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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
// Copyright 2014-2020 bluss and ndarray developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
#![crate_name = "ndarray"]
#![doc(html_root_url = "https://docs.rs/ndarray/0.15/")]
#![doc(html_logo_url = "https://rust-ndarray.github.io/images/rust-ndarray_logo.svg")]
#![allow(
    clippy::many_single_char_names,
    clippy::deref_addrof,
    clippy::unreadable_literal,
    clippy::manual_map, // is not an error
    clippy::while_let_on_iterator, // is not an error
    clippy::from_iter_instead_of_collect, // using from_iter is good style
    clippy::redundant_closure, // false positives clippy #7812
)]
#![doc(test(attr(deny(warnings))))]
#![doc(test(attr(allow(unused_variables))))]
#![doc(test(attr(allow(deprecated))))]
#![cfg_attr(not(feature = "std"), no_std)]

//! The `ndarray` crate provides an *n*-dimensional container for general elements
//! and for numerics.
//!
//! In *n*-dimensional we include, for example, 1-dimensional rows or columns,
//! 2-dimensional matrices, and higher dimensional arrays. If the array has *n*
//! dimensions, then an element in the array is accessed by using that many indices.
//! Each dimension is also called an *axis*.
//!
//! - **[`ArrayBase`]**:
//!   The *n*-dimensional array type itself.<br>
//!   It is used to implement both the owned arrays and the views; see its docs
//!   for an overview of all array features.<br>
//! - The main specific array type is **[`Array`]**, which owns
//! its elements.
//!
//! ## Highlights
//!
//! - Generic *n*-dimensional array
//! - [Slicing](ArrayBase#slicing), also with arbitrary step size, and negative
//!   indices to mean elements from the end of the axis.
//! - Views and subviews of arrays; iterators that yield subviews.
//! - Higher order operations and arithmetic are performant
//! - Array views can be used to slice and mutate any `[T]` data using
//!   `ArrayView::from` and `ArrayViewMut::from`.
//! - [`Zip`] for lock step function application across two or more arrays or other
//!   item producers ([`NdProducer`] trait).
//!
//! ## Crate Status
//!
//! - Still iterating on and evolving the crate
//!   + The crate is continuously developing, and breaking changes are expected
//!     during evolution from version to version. We adopt the newest stable
//!     rust features if we need them.
//!   + Note that functions/methods/traits/etc. hidden from the docs are not
//!     considered part of the public API, so changes to them are not
//!     considered breaking changes.
//! - Performance:
//!   + Prefer higher order methods and arithmetic operations on arrays first,
//!     then iteration, and as a last priority using indexed algorithms.
//!   + The higher order functions like [`.map()`](ArrayBase::map),
//!     [`.map_inplace()`](ArrayBase::map_inplace), [`.zip_mut_with()`](ArrayBase::zip_mut_with),
//!     [`Zip`] and [`azip!()`](azip) are the most efficient ways
//!     to perform single traversal and lock step traversal respectively.
//!   + Performance of an operation depends on the memory layout of the array
//!     or array view. Especially if it's a binary operation, which
//!     needs matching memory layout to be efficient (with some exceptions).
//!   + Efficient floating point matrix multiplication even for very large
//!     matrices; can optionally use BLAS to improve it further.
//! - **Requires Rust 1.49 or later**
//!
//! ## Crate Feature Flags
//!
//! The following crate feature flags are available. They are configured in your
//! `Cargo.toml`. See [`doc::crate_feature_flags`] for more information.
//!
//! - `std`: Rust standard library-using functionality (enabled by default)
//! - `serde`: serialization support for serde 1.x
//! - `rayon`: Parallel iterators, parallelized methods, the [`parallel`] module and [`par_azip!`].
//! - `approx` Implementations of traits from version 0.4 of the [`approx`] crate.
//! - `approx-0_5`: Implementations of traits from version 0.5 of the [`approx`] crate.
//! - `blas`: transparent BLAS support for matrix multiplication, needs configuration.
//! - `matrixmultiply-threading`: Use threading from `matrixmultiply`.
//!
//! ## Documentation
//!
//! * The docs for [`ArrayBase`] provide an overview of
//!   the *n*-dimensional array type. Other good pages to look at are the
//!   documentation for the [`s![]`](s!) and
//!   [`azip!()`](azip!) macros.
//!
//! * If you have experience with NumPy, you may also be interested in
//!   [`ndarray_for_numpy_users`](doc::ndarray_for_numpy_users).
//!
//! ## The ndarray ecosystem
//!
//! `ndarray` provides a lot of functionality, but it's not a one-stop solution.
//!
//! `ndarray` includes matrix multiplication and other binary/unary operations out of the box.
//! More advanced linear algebra routines (e.g. SVD decomposition or eigenvalue computation)
//! can be found in [`ndarray-linalg`](https://crates.io/crates/ndarray-linalg).
//!
//! The same holds for statistics: `ndarray` provides some basic functionalities (e.g. `mean`)
//! but more advanced routines can be found in [`ndarray-stats`](https://crates.io/crates/ndarray-stats).
//!
//! If you are looking to generate random arrays instead, check out [`ndarray-rand`](https://crates.io/crates/ndarray-rand).
//!
//! For conversion between `ndarray`, [`nalgebra`](https://crates.io/crates/nalgebra) and
//! [`image`](https://crates.io/crates/image) check out [`nshare`](https://crates.io/crates/nshare).


extern crate alloc;

#[cfg(feature = "std")]
extern crate std;
#[cfg(not(feature = "std"))]
extern crate core as std;

#[cfg(feature = "blas")]
extern crate cblas_sys;

#[cfg(feature = "docs")]
pub mod doc;

use std::marker::PhantomData;
use alloc::sync::Arc;

pub use crate::dimension::dim::*;
pub use crate::dimension::{Axis, AxisDescription, Dimension, IntoDimension, RemoveAxis};
pub use crate::dimension::{DimAdd, DimMax};

pub use crate::dimension::IxDynImpl;
pub use crate::dimension::NdIndex;
pub use crate::error::{ErrorKind, ShapeError};
pub use crate::indexes::{indices, indices_of};
pub use crate::order::Order;
pub use crate::slice::{
    MultiSliceArg, NewAxis, Slice, SliceArg, SliceInfo, SliceInfoElem, SliceNextDim,
};

use crate::iterators::Baseiter;
use crate::iterators::{ElementsBase, ElementsBaseMut, Iter, IterMut};

pub use crate::arraytraits::AsArray;
#[cfg(feature = "std")]
pub use crate::linalg_traits::NdFloat;
pub use crate::linalg_traits::LinalgScalar;

#[allow(deprecated)] // stack_new_axis
pub use crate::stacking::{concatenate, stack, stack_new_axis};

pub use crate::math_cell::MathCell;
pub use crate::impl_views::IndexLonger;
pub use crate::shape_builder::{Shape, ShapeBuilder, ShapeArg, StrideShape};

#[macro_use]
mod macro_utils;
#[macro_use]
mod private;
mod aliases;
#[macro_use]
mod itertools;
mod argument_traits;
#[cfg(feature = "serde")]
mod array_serde;
mod arrayformat;
mod arraytraits;
pub use crate::argument_traits::AssignElem;
mod data_repr;
mod data_traits;

pub use crate::aliases::*;

pub use crate::data_traits::{
    Data, DataMut, DataOwned, DataShared, RawData, RawDataClone, RawDataMut,
    RawDataSubst,
};

mod free_functions;
pub use crate::free_functions::*;
pub use crate::iterators::iter;

mod error;
mod extension;
mod geomspace;
mod indexes;
mod iterators;
mod layout;
mod linalg_traits;
mod linspace;
mod logspace;
mod math_cell;
mod numeric_util;
mod order;
mod partial;
mod shape_builder;
#[macro_use]
mod slice;
mod split_at;
mod stacking;
mod low_level_util;
#[macro_use]
mod zip;

mod dimension;

pub use crate::zip::{FoldWhile, IntoNdProducer, NdProducer, Zip};

pub use crate::layout::Layout;

/// Implementation's prelude. Common types used everywhere.
mod imp_prelude {
    pub use crate::dimension::DimensionExt;
    pub use crate::prelude::*;
    pub use crate::ArcArray;
    pub use crate::{
        CowRepr, Data, DataMut, DataOwned, DataShared, Ix, Ixs, RawData, RawDataMut, RawViewRepr,
        RemoveAxis, ViewRepr,
    };
}

pub mod prelude;

/// Array index type
pub type Ix = usize;
/// Array index type (signed)
pub type Ixs = isize;

/// An *n*-dimensional array.
///
/// The array is a general container of elements.
/// The array supports arithmetic operations by applying them elementwise, if the
/// elements are numeric, but it supports non-numeric elements too.
///
/// The arrays rarely grow or shrink, since those operations can be costly. On
/// the other hand there is a rich set of methods and operations for taking views,
/// slices, and making traversals over one or more arrays.
///
/// In *n*-dimensional we include for example 1-dimensional rows or columns,
/// 2-dimensional matrices, and higher dimensional arrays. If the array has *n*
/// dimensions, then an element is accessed by using that many indices.
///
/// The `ArrayBase<S, D>` is parameterized by `S` for the data container and
/// `D` for the dimensionality.
///
/// Type aliases [`Array`], [`ArcArray`], [`CowArray`], [`ArrayView`], and
/// [`ArrayViewMut`] refer to `ArrayBase` with different types for the data
/// container: arrays with different kinds of ownership or different kinds of array views.
///
/// ## Contents
///
/// + [Array](#array)
/// + [ArcArray](#arcarray)
/// + [CowArray](#cowarray)
/// + [Array Views](#array-views)
/// + [Indexing and Dimension](#indexing-and-dimension)
/// + [Loops, Producers and Iterators](#loops-producers-and-iterators)
/// + [Slicing](#slicing)
/// + [Subviews](#subviews)
/// + [Arithmetic Operations](#arithmetic-operations)
/// + [Broadcasting](#broadcasting)
/// + [Conversions](#conversions)
/// + [Constructor Methods for Owned Arrays](#constructor-methods-for-owned-arrays)
/// + [Methods For All Array Types](#methods-for-all-array-types)
/// + [Methods For 1-D Arrays](#methods-for-1-d-arrays)
/// + [Methods For 2-D Arrays](#methods-for-2-d-arrays)
/// + [Methods for Dynamic-Dimensional Arrays](#methods-for-dynamic-dimensional-arrays)
/// + [Numerical Methods for Arrays](#numerical-methods-for-arrays)
///
/// ## `Array`
///
/// [`Array`] is an owned array that owns the underlying array
/// elements directly (just like a `Vec`) and it is the default way to create and
/// store n-dimensional data. `Array<A, D>` has two type parameters: `A` for
/// the element type, and `D` for the dimensionality. A particular
/// dimensionality's type alias like `Array3<A>` just has the type parameter
/// `A` for element type.
///
/// An example:
///
/// ```
/// // Create a three-dimensional f64 array, initialized with zeros
/// use ndarray::Array3;
/// let mut temperature = Array3::<f64>::zeros((3, 4, 5));
/// // Increase the temperature in this location
/// temperature[[2, 2, 2]] += 0.5;
/// ```
///
/// ## `ArcArray`
///
/// [`ArcArray`] is an owned array with reference counted
/// data (shared ownership).
/// Sharing requires that it uses copy-on-write for mutable operations.
/// Calling a method for mutating elements on `ArcArray`, for example
/// [`view_mut()`](Self::view_mut) or [`get_mut()`](Self::get_mut),
/// will break sharing and require a clone of the data (if it is not uniquely held).
///
/// ## `CowArray`
///
/// [`CowArray`] is analogous to [`std::borrow::Cow`].
/// It can represent either an immutable view or a uniquely owned array. If a
/// `CowArray` instance is the immutable view variant, then calling a method
/// for mutating elements in the array will cause it to be converted into the
/// owned variant (by cloning all the elements) before the modification is
/// performed.
///
/// ## Array Views
///
/// [`ArrayView`] and [`ArrayViewMut`] are read-only and read-write array views
/// respectively. They use dimensionality, indexing, and almost all other
/// methods the same way as the other array types.
///
/// Methods for `ArrayBase` apply to array views too, when the trait bounds
/// allow.
///
/// Please see the documentation for the respective array view for an overview
/// of methods specific to array views: [`ArrayView`], [`ArrayViewMut`].
///
/// A view is created from an array using [`.view()`](ArrayBase::view),
/// [`.view_mut()`](ArrayBase::view_mut), using
/// slicing ([`.slice()`](ArrayBase::slice), [`.slice_mut()`](ArrayBase::slice_mut)) or from one of
/// the many iterators that yield array views.
///
/// You can also create an array view from a regular slice of data not
/// allocated with `Array` — see array view methods or their `From` impls.
///
/// Note that all `ArrayBase` variants can change their view (slicing) of the
/// data freely, even when their data can’t be mutated.
///
/// ## Indexing and Dimension
///
/// The dimensionality of the array determines the number of *axes*, for example
/// a 2D array has two axes. These are listed in “big endian” order, so that
/// the greatest dimension is listed first, the lowest dimension with the most
/// rapidly varying index is the last.
///
/// In a 2D array the index of each element is `[row, column]` as seen in this
/// 4 × 3 example:
///
/// ```ignore
/// [[ [0, 0], [0, 1], [0, 2] ],  // row 0
///  [ [1, 0], [1, 1], [1, 2] ],  // row 1
///  [ [2, 0], [2, 1], [2, 2] ],  // row 2
///  [ [3, 0], [3, 1], [3, 2] ]]  // row 3
/// //    \       \       \
/// //   column 0  \     column 2
/// //            column 1
/// ```
///
/// The number of axes for an array is fixed by its `D` type parameter: `Ix1`
/// for a 1D array, `Ix2` for a 2D array etc. The dimension type `IxDyn` allows
/// a dynamic number of axes.
///
/// A fixed size array (`[usize; N]`) of the corresponding dimensionality is
/// used to index the `Array`, making the syntax `array[[` i, j,  ...`]]`
///
/// ```
/// use ndarray::Array2;
/// let mut array = Array2::zeros((4, 3));
/// array[[1, 1]] = 7;
/// ```
///
/// Important traits and types for dimension and indexing:
///
/// - A [`struct@Dim`] value represents a dimensionality or index.
/// - Trait [`Dimension`] is implemented by all
/// dimensionalities. It defines many operations for dimensions and indices.
/// - Trait [`IntoDimension`] is used to convert into a
/// `Dim` value.
/// - Trait [`ShapeBuilder`] is an extension of
/// `IntoDimension` and is used when constructing an array. A shape describes
/// not just the extent of each axis but also their strides.
/// - Trait [`NdIndex`] is an extension of `Dimension` and is
/// for values that can be used with indexing syntax.
///
///
/// The default memory order of an array is *row major* order (a.k.a “c” order),
/// where each row is contiguous in memory.
/// A *column major* (a.k.a. “f” or fortran) memory order array has
/// columns (or, in general, the outermost axis) with contiguous elements.
///
/// The logical order of any array’s elements is the row major order
/// (the rightmost index is varying the fastest).
/// The iterators `.iter(), .iter_mut()` always adhere to this order, for example.
///
/// ## Loops, Producers and Iterators
///
/// Using [`Zip`] is the most general way to apply a procedure
/// across one or several arrays or *producers*.
///
/// [`NdProducer`] is like an iterable but for
/// multidimensional data. All producers have dimensions and axes, like an
/// array view, and they can be split and used with parallelization using `Zip`.
///
/// For example, `ArrayView<A, D>` is a producer, it has the same dimensions
/// as the array view and for each iteration it produces a reference to
/// the array element (`&A` in this case).
///
/// Another example, if we have a 10 × 10 array and use `.exact_chunks((2, 2))`
/// we get a producer of chunks which has the dimensions 5 × 5 (because
/// there are *10 / 2 = 5* chunks in either direction). The 5 × 5 chunks producer
/// can be paired with any other producers of the same dimension with `Zip`, for
/// example 5 × 5 arrays.
///
/// ### `.iter()` and `.iter_mut()`
///
/// These are the element iterators of arrays and they produce an element
/// sequence in the logical order of the array, that means that the elements
/// will be visited in the sequence that corresponds to increasing the
/// last index first: *0, ..., 0,  0*; *0, ..., 0, 1*; *0, ...0, 2* and so on.
///
/// ### `.outer_iter()` and `.axis_iter()`
///
/// These iterators produce array views of one smaller dimension.
///
/// For example, for a 2D array, `.outer_iter()` will produce the 1D rows.
/// For a 3D array, `.outer_iter()` produces 2D subviews.
///
/// `.axis_iter()` is like `outer_iter()` but allows you to pick which
/// axis to traverse.
///
/// The `outer_iter` and `axis_iter` are one dimensional producers.
///
/// ## `.rows()`, `.columns()` and `.lanes()`
///
/// [`.rows()`][gr] is a producer (and iterable) of all rows in an array.
///
/// ```
/// use ndarray::Array;
///
/// // 1. Loop over the rows of a 2D array
/// let mut a = Array::zeros((10, 10));
/// for mut row in a.rows_mut() {
///     row.fill(1.);
/// }
///
/// // 2. Use Zip to pair each row in 2D `a` with elements in 1D `b`
/// use ndarray::Zip;
/// let mut b = Array::zeros(a.nrows());
///
/// Zip::from(a.rows())
///     .and(&mut b)
///     .for_each(|a_row, b_elt| {
///         *b_elt = a_row[a.ncols() - 1] - a_row[0];
///     });
/// ```
///
/// The *lanes* of an array are 1D segments along an axis and when pointed
/// along the last axis they are *rows*, when pointed along the first axis
/// they are *columns*.
///
/// A *m* × *n* array has *m* rows each of length *n* and conversely
/// *n* columns each of length *m*.
///
/// To generalize this, we say that an array of dimension *a* × *m* × *n*
/// has *a m* rows. It's composed of *a* times the previous array, so it
/// has *a* times as many rows.
///
/// All methods: [`.rows()`][gr], [`.rows_mut()`][grm],
/// [`.columns()`][gc], [`.columns_mut()`][gcm],
/// [`.lanes(axis)`][l], [`.lanes_mut(axis)`][lm].
///
/// [gr]: Self::rows
/// [grm]: Self::rows_mut
/// [gc]: Self::columns
/// [gcm]: Self::columns_mut
/// [l]: Self::lanes
/// [lm]: Self::lanes_mut
///
/// Yes, for 2D arrays `.rows()` and `.outer_iter()` have about the same
/// effect:
///
///  + `rows()` is a producer with *n* - 1 dimensions of 1 dimensional items
///  + `outer_iter()` is a producer with 1 dimension of *n* - 1 dimensional items
///
/// ## Slicing
///
/// You can use slicing to create a view of a subset of the data in
/// the array. Slicing methods include [`.slice()`], [`.slice_mut()`],
/// [`.slice_move()`], and [`.slice_collapse()`].
///
/// The slicing argument can be passed using the macro [`s![]`](s!),
/// which will be used in all examples. (The explicit form is an instance of
/// [`SliceInfo`] or another type which implements [`SliceArg`]; see their docs
/// for more information.)
///
/// If a range is used, the axis is preserved. If an index is used, that index
/// is selected and the axis is removed; this selects a subview. See
/// [*Subviews*](#subviews) for more information about subviews. If a
/// [`NewAxis`] instance is used, a new axis is inserted. Note that
/// [`.slice_collapse()`] panics on `NewAxis` elements and behaves like
/// [`.collapse_axis()`] by preserving the number of dimensions.
///
/// [`.slice()`]: Self::slice
/// [`.slice_mut()`]: Self::slice_mut
/// [`.slice_move()`]: Self::slice_move
/// [`.slice_collapse()`]: Self::slice_collapse
///
/// When slicing arrays with generic dimensionality, creating an instance of
/// [`SliceInfo`] to pass to the multi-axis slicing methods like [`.slice()`]
/// is awkward. In these cases, it's usually more convenient to use
/// [`.slice_each_axis()`]/[`.slice_each_axis_mut()`]/[`.slice_each_axis_inplace()`]
/// or to create a view and then slice individual axes of the view using
/// methods such as [`.slice_axis_inplace()`] and [`.collapse_axis()`].
///
/// [`.slice_each_axis()`]: Self::slice_each_axis
/// [`.slice_each_axis_mut()`]: Self::slice_each_axis_mut
/// [`.slice_each_axis_inplace()`]: Self::slice_each_axis_inplace
/// [`.slice_axis_inplace()`]: Self::slice_axis_inplace
/// [`.collapse_axis()`]: Self::collapse_axis
///
/// It's possible to take multiple simultaneous *mutable* slices with
/// [`.multi_slice_mut()`] or (for [`ArrayViewMut`] only)
/// [`.multi_slice_move()`].
///
/// [`.multi_slice_mut()`]: Self::multi_slice_mut
/// [`.multi_slice_move()`]: ArrayViewMut#method.multi_slice_move
///
/// ```
/// use ndarray::{arr2, arr3, s, ArrayBase, DataMut, Dimension, NewAxis, Slice};
///
/// // 2 submatrices of 2 rows with 3 elements per row, means a shape of `[2, 2, 3]`.
///
/// let a = arr3(&[[[ 1,  2,  3],     // -- 2 rows  \_
///                 [ 4,  5,  6]],    // --         /
///                [[ 7,  8,  9],     //            \_ 2 submatrices
///                 [10, 11, 12]]]);  //            /
/// //  3 columns ..../.../.../
///
/// assert_eq!(a.shape(), &[2, 2, 3]);
///
/// // Let’s create a slice with
/// //
/// // - Both of the submatrices of the greatest dimension: `..`
/// // - Only the first row in each submatrix: `0..1`
/// // - Every element in each row: `..`
///
/// let b = a.slice(s![.., 0..1, ..]);
/// let c = arr3(&[[[ 1,  2,  3]],
///                [[ 7,  8,  9]]]);
/// assert_eq!(b, c);
/// assert_eq!(b.shape(), &[2, 1, 3]);
///
/// // Let’s create a slice with
/// //
/// // - Both submatrices of the greatest dimension: `..`
/// // - The last row in each submatrix: `-1..`
/// // - Row elements in reverse order: `..;-1`
/// let d = a.slice(s![.., -1.., ..;-1]);
/// let e = arr3(&[[[ 6,  5,  4]],
///                [[12, 11, 10]]]);
/// assert_eq!(d, e);
/// assert_eq!(d.shape(), &[2, 1, 3]);
///
/// // Let’s create a slice while selecting a subview and inserting a new axis with
/// //
/// // - Both submatrices of the greatest dimension: `..`
/// // - The last row in each submatrix, removing that axis: `-1`
/// // - Row elements in reverse order: `..;-1`
/// // - A new axis at the end.
/// let f = a.slice(s![.., -1, ..;-1, NewAxis]);
/// let g = arr3(&[[ [6],  [5],  [4]],
///                [[12], [11], [10]]]);
/// assert_eq!(f, g);
/// assert_eq!(f.shape(), &[2, 3, 1]);
///
/// // Let's take two disjoint, mutable slices of a matrix with
/// //
/// // - One containing all the even-index columns in the matrix
/// // - One containing all the odd-index columns in the matrix
/// let mut h = arr2(&[[0, 1, 2, 3],
///                    [4, 5, 6, 7]]);
/// let (s0, s1) = h.multi_slice_mut((s![.., ..;2], s![.., 1..;2]));
/// let i = arr2(&[[0, 2],
///                [4, 6]]);
/// let j = arr2(&[[1, 3],
///                [5, 7]]);
/// assert_eq!(s0, i);
/// assert_eq!(s1, j);
///
/// // Generic function which assigns the specified value to the elements which
/// // have indices in the lower half along all axes.
/// fn fill_lower<S, D>(arr: &mut ArrayBase<S, D>, x: S::Elem)
/// where
///     S: DataMut,
///     S::Elem: Clone,
///     D: Dimension,
/// {
///     arr.slice_each_axis_mut(|ax| Slice::from(0..ax.len / 2)).fill(x);
/// }
/// fill_lower(&mut h, 9);
/// let k = arr2(&[[9, 9, 2, 3],
///                [4, 5, 6, 7]]);
/// assert_eq!(h, k);
/// ```
///
/// ## Subviews
///
/// Subview methods allow you to restrict the array view while removing one
/// axis from the array. Methods for selecting individual subviews include
/// [`.index_axis()`], [`.index_axis_mut()`], [`.index_axis_move()`], and
/// [`.index_axis_inplace()`]. You can also select a subview by using a single
/// index instead of a range when slicing. Some other methods, such as
/// [`.fold_axis()`], [`.axis_iter()`], [`.axis_iter_mut()`],
/// [`.outer_iter()`], and [`.outer_iter_mut()`] operate on all the subviews
/// along an axis.
///
/// A related method is [`.collapse_axis()`], which modifies the view in the
/// same way as [`.index_axis()`] except for removing the collapsed axis, since
/// it operates *in place*. The length of the axis becomes 1.
///
/// Methods for selecting an individual subview take two arguments: `axis` and
/// `index`.
///
/// [`.axis_iter()`]: Self::axis_iter
/// [`.axis_iter_mut()`]: Self::axis_iter_mut
/// [`.fold_axis()`]: Self::fold_axis
/// [`.index_axis()`]: Self::index_axis
/// [`.index_axis_inplace()`]: Self::index_axis_inplace
/// [`.index_axis_mut()`]: Self::index_axis_mut
/// [`.index_axis_move()`]: Self::index_axis_move
/// [`.collapse_axis()`]: Self::collapse_axis
/// [`.outer_iter()`]: Self::outer_iter
/// [`.outer_iter_mut()`]: Self::outer_iter_mut
///
/// ```
///
/// use ndarray::{arr3, aview1, aview2, s, Axis};
///
///
/// // 2 submatrices of 2 rows with 3 elements per row, means a shape of `[2, 2, 3]`.
///
/// let a = arr3(&[[[ 1,  2,  3],    // \ axis 0, submatrix 0
///                 [ 4,  5,  6]],   // /
///                [[ 7,  8,  9],    // \ axis 0, submatrix 1
///                 [10, 11, 12]]]); // /
///         //        \
///         //         axis 2, column 0
///
/// assert_eq!(a.shape(), &[2, 2, 3]);
///
/// // Let’s take a subview along the greatest dimension (axis 0),
/// // taking submatrix 0, then submatrix 1
///
/// let sub_0 = a.index_axis(Axis(0), 0);
/// let sub_1 = a.index_axis(Axis(0), 1);
///
/// assert_eq!(sub_0, aview2(&[[ 1,  2,  3],
///                            [ 4,  5,  6]]));
/// assert_eq!(sub_1, aview2(&[[ 7,  8,  9],
///                            [10, 11, 12]]));
/// assert_eq!(sub_0.shape(), &[2, 3]);
///
/// // This is the subview picking only axis 2, column 0
/// let sub_col = a.index_axis(Axis(2), 0);
///
/// assert_eq!(sub_col, aview2(&[[ 1,  4],
///                              [ 7, 10]]));
///
/// // You can take multiple subviews at once (and slice at the same time)
/// let double_sub = a.slice(s![1, .., 0]);
/// assert_eq!(double_sub, aview1(&[7, 10]));
/// ```
///
/// ## Arithmetic Operations
///
/// Arrays support all arithmetic operations the same way: they apply elementwise.
///
/// Since the trait implementations are hard to overview, here is a summary.
///
/// ### Binary Operators with Two Arrays
///
/// Let `A` be an array or view of any kind. Let `B` be an array
/// with owned storage (either `Array` or `ArcArray`).
/// Let `C` be an array with mutable data (either `Array`, `ArcArray`
/// or `ArrayViewMut`).
/// The following combinations of operands
/// are supported for an arbitrary binary operator denoted by `@` (it can be
/// `+`, `-`, `*`, `/` and so on).
///
/// - `&A @ &A` which produces a new `Array`
/// - `B @ A` which consumes `B`, updates it with the result, and returns it
/// - `B @ &A` which consumes `B`, updates it with the result, and returns it
/// - `C @= &A` which performs an arithmetic operation in place
///
/// Note that the element type needs to implement the operator trait and the
/// `Clone` trait.
///
/// ```
/// use ndarray::{array, ArrayView1};
///
/// let owned1 = array![1, 2];
/// let owned2 = array![3, 4];
/// let view1 = ArrayView1::from(&[5, 6]);
/// let view2 = ArrayView1::from(&[7, 8]);
/// let mut mutable = array![9, 10];
///
/// let sum1 = &view1 + &view2;   // Allocates a new array. Note the explicit `&`.
/// // let sum2 = view1 + &view2; // This doesn't work because `view1` is not an owned array.
/// let sum3 = owned1 + view1;    // Consumes `owned1`, updates it, and returns it.
/// let sum4 = owned2 + &view2;   // Consumes `owned2`, updates it, and returns it.
/// mutable += &view2;            // Updates `mutable` in-place.
/// ```
///
/// ### Binary Operators with Array and Scalar
///
/// The trait [`ScalarOperand`] marks types that can be used in arithmetic
/// with arrays directly. For a scalar `K` the following combinations of operands
/// are supported (scalar can be on either the left or right side, but
/// `ScalarOperand` docs has the detailed conditions).
///
/// - `&A @ K` or `K @ &A` which produces a new `Array`
/// - `B @ K` or `K @ B` which consumes `B`, updates it with the result and returns it
/// - `C @= K` which performs an arithmetic operation in place
///
/// ### Unary Operators
///
/// Let `A` be an array or view of any kind. Let `B` be an array with owned
/// storage (either `Array` or `ArcArray`). The following operands are supported
/// for an arbitrary unary operator denoted by `@` (it can be `-` or `!`).
///
/// - `@&A` which produces a new `Array`
/// - `@B` which consumes `B`, updates it with the result, and returns it
///
/// ## Broadcasting
///
/// Arrays support limited *broadcasting*, where arithmetic operations with
/// array operands of different sizes can be carried out by repeating the
/// elements of the smaller dimension array. See
/// [`.broadcast()`](Self::broadcast) for a more detailed
/// description.
///
/// ```
/// use ndarray::arr2;
///
/// let a = arr2(&[[1., 1.],
///                [1., 2.],
///                [0., 3.],
///                [0., 4.]]);
///
/// let b = arr2(&[[0., 1.]]);
///
/// let c = arr2(&[[1., 2.],
///                [1., 3.],
///                [0., 4.],
///                [0., 5.]]);
/// // We can add because the shapes are compatible even if not equal.
/// // The `b` array is shape 1 × 2 but acts like a 4 × 2 array.
/// assert!(
///     c == a + b
/// );
/// ```
///
/// ## Conversions
///
/// ### Conversions Between Array Types
///
/// This table is a summary of the conversions between arrays of different
/// ownership, dimensionality, and element type. All of the conversions in this
/// table preserve the shape of the array.
///
/// <table>
/// <tr>
/// <th rowspan="2">Output</th>
/// <th colspan="5">Input</th>
/// </tr>
///
/// <tr>
/// <td>
///
/// `Array<A, D>`
///
/// </td>
/// <td>
///
/// `ArcArray<A, D>`
///
/// </td>
/// <td>
///
/// `CowArray<'a, A, D>`
///
/// </td>
/// <td>
///
/// `ArrayView<'a, A, D>`
///
/// </td>
/// <td>
///
/// `ArrayViewMut<'a, A, D>`
///
/// </td>
/// </tr>
///
/// <!--Conversions to `Array<A, D>`-->
///
/// <tr>
/// <td>
///
/// `Array<A, D>`
///
/// </td>
/// <td>
///
/// no-op
///
/// </td>
/// <td>
///
/// [`a.into_owned()`][.into_owned()]
///
/// </td>
/// <td>
///
/// [`a.into_owned()`][.into_owned()]
///
/// </td>
/// <td>
///
/// [`a.to_owned()`][.to_owned()]
///
/// </td>
/// <td>
///
/// [`a.to_owned()`][.to_owned()]
///
/// </td>
/// </tr>
///
/// <!--Conversions to `ArcArray<A, D>`-->
///
/// <tr>
/// <td>
///
/// `ArcArray<A, D>`
///
/// </td>
/// <td>
///
/// [`a.into_shared()`][.into_shared()]
///
/// </td>
/// <td>
///
/// no-op
///
/// </td>
/// <td>
///
/// [`a.into_owned().into_shared()`][.into_shared()]
///
/// </td>
/// <td>
///
/// [`a.to_owned().into_shared()`][.into_shared()]
///
/// </td>
/// <td>
///
/// [`a.to_owned().into_shared()`][.into_shared()]
///
/// </td>
/// </tr>
///
/// <!--Conversions to `CowArray<'a, A, D>`-->
///
/// <tr>
/// <td>
///
/// `CowArray<'a, A, D>`
///
/// </td>
/// <td>
///
/// [`CowArray::from(a)`](CowArray#impl-From<ArrayBase<OwnedRepr<A>%2C%20D>>)
///
/// </td>
/// <td>
///
/// [`CowArray::from(a.into_owned())`](CowArray#impl-From<ArrayBase<OwnedRepr<A>%2C%20D>>)
///
/// </td>
/// <td>
///
/// no-op
///
/// </td>
/// <td>
///
/// [`CowArray::from(a)`](CowArray#impl-From<ArrayBase<ViewRepr<%26%27a%20A>%2C%20D>>)
///
/// </td>
/// <td>
///
/// [`CowArray::from(a.view())`](CowArray#impl-From<ArrayBase<ViewRepr<%26%27a%20A>%2C%20D>>)
///
/// </td>
/// </tr>
///
/// <!--Conversions to `ArrayView<'b, A, D>`-->
///
/// <tr>
/// <td>
///
/// `ArrayView<'b, A, D>`
///
/// </td>
/// <td>
///
/// [`a.view()`][.view()]
///
/// </td>
/// <td>
///
/// [`a.view()`][.view()]
///
/// </td>
/// <td>
///
/// [`a.view()`][.view()]
///
/// </td>
/// <td>
///
/// [`a.view()`][.view()] or [`a.reborrow()`][ArrayView::reborrow()]
///
/// </td>
/// <td>
///
/// [`a.view()`][.view()]
///
/// </td>
/// </tr>
///
/// <!--Conversions to `ArrayViewMut<'b, A, D>`-->
///
/// <tr>
/// <td>
///
/// `ArrayViewMut<'b, A, D>`
///
/// </td>
/// <td>
///
/// [`a.view_mut()`][.view_mut()]
///
/// </td>
/// <td>
///
/// [`a.view_mut()`][.view_mut()]
///
/// </td>
/// <td>
///
/// [`a.view_mut()`][.view_mut()]
///
/// </td>
/// <td>
///
/// illegal
///
/// </td>
/// <td>
///
/// [`a.view_mut()`][.view_mut()] or [`a.reborrow()`][ArrayViewMut::reborrow()]
///
/// </td>
/// </tr>
///
/// <!--Conversions to equivalent with dim `D2`-->
///
/// <tr>
/// <td>
///
/// equivalent with dim `D2` (e.g. converting from dynamic dim to const dim)
///
/// </td>
/// <td colspan="5">
///
/// [`a.into_dimensionality::<D2>()`][.into_dimensionality()]
///
/// </td>
/// </tr>
///
/// <!--Conversions to equivalent with dim `IxDyn`-->
///
/// <tr>
/// <td>
///
/// equivalent with dim `IxDyn`
///
/// </td>
/// <td colspan="5">
///
/// [`a.into_dyn()`][.into_dyn()]
///
/// </td>
/// </tr>
///
/// <!--Conversions to `Array<B, D>`-->
///
/// <tr>
/// <td>
///
/// `Array<B, D>` (new element type)
///
/// </td>
/// <td colspan="5">
///
/// [`a.map(|x| x.do_your_conversion())`][.map()]
///
/// </td>
/// </tr>
/// </table>
///
/// ### Conversions Between Arrays and `Vec`s/Slices/Scalars
///
/// This is a table of the safe conversions between arrays and
/// `Vec`s/slices/scalars. Note that some of the return values are actually
/// `Result`/`Option` wrappers around the indicated output types.
///
/// Input | Output | Methods
/// ------|--------|--------
/// `Vec<A>` | `ArrayBase<S: DataOwned, Ix1>` | [`::from_vec()`](Self::from_vec)
/// `Vec<A>` | `ArrayBase<S: DataOwned, D>` | [`::from_shape_vec()`](Self::from_shape_vec)
/// `&[A]` | `ArrayView1<A>` | [`::from()`](ArrayView#method.from)
/// `&[A]` | `ArrayView<A, D>` | [`::from_shape()`](ArrayView#method.from_shape)
/// `&mut [A]` | `ArrayViewMut1<A>` | [`::from()`](ArrayViewMut#method.from)
/// `&mut [A]` | `ArrayViewMut<A, D>` | [`::from_shape()`](ArrayViewMut#method.from_shape)
/// `&ArrayBase<S, Ix1>` | `Vec<A>` | [`.to_vec()`](Self::to_vec)
/// `Array<A, D>` | `Vec<A>` | [`.into_raw_vec()`](Array#method.into_raw_vec)<sup>[1](#into_raw_vec)</sup>
/// `&ArrayBase<S, D>` | `&[A]` | [`.as_slice()`](Self::as_slice)<sup>[2](#req_contig_std)</sup>, [`.as_slice_memory_order()`](Self::as_slice_memory_order)<sup>[3](#req_contig)</sup>
/// `&mut ArrayBase<S: DataMut, D>` | `&mut [A]` | [`.as_slice_mut()`](Self::as_slice_mut)<sup>[2](#req_contig_std)</sup>, [`.as_slice_memory_order_mut()`](Self::as_slice_memory_order_mut)<sup>[3](#req_contig)</sup>
/// `ArrayView<A, D>` | `&[A]` | [`.to_slice()`](ArrayView#method.to_slice)<sup>[2](#req_contig_std)</sup>
/// `ArrayViewMut<A, D>` | `&mut [A]` | [`.into_slice()`](ArrayViewMut#method.into_slice)<sup>[2](#req_contig_std)</sup>
/// `Array0<A>` | `A` | [`.into_scalar()`](Array#method.into_scalar)
///
/// <sup><a name="into_raw_vec">1</a></sup>Returns the data in memory order.
///
/// <sup><a name="req_contig_std">2</a></sup>Works only if the array is
/// contiguous and in standard order.
///
/// <sup><a name="req_contig">3</a></sup>Works only if the array is contiguous.
///
/// The table above does not include all the constructors; it only shows
/// conversions to/from `Vec`s/slices. See
/// [below](#constructor-methods-for-owned-arrays) for more constructors.
///
/// [ArrayView::reborrow()]: ArrayView#method.reborrow
/// [ArrayViewMut::reborrow()]: ArrayViewMut#method.reborrow
/// [.into_dimensionality()]: Self::into_dimensionality
/// [.into_dyn()]: Self::into_dyn
/// [.into_owned()]: Self::into_owned
/// [.into_shared()]: Self::into_shared
/// [.to_owned()]: Self::to_owned
/// [.map()]: Self::map
/// [.view()]: Self::view
/// [.view_mut()]: Self::view_mut
///
/// ### Conversions from Nested `Vec`s/`Array`s
///
/// It's generally a good idea to avoid nested `Vec`/`Array` types, such as
/// `Vec<Vec<A>>` or `Vec<Array2<A>>` because:
///
/// * they require extra heap allocations compared to a single `Array`,
///
/// * they can scatter data all over memory (because of multiple allocations),
///
/// * they cause unnecessary indirection (traversing multiple pointers to reach
///   the data),
///
/// * they don't enforce consistent shape within the nested
///   `Vec`s/`ArrayBase`s, and
///
/// * they are generally more difficult to work with.
///
/// The most common case where users might consider using nested
/// `Vec`s/`Array`s is when creating an array by appending rows/subviews in a
/// loop, where the rows/subviews are computed within the loop. However, there
/// are better ways than using nested `Vec`s/`Array`s.
///
/// If you know ahead-of-time the shape of the final array, the cleanest
/// solution is to allocate the final array before the loop, and then assign
/// the data to it within the loop, like this:
///
/// ```rust
/// use ndarray::{array, Array2, Axis};
///
/// let mut arr = Array2::zeros((2, 3));
/// for (i, mut row) in arr.axis_iter_mut(Axis(0)).enumerate() {
///     // Perform calculations and assign to `row`; this is a trivial example:
///     row.fill(i);
/// }
/// assert_eq!(arr, array![[0, 0, 0], [1, 1, 1]]);
/// ```
///
/// If you don't know ahead-of-time the shape of the final array, then the
/// cleanest solution is generally to append the data to a flat `Vec`, and then
/// convert it to an `Array` at the end with
/// [`::from_shape_vec()`](Self::from_shape_vec). You just have to be careful
/// that the layout of the data (the order of the elements in the flat `Vec`)
/// is correct.
///
/// ```rust
/// use ndarray::{array, Array2};
///
/// let ncols = 3;
/// let mut data = Vec::new();
/// let mut nrows = 0;
/// for i in 0..2 {
///     // Compute `row` and append it to `data`; this is a trivial example:
///     let row = vec![i; ncols];
///     data.extend_from_slice(&row);
///     nrows += 1;
/// }
/// let arr = Array2::from_shape_vec((nrows, ncols), data)?;
/// assert_eq!(arr, array![[0, 0, 0], [1, 1, 1]]);
/// # Ok::<(), ndarray::ShapeError>(())
/// ```
///
/// If neither of these options works for you, and you really need to convert
/// nested `Vec`/`Array` instances to an `Array`, the cleanest solution is
/// generally to use [`Iterator::flatten()`]
/// to get a flat `Vec`, and then convert the `Vec` to an `Array` with
/// [`::from_shape_vec()`](Self::from_shape_vec), like this:
///
/// ```rust
/// use ndarray::{array, Array2, Array3};
///
/// let nested: Vec<Array2<i32>> = vec![
///     array![[1, 2, 3], [4, 5, 6]],
///     array![[7, 8, 9], [10, 11, 12]],
/// ];
/// let inner_shape = nested[0].dim();
/// let shape = (nested.len(), inner_shape.0, inner_shape.1);
/// let flat: Vec<i32> = nested.iter().flatten().cloned().collect();
/// let arr = Array3::from_shape_vec(shape, flat)?;
/// assert_eq!(arr, array![
///     [[1, 2, 3], [4, 5, 6]],
///     [[7, 8, 9], [10, 11, 12]],
/// ]);
/// # Ok::<(), ndarray::ShapeError>(())
/// ```
///
/// Note that this implementation assumes that the nested `Vec`s are all the
/// same shape and that the `Vec` is non-empty. Depending on your application,
/// it may be a good idea to add checks for these assumptions and possibly
/// choose a different way to handle the empty case.
///
// # For implementors
//
// All methods must uphold the following constraints:
//
// 1. `data` must correctly represent the data buffer / ownership information,
//    `ptr` must point into the data represented by `data`, and the `dim` and
//    `strides` must be consistent with `data`. For example,
//
//    * If `data` is `OwnedRepr<A>`, all elements represented by `ptr`, `dim`,
//      and `strides` must be owned by the `Vec` and not aliased by multiple
//      indices.
//
//    * If `data` is `ViewRepr<&'a mut A>`, all elements represented by `ptr`,
//      `dim`, and `strides` must be exclusively borrowed and not aliased by
//      multiple indices.
//
// 2. If the type of `data` implements `Data`, then `ptr` must be aligned.
//
// 3. `ptr` must be non-null, and it must be safe to [`.offset()`] `ptr` by
//    zero.
//
// 4. It must be safe to [`.offset()`] the pointer repeatedly along all axes
//    and calculate the `count`s for the `.offset()` calls without overflow,
//    even if the array is empty or the elements are zero-sized.
//
//    More specifically, the set of all possible (signed) offset counts
//    relative to `ptr` can be determined by the following (the casts and
//    arithmetic must not overflow):
//
//    ```rust
//    /// Returns all the possible offset `count`s relative to `ptr`.
//    fn all_offset_counts(shape: &[usize], strides: &[isize]) -> BTreeSet<isize> {
//        assert_eq!(shape.len(), strides.len());
//        let mut all_offsets = BTreeSet::<isize>::new();
//        all_offsets.insert(0);
//        for axis in 0..shape.len() {
//            let old_offsets = all_offsets.clone();
//            for index in 0..shape[axis] {
//                assert!(index <= isize::MAX as usize);
//                let off = (index as isize).checked_mul(strides[axis]).unwrap();
//                for &old_offset in &old_offsets {
//                    all_offsets.insert(old_offset.checked_add(off).unwrap());
//                }
//            }
//        }
//        all_offsets
//    }
//    ```
//
//    Note that it must be safe to offset the pointer *repeatedly* along all
//    axes, so in addition for it being safe to offset `ptr` by each of these
//    counts, the difference between the least and greatest address reachable
//    by these offsets in units of `A` and in units of bytes must not be
//    greater than `isize::MAX`.
//
//    In other words,
//
//    * All possible pointers generated by moving along all axes must be in
//      bounds or one byte past the end of a single allocation with element
//      type `A`. The only exceptions are if the array is empty or the element
//      type is zero-sized. In these cases, `ptr` may be dangling, but it must
//      still be safe to [`.offset()`] the pointer along the axes.
//
//    * The offset in units of bytes between the least address and greatest
//      address by moving along all axes must not exceed `isize::MAX`. This
//      constraint prevents the computed offset, in bytes, from overflowing
//      `isize` regardless of the starting point due to past offsets.
//
//    * The offset in units of `A` between the least address and greatest
//      address by moving along all axes must not exceed `isize::MAX`. This
//      constraint prevents overflow when calculating the `count` parameter to
//      [`.offset()`] regardless of the starting point due to past offsets.
//
//    For example, if the shape is [2, 0, 3] and the strides are [3, 6, -1],
//    the offsets of interest relative to `ptr` are -2, -1, 0, 1, 2, 3. So,
//    `ptr.offset(-2)`, `ptr.offset(-1)`, …, `ptr.offset(3)` must be pointers
//    within a single allocation with element type `A`; `(3 - (-2)) *
//    size_of::<A>()` must not exceed `isize::MAX`, and `3 - (-2)` must not
//    exceed `isize::MAX`. Note that this is a requirement even though the
//    array is empty (axis 1 has length 0).
//
//    A dangling pointer can be used when creating an empty array, but this
//    usually means all the strides have to be zero. A dangling pointer that
//    can safely be offset by zero bytes can be constructed with
//    `::std::ptr::NonNull::<A>::dangling().as_ptr()`. (It isn't entirely clear
//    from the documentation that a pointer created this way is safe to
//    `.offset()` at all, even by zero bytes, but the implementation of
//    `Vec<A>` does this, so we can too. See rust-lang/rust#54857 for details.)
//
// 5. The product of non-zero axis lengths must not exceed `isize::MAX`. (This
//    also implies that the length of any individual axis must not exceed
//    `isize::MAX`, and an array can contain at most `isize::MAX` elements.)
//    This constraint makes various calculations easier because they don't have
//    to worry about overflow and axis lengths can be freely cast to `isize`.
//
// Constraints 2–5 are carefully designed such that if they're upheld for the
// array, they're also upheld for any subset of axes of the array as well as
// slices/subviews/reshapes of the array. This is important for iterators that
// produce subviews (and other similar cases) to be safe without extra (easy to
// forget) checks for zero-length axes. Constraint 1 is similarly upheld for
// any subset of axes and slices/subviews/reshapes, except when removing a
// zero-length axis (since if the other axes are non-zero-length, that would
// allow accessing elements that should not be possible to access).
//
// Method/function implementations can rely on these constraints being upheld.
// The constraints can be temporarily violated within a method/function
// implementation since `ArrayBase` doesn't implement `Drop` and `&mut
// ArrayBase` is `!UnwindSafe`, but the implementation must not call
// methods/functions on the array while it violates the constraints.
//
// Users of the `ndarray` crate cannot rely on these constraints because they
// may change in the future.
//
// [`.offset()`]: https://doc.rust-lang.org/stable/std/primitive.pointer.html#method.offset-1
pub struct ArrayBase<S, D>
where
    S: RawData,
{
    /// Data buffer / ownership information. (If owned, contains the data
    /// buffer; if borrowed, contains the lifetime and mutability.)
    data: S,
    /// A non-null pointer into the buffer held by `data`; may point anywhere
    /// in its range. If `S: Data`, this pointer must be aligned.
    ptr: std::ptr::NonNull<S::Elem>,
    /// The lengths of the axes.
    dim: D,
    /// The element count stride per axis. To be parsed as `isize`.
    strides: D,
}

/// An array where the data has shared ownership and is copy on write.
///
/// The `ArcArray<A, D>` is parameterized by `A` for the element type and `D` for
/// the dimensionality.
///
/// It can act as both an owner as the data as well as a shared reference (view
/// like).
/// Calling a method for mutating elements on `ArcArray`, for example
/// [`view_mut()`](ArrayBase::view_mut) or
/// [`get_mut()`](ArrayBase::get_mut), will break sharing and
/// require a clone of the data (if it is not uniquely held).
///
/// `ArcArray` uses atomic reference counting like `Arc`, so it is `Send` and
/// `Sync` (when allowed by the element type of the array too).
///
/// **[`ArrayBase`]** is used to implement both the owned
/// arrays and the views; see its docs for an overview of all array features.
///
/// See also:
///
/// + [Constructor Methods for Owned Arrays](ArrayBase#constructor-methods-for-owned-arrays)
/// + [Methods For All Array Types](ArrayBase#methods-for-all-array-types)
pub type ArcArray<A, D> = ArrayBase<OwnedArcRepr<A>, D>;

/// An array that owns its data uniquely.
///
/// `Array` is the main n-dimensional array type, and it owns all its array
/// elements.
///
/// The `Array<A, D>` is parameterized by `A` for the element type and `D` for
/// the dimensionality.
///
/// **[`ArrayBase`]** is used to implement both the owned
/// arrays and the views; see its docs for an overview of all array features.
///
/// See also:
///
/// + [Constructor Methods for Owned Arrays](ArrayBase#constructor-methods-for-owned-arrays)
/// + [Methods For All Array Types](ArrayBase#methods-for-all-array-types)
/// + Dimensionality-specific type alises
/// [`Array1`],
/// [`Array2`],
/// [`Array3`], ...,
/// [`ArrayD`],
/// and so on.
pub type Array<A, D> = ArrayBase<OwnedRepr<A>, D>;

/// An array with copy-on-write behavior.
///
/// An `CowArray` represents either a uniquely owned array or a view of an
/// array. The `'a` corresponds to the lifetime of the view variant.
///
/// This type is analogous to [`std::borrow::Cow`].
/// If a `CowArray` instance is the immutable view variant, then calling a
/// method for mutating elements in the array will cause it to be converted
/// into the owned variant (by cloning all the elements) before the
/// modification is performed.
///
/// Array views have all the methods of an array (see [`ArrayBase`]).
///
/// See also [`ArcArray`], which also provides
/// copy-on-write behavior but has a reference-counted pointer to the data
/// instead of either a view or a uniquely owned copy.
pub type CowArray<'a, A, D> = ArrayBase<CowRepr<'a, A>, D>;

/// A read-only array view.
///
/// An array view represents an array or a part of it, created from
/// an iterator, subview or slice of an array.
///
/// The `ArrayView<'a, A, D>` is parameterized by `'a` for the scope of the
/// borrow, `A` for the element type and `D` for the dimensionality.
///
/// Array views have all the methods of an array (see [`ArrayBase`]).
///
/// See also [`ArrayViewMut`].
pub type ArrayView<'a, A, D> = ArrayBase<ViewRepr<&'a A>, D>;

/// A read-write array view.
///
/// An array view represents an array or a part of it, created from
/// an iterator, subview or slice of an array.
///
/// The `ArrayViewMut<'a, A, D>` is parameterized by `'a` for the scope of the
/// borrow, `A` for the element type and `D` for the dimensionality.
///
/// Array views have all the methods of an array (see [`ArrayBase`]).
///
/// See also [`ArrayView`].
pub type ArrayViewMut<'a, A, D> = ArrayBase<ViewRepr<&'a mut A>, D>;

/// A read-only array view without a lifetime.
///
/// This is similar to [`ArrayView`] but does not carry any lifetime or
/// ownership information, and its data cannot be read without an unsafe
/// conversion into an [`ArrayView`]. The relationship between `RawArrayView`
/// and [`ArrayView`] is somewhat analogous to the relationship between `*const
/// T` and `&T`, but `RawArrayView` has additional requirements that `*const T`
/// does not, such as non-nullness.
///
/// The `RawArrayView<A, D>` is parameterized by `A` for the element type and
/// `D` for the dimensionality.
///
/// Raw array views have all the methods of an array (see
/// [`ArrayBase`]).
///
/// See also [`RawArrayViewMut`].
///
/// # Warning
///
/// You can't use this type with an arbitrary raw pointer; see
/// [`from_shape_ptr`](#method.from_shape_ptr) for details.
pub type RawArrayView<A, D> = ArrayBase<RawViewRepr<*const A>, D>;

/// A mutable array view without a lifetime.
///
/// This is similar to [`ArrayViewMut`] but does not carry any lifetime or
/// ownership information, and its data cannot be read/written without an
/// unsafe conversion into an [`ArrayViewMut`]. The relationship between
/// `RawArrayViewMut` and [`ArrayViewMut`] is somewhat analogous to the
/// relationship between `*mut T` and `&mut T`, but `RawArrayViewMut` has
/// additional requirements that `*mut T` does not, such as non-nullness.
///
/// The `RawArrayViewMut<A, D>` is parameterized by `A` for the element type
/// and `D` for the dimensionality.
///
/// Raw array views have all the methods of an array (see
/// [`ArrayBase`]).
///
/// See also [`RawArrayView`].
///
/// # Warning
///
/// You can't use this type with an arbitrary raw pointer; see
/// [`from_shape_ptr`](#method.from_shape_ptr) for details.
pub type RawArrayViewMut<A, D> = ArrayBase<RawViewRepr<*mut A>, D>;

pub use data_repr::OwnedRepr;

/// ArcArray's representation.
///
/// *Don’t use this type directly—use the type alias
/// [`ArcArray`] for the array type!*
#[derive(Debug)]
pub struct OwnedArcRepr<A>(Arc<OwnedRepr<A>>);

impl<A> Clone for OwnedArcRepr<A> {
    fn clone(&self) -> Self {
        OwnedArcRepr(self.0.clone())
    }
}

/// Array pointer’s representation.
///
/// *Don’t use this type directly—use the type aliases
/// [`RawArrayView`] / [`RawArrayViewMut`] for the array type!*
#[derive(Copy, Clone)]
// This is just a marker type, to carry the mutability and element type.
pub struct RawViewRepr<A> {
    ptr: PhantomData<A>,
}

impl<A> RawViewRepr<A> {
    #[inline(always)]
    fn new() -> Self {
        RawViewRepr { ptr: PhantomData }
    }
}

/// Array view’s representation.
///
/// *Don’t use this type directly—use the type aliases
/// [`ArrayView`] / [`ArrayViewMut`] for the array type!*
#[derive(Copy, Clone)]
// This is just a marker type, to carry the lifetime parameter.
pub struct ViewRepr<A> {
    life: PhantomData<A>,
}

impl<A> ViewRepr<A> {
    #[inline(always)]
    fn new() -> Self {
        ViewRepr { life: PhantomData }
    }
}

/// CowArray's representation.
///
/// *Don't use this type directly—use the type alias
/// [`CowArray`] for the array type!*
pub enum CowRepr<'a, A> {
    /// Borrowed data.
    View(ViewRepr<&'a A>),
    /// Owned data.
    Owned(OwnedRepr<A>),
}

impl<'a, A> CowRepr<'a, A> {
    /// Returns `true` iff the data is the `View` variant.
    pub fn is_view(&self) -> bool {
        match self {
            CowRepr::View(_) => true,
            CowRepr::Owned(_) => false,
        }
    }

    /// Returns `true` iff the data is the `Owned` variant.
    pub fn is_owned(&self) -> bool {
        match self {
            CowRepr::View(_) => false,
            CowRepr::Owned(_) => true,
        }
    }
}

// NOTE: The order of modules decides in which order methods on the type ArrayBase
// (mainly mentioning that as the most relevant type) show up in the documentation.
// Consider the doc effect of ordering modules here.
mod impl_clone;

mod impl_internal_constructors;
mod impl_constructors;

mod impl_methods;
mod impl_owned_array;
mod impl_special_element_types;

/// Private Methods
impl<A, S, D> ArrayBase<S, D>
where
    S: Data<Elem = A>,
    D: Dimension,
{
    #[inline]
    fn broadcast_unwrap<E>(&self, dim: E) -> ArrayView<'_, A, E>
    where
        E: Dimension,
    {
        #[cold]
        #[inline(never)]
        fn broadcast_panic<D, E>(from: &D, to: &E) -> !
        where
            D: Dimension,
            E: Dimension,
        {
            panic!(
                "ndarray: could not broadcast array from shape: {:?} to: {:?}",
                from.slice(),
                to.slice()
            )
        }

        match self.broadcast(dim.clone()) {
            Some(it) => it,
            None => broadcast_panic(&self.dim, &dim),
        }
    }

    // Broadcast to dimension `E`, without checking that the dimensions match
    // (Checked in debug assertions).
    #[inline]
    fn broadcast_assume<E>(&self, dim: E) -> ArrayView<'_, A, E>
    where
        E: Dimension,
    {
        let dim = dim.into_dimension();
        debug_assert_eq!(self.shape(), dim.slice());
        let ptr = self.ptr;
        let mut strides = dim.clone();
        strides.slice_mut().copy_from_slice(self.strides.slice());
        unsafe { ArrayView::new(ptr, dim, strides) }
    }

    fn raw_strides(&self) -> D {
        self.strides.clone()
    }

    /// Remove array axis `axis` and return the result.
    fn try_remove_axis(self, axis: Axis) -> ArrayBase<S, D::Smaller> {
        let d = self.dim.try_remove_axis(axis);
        let s = self.strides.try_remove_axis(axis);
        // safe because new dimension, strides allow access to a subset of old data
        unsafe {
            self.with_strides_dim(s, d)
        }
    }
}

// parallel methods
#[cfg(feature = "rayon")]
extern crate rayon_ as rayon;
#[cfg(feature = "rayon")]
pub mod parallel;

mod impl_1d;
mod impl_2d;
mod impl_dyn;

mod numeric;

pub mod linalg;

mod impl_ops;
pub use crate::impl_ops::ScalarOperand;

#[cfg(any(feature = "approx", feature = "approx-0_5"))]
mod array_approx;

// Array view methods
mod impl_views;

// Array raw view methods
mod impl_raw_views;

// Copy-on-write array methods
mod impl_cow;

/// Returns `true` if the pointer is aligned.
pub(crate) fn is_aligned<T>(ptr: *const T) -> bool {
    (ptr as usize) % ::std::mem::align_of::<T>() == 0
}