Numjs

NumJs is a npm/bower package for scientific computing with JavaScript. It contains among other things:

• a powerful N-dimensional array object
• linear algebra function
• fast Fourier transform
• tools for basic image processing

Besides its obvious scientific uses, NumJs can also be used as an efficient multi-dimensional container of generic data.

It works both in node.js and in the browser (with or without browserify)

NumJs is licensed under the MIT license, enabling reuse with almost no restrictions.

See this jsfiddle for a concrete example of how to use the library to manipulate images in the browser.

Installation

on node.js

npm install numjs

var nj = require('numjs');
...

on the browser

bower install numjs

<script src="bower_packages/numjs/dist/numjs.min.js"></script>
<!-- or include it directly from a CDN -->
<script src="https://cdn.jsdelivr.net/gh/nicolaspanel/numjs@0.15.1/dist/numjs.min.js"></script>

Basics

Array Creation

> var a = nj.array([2,3,4]);
> a
array([ 2, 3, 4])
> var b = nj.array([[1,2,3], [4,5,6]]);
> b
array([[ 1, 2, 3],
       [ 4, 5, 6]])

Note: Default data container is Javascript Array object. If needed, you can also use typed array such as Uint8Array:

> var a = nj.uint8([1,2,3]);
> a
array([ 1, 2, 3], dtype=uint8)

Note: possible types are int8, uint8, int16, uint16, int32, uint32, float32, float64 and array (the default)

To create arrays with a given shape, you can use zeros, ones or random functions:

> nj.zeros([2,3]);
array([[ 0, 0, 0],
       [ 0, 0, 0]])
> nj.ones([2,3,4], 'int32')     // dtype can also be specified
array([[[ 1, 1, 1, 1],
        [ 1, 1, 1, 1],
        [ 1, 1, 1, 1]],
       [[ 1, 1, 1, 1],
        [ 1, 1, 1, 1],
        [ 1, 1, 1, 1]]], dtype=int32)

> nj.random([4,3])
array([[ 0.9182 , 0.85176, 0.22587],
       [ 0.50088, 0.74376, 0.84024],
       [ 0.74045, 0.23345, 0.20289],
       [ 0.00612, 0.37732, 0.06932]])

To create sequences of numbers, NumJs provides a function called arange:

> nj.arange(4);
array([ 0, 1, 2, 3])

> nj.arange( 10, 30, 5 )
array([ 10, 15, 20, 25])

> nj.arange(1, 5, 'uint8');
array([ 1, 2, 3, 4], dtype=uint8)

More info about the array

NumJs’s array class is called NdArray. It is also known by the alias array. The more important properties of an NdArray object are:

• NdArray#ndim: the number of axes (dimensions) of the array.
• NdArray#shape: the dimensions of the array. This is a list of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be [n,m]. The length of the shape is therefore the number of dimensions, ndim.
• NdArray#size: the total number of elements of the array. This is equal to the product of the elements of shape.
• NdArray#dtype: a string describing the type of the elements in the array. int32, int16, and float64 are some examples. Default dtype is array.

An NdArray can always be converted to a native JavaScript Array using NdArray#tolist() method.

Example:

> a = nj.arange(15).reshape(3, 5);
array([[  0,  1,  2,  3,  4],
       [  5,  6,  7,  8,  9],
       [ 10, 11, 12, 13, 14]])

> a.shape
[ 3, 5]
> a.ndim
2
> a.dtype
'array'
> a instanceof nj.NdArray
true
> a.tolist() instanceof Array
true
> a.get(1,1)
6
> a.set(0,0,1)
> a
array([[  1,  1,  2,  3,  4],
       [  5,  6,  7,  8,  9],
       [ 10, 11, 12, 13, 14]])

Printing arrays

When you print an array, NumJs displays it in a similar way to nested lists, but with the following layout:

• the last axis is printed from left to right,
• the second-to-last is printed from top to bottom,
• the rest are also printed from top to bottom, with each slice separated from the next by an empty line.

One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices.

> var a = nj.arange(6);                 // 1d array
> console.log(a);
array([ 0, 1, 2, 3, 4, 5])
>
> var b = nj.arange(12).reshape(4,3);   // 2d array
> console.log(b);
array([[  0,  1,  2],
       [  3,  4,  5],
       [  6,  7,  8],
       [  9, 10, 11]])
>
> var c = nj.arange(24).reshape(2,3,4); // 3d array
> console.log(c);
array([[[  0,  1,  2,  3],
        [  4,  5,  6,  7],
        [  8,  9, 10, 11]],
       [[ 12, 13, 14, 15],
        [ 16, 17, 18, 19],
        [ 20, 21, 22, 23]]])

If an array is too large to be printed, NumJs automatically skips the central part of the array and only prints the corners:

> console.log(nj.arange(10000).reshape(100,100))
array([[    0,    1, ...,   98,   99],
       [  100,  101, ...,  198,  199],
        ...
       [ 9800, 9801, ..., 9898, 9899],
       [ 9900, 9901, ..., 9998, 9999]])

To customize this behaviour, you can change the printing options using nj.config.printThreshold (default is 7):

> nj.config.printThreshold = 9;
> console.log(nj.arange(10000).reshape(100,100))
array([[    0,    1,    2,    3, ...,   96,   97,   98,   99],
       [  100,  101,  102,  103, ...,  196,  197,  198,  199],
       [  200,  201,  202,  203, ...,  296,  297,  298,  299],
       [  300,  301,  302,  303, ...,  396,  397,  398,  399],
        ...
       [ 9600, 9601, 9602, 9603, ..., 9696, 9697, 9698, 9699],
       [ 9700, 9701, 9702, 9703, ..., 9796, 9797, 9798, 9799],
       [ 9800, 9801, 9802, 9803, ..., 9896, 9897, 9898, 9899],
       [ 9900, 9901, 9902, 9903, ..., 9996, 9997, 9998, 9999]])

Indexing

Single element indexing uses get and set methods. It is 0-based, and accepts negative indices for indexing from the end of the array:

> var a = nj.array([0,1,2]);
> a.get(1)
1
>
> a.get(-1)
2
>
> var b = nj.arange(3*3).reshape(3,3);
> b
array([[  0,  1,  2],
       [  3,  4,  5],
       [  6,  7,  8])
>
> b.get(1, 1);
4
>
> b.get(-1, -1);
8
> b.set(0,0,1);
> b
array([[ 1, 1, 2],
       [ 3, 4, 5],
       [ 6, 7, 8]])

Slicing and Striding

It is possible to slice and stride arrays to extract arrays of the same number of dimensions, but of different sizes than the original. The slicing and striding works exactly the same way it does in NumPy:

> var a = nj.arange(5);
> a
array([  0,  1,  2,  3,  4])
>
> a.slice(1) // skip the first item, same as a[1:]
array([ 1, 2, 3, 4])
>
> a.slice(-3) // takes the last 3 items, same as a[-3:]
array([ 2, 3, 4])
>
> a.slice([4]) // takes the first 4 items, same as a[:4]
array([ 0, 1, 2, 3])
>
> a.slice([-2]) // skip the last 2 items, same as a[:-2]
array([ 0, 1, 2])
>
> a.slice([1,4]) // same as a[1:4]
array([ 1, 2, 3])
>
> a.slice([1,4,-1]) // same as a[1:4:-1]
array([ 3, 2, 1])
>
> a.slice([null,null,-1]) // same as a[::-1]
array([ 4, 3, 2, 1, 0])
>
> var b = nj.arange(5*5).reshape(5,5);
> b
array([[  0,  1,  2,  3,  4],
       [  5,  6,  7,  8,  9],
       [ 10, 11, 12, 13, 14],
       [ 15, 16, 17, 18, 19],
       [ 20, 21, 22, 23, 24]])
>
> b.slice(1,2) //  skip the first row and the 2 first  columns, same as b[1:,2:]
array([[  7,  8,  9],
       [ 12, 13, 14],
       [ 17, 18, 19],
       [ 22, 23, 24]])
>
> b.slice(null, [null, null, -1]) // reverse rows, same as b[:, ::-1]
array([[  4,  3,  2,  1,  0],
       [  9,  8,  7,  6,  5],
       [ 14, 13, 12, 11, 10],
       [ 19, 18, 17, 16, 15],
       [ 24, 23, 22, 21, 20]])

Note that slices do not copy the internal array data, it produces a new views of the original data.

Basic operations

Arithmetic operators such as * (multiply), + (add), - (subtract), / (divide), ** (pow), = (assign) apply elemen-twise. A new array is created and filled with the result:

> zeros = nj.zeros([3,4]);
array([[ 0, 0, 0, 0],
       [ 0, 0, 0, 0],
       [ 0, 0, 0, 0]])
>
> ones = nj.ones([3,4]);
array([[ 1, 1, 1, 1],
       [ 1, 1, 1, 1],
       [ 1, 1, 1, 1]])
>
> ones.add(ones)
array([[ 2, 2, 2, 2],
       [ 2, 2, 2, 2],
       [ 2, 2, 2, 2]])
>
> ones.subtract(ones)
array([[ 0, 0, 0, 0],
       [ 0, 0, 0, 0],
       [ 0, 0, 0, 0]])
>
> zeros.pow(zeros)
array([[ 1, 1, 1, 1],
       [ 1, 1, 1, 1],
       [ 1, 1, 1, 1]])
>

To modify an existing array rather than create a new one you can set the copy parameter to false:

> ones = nj.ones([3,4]);
array([[ 1, 1, 1, 1],
       [ 1, 1, 1, 1],
       [ 1, 1, 1, 1]])
>
> ones.add(ones, false)
array([[ 2, 2, 2, 2],
       [ 2, 2, 2, 2],
       [ 2, 2, 2, 2]])
>
> ones
array([[ 2, 2, 2, 2],
       [ 2, 2, 2, 2],
       [ 2, 2, 2, 2]])
>
> zeros = nj.zeros([3,4])
> zeros.slice([1,-1],[1,-1]).assign(1, false);
> zeros
array([[ 0, 0, 0, 0],
       [ 0, 1, 1, 0],
       [ 0, 0, 0, 0]])

Note: available for add, subtract, multiply, divide, assign and pow methods.

The matrix product can be performed using the dot function:

> a = nj.arange(12).reshape(3,4);
array([[  0,  1,  2,  3],
       [  4,  5,  6,  7],
       [  8,  9, 10, 11]])
>
> nj.dot(a.T, a)
array([[  80,  92, 104, 116],
       [  92, 107, 122, 137],
       [ 104, 122, 140, 158],
       [ 116, 137, 158, 179]])
>
> nj.dot(a, a.T)
array([[  14,  38,  62],
       [  38, 126, 214],
       [  62, 214, 366]])

Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the NdArray class:

> a = nj.random([2,3])
array([[0.62755, 0.8278,0.21384],
       [ 0.7029,0.27584,0.46472]])
> a.sum()
3.11