@theoxiong/numjs

NumJs

Note

This repository is forked from nicolaspanel/numjs, and removed image-related features.

Feature

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

• a powerful N-dimensional array object
• linear algebra function
• fast Fourier transform

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

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

Installation

on node.js

npm install @theoxiong/numjs

const nj = require('@theoxiong/numjs')
...

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()
3.1126488673035055
>
> a.min()
0.2138431086204946
>
> a.max()
0.8278025290928781
>
> a.mean()
0.5187748112172509
>
> a.std()
0.22216977543691244

Universal Functions

NumJs provides familiar mathematical functions such as sin, cos, and exp. These functions operate element-wise on an array, producing an NdArray as output:

> a = nj.array([-1, 0, 1])
array([-1, 0, 1])
>
> nj.negative(a)
array([ 1, 0,-1])
>
> nj.abs(a)
array([ 1, 0, 1])
>
> nj.exp(a)
array([ 0.36788,       1, 2.71828])
>
> nj.tanh(a)
array([-0.76159,       0, 0.76159])
>
> nj.softmax(a)
array([ 0.09003, 0.24473, 0.66524])
>
> nj.sigmoid(a)
array([ 0.26894,     0.5, 0.73106])
>
> nj.exp(a)
array([ 0.36788,       1, 2.71828])
>
> nj.log(nj.exp(a))
array([-1, 0, 1])
>
> nj.sqrt(nj.abs(a))
array([ 1, 0, 1])
>
> nj.sin(nj.arcsin(a))
array([-1, 0, 1])
>
> nj.cos(nj.arccos(a))
array([-1, 0, 1])
>
> nj.tan(nj.arctan(a))
array([-1, 0, 1])

Shape Manipulation

An array has a shape given by the number of elements along each axis:

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

> a.shape
[ 3, 4 ]

The shape of an array can be changed with various commands:

> a.flatten();
array([  0,  1,  2, ...,  9, 10, 11])
>
> a.T                   // equivalent to a.transpose(1,0)
array([[  0,  4,  8],
       [  1,  5,  9],
       [  2,  6, 10],
       [  3,  7, 11]])
>
> a.reshape(4,3)
array([[  0,  1,  2],
       [  3,  4,  5],
       [  6,  7,  8],
       [  9, 10, 11]])
>

Since a is matrix we may want its diagonal:

> nj.diag(a)
array([  0,  5, 10])
>

Identity matrix

The identity array is a square array with ones on the main diagonal:

> nj.identity(3)
array([[ 1, 0, 0],
       [ 0, 1, 0],
       [ 0, 0, 1]])

Concatenate different arrays

Several arrays can be stacked together using concatenate function:

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

Notes:

• the arrays must have the same shape, except in the last dimension
• arrays are concatenated along the last axis

It is still possible to concatenate along other dimensions using transpositions:

> a = nj.arange(12).reshape(3,4)
array([[  0,  1,  2,  3],
       [  4,  5,  6,  7],
       [  8,  9, 10, 11]])
>
> b = nj.arange(4)
array([ 0, 1, 2, 3])
>
> nj.concatenate(a.T,b.reshape(4,1)).T
array([[  0,  1,  2,  3],
       [  4,  5,  6,  7],
       [  8,  9, 10, 11],
       [  0,  1,  2,  3]])

Stack multiple arrays

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

> np.stack([a, b])
array([[1, 2, 3],
       [2, 3, 4]])
> np.stack([a, b], -1)
array([[1, 2],
       [2, 3],
       [3, 4]])

Notes:

• the arrays must have the same shape
• take an optional axis argument which can be negative

Deep Copy

The clone method makes a complete copy of the array and its data.

> a = nj.arange(12).reshape(3,4)
array([[  0,  1,  2,  3],
       [  4,  5,  6,  7],
       [  8,  9, 10, 11]])
>
> b = a.clone()
array([[  0,  1,  2,  3],
       [  4,  5,  6,  7],
       [  8,  9, 10, 11]])
>
> a === b
false
>
> a.set(0,0,1)
> a
array([[  1,  1,  2,  3],
       [  4,  5,  6,  7],
       [  8,  9, 10, 11]])
> b
array([[  0,  1,  2,  3],
       [  4,  5,  6,  7],
       [  8,  9, 10, 11]])

Fast Fourier Transform (FFT)

fft and ifft functions can be used to compute the N-dimensional discrete Fourier Transform and its inverse.

Example:

> RI = nj.concatenate(nj.ones([10,1]), nj.zeros([10,1]))
array([[ 1, 0],
       [ 1, 0],
       [ 1, 0],
        ...
       [ 1, 0],
       [ 1, 0],
       [ 1, 0]])
>
> fft = nj.fft(RI)
array([[ 10,  0],
       [  0,  0],
       [  0,  0],
        ...
       [  0,  0],
       [  0,  0],
       [  0,  0]])
>
> nj.ifft(fft)
array([[ 1, 0],
       [ 1, 0],
       [ 1, 0],
        ...
       [ 1, 0],
       [ 1, 0],
       [ 1, 0]])

Note: both fft and ifft expect last dimension of the array to contain 2 values: the real and the imaginary value

Convolution

convolve function compute the discrete, linear convolution of two multi-dimensional arrays.

Note: The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect. This behaviour is also known as the 'valid' mode.

Example:

> x = nj.array([0,0,1,2,1,0,0])
array([ 0, 0, 1, 2, 1, 0, 0])
>
> nj.convolve(x, [-1,0,1])
array([-1,-2, 0, 2, 1])
>
> var a = nj.arange(25).reshape(5,5)
> a
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]])
> nj.convolve(a, [[ 1, 2, 1], [ 0, 0, 0], [-1,-2,-1]])
array([[ 40, 40, 40],
       [ 40, 40, 40],
       [ 40, 40, 40]])
> nj.convolve(nj.convolve(a, [[1, 2, 1]]), [[1],[0],[-1]])
array([[ 40, 40, 40],
       [ 40, 40, 40],
       [ 40, 40, 40]])

Note: convolve uses Fast Fourier Transform (FFT) to speed up computation on large arrays.

Other utils

rot90

> m = nj.array([[1,2],[3,4]], 'int')
> m
array([[1, 2],
       [3, 4]])
> nj.rot90(m)
array([[2, 4],
       [1, 3]])
> nj.rot90(m, 2)
array([[4, 3],
       [2, 1]])
> m = nj.arange(8).reshape([2,2,2])
> nj.rot90(m, 1, [1,2])
array([[[1, 3],
        [0, 2]],
      [[5, 7],
       [4, 6]]])

mod (since v0.16.0)

> nj.mod(nj.arange(7), 5)
> m
array([0, 1, 2, 3, 4, 0, 1])

More ?

See documentation on numjs globals and NdArray methods.

Credits

NumJs is built on top of ndarray and uses many scijs packages