-
Notifications
You must be signed in to change notification settings - Fork 5
/
mo_histo.f90
920 lines (770 loc) · 34.2 KB
/
mo_histo.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
MODULE mo_histo
! This module calculates the Histogram of data
! and is part of the JAMS Fortran library.
!
! Written Juliane Mai, Feb 2012
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2012 Juliane Mai
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in all
! copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
! SOFTWARE.
USE mo_kind, ONLY: i4, sp, dp
IMPLICIT NONE
#ifndef __ABSOFT__
PUBLIC :: histo ! Histogram of 1D data
PUBLIC :: histo2d ! Histogram of 2D data
! ------------------------------------------------------------------
! NAME
! histo
! PURPOSE
! Calculates the histogram of n data 1D points (Xi),i=1,n ,
! i.e. the n data points are sorted into k categories (bins).
! In case of multidimensional data points (Xij),j=1,n ,
! only the first coordinate (X1j) is taken for determination of the category,
! while the other coordinates are averged per bin.
!
! With no optional arguments the number of bins k is the integer part of Sqrt(n)
! where n is the number of data points. E.g. n=15 will create k=3 bins.
! The bin width w is calculated depending on the minimal and maximal value of
! the first coordinate):
! w = (maxval(X) - minval(X)) / k
!
! Optionally, one can fix the number of bins k (integer i4)
! while the width of the bins is determined.
! Or, on can fix the binwidth w (float sp/dp) while k is determined automatically.
! If an optional mask is given, the histogram is taken into account only data points (Xij)
! which have a true value in the mask.
! (Xij) can be single or double precision. The result will have the same numerical precision.
! CALLING SEQUENCE
! call hist(x, binx, bincount, width) ! with no optional arguments
! call hist(x, binx, bincount, width, bins=k, mask=maske) ! to fix the number of bins k
! call hist(x, binx, bincount, width, binwidth=w, mask=maske) ! to fix the bin width w
! INTENT(IN)
! real(sp/dp) :: x(:) 1D array of x values
! or
! real(sp/dp) :: x(:,:) 2D array of x values
! INTENT(INOUT)
! None
! INTENT(OUT)
! real(sp/dp) :: binx(:) x-values of the histogram (center of the bin)
! or
! real(sp/dp) :: binx(:,:) center of the bins and the averaged 2nd, 3rd... coordinates
! and
! integer(i4) :: bincount(:) number of values within each bin
! real(sp/dp) :: width width of a bin
! INTENT(IN), OPTIONAL
! logical :: mask(:) 1D-array of logical values with size(x,1).
! If present, only the data points in (Xij) corresponding
! to the true values in mask are used.
! integer(i4) :: bins Number of bins to be generated.
! If present, the number of bins will be fixed to this value.
! Otherwise, is set to integer part of sqrt(size(x)) or
! using the optionally set binwidth.
! real(sp/dp) :: binwidth Width of the bins to be generated.
! If present, the width of bins will be fixed to this value and
! the INTENT(OUT) width will be set to this value.
! Otherwise, will be determined using the number of bins.
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! Input values must be floating points.
! Use more than one data point: Size(x,1) > 1.
! If you fix the number of bins, it has to be larger than 1: bins > 1.
! If you fix the width of the bins, it has to be larger than 0: binwidth > 0.
! Either the number of bins or the width of the bins can be fixed, not both.
! Not all values of the first coordinate should be equal.
! Dimension of x and mask have to match: Size(x,1) = Size(mask).
! EXAMPLE
! x = (/3.0, 4.0, 6.0, 7.0/)
!
! binx = (/4.0, 6.0/)
! bincount = (/2, 2/)
! width = 2.0
!
! x = (/ (/3.0, 4.0, 6.0, 7.0/) , (/1.0, 2.0, 5.0, 2.0/) /)
!
! binx = (/ (/4.0, 6.0/) , (/1.5, 3.5/) /)
! bincount = (/2, 2/)
! width = 2.0
!
! -> see also example in test directory
! LITERATURE
!
! HISTORY
! Written, Juliane Mai, Feb 2012
INTERFACE histo
MODULE PROCEDURE histo_sp_1d, histo_dp_1d, histo_sp_2d, histo_dp_2d
END INTERFACE histo
! ------------------------------------------------------------------
! NAME
! histo2d
! PURPOSE
! Calculates the 2D histogram of n data 2D points (Xi,Yi),i=1,n ,
! i.e. the n data points are sorted into k x k categories (bins).
!
! With no optional arguments the number of bins k per dimension
! is the integer part of n**(1/4) where n is the number of data points.
! E.g. n=20 will create k=2 bins in each direction (= 4 bins in sum).
! The bin width w is calculated depending on the minimal and maximal value of
! the first coordinate):
! w = (maxval(X) - minval(X)) / k
!
! Optionally, one can fix the number of bins k (integer i4)
! while the width of the bins is determined.
! Or, on can fix the binwidth w (float sp/dp) while k is determined automatically.
! If an optional mask is given, the histogram is taken into account only data points
! (Xi, Yi) which have a true value in the mask.
! (Xi, Yi) can be single or double precision.
! The result will have the same numerical precision.
! CALLING SEQUENCE
! with no optional arguments
! call hist2d(x, binx, bincount, width)
! to fix the number of bins k
! call hist2d(x, binx, bincount, width, bins=k, mask=maske)
! to fix the bin width w
! call hist2d(x, binx, bincount, width, binwidth=w, mask=maske)
! INTENT(IN)
! real(sp/dp) :: x(:,2) 2D array of (x,y) values
! INTENT(INOUT)
! None
! INTENT(OUT)
! real(sp/dp) :: binx(:,2) (x,y)-values of the histogram (center of the bin)
! integer(i4) :: bincount(:) number of values within each bin
! real(sp/dp) :: width width of a bin
! INTENT(IN), OPTIONAL
! logical :: mask(:) 1D-array of logical values with size(x,1).
! If present, only the data points in (Xij) corresponding
! to the true values in mask are used.
! integer(i4) :: bins Number of bins to be generated.
! If present, the number of bins will be fixed to this value.
! Otherwise, is set to integer part of sqrt(size(x)) or
! using the optionally set binwidth.
! real(sp/dp) :: binwidth(2) Width of the bins to be generated.
! One value for each direction.
! If present, the width of bins will be fixed to this value
! and the INTENT(OUT) width will be set to this value.
! Otherwise, will be determined using the number of bins.
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! The number of bins is equal in each direction, i.e. x and y.
! Input values must be floating points.
! Use more than one data point: Size(x,1) > 1.
! If you fix the number of bins, it has to be larger than 1: bins > 1.
! If you fix the width of the bins, it has to be larger than 0: binwidth > 0.
! Either the number of bins or the width of the bins can be fixed, not both.
! Not all values of the first coordinate should be equal.
! Dimension of x and mask have to match: Size(x,1) = Size(mask).
! EXAMPLE
! REAL(DP), DIMENSION(4,2) :: x
! REAL(DP), DIMENSION(:,:), ALLOCATABLE :: testbinx
! INTEGER(I4), DIMENSION(:), ALLOCATABLE :: testbincount
! REAL(DP), DIMENSION(2) :: testwidth
! x(1,:) = (/3.0_dp, 1.0_dp/)
! x(2,:) = (/6.0_dp, 4.0_dp/)
! x(3,:) = (/2.0_dp, 3.0_dp/)
! x(4,:) = (/1.0_dp, 1.0_dp/)
!
! call histo2d(x, testbinx, testbincount, testwidth)
!
! ^
! | x ... data points
! 4 | ********************x * ... edge of bin
! | * * *
! 3 | * x * *
! | *********************
! 2 | * * *
! | * * *
! 1 | x*******x************
! |
! |- - - - - - - - - - - - - >
! 1 2 3 4 5 6
!
! print*, 'testbinx(1) = ',testbinx(1,:) --> (/2.25, 1.75/)
! print*, 'testbinx(2) = ',testbinx(2,:) --> (/4.75, 1.75/)
! print*, 'testbinx(3) = ',testbinx(3,:) --> (/2.25, 3.25/)
! print*, 'testbinx(4) = ',testbinx(4,:) --> (/4.75, 3.25/)
! print*, 'testbincount = ',testbincount --> (/ 2, 0, 1, 1/)
! print*, 'testwidth = ',testwidth --> (/ 2.5, 1.5 /)
!
! LITERATURE
!
! HISTORY
! Written, Juliane Mai, Mar 2012
INTERFACE histo2d
MODULE PROCEDURE histo2d_sp, histo2d_dp
END INTERFACE histo2d
! ------------------------------------------------------------------
PRIVATE
! ------------------------------------------------------------------
CONTAINS
! ------------------------------------------------------------------
SUBROUTINE histo_dp_1d(x, binx, bincount, width, mask, bins, binwidth)
IMPLICIT NONE
REAL(DP), DIMENSION(:), INTENT(IN) :: x
REAL(DP), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: binx
INTEGER(I4), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: bincount
REAL(DP), INTENT(OUT) :: width
INTEGER(I4), OPTIONAL, INTENT(IN) :: bins
REAL(DP), OPTIONAL, INTENT(IN) :: binwidth
LOGICAL, DIMENSION(:), OPTIONAL, INTENT(IN) :: mask
! Local variables
LOGICAL, DIMENSION(size(x)) :: maske
INTEGER(I4) :: n ! number of data points
INTEGER(I4) :: k ! number of bins
REAL(DP) :: w ! binwidth
REAL(DP) :: minimalvalue
INTEGER(I4) :: i, binnr
REAL(DP), DIMENSION(:),ALLOCATABLE :: helpbinx
INTEGER(I4), DIMENSION(:),ALLOCATABLE :: helpbincount
if (present(mask)) then
if (size(mask) /= size(x)) stop 'Error histo_dp: size(mask) /= size(x)'
maske = mask
n = count(maske)
else
maske(:) = .true.
n = size(x)
endif
if (n .le. (1.0_dp+tiny(1.0_dp))) then
stop 'Error histo_dp: size(x) must be at least 2'
end if
if (maxval(x(:), mask=maske)-minval(x(:), mask=maske) <= tiny(1.0_dp)) then
stop 'Error histo_dp: all entries of x(:) are equal'
end if
if (present(bins) .and. present(binwidth)) then
stop 'Error histo_dp: Either fix number of bins or binwidth, not both.'
end if
if (present(bins)) then
if (bins .le. 1_i4) stop 'Error histo_dp: number of bins <= 1'
k = bins
w = (maxval(x(:), mask=maske)-minval(x(:), mask=maske)) / real(k,dp)
else
if (present(binwidth)) then
if (binwidth .le. tiny(1.0_dp)) stop 'Error histo_dp: width of bins too small'
w = binwidth
k = Ceiling( (maxval(x(:), mask=maske)-minval(x(:), mask=maske)) / w )
else
k = Floor(Sqrt(real(n,dp)))
w = (maxval(x(:), mask=maske)-minval(x(:), mask=maske)) / real(k,dp)
end if
endif
! Histogram
allocate (binx(k),bincount(k))
minimalvalue=minval(x(:), mask=maske)
do i=1,k
binx(i) = minimalvalue + real(2*i-1,dp)/2.0_dp*w
bincount(i) = 0_i4
end do
do i=1,size(x)
If (maske(i)) then
binnr = Floor((x(i)-minimalvalue)/w )
! maxval(x) has to be assigned to last bin k not k+1
binnr = binnr - Floor(real(binnr,dp)/real(k,dp)) + 1_i4
bincount(binnr) = bincount(binnr) + 1_i4
end if
end do
width = w
if (count(bincount .gt. 0_i4) .lt. k) then
print *, ' '
print *, 'WARNING histo_dp: Empty bins have been deleted. size(binx) < bins'
print *, ' '
allocate(helpbinx(count(bincount .gt. 0_i4)))
allocate(helpbincount(count(bincount .gt. 0_i4)))
binnr=1_i4
do i=1,k
if (bincount(i) .gt. 0_i4) then
helpbinx(binnr) = binx(i)
helpbincount(binnr) = bincount(i)
binnr=binnr+1_i4
end if
end do
deallocate(binx,bincount)
allocate(binx(size(helpbinx)))
allocate(bincount(size(helpbinx)))
binx=helpbinx
bincount=helpbincount
deallocate(helpbinx,helpbincount)
end if
END SUBROUTINE histo_dp_1d
SUBROUTINE histo_sp_1d(x, binx, bincount, width, mask, bins, binwidth)
IMPLICIT NONE
REAL(SP), DIMENSION(:), INTENT(IN) :: x
REAL(SP), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: binx
INTEGER(I4), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: bincount
REAL(SP), INTENT(OUT) :: width
INTEGER(I4), OPTIONAL, INTENT(IN) :: bins
REAL(SP), OPTIONAL, INTENT(IN) :: binwidth
LOGICAL, DIMENSION(:), OPTIONAL, INTENT(IN) :: mask
! Local variables
LOGICAL, DIMENSION(size(x)) :: maske
INTEGER(I4) :: n ! number of data points
INTEGER(I4) :: k ! number of bins
REAL(SP) :: w ! binwidth
REAL(SP) :: minimalvalue
INTEGER(I4) :: i, binnr
REAL(SP), DIMENSION(:),ALLOCATABLE :: helpbinx
INTEGER(I4), DIMENSION(:),ALLOCATABLE :: helpbincount
if (present(mask)) then
if (size(mask) /= size(x)) stop 'Error histo_sp: size(mask) /= size(x)'
maske = mask
n = count(maske)
else
maske(:) = .true.
n = size(x)
endif
if (n .le. (1.0_sp+tiny(1.0_sp))) then
stop 'Error histo_sp: size(x) must be at least 2'
end if
if (maxval(x(:), mask=maske)-minval(x(:), mask=maske) <= tiny(1.0_sp)) then
stop 'Error histo_sp: all entries of x(:) are equal'
end if
if (present(bins) .and. present(binwidth)) then
stop 'Error histo_sp: Either fix number of bins or binwidth, not both.'
end if
if (present(bins)) then
if (bins .le. 1_i4) stop 'Error histo_sp: number of bins <= 1'
k = bins
w = (maxval(x(:), mask=maske)-minval(x(:), mask=maske)) / real(k,sp)
else
if (present(binwidth)) then
if (binwidth .le. tiny(1.0_sp)) stop 'Error histo_sp: width of bins too small'
w = binwidth
k = Ceiling( (maxval(x(:), mask=maske)-minval(x(:), mask=maske)) / w )
else
k = Floor(Sqrt(real(n,sp)))
w = (maxval(x(:), mask=maske)-minval(x(:), mask=maske)) / real(k,sp)
end if
endif
! Histogram
allocate (binx(k),bincount(k))
minimalvalue = minval(x(:), mask=maske)
do i=1,k
binx(i) = minimalvalue + real(2*i-1,sp)/2.0_sp*w
bincount(i) = 0_i4
end do
do i=1,size(x)
If (maske(i)) then
binnr = Floor((x(i)-minimalvalue)/w )
! maxval(x) has to be assigned to last bin k not k+1
binnr = binnr - Floor(real(binnr,sp)/real(k,sp)) + 1_i4
bincount(binnr) = bincount(binnr) + 1_i4
end if
end do
width = w
if (count(bincount .gt. 0_i4) .lt. k) then
print *, ' '
print *, 'WARNING histo_sp: Empty bins have been deleted. size(binx) < bins'
print *, ' '
allocate(helpbinx(count(bincount .gt. 0_i4)))
allocate(helpbincount(count(bincount .gt. 0_i4)))
binnr=1_i4
do i=1,k
if (bincount(i) .gt. 0_i4) then
helpbinx(binnr) = binx(i)
helpbincount(binnr) = bincount(i)
binnr=binnr+1_i4
end if
end do
deallocate(binx,bincount)
allocate(binx(size(helpbinx)))
allocate(bincount(size(helpbinx)))
binx=helpbinx
bincount=helpbincount
deallocate(helpbinx,helpbincount)
end if
END SUBROUTINE histo_sp_1d
SUBROUTINE histo_dp_2d(x, binx, bincount, width, mask, bins, binwidth)
IMPLICIT NONE
REAL(DP), DIMENSION(:,:), INTENT(IN) :: x
REAL(DP), DIMENSION(:,:), ALLOCATABLE, INTENT(OUT) :: binx
INTEGER(I4), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: bincount
REAL(DP), INTENT(OUT) :: width
INTEGER(I4), OPTIONAL, INTENT(IN) :: bins
REAL(DP), OPTIONAL, INTENT(IN) :: binwidth
LOGICAL, DIMENSION(:), OPTIONAL, INTENT(IN) :: mask
! Local variables
LOGICAL, DIMENSION(size(x,1)) :: maske
INTEGER(I4) :: n ! number of data points
INTEGER(I4) :: k ! number of bins
REAL(DP) :: w ! binwidth
REAL(DP) :: minimalvalue
INTEGER(I4) :: i, j, binnr
REAL(DP), DIMENSION(:,:),ALLOCATABLE :: helpbinx
INTEGER(I4), DIMENSION(:),ALLOCATABLE :: helpbincount
if (present(mask)) then
if (size(mask) /= size(x,1)) stop 'Error histo_dp: size(mask) /= size(x,1)'
maske = mask
n = count(maske)
else
maske(:) = .true.
n = size(x,1)
endif
if (n .le. (1.0_dp+tiny(1.0_dp))) then
stop 'Error histo_dp: size(x,1) must be at least 2'
end if
if (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske) <= tiny(1.0_dp)) then
stop 'Error histo_dp: all entries of x(:,1) are equal'
end if
if (present(bins) .and. present(binwidth)) then
stop 'Error histo_dp: Either fix number of bins or binwidth, not both.'
end if
if (present(bins)) then
if (bins .le. 1_i4) stop 'Error histo_dp: number of bins <= 1'
k = bins
w = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,dp)
else
if (present(binwidth)) then
if (binwidth .le. tiny(1.0_dp)) stop 'Error histo_dp: width of bins too small'
w = binwidth
k = Ceiling( (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / w )
else
k = Floor(Sqrt(real(n,dp)))
w = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,dp)
end if
endif
! Histogram
allocate (binx(k,size(x,2)),bincount(k))
minimalvalue = minval(x(:,1), mask=maske)
binx = 0.0_dp
bincount = 0_i4
do i=1,k
binx(i,1) = minimalvalue + real(2*i-1,dp)/2.0_dp*w
end do
do i=1,size(x,1)
If (maske(i)) then
binnr = Floor((x(i,1)-minimalvalue)/w )
! maxval(x) has to be assigned to last bin k not k+1
binnr = binnr - Floor(real(binnr,dp)/real(k,dp)) + 1_i4
bincount(binnr) = bincount(binnr) + 1_i4
do j=2,size(x,2)
binx(binnr,j) = binx(binnr,j) + x(i,j)
end do
end if
end do
width = w
if (count(bincount .gt. 0_i4) .lt. k) then
print *, ' '
print *, 'WARNING histo_dp: Empty bins have been deleted. size(binx) < bins'
print *, ' '
allocate(helpbinx(count(bincount .gt. 0_i4),size(x,2)))
allocate(helpbincount(count(bincount .gt. 0_i4)))
binnr=1_i4
do i=1,k
if (bincount(i) .gt. 0_i4) then
helpbinx(binnr,1) = binx(i,1)
do j=2,size(x,2)
helpbinx(binnr,j) = binx(i,j)/real(bincount(i),dp)
end do
helpbincount(binnr) = bincount(i)
binnr=binnr+1_i4
!else
! print*, 'Delete binx = ', binx(i,1)
end if
end do
deallocate(binx,bincount)
allocate(binx(size(helpbinx,1),size(helpbinx,2)))
allocate(bincount(size(helpbinx)))
binx=helpbinx
bincount=helpbincount
deallocate(helpbinx,helpbincount)
else
do i=1,k
do j=2,size(x,2)
binx(i,j) = binx(i,j) / real(bincount(i),dp)
end do
end do
end if
END SUBROUTINE histo_dp_2d
SUBROUTINE histo_sp_2d(x, binx, bincount, width, mask, bins, binwidth)
IMPLICIT NONE
REAL(SP), DIMENSION(:,:), INTENT(IN) :: x
REAL(SP), DIMENSION(:,:), ALLOCATABLE, INTENT(OUT) :: binx
INTEGER(I4), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: bincount
REAL(SP), INTENT(OUT) :: width
INTEGER(I4), OPTIONAL, INTENT(IN) :: bins
REAL(SP), OPTIONAL, INTENT(IN) :: binwidth
LOGICAL, DIMENSION(:), OPTIONAL, INTENT(IN) :: mask
! Local variables
LOGICAL, DIMENSION(size(x,1)) :: maske
INTEGER(I4) :: n ! number of data points
INTEGER(I4) :: k ! number of bins
REAL(SP) :: w ! binwidth
REAL(SP) :: minimalvalue
INTEGER(I4) :: i, j, binnr
REAL(SP), DIMENSION(:,:),ALLOCATABLE :: helpbinx
INTEGER(I4), DIMENSION(:),ALLOCATABLE :: helpbincount
if (present(mask)) then
if (size(mask) /= size(x,1)) stop 'Error histo_sp: size(mask) /= size(x,1)'
maske = mask
n = count(maske)
else
maske(:) = .true.
n = size(x,1)
endif
if (n .le. (1.0_sp+tiny(1.0_sp))) then
stop 'Error histo_sp: size(x,1) must be at least 2'
end if
if (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske) <= tiny(1.0_sp)) then
stop 'Error histo_sp: all entries of x(:,1) are equal'
end if
if (present(bins) .and. present(binwidth)) then
stop 'Error histo_sp: Either fix number of bins or binwidth, not both.'
end if
if (present(bins)) then
if (bins .le. 1_i4) stop 'Error histo_sp: number of bins <= 1'
k = bins
w = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,sp)
else
if (present(binwidth)) then
if (binwidth .le. tiny(1.0_sp)) stop 'Error histo_sp: width of bins too small'
w = binwidth
k = Ceiling( (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / w )
else
k = Floor(Sqrt(real(n,sp)))
w = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,sp)
end if
endif
! Histogram
allocate (binx(k,size(x,2)),bincount(k))
minimalvalue = minval(x(:,1), mask=maske)
binx = 0.0_sp
bincount = 0_i4
do i=1,k
binx(i,1) = minimalvalue + real(2*i-1,sp)/2.0_sp*w
end do
do i=1,size(x,1)
If (maske(i)) then
binnr = Floor((x(i,1)-minimalvalue)/w )
! maxval(x) has to be assigned to last bin k not k+1
binnr = binnr - Floor(real(binnr,sp)/real(k,sp)) + 1_i4
bincount(binnr) = bincount(binnr) + 1_i4
do j=2,size(x,2)
binx(binnr,j) = binx(binnr,j) + x(i,j)
end do
end if
end do
width = w
if (count(bincount .gt. 0_i4) .lt. k) then
print *, ' '
print *, 'WARNING histo_sp: Empty bins have been deleted. size(binx) < bins'
print *, ' '
allocate(helpbinx(count(bincount .gt. 0_i4),size(x,2)))
allocate(helpbincount(count(bincount .gt. 0_i4)))
binnr=1_i4
do i=1,k
if (bincount(i) .gt. 0_i4) then
helpbinx(binnr,1) = binx(i,1)
do j=2,size(x,2)
helpbinx(binnr,j) = binx(i,j)/real(bincount(i),sp)
end do
helpbincount(binnr) = bincount(i)
binnr=binnr+1_i4
!else
! print*, 'Delete binx = ', binx(i,1)
end if
end do
deallocate(binx,bincount)
allocate(binx(size(helpbinx,1),size(helpbinx,2)))
allocate(bincount(size(helpbinx)))
binx=helpbinx
bincount=helpbincount
deallocate(helpbinx,helpbincount)
else
do i=1,k
do j=2,size(x,2)
binx(i,j) = binx(i,j) / real(bincount(i),sp)
end do
end do
end if
END SUBROUTINE histo_sp_2d
! ------------------------------------------------------------------
SUBROUTINE histo2d_dp(x, binx, bincount, width, mask, bins, binwidth)
IMPLICIT NONE
REAL(DP), DIMENSION(:,:), INTENT(IN) :: x
REAL(DP), DIMENSION(:,:), ALLOCATABLE, INTENT(OUT) :: binx
INTEGER(I4), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: bincount
REAL(DP), DIMENSION(2), INTENT(OUT) :: width
INTEGER(I4), OPTIONAL, INTENT(IN) :: bins
REAL(DP), DIMENSION(2), OPTIONAL, INTENT(IN) :: binwidth
LOGICAL, DIMENSION(:), OPTIONAL, INTENT(IN) :: mask
! Local variables
LOGICAL, DIMENSION(size(x,1)) :: maske
INTEGER(I4) :: n ! number of data points
INTEGER(I4) :: k ! number of bins
REAL(DP), DIMENSION(2) :: w ! binwidth
REAL(DP), DIMENSION(2) :: minimalvalue
INTEGER(I4) :: i, j
INTEGER(I4) :: binnr, binnr1, binnr2
!REAL(DP), DIMENSION(:),ALLOCATABLE :: helpbinx
!INTEGER(I4), DIMENSION(:),ALLOCATABLE :: helpbincount
if (present(mask)) then
if (size(mask) /= size(x,1)) stop 'Error histo_dp: size(mask) /= size(x)'
maske = mask
n = count(maske)
else
maske(:) = .true.
n = size(x,1)
endif
if (n .le. (1.0_dp+tiny(1.0_dp))) then
stop 'Error histo2d_dp: size(x) must be at least 2'
end if
!if (maxval(x(:), mask=maske)-minval(x(:), mask=maske) <= tiny(1.0_dp)) then
! stop 'Error histo_dp: all entries of x(:) are equal'
!end if
if (present(bins) .and. present(binwidth)) then
stop 'Error histo2d_dp: Either fix number of bins or binwidth, not both.'
end if
if (present(bins)) then
if (bins .le. 1_i4) stop 'Error histo2d_dp: number of bins <= 1'
k = bins
w(1) = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,dp)
w(2) = (maxval(x(:,2), mask=maske)-minval(x(:,2), mask=maske)) / real(k,dp)
else
if (present(binwidth)) then
if (any(binwidth .le. tiny(1.0_dp))) stop 'Error histo2d_dp: width of bins too small'
if (size(binwidth,1) .ne. 2_i4) stop 'Error histo2d_dp: size(width) has to be 2'
w(:) = binwidth(:)
k = Max( Ceiling( (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / w(1) ), &
Ceiling( (maxval(x(:,2), mask=maske)-minval(x(:,2), mask=maske)) / w(2) ) )
else
k = Floor(real(n,dp)**0.25_dp)
w(1) = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,dp)
w(2) = (maxval(x(:,2), mask=maske)-minval(x(:,2), mask=maske)) / real(k,dp)
end if
endif
! Histogram
allocate (binx(k*k,2),bincount(k*k))
minimalvalue(1)=minval(x(:,1), mask=maske)
minimalvalue(2)=minval(x(:,2), mask=maske)
do i=1,k
do j=1,k
binx((i-1)*k+j,1) = minimalvalue(1) + real(2*j-1,dp)/2.0_dp*w(1)
binx((i-1)*k+j,2) = minimalvalue(2) + real(2*i-1,dp)/2.0_dp*w(2)
bincount((i-1)*k+j) = 0_i4
end do
end do
do i=1,size(x,1)
If (maske(i)) then
!print*, 'x(i) = ',x(i,:)
binnr1 = Floor((x(i,1)-minimalvalue(1))/w(1) )
! maxval(x) has to be assigned to last bin k not k+1
binnr1 = binnr1 - Floor(real(binnr1,dp)/real(k,dp)) + 1_i4
!print*, 'i = ',i,' binnr 1 = ',binnr1
binnr2 = Floor((x(i,2)-minimalvalue(2))/w(2) )
! maxval(x) has to be assigned to last bin k not k+1
binnr2 = binnr2 - Floor(real(binnr2,dp)/real(k,dp)) + 1_i4
!print*, 'i = ',i,' binnr 2 = ',binnr2
binnr = (binnr2-1_i4)*k + binnr1
!print*, 'i = ',i,' binnr 3 = ',binnr
bincount(binnr) = bincount(binnr) + 1_i4
end if
end do
width(:) = w(:)
END SUBROUTINE histo2d_dp
SUBROUTINE histo2d_sp(x, binx, bincount, width, mask, bins, binwidth)
IMPLICIT NONE
REAL(SP), DIMENSION(:,:), INTENT(IN) :: x
REAL(SP), DIMENSION(:,:), ALLOCATABLE, INTENT(OUT) :: binx
INTEGER(I4), DIMENSION(:), ALLOCATABLE, INTENT(OUT) :: bincount
REAL(SP), DIMENSION(2), INTENT(OUT) :: width
INTEGER(I4), OPTIONAL, INTENT(IN) :: bins
REAL(SP), DIMENSION(2), OPTIONAL, INTENT(IN) :: binwidth
LOGICAL, DIMENSION(:), OPTIONAL, INTENT(IN) :: mask
! Local variables
LOGICAL, DIMENSION(size(x,1)) :: maske
INTEGER(I4) :: n ! number of data points
INTEGER(I4) :: k ! number of bins
REAL(SP), DIMENSION(2) :: w ! binwidth
REAL(SP), DIMENSION(2) :: minimalvalue
INTEGER(I4) :: i, j
INTEGER(I4) :: binnr, binnr1, binnr2
!REAL(SP), DIMENSION(:),ALLOCATABLE :: helpbinx
!INTEGER(I4), DIMENSION(:),ALLOCATABLE :: helpbincount
if (present(mask)) then
if (size(mask) /= size(x,1)) stop 'Error histo_sp: size(mask) /= size(x)'
maske = mask
n = count(maske)
else
maske(:) = .true.
n = size(x,1)
endif
if (n .le. (1.0_sp+tiny(1.0_sp))) then
stop 'Error histo2d_sp: size(x) must be at least 2'
end if
!if (maxval(x(:), mask=maske)-minval(x(:), mask=maske) <= tiny(1.0_sp)) then
! stop 'Error histo_sp: all entries of x(:) are equal'
!end if
if (present(bins) .and. present(binwidth)) then
stop 'Error histo2d_sp: Either fix number of bins or binwidth, not both.'
end if
if (present(bins)) then
if (bins .le. 1_i4) stop 'Error histo2d_sp: number of bins <= 1'
k = bins
w(1) = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,sp)
w(2) = (maxval(x(:,2), mask=maske)-minval(x(:,2), mask=maske)) / real(k,sp)
else
if (present(binwidth)) then
if (any(binwidth .le. tiny(1.0_sp))) stop 'Error histo2d_sp: width of bins too small'
if (size(binwidth,1) .ne. 2_i4) stop 'Error histo2d_sp: size(width) has to be 2'
w(:) = binwidth(:)
k = Max( Ceiling( (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / w(1) ), &
Ceiling( (maxval(x(:,2), mask=maske)-minval(x(:,2), mask=maske)) / w(2) ) )
else
k = Floor(Sqrt(real(n,sp)))
w(1) = (maxval(x(:,1), mask=maske)-minval(x(:,1), mask=maske)) / real(k,sp)
w(2) = (maxval(x(:,2), mask=maske)-minval(x(:,2), mask=maske)) / real(k,sp)
end if
endif
! Histogram
allocate (binx(k*k,2),bincount(k*k))
minimalvalue(1)=minval(x(:,1), mask=maske)
minimalvalue(2)=minval(x(:,2), mask=maske)
do i=1,k
do j=1,k
binx((i-1)*k+j,1) = minimalvalue(1) + real(2*j-1,sp)/2.0_sp*w(1)
binx((i-1)*k+j,2) = minimalvalue(2) + real(2*i-1,sp)/2.0_sp*w(2)
bincount((i-1)*k+j) = 0_i4
end do
end do
do i=1,size(x,1)
If (maske(i)) then
!print*, 'x(i) = ',x(i,:)
binnr1 = Floor((x(i,1)-minimalvalue(1))/w(1) )
! maxval(x) has to be assigned to last bin k not k+1
binnr1 = binnr1 - Floor(real(binnr1,sp)/real(k,sp)) + 1_i4
!print*, 'i = ',i,' binnr 1 = ',binnr1
binnr2 = Floor((x(i,2)-minimalvalue(2))/w(2) )
! maxval(x) has to be assigned to last bin k not k+1
binnr2 = binnr2 - Floor(real(binnr2,sp)/real(k,sp)) + 1_i4
!print*, 'i = ',i,' binnr 2 = ',binnr2
binnr = (binnr2-1_i4)*k + binnr1
!print*, 'i = ',i,' binnr 3 = ',binnr
bincount(binnr) = bincount(binnr) + 1_i4
end if
end do
width(:) = w(:)
END SUBROUTINE histo2d_sp
#endif
END MODULE mo_histo