forked from QcmPlab/CDMFT-LANC-ED
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathED_SETUP.f90
1098 lines (965 loc) · 33.6 KB
/
ED_SETUP.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
!|imp_up>|bath_up> * |imp_dw>|bath_dw>
!
!|imp_sigma>=
!| (1..Norb)_1 ... (1..Norb)_Nlat; <-- Nlat*Norb == stride, indices here: imp_state_index
! [(1..Norb)_1 ... (1..Norb)_Nlat]_1 <-- Nlat*Norb + Nlat*Norb, " " : imp_state_index
! ...
! [(1..Norb)_1 ... (1..Norb)_Nlat]_Nbath>; <-- Nbath*Norb*Nlat
!
!
MODULE ED_SETUP
USE ED_INPUT_VARS
USE ED_VARS_GLOBAL
USE ED_AUX_FUNX
USE SF_TIMER
USE SF_IOTOOLS, only:free_unit,reg,file_length
#ifdef _MPI
USE MPI
USE SF_MPI
#endif
implicit none
private
public :: init_ed_structure
public :: setup_global
!
public :: build_sector
public :: delete_sector
!
public :: get_Sector
public :: get_Indices
public :: get_Nup
public :: get_Ndw
public :: get_DimUp
public :: get_DimDw
!
public :: indices2state
public :: state2indices
public :: iup_index
public :: idw_index
!
public :: bdecomp
public :: breorder
public :: bjoin
!
public :: c,cdg
!
public :: twin_sector_order
public :: get_twin_sector
public :: flip_state
!
public :: imp_state_index
!
public :: binary_search
#ifdef _MPI
public :: scatter_vector_MPI
public :: scatter_basis_MPI
public :: gather_vector_MPI
public :: allgather_vector_MPI
#endif
contains
subroutine ed_checks_global
!
if(Lfit>Lmats)Lfit=Lmats
if(Nspin>2)stop "ED ERROR: Nspin > 2 is currently not supported"
if(Norb>5)stop "ED ERROR: Norb > 5 is currently not supported"
!
if(Nspin>1.AND.ed_twin.eqv..true.)then
write(LOGfile,"(A)")"WARNING: using twin_sector with Nspin>1"
call sleep(1)
end if
!
if(lanc_method=="lanczos")then
if(lanc_nstates_total>1)stop "ED ERROR: lanc_method==lanczos available only for lanc_nstates_total==1, T=0"
if(lanc_nstates_sector>1)stop "ED ERROR: lanc_method==lanczos available only for lanc_nstates_sector==1, T=0"
endif
!
end subroutine ed_checks_global
!+------------------------------------------------------------------+
!PURPOSE : Setup Dimensions of the problem
! Norb = # of impurity orbitals
! Nbath = # of bath levels (depending on bath_type)
! Ns = # of levels (per spin)
! Nlevels = 2*Ns = Total # of levels (counting spin degeneracy 2)
!+------------------------------------------------------------------+
subroutine ed_setup_dimensions()
!
Ns = Nlat*Norb*(Nbath+1)
!
Ns_Orb = Ns
Ns_Ud = 1
!
Nsectors = ((Ns_Orb+1)*(Ns_Orb+1))**Ns_Ud
end subroutine ed_setup_dimensions
!+------------------------------------------------------------------+
!PURPOSE : Init ED structure and calculation
!+------------------------------------------------------------------+
subroutine init_ed_structure()
logical :: control
integer :: i,iud,iorb,jorb,ispin,jspin
integer,dimension(:),allocatable :: DimUps,DimDws
!
call ed_checks_global
!
call ed_setup_dimensions
!
!
allocate(DimUps(Ns_Ud))
allocate(DimDws(Ns_Ud))
do iud=1,Ns_Ud
DimUps(iud) = get_sector_dimension(Ns_Orb,Ns_Orb/2)
DimDws(iud) = get_sector_dimension(Ns_Orb,Ns_Orb-Ns_Orb/2)
enddo
if(MpiMaster)then
write(LOGfile,"(A)")"Summary:"
write(LOGfile,"(A)")"--------------------------------------------"
write(LOGfile,"(A,I15)")'# of levels/spin = ',Ns
write(LOGfile,"(A,I15)")'Total size = ',2*Ns
write(LOGfile,"(A,I15)")'# of sites = ',Nlat
write(LOGfile,"(A,I15)")'# of impurities = ',Norb
write(LOGfile,"(A,I15)")'# of bath/impurity = ',Nbath
write(LOGfile,"(A,I15)")'Number of sectors = ',Nsectors
write(LOGfile,"(A,"//str(Ns_Ud)//"I8,2X,"//str(Ns_Ud)//"I8,I20)")&
'Largest Sector(s) = ',DimUps,DimDws,product(DimUps)*product(DimDws)
write(LOGfile,"(A)")"--------------------------------------------"
endif
call sleep(1)
!
!
allocate(spH0ups(Ns_Ud))
allocate(spH0dws(Ns_Ud))
!
!Allocate indexing arrays
allocate(getCsector(Ns_Ud,2,Nsectors)) ;getCsector =0
allocate(getCDGsector(Ns_Ud,2,Nsectors));getCDGsector=0
!
allocate(getDim(Nsectors));getDim=0
!
allocate(getBathStride(Nlat,Norb,Nbath));getBathStride=0
allocate(twin_mask(Nsectors))
allocate(sectors_mask(Nsectors))
allocate(neigen_sector(Nsectors))
!
!check finiteT
finiteT=.true. !assume doing finite T per default
if(lanc_nstates_total==1)then !is you only want to keep 1 state
finiteT=.false. !set to do zero temperature calculations
write(LOGfile,"(A)")"Required Lanc_nstates_total=1 => set T=0 calculation"
endif
!
!check whether lanc_nstates_sector and lanc_states are even (we do want to keep doublet among states)
if(finiteT)then
if(mod(lanc_nstates_sector,2)/=0)then
lanc_nstates_sector=lanc_nstates_sector+1
write(LOGfile,"(A,I10)")"Increased Lanc_nstates_sector:",lanc_nstates_sector
endif
if(mod(lanc_nstates_total,2)/=0)then
lanc_nstates_total=lanc_nstates_total+1
write(LOGfile,"(A,I10)")"Increased Lanc_nstates_total:",lanc_nstates_total
endif
write(LOGfile,"(A)")"Lanczos FINITE temperature calculation:"
!
write(LOGfile,"(A,I3)")"Nstates x Sector = ", lanc_nstates_sector
write(LOGfile,"(A,I3)")"Nstates Total = ", lanc_nstates_total
call sleep(1)
else
write(LOGfile,"(A)")"Lanczos ZERO temperature calculation:"
call sleep(1)
endif
!
Jhflag=.FALSE.
if(Norb>1.AND.(Jx/=0d0.OR.Jp/=0d0))Jhflag=.TRUE.
!
!
offdiag_gf_flag=.true.
!
if(nread/=0.d0)then
i=abs(floor(log10(abs(nerr)))) !modulus of the order of magnitude of nerror
niter=nloop/3
endif
!
!
!allocate functions
!allocate functions
allocate(impSmats(Nlat,Nlat,Nspin,Nspin,Norb,Norb,Lmats))
allocate(impSreal(Nlat,Nlat,Nspin,Nspin,Norb,Norb,Lreal))
impSmats=zero
impSreal=zero
!
allocate(impGmats(Nlat,Nlat,Nspin,Nspin,Norb,Norb,Lmats))
allocate(impGreal(Nlat,Nlat,Nspin,Nspin,Norb,Norb,Lreal))
impGmats=zero
impGreal=zero
!
!allocate functions
allocate(impG0mats(Nlat,Nlat,Nspin,Nspin,Norb,Norb,Lmats))
allocate(impG0real(Nlat,Nlat,Nspin,Nspin,Norb,Norb,Lreal))
impG0mats=zero
impG0real=zero
!
!allocate observables
allocate(ed_dens(Nlat,Norb),ed_docc(Nlat,Norb),ed_dens_up(Nlat,Norb),ed_dens_dw(Nlat,Norb))
ed_dens=0d0
ed_docc=0d0
ed_dens_up=0d0
ed_dens_dw=0d0
!
! if(chiflag)then
! allocate(spinChi_tau(Norb+1,0:Ltau))
! allocate(spinChi_w(Norb+1,Lreal))
! allocate(spinChi_iv(Norb+1,0:Lmats))
! !
! ! allocate(densChi_tau(Norb,Norb,0:Ltau))
! ! allocate(densChi_w(Norb,Norb,Lreal))
! ! allocate(densChi_iv(Norb,Norb,0:Lmats))
! ! allocate(densChi_mix_tau(Norb,Norb,0:Ltau))
! ! allocate(densChi_mix_w(Norb,Norb,Lreal))
! ! allocate(densChi_mix_iv(Norb,Norb,0:Lmats))
! ! allocate(densChi_tot_tau(0:Ltau))
! ! allocate(densChi_tot_w(Lreal))
! ! allocate(densChi_tot_iv(0:Lmats))
! ! !
! ! allocate(pairChi_tau(Norb,0:Ltau))
! ! allocate(pairChi_w(Norb,Lreal))
! ! allocate(pairChi_iv(Norb,0:Lmats))
! endif
!
end subroutine init_ed_structure
!+------------------------------------------------------------------+
!PURPOSE: SETUP THE GLOBAL POINTERS FOR THE ED CALCULAIONS.
!+------------------------------------------------------------------+
subroutine setup_global
integer :: DimUp,DimDw
integer :: DimUps(Ns_Ud),DimDws(Ns_Ud)
integer :: Indices(2*Ns_Ud),Jndices(2*Ns_Ud)
integer :: Nups(Ns_ud),Ndws(Ns_ud)
integer :: Jups(Ns_ud),Jdws(Ns_ud)
integer :: i,iud,iorb,ilat,stride,ibath
integer :: isector,jsector
integer :: unit,status,istate,ishift,isign
logical :: IOfile
integer :: list_len
integer,dimension(:),allocatable :: list_sector
!
!Store full dimension of the sectors:
do isector=1,Nsectors
call get_DimUp(isector,DimUps)
call get_DimDw(isector,DimDws)
DimUp = product(DimUps)
DimDw = product(DimDws)
getDim(isector) = DimUp*DimDw
enddo
!
!
inquire(file="state_list"//reg(ed_file_suffix)//".restart",exist=IOfile)
if(IOfile)then
write(LOGfile,"(A)")"Restarting from a state_list file:"
list_len=file_length("state_list"//reg(ed_file_suffix)//".restart")
allocate(list_sector(list_len))
!
open(free_unit(unit),file="state_list"//reg(ed_file_suffix)//".restart",status="old")
status=0
do while(status>=0)
read(unit,*,iostat=status)istate,isector,indices
list_sector(istate)=isector
call get_Nup(isector,Nups)
call get_Ndw(isector,Ndws)
if(any(Indices /= [Nups,Ndws]))&
stop "setup_global error: nups!=nups(isector).OR.ndws!=ndws(isector)"
enddo
close(unit)
!
lanc_nstates_total = list_len
do isector=1,Nsectors
neigen_sector(isector) = max(1,count(list_sector==isector))
enddo
else
do isector=1,Nsectors
neigen_sector(isector) = min(getDim(isector),lanc_nstates_sector) !init every sector to required eigenstates
enddo
endif
!
twin_mask=.true.
if(ed_twin)then
do isector=1,Nsectors
call get_Nup(isector,Nups)
call get_Ndw(isector,Ndws)
if(any(Nups < Ndws))twin_mask(isector)=.false.
enddo
write(LOGfile,"(A,I6,A,I9)")"Looking into ",count(twin_mask)," sectors out of ",Nsectors
call sleep(1)
endif
!
stride=Nlat*Norb
do ibath=1,Nbath
do ilat=1,Nlat
do iorb=1,Norb
getBathStride(ilat,iorb,ibath) = stride + imp_state_index(ilat,iorb) + (ibath-1)*Nlat*Norb
! getBathStride(ilat,iorb,ibath) = stride + iorb + (ilat-1)*Norb + (ibath-1)*Nlat*Norb
enddo
enddo
enddo
!
getCsector = 0
getCDGsector= 0
do isector=1,Nsectors
call get_Nup(isector,Nups)
call get_Ndw(isector,Ndws)
!
!UPs:
!DEL:
do iud=1,Ns_Ud
Jups=Nups
Jdws=Ndws
Jups(iud)=Jups(iud)-1; if(Jups(iud) < 0)cycle
call get_Sector([Jups,Jdws],Ns_Orb,jsector)
getCsector(iud,1,isector)=jsector
enddo
!ADD
do iud=1,Ns_Ud
Jups=Nups
Jdws=Ndws
Jups(iud)=Jups(iud)+1; if(Jups(iud) > Ns_Orb)cycle
call get_Sector([Jups,Jdws],Ns_Orb,jsector)
getCDGsector(iud,1,isector)=jsector
enddo
!
!DWs:
!DEL
do iud=1,Ns_Ud
Jups=Nups
Jdws=Ndws
Jdws(iud)=Jdws(iud)-1; if(Jdws(iud) < 0)cycle
call get_Sector([Jups,Jdws],Ns_Orb,jsector)
getCsector(iud,2,isector)=jsector
enddo
!DEL
do iud=1,Ns_Ud
Jups=Nups
Jdws=Ndws
Jdws(iud)=Jdws(iud)+1; if(Jdws(iud) > Ns_Orb)cycle
call get_Sector([Jups,Jdws],Ns_Orb,jsector)
getCDGsector(iud,2,isector)=jsector
enddo
enddo
return
end subroutine setup_global
!##################################################################
!##################################################################
!AUXILIARY PROCEDURES - Sectors,Nup,Ndw,DimUp,DimDw,...
!##################################################################
!##################################################################
elemental function get_sector_dimension(n,np) result(dim)
integer,intent(in) :: n,np
integer :: dim
dim = binomial(n,np)
end function get_sector_dimension
subroutine get_Sector(indices,N,isector)
integer,dimension(:) :: indices
integer :: N
integer :: isector
integer :: i,Nind,factor
Nind = size(indices)
Factor = N+1
isector = 1
do i=Nind,1,-1
isector = isector + indices(i)*(Factor)**(Nind-i)
enddo
end subroutine get_Sector
subroutine get_Indices(isector,N,indices)
integer :: isector,N
integer,dimension(:) :: indices
integer :: i,count,Dim
integer,dimension(size(indices)) :: indices_
!
Dim = size(indices)
if(mod(Dim,2)/=0)stop "get_Indices_main error: Dim%2 != 0"
count=isector-1
do i=1,Dim
indices_(i) = mod(count,N+1)
count = count/(N+1)
enddo
indices = indices_(Dim:1:-1)
end subroutine get_Indices
subroutine get_Nup(isector,Nup)
integer :: isector,Nup(Ns_Ud)
integer :: i,count
integer,dimension(2*Ns_Ud) :: indices_
count=isector-1
do i=1,2*Ns_Ud
indices_(i) = mod(count,Ns_Orb+1)
count = count/(Ns_Orb+1)
enddo
Nup = indices_(2*Ns_Ud:Ns_Ud+1:-1)
end subroutine get_Nup
subroutine get_Ndw(isector,Ndw)
integer :: isector,Ndw(Ns_Ud)
integer :: i,count
integer,dimension(2*Ns_Ud) :: indices_
count=isector-1
do i=1,2*Ns_Ud
indices_(i) = mod(count,Ns_Orb+1)
count = count/(Ns_Orb+1)
enddo
Ndw = indices_(Ns_Ud:1:-1)
end subroutine get_Ndw
subroutine get_DimUp(isector,DimUps)
integer :: isector,DimUps(Ns_Ud)
integer :: Nups(Ns_Ud),iud
call get_Nup(isector,Nups)
do iud=1,Ns_Ud
DimUps(iud) = binomial(Ns_Orb,Nups(iud))
enddo
end subroutine get_DimUp
subroutine get_DimDw(isector,DimDws)
integer :: isector,DimDws(Ns_Ud)
integer :: Ndws(Ns_Ud),iud
call get_Ndw(isector,Ndws)
do iud=1,Ns_Ud
DimDws(iud) = binomial(Ns_Orb,Ndws(iud))
enddo
end subroutine get_DimDw
subroutine indices2state(ivec,Nvec,istate)
integer,dimension(:) :: ivec
integer,dimension(size(ivec)) :: Nvec
integer :: istate,i
istate=ivec(1)
do i=2,size(ivec)
istate = istate + (ivec(i)-1)*product(Nvec(1:i-1))
enddo
end subroutine indices2state
subroutine state2indices(istate,Nvec,ivec)
integer :: istate
integer,dimension(:) :: Nvec
integer,dimension(size(Nvec)) :: Ivec
integer :: i,count,N
count = istate-1
N = size(Nvec)
do i=1,N
Ivec(i) = mod(count,Nvec(i))+1
count = count/Nvec(i)
enddo
end subroutine state2indices
function iup_index(i,DimUp) result(iup)
integer :: i
integer :: DimUp
integer :: iup
iup = mod(i,DimUp);if(iup==0)iup=DimUp
end function iup_index
function idw_index(i,DimUp) result(idw)
integer :: i
integer :: DimUp
integer :: idw
idw = (i-1)/DimUp+1
end function idw_index
!> Find position in the state vector for a given lattice-spin-orbital position for the cluster (no bath considered)
function imp_state_index(ilat,iorb) result(indx)
integer :: ilat
integer :: iorb
integer :: indx
indx = iorb + (ilat-1)*Norb
end function imp_state_index
#ifdef _MPI
!! Scatter V into the arrays Vloc on each thread: sum_threads(size(Vloc)) must be equal to size(v)
subroutine scatter_vector_MPI(MpiComm,v,vloc)
integer :: MpiComm
complex(8),dimension(:) :: v !size[N]
complex(8),dimension(:) :: vloc !size[Nloc]
integer :: i,irank,Nloc,N
integer,dimension(:),allocatable :: Counts,Offset
integer :: MpiSize,MpiIerr
logical :: MpiMaster
!
if( MpiComm == MPI_UNDEFINED .OR. MpiComm == Mpi_Comm_Null )return
! stop "scatter_vector_MPI error: MpiComm == MPI_UNDEFINED"
!
MpiSize = get_size_MPI(MpiComm)
MpiMaster = get_master_MPI(MpiComm)
!
Nloc = size(Vloc)
N = 0
call AllReduce_MPI(MpiComm,Nloc,N)
if(MpiMaster.AND.N /= size(V)) stop "scatter_vector_MPI error: size(V) != Mpi_Allreduce(Nloc)"
!
allocate(Counts(0:MpiSize-1)) ; Counts=0
allocate(Offset(0:MpiSize-1)) ; Offset=0
!
!Get Counts;
call MPI_AllGather(Nloc,1,MPI_INTEGER,Counts,1,MPI_INTEGER,MpiComm,MpiIerr)
!
!Get Offset:
Offset(0)=0
do i=1,MpiSize-1
Offset(i) = Offset(i-1) + Counts(i-1)
enddo
!
Vloc=0
call MPI_Scatterv(V,Counts,Offset,MPI_DOUBLE_COMPLEX,Vloc,Nloc,MPI_DOUBLE_COMPLEX,0,MpiComm,MpiIerr)
!
return
end subroutine scatter_vector_MPI
subroutine scatter_basis_MPI(MpiComm,v,vloc)
integer :: MpiComm
complex(8),dimension(:,:) :: v !size[N,N]
complex(8),dimension(:,:) :: vloc !size[Nloc,Neigen]
integer :: N,Nloc,Neigen,i
N = size(v,1)
Nloc = size(vloc,1)
Neigen = size(vloc,2)
if( size(v,2) < Neigen ) stop "error scatter_basis_MPI: size(v,2) < Neigen"
!
do i=1,Neigen
call scatter_vector_MPI(MpiComm,v(:,i),vloc(:,i))
end do
!
return
end subroutine scatter_basis_MPI
!! AllGather Vloc on each thread into the array V: sum_threads(size(Vloc)) must be equal to size(v)
subroutine gather_vector_MPI(MpiComm,vloc,v)
integer :: MpiComm
complex(8),dimension(:) :: vloc !size[Nloc]
complex(8),dimension(:) :: v !size[N]
integer :: i,irank,Nloc,N
integer,dimension(:),allocatable :: Counts,Offset
integer :: MpiSize,MpiIerr
logical :: MpiMaster
!
if( MpiComm == MPI_UNDEFINED .OR. MpiComm == Mpi_Comm_Null ) return
!stop "gather_vector_MPI error: MpiComm == MPI_UNDEFINED"
!
MpiSize = get_size_MPI(MpiComm)
MpiMaster = get_master_MPI(MpiComm)
!
Nloc = size(Vloc)
N = 0
call AllReduce_MPI(MpiComm,Nloc,N)
if(MpiMaster.AND.N /= size(V)) stop "gather_vector_MPI error: size(V) != Mpi_Allreduce(Nloc)"
!
allocate(Counts(0:MpiSize-1)) ; Counts=0
allocate(Offset(0:MpiSize-1)) ; Offset=0
!
!Get Counts;
call MPI_AllGather(Nloc,1,MPI_INTEGER,Counts,1,MPI_INTEGER,MpiComm,MpiIerr)
!
!Get Offset:
Offset(0)=0
do i=1,MpiSize-1
Offset(i) = Offset(i-1) + Counts(i-1)
enddo
!
call MPI_Gatherv(Vloc,Nloc,MPI_DOUBLE_COMPLEX,V,Counts,Offset,MPI_DOUBLE_COMPLEX,0,MpiComm,MpiIerr)
!
return
end subroutine gather_vector_MPI
!! AllGather Vloc on each thread into the array V: sum_threads(size(Vloc)) must be equal to size(v)
subroutine allgather_vector_MPI(MpiComm,vloc,v)
integer :: MpiComm
complex(8),dimension(:) :: vloc !size[Nloc]
complex(8),dimension(:) :: v !size[N]
integer :: i,irank,Nloc,N
integer,dimension(:),allocatable :: Counts,Offset
integer :: MpiSize,MpiIerr
logical :: MpiMaster
!
if( MpiComm == MPI_UNDEFINED .OR. MpiComm == Mpi_Comm_Null ) return
! stop "gather_vector_MPI error: MpiComm == MPI_UNDEFINED"
!
MpiSize = get_size_MPI(MpiComm)
MpiMaster = get_master_MPI(MpiComm)
!
Nloc = size(Vloc)
N = 0
call AllReduce_MPI(MpiComm,Nloc,N)
if(MpiMaster.AND.N /= size(V)) stop "allgather_vector_MPI error: size(V) != Mpi_Allreduce(Nloc)"
!
allocate(Counts(0:MpiSize-1)) ; Counts=0
allocate(Offset(0:MpiSize-1)) ; Offset=0
!
!Get Counts;
call MPI_AllGather(Nloc,1,MPI_INTEGER,Counts,1,MPI_INTEGER,MpiComm,MpiIerr)
!
!Get Offset:
Offset(0)=0
do i=1,MpiSize-1
Offset(i) = Offset(i-1) + Counts(i-1)
enddo
!
V = 0d0
call MPI_AllGatherv(Vloc,Nloc,MPI_DOUBLE_COMPLEX,V,Counts,Offset,MPI_DOUBLE_COMPLEX,MpiComm,MpiIerr)
!
return
end subroutine Allgather_vector_MPI
#endif
!##################################################################
!##################################################################
!BUILD SECTORS
!##################################################################
!##################################################################
subroutine build_sector(isector,H)
integer :: isector
type(sector_map),dimension(2*Ns_Ud) :: H
integer,dimension(Ns_Ud) :: Nups,Ndws
integer,dimension(Ns_Ud) :: DimUps,DimDws
integer :: iup,idw
integer :: nup_,ndw_
integer :: dim,iud
!
!
call get_Nup(isector,Nups)
call get_Ndw(isector,Ndws)
call get_DimUp(isector,DimUps)
call get_DimDw(isector,DimDws)
!
call map_allocate(H,[DimUps,DimDws])
do iud=1,Ns_Ud
!UP
dim=0
do iup=0,2**Ns_Orb-1
nup_ = popcnt(iup)
if(nup_ /= Nups(iud))cycle
dim = dim+1
H(iud)%map(dim) = iup
enddo
!DW
dim=0
do idw=0,2**Ns_Orb-1
ndw_= popcnt(idw)
if(ndw_ /= Ndws(iud))cycle
dim = dim+1
H(iud+Ns_Ud)%map(dim) = idw
enddo
enddo
!
end subroutine build_sector
subroutine delete_sector(isector,H)
integer :: isector
type(sector_map) :: H(:)
call map_deallocate(H)
end subroutine delete_sector
!##################################################################
!##################################################################
!CREATION / DESTRUCTION OPERATORS
!##################################################################
!##################################################################
!+-------------------------------------------------------------------+
!PURPOSE: input state |in> of the basis and calculates
! |out>=C_pos|in> OR |out>=C^+_pos|in> ;
! the sign of |out> has the phase convention, pos labels the sites
!+-------------------------------------------------------------------+
subroutine c(pos,in,out,fsgn)
integer,intent(in) :: pos
integer,intent(in) :: in
integer,intent(inout) :: out
real(8),intent(inout) :: fsgn
integer :: l
if(.not.btest(in,pos-1))stop "C error: C_i|...0_i...>"
fsgn=1d0
do l=1,pos-1
if(btest(in,l-1))fsgn=-fsgn
enddo
out = ibclr(in,pos-1)
end subroutine c
subroutine cdg(pos,in,out,fsgn)
integer,intent(in) :: pos
integer,intent(in) :: in
integer,intent(inout) :: out
real(8),intent(inout) :: fsgn
integer :: l
if(btest(in,pos-1))stop "C^+ error: C^+_i|...1_i...>"
fsgn=1d0
do l=1,pos-1
if(btest(in,l-1))fsgn=-fsgn
enddo
out = ibset(in,pos-1)
end subroutine cdg
!##################################################################
!##################################################################
!TWIN SECTORS ROUTINES:
!##################################################################
!##################################################################
!+------------------------------------------------------------------+
!PURPOSE : Build the re-ordering map to go from sector A(nup,ndw)
! to its twin sector B(ndw,nup), with nup!=ndw.
!
!- build the map from the A-sector to \HHH
!- get the list of states in \HHH corresponding to sector B twin of A
!- return the ordering of B-states in \HHH with respect to those of A
!+------------------------------------------------------------------+
subroutine twin_sector_order(isector,order)
integer :: isector
integer,dimension(:) :: order
type(sector_map),dimension(2*Ns_Ud) :: H
integer,dimension(2*Ns_Ud) :: Indices,Istates
integer,dimension(Ns_Ud) :: DimUps,DimDws
integer :: Dim
integer :: i,iud
!
Dim = GetDim(isector)
if(size(Order)/=Dim)stop "twin_sector_order error: wrong dimensions of *order* array"
call get_DimUp(isector,DimUps)
call get_DimDw(isector,DimDws)
!
call build_sector(isector,H)
do i=1,Dim
call state2indices(i,[DimUps,DimDws],Indices)
forall(iud=1:2*Ns_Ud)Istates(iud) = H(iud)%map(Indices(iud))
Order(i) = flip_state( Istates )
enddo
call delete_sector(isector,H)
!
call sort_array(Order)
!
end subroutine twin_sector_order
!+------------------------------------------------------------------+
!PURPOSE : Flip an Hilbert space state m=|{up}>|{dw}> into:
!
! normal: j=|{dw}>|{up}> , nup --> ndw
!+------------------------------------------------------------------+
function flip_state(istate) result(j)
integer,dimension(2*Ns_Ud) :: istate
integer :: j
integer,dimension(Ns_Ud) :: jups,jdws
integer,dimension(2*Ns_Ud) :: dims
!
jups = istate(Ns_Ud+1:2*Ns_Ud)
jdws = istate(1:Ns_Ud)
dims = 2**Ns_Orb
call indices2state([jups,jdws],Dims,j)
!
end function flip_state
!+------------------------------------------------------------------+
!PURPOSE : get the twin of a given sector (the one with opposite
! quantum numbers):
! nup,ndw ==> ndw,nup (spin-exchange)
!+------------------------------------------------------------------+
function get_twin_sector(isector) result(jsector)
integer,intent(in) :: isector
integer :: jsector
integer,dimension(Ns_Ud) :: Iups,Idws
call get_Nup(isector,iups)
call get_Ndw(isector,idws)
call get_Sector([idws,iups],Ns_Orb,jsector)
end function get_twin_sector
!##################################################################
!##################################################################
!AUXILIARY COMPUTATIONAL ROUTINES ARE HERE BELOW:
!##################################################################
!##################################################################
!+------------------------------------------------------------------+
!PURPOSE : input a state |i> and output a vector ivec(Nlevels)
!with its binary decomposition
!(corresponds to the decomposition of the number i-1)
!+------------------------------------------------------------------+
function bdecomp(i,Ntot) result(ivec)
integer :: Ntot,ivec(Ntot),l,i
logical :: busy
!this is the configuration vector |1,..,Ns,Ns+1,...,Ntot>
!obtained from binary decomposition of the state/number i\in 2^Ntot
do l=0,Ntot-1
busy=btest(i,l)
ivec(l+1)=0
if(busy)ivec(l+1)=1
enddo
end function bdecomp
!+------------------------------------------------------------------+
! Reorder a binary decomposition so to have a state of the form:
! default: |(1:Norb),([1:Nbath]_1, [1:Nbath]_2, ... ,[1:Nbath]_Norb)>_spin
! hybrid: |(1:Norb),([1:Nbath])_spin
! replica: |(1:Norb),([1:Norb]_1, [1:Norb]_2, ... , [1:Norb]_Nbath)>_spin
!
!> case (ed_total_ud):
! (T): Ns_Ud=1, Ns_Orb=Ns.
! bdecomp is already of the form above [1:Ns]
! (F): Ns_Ud=Norb, Ns_Orb=Ns/Norb==1+Nbath
! bdecomp is
! |( [1:1+Nbath]_1,...,[1:1+Nbath]_Norb)>_spin
!+------------------------------------------------------------------+
function breorder(Nins) result(Ivec)
integer,intent(in),dimension(Ns_Ud,Ns_Orb) :: Nins ![1,Ns] - [Norb,1+Nbath]
integer,dimension(Ns) :: Ivec ![Ns]
integer :: iud,ibath,indx
! select case (ed_total_ud)
! case (.true.)
Ivec = Nins(1,:)
! case (.false.)
! do iud=1,Ns_Ud ![1:Norb]
! Ivec(iud) = Nins(iud,1)
! do ibath=1,Nbath
! indx = getBathStride(iud,ibath) !take care of normal/
! Ivec(indx) = Nins(iud,1+ibath)
! enddo
! enddo
! end select
end function breorder
!+------------------------------------------------------------------+
!PURPOSE : input a vector ib(Nlevels) with the binary sequence
! and output the corresponding state |i>
!(corresponds to the recomposition of the number i-1)
!+------------------------------------------------------------------+
function bjoin(ib,Ntot) result(i)
integer :: Ntot
integer,dimension(Ntot) :: ib
integer :: i,j
i=0
do j=0,Ntot-1
i=i+ib(j+1)*2**j
enddo
end function bjoin
!+------------------------------------------------------------------+
!PURPOSE : calculate the factorial of an integer N!=1.2.3...(N-1).N
!+------------------------------------------------------------------+
recursive function factorial(n) result(f)
integer :: f
integer,intent(in) :: n
if(n<=0)then
f=1
else
f=n*factorial(n-1)
end if
end function factorial
!+------------------------------------------------------------------+
!PURPOSE : calculate the binomial factor n1 over n2
!+------------------------------------------------------------------+
elemental function binomial(n1,n2) result(nchoos)
integer,intent(in) :: n1,n2
real(8) :: xh
integer :: i
integer nchoos
xh = 1.d0
if(n2<0) then
nchoos = 0
return
endif
if(n2==0) then
nchoos = 1
return
endif
do i = 1,n2
xh = xh*dble(n1+1-i)/dble(i)
enddo
nchoos = int(xh + 0.5d0)
end function binomial
!+------------------------------------------------------------------+
!PURPOSE : binary search of a value in an array
!+------------------------------------------------------------------+
recursive function binary_search(a,value) result(bsresult)
integer,intent(in) :: a(:), value
integer :: bsresult, mid
mid = size(a)/2 + 1
if (size(a) == 0) then
bsresult = 0 ! not found
!stop "binary_search error: value not found"
else if (a(mid) > value) then
bsresult= binary_search(a(:mid-1), value)
else if (a(mid) < value) then
bsresult = binary_search(a(mid+1:), value)
if (bsresult /= 0) then
bsresult = mid + bsresult
end if
else
bsresult = mid ! SUCCESS!!
end if
end function binary_search
!+------------------------------------------------------------------+
!PURPOSE : sort array of integer using random algorithm
!+------------------------------------------------------------------+
subroutine sort_array(array)
integer,dimension(:),intent(inout) :: array
integer,dimension(size(array)) :: order
integer :: i
forall(i=1:size(array))order(i)=i
call qsort_sort( array, order, 1, size(array) )
array=order
contains
recursive subroutine qsort_sort( array, order, left, right )
integer, dimension(:) :: array
integer, dimension(:) :: order
integer :: left
integer :: right
integer :: i
integer :: last
if ( left .ge. right ) return
call qsort_swap( order, left, qsort_rand(left,right) )
last = left
do i = left+1, right
if ( compare(array(order(i)), array(order(left)) ) .lt. 0 ) then
last = last + 1