# ndarray 0.15.6

An n-dimensional array for general elements and for numerics. Lightweight array views and slicing; views support chunking and splitting.
Documentation
``````# Quickstart tutorial

If you are familiar with Python Numpy, do check out this [For Numpy User Doc](https://docs.rs/ndarray/0.13.0/ndarray/doc/ndarray_for_numpy_users/index.html)
after you go through this tutorial.

You can use [play.integer32.com](https://play.integer32.com/) to immediately try out the examples.

## The Basics

Just create your first 2x3 floating-point ndarray
```rust
use ndarray::prelude::*;

fn main() {
let a = array![
[1.,2.,3.],
[4.,5.,6.],
];
assert_eq!(a.ndim(), 2);         // get the number of dimensions of array a
assert_eq!(a.len(), 6);          // get the number of elements in array a
assert_eq!(a.shape(), [2, 3]);   // get the shape of array a
assert_eq!(a.is_empty(), false); // check if the array has zero elements

println!("{:?}", a);
}
```
This code will create a simple array and output to stdout:
```
[[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0]], shape=[2, 3], strides=[3, 1], layout=C (0x1), const ndim=2
```

## Array Creation

### Element type and dimensionality

Now let's create more arrays. How about try make a zero array with dimension of (3, 2, 4)?

```rust
use ndarray::prelude::*;
use ndarray::Array;
fn main() {
let a = Array::zeros((3, 2, 4).f());
println!("{:?}", a);
}
```
gives
```
|    let a = Array::zeros((3, 2, 4).f());
|        -   ^^^^^^^^^^^^ cannot infer type for type parameter `A`
```
Note that the compiler needs to infer the element type and dimensionality from context. In this
case the compiler failed to do that. Now we give it the type and let it infer dimensionality

```rust
use ndarray::prelude::*;
use ndarray::Array;
fn main() {
let a = Array::<f64, _>::zeros((3, 2, 4).f());
println!("{:?}", a);
}
```
and now it works:
```
[[[0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0]],

[[0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0]],

[[0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0]]], shape=[3, 2, 4], strides=[1, 3, 6], layout=F (0x2), const ndim=3
```

We can also specify its dimensionality

```rust
use ndarray::prelude::*;
use ndarray::{Array, Ix3};
fn main() {
let a = Array::<f64, Ix3>::zeros((3, 2, 4).f());
println!("{:?}", a);
}
```
`Ix3` stands for 3D array.

And now we are type checked. Try change the code above to `Array::<f64, Ix3>::zeros((3, 2, 4, 5).f());`
and compile, see what happens.

### How about create array of different type and having different initial values?

The [`from_elem`](http://docs.rs/ndarray/latest/ndarray/struct.ArrayBase.html#method.from_elem) method can be handy here:

```rust
use ndarray::{Array, Ix3};
fn main() {
let a = Array::<bool, Ix3>::from_elem((3, 2, 4), false);
println!("{:?}", a);
}
```

### Some common create helper functions
`linspace` - Create a 1-D array with 11 elements with values 0., …, 5.
```rust
use ndarray::prelude::*;
use ndarray::{Array, Ix3};
fn main() {
let a = Array::<f64, _>::linspace(0., 5., 11);
println!("{:?}", a);
}
```
The output is:
```
[0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0], shape=[11], strides=[1], layout=C | F (0x3), const ndim=1
```

And there are also `range`, `logspace`, `ones`, `eye` and so on you can choose to use.

## Basic operations

```rust
use ndarray::prelude::*;
use ndarray::Array;
use std::f64::INFINITY as inf;

fn main() {
let a = array![
[10.,20.,30., 40.,],
];
let b = Array::range(0., 4., 1.);  // [0., 1., 2., 3, ]

assert_eq!(&a + &b, array![[10., 21., 32., 43.,]]);  // Allocates a new array. Note the explicit `&`.
assert_eq!(&a - &b, array![[10., 19., 28., 37.,]]);
assert_eq!(&a * &b, array![[0., 20., 60., 120.,]]);
assert_eq!(&a / &b, array![[inf, 20., 15., 13.333333333333334,]]);
}
```

Try remove all the `&` sign in front of `a` and `b`, does it still compile? Why?

Note that
* `&A @ &A` produces a new `Array`
* `B @ A` consumes `B`, updates it with the result, and returns it
* `B @ &A` consumes `B`, updates it with the result, and returns it
* `C @= &A` performs an arithmetic operation in place

Some operations have `_axis` appended to the function name: they generally take in a parameter of type `Axis` as one of their inputs,
such as `sum_axis`:

```rust
use ndarray::{aview0, aview1, arr2, Axis};

fn main() {
let a = arr2(&[[1., 2., 3.],
[4., 5., 6.]]);
assert!(
a.sum_axis(Axis(0)) == aview1(&[5., 7., 9.]) &&
a.sum_axis(Axis(1)) == aview1(&[6., 15.]) &&

a.sum_axis(Axis(0)).sum_axis(Axis(0)) == aview0(&21.) &&
a.sum_axis(Axis(0)).sum_axis(Axis(0)) == aview0(&a.sum())
);
}
```

### Matrix product

```rust
use ndarray::prelude::*;
use ndarray::Array;

fn main() {
let a = array![
[10.,20.,30., 40.,],
];
let b = Array::range(0., 4., 1.);     // b = [0., 1., 2., 3, ]
println!("a shape {:?}", &a.shape());
println!("b shape {:?}", &b.shape());

let b = b.into_shape((4,1)).unwrap(); // reshape b to shape [4, 1]
println!("b shape {:?}", &b.shape());

println!("{}", a.dot(&b));            // [1, 4] x [4, 1] -> [1, 1]
println!("{}", a.t().dot(&b.t()));    // [4, 1] x [1, 4] -> [4, 4]
}
```
The output is:
```
a shape [1, 4]
b shape [4]
b shape after reshape [4, 1]
[[200]]
[[0, 10, 20, 30],
[0, 20, 40, 60],
[0, 30, 60, 90],
[0, 40, 80, 120]]
```

## Indexing, Slicing and Iterating
One-dimensional arrays can be indexed, sliced and iterated over, much like `numpy` arrays

```rust
use ndarray::prelude::*;
use ndarray::Array;

fn main() {
let a = Array::range(0., 10., 1.);

let mut a = a.mapv(|a: f64| a.powi(3));  // numpy equivlant of `a ** 3`; https://doc.rust-lang.org/nightly/std/primitive.f64.html#method.powi

println!("{}", a);

println!("{}", a[[2]]);
println!("{}", a.slice(s![2]));

println!("{}", a.slice(s![2..5]));

a.slice_mut(s![..6;2]).fill(1000.);  // numpy equivlant of `a[:6:2] = 1000`
println!("{}", a);

for i in a.iter() {
print!("{}, ", i.powf(1./3.))
}
}
```
The output is:
```
[0, 1, 8, 27, 64, 125, 216, 343, 512, 729]
8
8
[8, 27, 64]
[1000, 1, 1000, 27, 1000, 125, 216, 343, 512, 729]
9.999999999999998, 1, 9.999999999999998, 3, 9.999999999999998, 4.999999999999999, 5.999999999999999, 6.999999999999999, 7.999999999999999, 8.999999999999998,
```

For more info about iteration see [Loops, Producers, and Iterators](https://docs.rs/ndarray/0.13.0/ndarray/struct.ArrayBase.html#loops-producers-and-iterators)

Let's try a 3D array with elements of type `isize`. This is how you index it:
```rust
use ndarray::prelude::*;

fn main() {
let a = array![
[[  0,  1,  2],         // a 3D array  2 x 2 x 3
[ 10, 12, 13]],

[[100,101,102],
[110,112,113]]
];

let a = a.mapv(|a: isize| a.pow(1));  // numpy equivlant of `a ** 1`;
// This line does nothing but illustrate mapv with isize type
println!("a -> \n{}\n", a);

println!("`a.slice(s![1, .., ..])` -> \n{}\n", a.slice(s![1, .., ..]));

println!("`a.slice(s![.., .., 2])` -> \n{}\n", a.slice(s![.., .., 2]));

println!("`a.slice(s![.., 1, 0..2])` -> \n{}\n", a.slice(s![.., 1, 0..2]));

println!("`a.iter()` ->");
for i in a.iter() {
print!("{}, ", i)  // flat out to every element
}

println!("\n\n`a.outer_iter()` ->");
for i in a.outer_iter() {
print!("row: {}, \n", i)  // iterate through first dimension
}
}
```
The output is:
```
a ->
[[[0, 1, 2],
[10, 12, 13]],

[[100, 101, 102],
[110, 112, 113]]]

`a.slice(s![1, .., ..])` ->
[[100, 101, 102],
[110, 112, 113]]

`a.slice(s![.., .., 2])` ->
[[2, 13],
[102, 113]]

`a.slice(s![.., 1, 0..2])` ->
[[10, 12],
[110, 112]]

`a.iter()` ->
0, 1, 2, 10, 12, 13, 100, 101, 102, 110, 112, 113,

`a.outer_iter()` ->
row: [[0, 1, 2],
[10, 12, 13]],
row: [[100, 101, 102],
[110, 112, 113]],
```

## Shape Manipulation

### Changing the shape of an array
The shape of an array can be changed with `into_shape` method.

````rust
use ndarray::prelude::*;
use ndarray::Array;
use std::iter::FromIterator;
// use ndarray_rand::RandomExt;
// use ndarray_rand::rand_distr::Uniform;

fn main() {
// Or you may use ndarray_rand crate to generate random arrays
// let a = Array::random((2, 5), Uniform::new(0., 10.));

let a = array![
[3., 7., 3., 4.],
[1., 4., 2., 2.],
[7., 2., 4., 9.]];

println!("a = \n{:?}\n", a);

// use trait FromIterator to flatten a matrix to a vector
let b = Array::from_iter(a.iter());
println!("b = \n{:?}\n", b);

let c = b.into_shape([6, 2]).unwrap(); // consume b and generate c with new shape
println!("c = \n{:?}", c);
}
````
The output is:
```
a =
[[3.0, 7.0, 3.0, 4.0],
[1.0, 4.0, 2.0, 2.0],
[7.0, 2.0, 4.0, 9.0]], shape=[3, 4], strides=[4, 1], layout=C (0x1), const ndim=2

b =
[3.0, 7.0, 3.0, 4.0, 1.0, 4.0, 2.0, 2.0, 7.0, 2.0, 4.0, 9.0], shape=[12], strides=[1], layout=C | F (0x3), const ndim=1

c =
[[3.0, 7.0],
[3.0, 4.0],
[1.0, 4.0],
[2.0, 2.0],
[7.0, 2.0],
[4.0, 9.0]], shape=[6, 2], strides=[2, 1], layout=C (0x1), const ndim=2
```

### Stacking/concatenating together different arrays

The `stack!` and `concatenate!` macros are helpful for stacking/concatenating
arrays. The `stack!` macro stacks arrays along a new axis, while the
`concatenate!` macro concatenates arrays along an existing axis:

```rust
use ndarray::prelude::*;
use ndarray::{concatenate, stack, Axis};

fn main() {
let a = array![
[3., 7., 8.],
[5., 2., 4.],
];

let b = array![
[1., 9., 0.],
[5., 4., 1.],
];

println!("stack, axis 0:\n{:?}\n", stack![Axis(0), a, b]);
println!("stack, axis 1:\n{:?}\n", stack![Axis(1), a, b]);
println!("stack, axis 2:\n{:?}\n", stack![Axis(2), a, b]);
println!("concatenate, axis 0:\n{:?}\n", concatenate![Axis(0), a, b]);
println!("concatenate, axis 1:\n{:?}\n", concatenate![Axis(1), a, b]);
}
```
The output is:
```
stack, axis 0:
[[[3.0, 7.0, 8.0],
[5.0, 2.0, 4.0]],

[[1.0, 9.0, 0.0],
[5.0, 4.0, 1.0]]], shape=[2, 2, 3], strides=[6, 3, 1], layout=Cc (0x5), const ndim=3

stack, axis 1:
[[[3.0, 7.0, 8.0],
[1.0, 9.0, 0.0]],

[[5.0, 2.0, 4.0],
[5.0, 4.0, 1.0]]], shape=[2, 2, 3], strides=[3, 6, 1], layout=c (0x4), const ndim=3

stack, axis 2:
[[[3.0, 1.0],
[7.0, 9.0],
[8.0, 0.0]],

[[5.0, 5.0],
[2.0, 4.0],
[4.0, 1.0]]], shape=[2, 3, 2], strides=[1, 2, 6], layout=Ff (0xa), const ndim=3

concatenate, axis 0:
[[3.0, 7.0, 8.0],
[5.0, 2.0, 4.0],
[1.0, 9.0, 0.0],
[5.0, 4.0, 1.0]], shape=[4, 3], strides=[3, 1], layout=Cc (0x5), const ndim=2

concatenate, axis 1:
[[3.0, 7.0, 8.0, 1.0, 9.0, 0.0],
[5.0, 2.0, 4.0, 5.0, 4.0, 1.0]], shape=[2, 6], strides=[1, 2], layout=Ff (0xa), const ndim=2
```

### Splitting one array into several smaller ones

More to see here [ArrayView::split_at](https://docs.rs/ndarray/latest/ndarray/type.ArrayView.html#method.split_at)
```rust
use ndarray::prelude::*;
use ndarray::Axis;

fn main() {

let a = array![
[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.],
[8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]];

let (s1, s2) = a.view().split_at(Axis(0), 1);
println!("Split a from Axis(0), at index 1:");
println!("s1  = \n{}", s1);
println!("s2  = \n{}\n", s2);

let (s1, s2) = a.view().split_at(Axis(1), 4);
println!("Split a from Axis(1), at index 4:");
println!("s1  = \n{}", s1);
println!("s2  = \n{}\n", s2);
}
```
The output is:
```
Split a from Axis(0), at index 1:
s1  =
[[6, 7, 6, 9, 0, 5, 4, 0, 6, 8, 5, 2]]
s2  =
[[8, 5, 5, 7, 1, 8, 6, 7, 1, 8, 1, 0]]

Split a from Axis(1), at index 4:
s1  =
[[6, 7, 6, 9],
[8, 5, 5, 7]]
s2  =
[[0, 5, 4, 0, 6, 8, 5, 2],
[1, 8, 6, 7, 1, 8, 1, 0]]

```

## Copies and Views
### View, Ref or Shallow Copy
As in Rust we have owner ship, so we cannot simply
update an element of an array while we have a
shared view of it. This will help us write more
robust code.

```rust
use ndarray::prelude::*;
use ndarray::{Array, Axis};

fn main() {

let mut a = Array::range(0., 12., 1.).into_shape([3 ,4]).unwrap();
println!("a = \n{}\n", a);

{
let (s1, s2) = a.view().split_at(Axis(1), 2);

// with s as a view sharing the ref of a, we cannot update a here
// a.slice_mut(s![1, 1]).fill(1234.);

println!("Split a from Axis(0), at index 1:");
println!("s1  = \n{}", s1);
println!("s2  = \n{}\n", s2);
}

// now we can update a again here, as views of s1, s2 are dropped already
a.slice_mut(s![1, 1]).fill(1234.);

let (s1, s2) = a.view().split_at(Axis(1), 2);
println!("Split a from Axis(0), at index 1:");
println!("s1  = \n{}", s1);
println!("s2  = \n{}\n", s2);
}
```
The output is:
```
a =
[[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11]]

Split a from Axis(0), at index 1:
s1  =
[[0, 1],
[4, 5],
[8, 9]]
s2  =
[[2, 3],
[6, 7],
[10, 11]]

Split a from Axis(0), at index 1:
s1  =
[[0, 1],
[4, 1234],
[8, 9]]
s2  =
[[2, 3],
[6, 7],
[10, 11]]
```

### Deep Copy
As the usual way in Rust, a `clone()` call will
make a copy of your array:
```rust
use ndarray::prelude::*;
use ndarray::Array;

fn main() {

let mut a = Array::range(0., 4., 1.).into_shape([2 ,2]).unwrap();
let b = a.clone();

println!("a = \n{}\n", a);
println!("b clone of a = \n{}\n", a);

a.slice_mut(s![1, 1]).fill(1234.);

println!("a updated...");
println!("a = \n{}\n", a);
println!("b clone of a = \n{}\n", b);
}
```

The output is:
```
a =
[[0, 1],
[2, 3]]

b clone of a =
[[0, 1],
[2, 3]]

a updated...
a =
[[0, 1],
[2, 1234]]

b clone of a =
[[0, 1],
[2, 3]]
```

Noticing that using `clone()` (or cloning) an `Array` type also copies the array's elements. It creates an independently owned array of the same type.

Cloning an `ArrayView` does not clone or copy the underlying elements - it just clones the view reference (as it happens in Rust when cloning a `&` reference).

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.

```rust
use ndarray::prelude::*;

fn main() {
let a = array![
[1., 1.],
[1., 2.],
[0., 3.],
[0., 4.]];

let b = array![[0., 1.]];

let c = array![
[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);
}
```

See [.broadcast()](https://docs.rs/ndarray/latest/ndarray/struct.ArrayBase.html#method.broadcast) for a more detailed description.

And there is a short example of it:
```rust
use ndarray::prelude::*;

fn main() {
let a = array![
[1., 2.],
[3., 4.],
];

let b =  a.broadcast((3, 2, 2)).unwrap();
println!("shape of a is {:?}", a.shape());
println!("a is broadcased to 3x2x2 = \n{}", b);
}
```
The output is:
```
shape of a is [2, 2]
a is broadcased to 3x2x2 =
[[[1, 2],
[3, 4]],

[[1, 2],
[3, 4]],

[[1, 2],
[3, 4]]]
```