess4(max_bes_ix))
allocate(Bess6(max_bes_ix),ddBess6(max_bes_ix))
allocate(x(max_bes_ix))
Bess0(1)=1
Bess2(1)=0; Bess4(1)=0; Bess6(1)=0
x(1)=0
do i=2, max_bes_ix
x(i) = (i-1)*dbessel
Bess0(i) = Bessj0(x(i))
Bess2(i) = Bessj(2,x(i))
Bess4(i) = Bessj(4,x(i))
Bess6(i) = Bessj(6,x(i))
end do
call spline(x,Bess0,max_bes_ix,spl_large,spl_large,ddBess0)
call spline(x,Bess2,max_bes_ix,spl_large,spl_large,ddBess2)
call spline(x,Bess4,max_bes_ix,spl_large,spl_large,ddBess4)
call spline(x,Bess6,max_bes_ix,spl_large,spl_large,ddBess6)
deallocate(x)
end if
end subroutine GetBessels
!Wrap standard built-in F2008 funcitons (appear OK for ifort and gfortran)
FUNCTION bessj0(x)
real(dl) bessj0,x
bessj0 = bessel_j0(x)
END FUNCTION bessj0
FUNCTION bessj(n,x)
real(dl) bessj,x
integer n
bessj = bessel_jn(n,x)
END FUNCTION bessj
! ----------------------------------------------------------------------
! Auxiliary Bessel functions for N=0, N=1
FUNCTION BESSI0(X)