forked from stefanocampanella/TourOfJulia.jl
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy path05_arrays.jl
1236 lines (995 loc) · 43.5 KB
/
05_arrays.jl
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
### A Pluto.jl notebook ###
# v0.19.22
using Markdown
using InteractiveUtils
# ╔═╡ aa3574f9-5ff4-4244-857e-79ab7cbbfd23
using BenchmarkTools
# ╔═╡ ff2f2b4e-3d12-4e78-a47d-5677f18a7d0b
using Plots
# ╔═╡ 15c50a5b-ea9e-4e7c-a3d1-0470eeed489c
using PlutoUI
# ╔═╡ 3e1a5e86-9cc8-11ed-35da-5f21a6e28fb6
md"""
# Multi-dimensional arrays
Being a programming language designed for technical computing, Julia has a comprehensive support for multi-dimensional arrays. Furthermore, since the implementation of arrays is written in Julia, the array interface is easily extendible to data structures that exibhit similar behavior.
The crucial point is that the performance comes from Julia design and, in contrast to other languages like Matlab of Python, there is no need to use vectorized operations. Although array-programming might make more readable certain implementation (and more easily portable to accelerators, for example), you can write loops and use scalar indexing in Julia obtaining good performance.
"""
# ╔═╡ 890b8096-972b-4c88-bf35-5d2fc54a3aeb
md"""
## Construction, initialization and basic functions
The array type `Array{T, N}` is a parametric type having two parameters, the rank (number of dimensions) of the array and the type of the elements of the array. The elements can be any object and will be stored in contigous memory locations. Notice that the size of the array along each dimension is not a parameter of the array type. Indeed, arrays can be resized without changing their type and are mutable objects. However, if you have to deal with small arrays of known size you might consider using [`StaticArrays`](https://github.com/JuliaArrays/StaticArrays.jl), which have fixed lenght and, in certain algorithms, can show a considerable speedup.
Arrays can be constructed using the `Array{T}(initializer, sizes...)` constructor. The rank of the array is deduced from the sizes. The initializer can be `undef`, an object of the singleton type `UndefInitializer` that will not initialize the array. If `Missing <: T` or `Noting <: T` the initializer can be respectively `missing` or `nothing`.
If you want to create an array containing elements you can use `fill(value, sizes...)`, or the convenience functions `zeros(T, sizes...)`, `ones(T, sizes...)`, `rand(T, sizes...)`, `randn(T, sizes...)` and `trues` and `falses` (the type of the element `T` defaults to `Float64` when the argument is omitted). You can also `copy` or `deepcopy` an array or crate a new empty un-initialized array with `similar`.
Many useful functions are available to inquire the element type, the number of dimensions, the size, the stride and the index ranges along each dimension. Probably the most important one is `eachindex`, which return an iterator yielding a linear index for accessing and writing to the array with best performance.
"""
# ╔═╡ e38c43ca-7d90-40ec-88b4-86102527e585
methods(Array{Float64, 3})
# ╔═╡ 1680ace1-3ea2-46ed-8310-599f4a0cd85a
xs = Array{Float32}(undef, 3, 3, 3)
# ╔═╡ 4f2d5791-d2ac-4a47-9bd2-2d10fdf862c9
ts = trues(10)
# ╔═╡ 0dc39f83-ece7-4e35-b48b-2c809f16ba39
rs = randn(100, 100)
# ╔═╡ 80b326c0-90e4-4c10-bd13-baaa8063947b
stride(xs, 2)
# ╔═╡ 15202463-4d62-4e37-a50a-9275292e4097
let
strings = Array{String}(undef, 10)
fill!(strings, "They're taking the hobbits to Isengard!")
end
# ╔═╡ 2bd2cebc-d8cc-411a-8df8-2adb9aaf6778
function slowfunc(matrix::Matrix{T}) where T
acc = zero(T)
@simd for i in axes(matrix, 1)
@simd for j in axes(matrix, 2)
@inbounds acc += matrix[i, j]
end
end
acc
end
# ╔═╡ ffbf1dd4-153c-4a1f-8a72-e5f5f86c927b
function fastfunc(matrix::Matrix{T}) where T
acc = zero(T)
@simd for n in eachindex(matrix)
@inbounds acc += matrix[n]
end
acc
end
# ╔═╡ 21b33680-694a-438e-b093-31b32e651091
# Notice: in floating point addition the order of the operads matter
slowfunc(rs) ≈ fastfunc(rs) ≈ sum(rs)
# ╔═╡ 67561d62-0a27-43f1-9c0e-e122b1306eec
@benchmark slowfunc($rs)
# ╔═╡ 9eccdb07-b5c3-4285-a1bd-f90f71237558
@benchmark fastfunc($rs)
# ╔═╡ 3f7af6e3-5555-4b20-89ff-bf952a0618d6
@benchmark sum($rs)
# ╔═╡ f9a4ab44-3e70-47fd-a5d8-017c573e369f
md"""
## Array literals and concatenation
Array literals are declared using square brackets and applying the following rules
1. Prepending a type (no space) to the square brackets automatically creates an array of that type and tries to convert the elements.
2. Comma separated values creates a column vector.
3. Space (or tab) separated values creates a row vector (1xN matrix)
3. Single semicolons (or newlines) and spaces (or tabs) can be combnined to caoncatenate both horizonatlly and vertically at the same time.
4. Semi-colons can be used to concatenate along a dimension equal to the number of consecutive semicolons.
5. Space (and tabs) have higher precedence than semicolons.
"""
# ╔═╡ bea6cd29-a39c-4736-8ed0-46579a082fe1
Float64[1, 2, 3]
# ╔═╡ cd3ea6c0-9641-4843-a1c9-e39df0d0e024
Float64[1 2 3]
# ╔═╡ 7f95d9a9-5fa8-4934-be89-eea59d820d9c
[1 2 3; 4 5 6; 7 8 9]
# ╔═╡ 8a199bd4-1edb-40a0-b3bb-38189e6c1d4b
[1 2 3
4 5 6
7 8 9]
# ╔═╡ d41f1bbc-2cdb-4bcc-946a-94ca74f3eb04
[[1 2; 3 4];;; [5 6; 7 8]]
# ╔═╡ 0494939d-0f66-4b1f-8cbb-7f00e9f2c767
md"""
## Comprehensions and generators
List comprehensions can be created using the `[f(x) for x in xs]` syntax. The comprehension can loop over multiple iterators, in that case a multi-dimensional or a one-dimensional iterator is constructed based on the repetition of the `for` keyword. They can contain also guards (conditions), in presence of such a one-dimensional array is created automatically. The element type can be enforced with the same syntax of array literals.
Omitting the square brackets (or using parenthesis) a generator is instantiated. Generators are iterators that lazily produce elements, without allocating and creating an array to store all the elements.
"""
# ╔═╡ 37067e15-0110-4dc9-8284-994fd659e8cf
[cos(x^2 + y^2) for x in range(-1, 1, length=10), y in range(-1, 1, length=10)]
# ╔═╡ 40e23ea2-3634-44db-8bf8-b3b3002a5822
[cos(x^2 + y^2) for x in range(-1, 1, length=10) for y in range(-1, 1, length=10)]
# ╔═╡ 3253722d-5e7a-4e31-b3dd-ca842c1e7b02
[n for n = 1:50 if (mod(n, 3) == 0 || mod(n, 5) == 0) && mod(n, 15) != 0]
# ╔═╡ 39708ca1-48c5-4499-a299-59c12ffe6c6b
prod("They're taking the hobbits to Isengard! " for _ = 1:10)
# ╔═╡ cb564a78-8c2f-4796-b6dd-ebddd24ed845
md"""
## Broadcasting
Julia has broadcasting, has Python does with Numpy. But in Julia broadcasting is explicit, and use the dot sintax. A function postfixed with a dot or an operator prefixed with a dot is broadcasted on its arguments. Furthermore, broadcasted operator are fused in a single loop (_loop fusion_) and the `@.` automatically broadcast all operations in the expression.
Arithmetic operators and comparisons are also vectorized for convenience (they act on arrays, of the same shape). With matrices, multiplication and powers (including with negative integer exponents) are to be intended with respect to internal product, not element-wise. When mixing matrices and vectors multiplication and division symbols means row-by-column products and solution of a system of linear equations respectively. The `'` symbol is the adjoint (a lazy wrapper), the product of an adjoint with a vector is a scalar.
"""
# ╔═╡ f87638dd-4961-4352-8fd3-0a4dccab2309
let ϕ = (1 + √5) / 2
round.(Int, (ϕ^n/ √5 for n = 1:20))
end
# ╔═╡ 2b1d4cba-f6e0-491d-903a-e7cf61ae6c59
let N = 100_000_000
4count(<(1.0), rand(N).^2 + rand(N).^2) / N
end
# ╔═╡ 0bc6f709-ff25-45be-b97e-c1c6306dc2ac
let xs = range(0, π, length=100)
plot(xs, @. √(1 - cos(xs)^2) / xs)
end
# ╔═╡ 2c2ce4c5-1868-40c6-ae87-4d59ad1a81d6
[1/2, √3/2]' * [0 -1; 1 0] * [√3/2, -1/2]
# ╔═╡ 5dfa0009-f8ff-4049-aebb-f98ddd711d59
md"""
## Indexing and array views
An array can be indexed, as in Numpy, with scalars or vectors (of indices or booleans). The `end` keyword means the last index, the `:` symbol means the whole range of indices along that dimension.
When assigning or accessing an array using vectors, Julia allocates a new object by default. It is possible to avoid it using the `view` function or the `@view` macro.
"""
# ╔═╡ 7ac90260-64fc-4b7e-b81e-b98930663a62
function slowfunc_v2(xs, indxs)
ys = xs[indxs]
sum(ys)
end
# ╔═╡ 17d13076-231e-4207-a17a-36c22d1f4a0d
function fastfunc_v2(xs, indxs)
ys = view(xs, indxs)
sum(ys)
end
# ╔═╡ ca5cc16a-2efd-4c54-9e80-da783c0f52d1
@benchmark slowfunc_v2($rs, $100:600)
# ╔═╡ c908e25c-f8e1-49d9-acd7-fdf7b82f67c1
@benchmark fastfunc_v2($rs, $100:600)
# ╔═╡ 1cdf1772-3755-49ff-8bd3-fd95ab341ef6
PlutoUI.TableOfContents()
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
[compat]
BenchmarkTools = "~1.3.2"
Plots = "~1.38.4"
PlutoUI = "~0.7.49"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
julia_version = "1.8.5"
manifest_format = "2.0"
project_hash = "2027106876308ea187edd906d8ca120921c67a0d"
[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.4"
[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"
[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
[[deps.BenchmarkTools]]
deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"]
git-tree-sha1 = "d9a9701b899b30332bbcb3e1679c41cce81fb0e8"
uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
version = "1.3.2"
[[deps.BitFlags]]
git-tree-sha1 = "43b1a4a8f797c1cddadf60499a8a077d4af2cd2d"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.7"
[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"
[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"
[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "c6d890a52d2c4d55d326439580c3b8d0875a77d9"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.15.7"
[[deps.ChangesOfVariables]]
deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
git-tree-sha1 = "844b061c104c408b24537482469400af6075aae4"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.5"
[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "9c209fb7536406834aa938fb149964b985de6c83"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.1"
[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "Random", "SnoopPrecompile"]
git-tree-sha1 = "aa3edc8f8dea6cbfa176ee12f7c2fc82f0608ed3"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.20.0"
[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.4"
[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
git-tree-sha1 = "600cc5508d66b78aae350f7accdb58763ac18589"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.9.10"
[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.10"
[[deps.Compat]]
deps = ["Dates", "LinearAlgebra", "UUIDs"]
git-tree-sha1 = "61fdd77467a5c3ad071ef8277ac6bd6af7dd4c04"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "4.6.0"
[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.0.1+0"
[[deps.Contour]]
git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.2"
[[deps.DataAPI]]
git-tree-sha1 = "e8119c1a33d267e16108be441a287a6981ba1630"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.14.0"
[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "d1fff3a548102f48987a52a2e0d114fa97d730f0"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.13"
[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
[[deps.DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
[[deps.DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.9.3"
[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"
[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bad72f730e9e91c08d9427d5e8db95478a3c323d"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.4.8+0"
[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"
[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Pkg", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "74faea50c1d007c85837327f6775bea60b5492dd"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.2+2"
[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"
[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"
[[deps.Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"
[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"
[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"
[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "d972031d28c8c8d9d7b41a536ad7bb0c2579caca"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.8+0"
[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
git-tree-sha1 = "9e23bd6bb3eb4300cb567bdf63e2c14e5d2ffdbc"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.71.5"
[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "aa23c9f9b7c0ba6baeabe966ea1c7d2c7487ef90"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.71.5+0"
[[deps.Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"
[[deps.Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "d3b3624125c1474292d0d8ed0f65554ac37ddb23"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.74.0+2"
[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"
[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"
[[deps.HTTP]]
deps = ["Base64", "CodecZlib", "Dates", "IniFile", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "37e4657cd56b11abe3d10cd4a1ec5fbdb4180263"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.7.4"
[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+1"
[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.4"
[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "c47c5fa4c5308f27ccaac35504858d8914e102f9"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.4"
[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.2"
[[deps.IniFile]]
git-tree-sha1 = "f550e6e32074c939295eb5ea6de31849ac2c9625"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.1"
[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
[[deps.InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "49510dfcb407e572524ba94aeae2fced1f3feb0f"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.8"
[[deps.IrrationalConstants]]
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"
[[deps.JLFzf]]
deps = ["Pipe", "REPL", "Random", "fzf_jll"]
git-tree-sha1 = "f377670cda23b6b7c1c0b3893e37451c5c1a2185"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.5"
[[deps.JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.4.1"
[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "3c837543ddb02250ef42f4738347454f95079d4e"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.3"
[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b53380851c6e6664204efb2e62cd24fa5c47e4ba"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.2+0"
[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"
[[deps.LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "3.0.0+1"
[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"
[[deps.LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"
[[deps.Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
git-tree-sha1 = "2422f47b34d4b127720a18f86fa7b1aa2e141f29"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.18"
[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.3"
[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "7.84.0+0"
[[deps.LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.10.2+0"
[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"
[[deps.Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"
[[deps.Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.6.0+0"
[[deps.Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"
[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c7cb1f5d892775ba13767a87c7ada0b980ea0a71"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+2"
[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"
[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.4.0+0"
[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"
[[deps.LinearAlgebra]]
deps = ["Libdl", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
[[deps.LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "45b288af6956e67e621c5cbb2d75a261ab58300b"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.20"
[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "cedb76b37bc5a6c702ade66be44f831fa23c681e"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "1.0.0"
[[deps.MIMEs]]
git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb"
uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
version = "0.1.4"
[[deps.MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "42324d08725e200c23d4dfb549e0d5d89dede2d2"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.10"
[[deps.Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "Random", "Sockets"]
git-tree-sha1 = "03a9b9718f5682ecb107ac9f7308991db4ce395b"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.7"
[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.0+0"
[[deps.Measures]]
git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.2"
[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "f66bdc5de519e8f8ae43bdc598782d35a25b1272"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.1.0"
[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2022.2.1"
[[deps.NaNMath]]
deps = ["OpenLibm_jll"]
git-tree-sha1 = "a7c3d1da1189a1c2fe843a3bfa04d18d20eb3211"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.0.1"
[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"
[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"
[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.20+0"
[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+0"
[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "6503b77492fd7fcb9379bf73cd31035670e3c509"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.3.3"
[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6e9dba33f9f2c44e08a020b0caf6903be540004"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.19+0"
[[deps.OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"
[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"
[[deps.OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"
[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.40.0+0"
[[deps.Parsers]]
deps = ["Dates", "SnoopPrecompile"]
git-tree-sha1 = "151d91d63d8d6c1a5789ecb7de51547e00480f1b"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.5.4"
[[deps.Pipe]]
git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
version = "1.3.0"
[[deps.Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"
[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.8.0"
[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.1.0"
[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "SnoopPrecompile", "Statistics"]
git-tree-sha1 = "c95373e73290cf50a8a22c3375e4625ded5c5280"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.3.4"
[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Preferences", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SnoopPrecompile", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
git-tree-sha1 = "87036ff7d1277aa624ce4d211ddd8720116f80bf"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.38.4"
[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "eadad7b14cf046de6eb41f13c9275e5aa2711ab6"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.49"
[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "47e5f437cc0e7ef2ce8406ce1e7e24d44915f88d"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.3.0"
[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
[[deps.Profile]]
deps = ["Printf"]
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
[[deps.Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "0c03844e2231e12fda4d0086fd7cbe4098ee8dc5"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+2"
[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
[[deps.Random]]
deps = ["SHA", "Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
[[deps.RecipesBase]]
deps = ["SnoopPrecompile"]
git-tree-sha1 = "261dddd3b862bd2c940cf6ca4d1c8fe593e457c8"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.3"
[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase", "SnoopPrecompile"]
git-tree-sha1 = "e974477be88cb5e3040009f3767611bc6357846f"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.6.11"
[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"
[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "90bc7a7c96410424509e4263e277e43250c05691"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.0"
[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"
[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"
[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "f94f779c94e58bf9ea243e77a37e16d9de9126bd"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.1"
[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"
[[deps.SimpleBufferStream]]
git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.1.0"
[[deps.SnoopPrecompile]]
deps = ["Preferences"]
git-tree-sha1 = "e760a70afdcd461cf01a575947738d359234665c"
uuid = "66db9d55-30c0-4569-8b51-7e840670fc0c"
version = "1.0.3"
[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "a4ada03f999bd01b3a25dcaa30b2d929fe537e00"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.1.0"
[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "d75bda01f8c31ebb72df80a46c88b25d1c79c56d"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.7"
[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f9af7f195fb13589dd2e2d57fdb401717d2eb1f6"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.5.0"
[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "d1bf48bfcc554a3761a133fe3a9bb01488e06916"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.21"
[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"
[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.1"
[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"
[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "94f38103c984f89cf77c402f2a68dbd870f8165f"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.11"
[[deps.Tricks]]
git-tree-sha1 = "6bac775f2d42a611cdfcd1fb217ee719630c4175"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.6"
[[deps.URIs]]
git-tree-sha1 = "ac00576f90d8a259f2c9d823e91d1de3fd44d348"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.1"
[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"
[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"
[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "ed8d92d9774b077c53e1da50fd81a36af3744c1c"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+0"
[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"
[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.10.3+0"
[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"
[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"
[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"
[[deps.Xorg_libXcursor_jll]]