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@0xcmdr/numjs 中文文档教程

发布于 5年前 浏览 35 项目主页 更新于 3年前

构建状态 npm 版本 凉亭版本Built with Grunt

NumJs 是一个 npm/bower 包，用于使用 JavaScript 进行科学计算。 除其他外，它包含：

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

除了明显的科学用途外，NumJs 还可以用作通用数据的高效多维容器。

它适用于 node.js 和浏览器（有或没有 browserify）

NumJs 是根据 MIT license，几乎没有限制地重用。

请参阅此 jsfiddle，了解如何使用该库在浏览器中操作图像的具体示例。

Installation (updated and fixed for NodeJS v13)

prerequsities

npm install -g node-gyp

install package

npm install @0xcmdr/numjs

or

yarn add @0xcmdr/numjs

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

on the browser (NOT UPDATED)

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]])

注意：默认数据容器是 Javascript Array 对象。 如果需要，您还可以使用类型化数组，例如 Uint8Array：

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

注意：可能的类型有 int8、uint8、int16、uint16、int32、uint32、float32、float64 和 array (默认值）

要创建具有给定形状的数组，您可以使用 zeros、ones 或 random 函数：

> 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]])

要创建数字序列，NumJs 提供了一个名为arange 的函数：

> 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 的数组类称为NdArray。 它也被称为 array 的别名。 NdArray 对象的更重要的属性是：

  • 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.

NdArray 总是可以使用 NdArray#tolist( ) 方法。

示例：

> 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

当您打印数组时，NumJs 以类似于嵌套列表的方式显示它，但具有以下布局：

  • 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.

然后将一维数组打印为行，将二维数组打印为矩阵，将三维数组打印为列表矩阵。

> 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]]])

如果数组太大而无法打印，NumJs 会自动跳过数组的中央部分，只打印边角：

> 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]])

要自定义此行为，您可以使用 nj.config 更改打印选项.printThreshold（默认为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

单元素索引使用get 和set 方法。 它是从 0 开始的，并且接受从数组末尾开始索引的负索引：

> 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

可以对数组进行切片和跨步以提取维数相同但大小与原始数组不同的数组。 切片和跨步的工作方式与它在 NumPy 中的工作方式完全相同：

> 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]])

请注意，切片不会复制内部数组数据，它会生成原始数据的新视图。

Basic operations

*（multiply）、+（add）、-等算术运算符(subtract), / (divide), ** (pow), = (assign) 按元素应用。 创建一个新数组并用结果填充：

> 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]])
>

要修改现有数组而不是创建一个新数组，您可以将 copy 参数设置为 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]])

注意< /strong>：可用于加法、减法、乘法、除法、赋值和 pow 方法。

可以使用 dot 函数执行矩阵乘积：

> 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]])

许多一元运算，例如计算数组中所有元素的总和，都是作为 NdArray 类的方法实现的:

> 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 提供熟悉的数学函数，例如 sin、cos 和 exp。 元素操作，生成 NdArray 作为输出

> 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

这些函数在数组上按

> 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 ]

：

> 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]])
>

由于 a 是矩阵，我们可能需要它的对角线：

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

Identity matrix

单位数组是一个正方形数组，其中一个在主对角线上：

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

Concatenate different arrays

可以使用 concatenate 函数将多个数组堆叠在一起：

> 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]])

注意：

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

仍然可以使用换位沿其他维度连接：

> 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]])

注意：

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

Deep Copy

clone 方法可完整复制数组及其数据。

> 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 和 ifft 函数可用于计算 N 维离散傅里叶变换及其逆变换。

示例：

> 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]])

注意：fft 和ifft 都期望数组的最后一维包含 2 个值：实值和虚值

Convolution

卷积 函数计算两个多维数组的离散线性卷积。

注意：卷积积仅针对信号完全重叠的点给出。 信号边界外的值无效。 此行为也称为“有效”模式。

示例：

> 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]])

注意：卷积 使用快速傅立叶变换 (FFT) 来加速大型数组的计算。

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])

Images manipulation

NumJs 具有强大的图像处理功能。 这些函数位于 nj.images 模块中。

使用 NdArray 对象存储不同的色带/通道，例如灰度图像是 [H,W]，RGB 图像是 [H, W,3] 而 RGBA 图像是 [H,W,4]。

使用 nj.images.read、nj.images.write 和 nj.images.resize 函数（分别）读取、写入或调整图像大小.

示例：

> nj.config.printThreshold = 28;
>
> var img = nj.images.data.digit;  // WARN: this is a property, not a function. See also `nj.images.data.moon`, `nj.images.data.lenna` and `nj.images.data.node`
>
> img
array([[   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,   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,   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,   0,   0,   0,   0,   0,   0,   0,   0,   3,  18,  18,  18, 126, 136, 175,  26, 166, 255, 247, 127,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,  30,  36,  94, 154, 170, 253, 253, 253, 253, 253, 225, 172, 253, 242, 195,  64,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,  49, 238, 253, 253, 253, 253, 253, 253, 253, 253, 251,  93,  82,  82,  56,  39,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,  18, 219, 253, 253, 253, 253, 253, 198, 182, 247, 241,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,  80, 156, 107, 253, 253, 205,  11,   0,  43, 154,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,  14,   1, 154, 253,  90,   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, 139, 253, 190,   2,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  11, 190, 253,  70,   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,  35, 241, 225, 160, 108,   1,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  81, 240, 253, 253, 119,  25,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  45, 186, 253, 253, 150,  27,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  16,  93, 252, 253, 187,   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, 249, 253, 249,  64,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  46, 130, 183, 253, 253, 207,   2,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  39, 148, 229, 253, 253, 253, 250, 182,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  24, 114, 221, 253, 253, 253, 253, 201,  78,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,  23,  66, 213, 253, 253, 253, 253, 198,  81,   2,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,  18, 171, 219, 253, 253, 253, 253, 195,  80,   9,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,  55, 172, 226, 253, 253, 253, 253, 244, 133,  11,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0, 136, 253, 253, 253, 212, 135, 132,  16,   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,   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,   0,   0,   0,   0]], dtype=uint8)
> var resized = nj.images.resize(img, 14, 12)
>
> resized.shape
[ 14, 12 ]
>
> resized
array([[   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,   6,   9,  66,  51, 106,  94,   0],
       [   0,   0,  13, 140, 189, 233, 253, 253, 143, 159,  75,   0],
       [   0,   0,   5, 178, 217, 241,  98, 172,   0,   0,   0,   0],
       [   0,   0,   0,   4,  74, 197,   1,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   3, 180, 114,  28,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,  21, 182, 220,  51,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   4, 149, 236,  16,   0,   0],
       [   0,   0,   0,   0,   0,  47, 165, 236, 224,   1,   0,   0],
       [   0,   0,   0,  23, 152, 245, 240, 135,  20,   0,   0,   0],
       [   0,  57, 167, 245, 251, 148,  23,   0,   0,   0,   0,   0],
       [   0,  98, 127,  87,  37,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0]], dtype=uint8)

另请参阅 this jsfiddle 以了解有关浏览器可能实现的功能的更多详细信息。

More ?

请参阅有关 numjs globals 和 NdArray 方法。

Credits

NumJs 建立在 ndarray 之上并使用了许多 scijs 包

原文

Build Statusnpm versionBower versionBuilt with Grunt

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 (updated and fixed for NodeJS v13)

prerequsities

npm install -g node-gyp

install package

npm install @0xcmdr/numjs

or

yarn add @0xcmdr/numjs

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

on the browser (NOT UPDATED)

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()
3.1126488673035055
>
> 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])

Images manipulation

NumJs’s comes with powerful functions for image processing. Theses function are located in nj.images module.

The different color bands/channels are stored using the NdArray object such that a grey-image is [H,W], an RGB-image is [H,W,3] and an RGBA-image is [H,W,4].

Use nj.images.read, nj.images.write and nj.images.resize functions to (respectively) read, write or resize images.

Example:

> nj.config.printThreshold = 28;
>
> var img = nj.images.data.digit;  // WARN: this is a property, not a function. See also `nj.images.data.moon`, `nj.images.data.lenna` and `nj.images.data.node`
>
> img
array([[   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,   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,   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,   0,   0,   0,   0,   0,   0,   0,   0,   3,  18,  18,  18, 126, 136, 175,  26, 166, 255, 247, 127,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,  30,  36,  94, 154, 170, 253, 253, 253, 253, 253, 225, 172, 253, 242, 195,  64,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,  49, 238, 253, 253, 253, 253, 253, 253, 253, 253, 251,  93,  82,  82,  56,  39,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,  18, 219, 253, 253, 253, 253, 253, 198, 182, 247, 241,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,  80, 156, 107, 253, 253, 205,  11,   0,  43, 154,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,  14,   1, 154, 253,  90,   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, 139, 253, 190,   2,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  11, 190, 253,  70,   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,  35, 241, 225, 160, 108,   1,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  81, 240, 253, 253, 119,  25,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  45, 186, 253, 253, 150,  27,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  16,  93, 252, 253, 187,   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, 249, 253, 249,  64,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  46, 130, 183, 253, 253, 207,   2,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  39, 148, 229, 253, 253, 253, 250, 182,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,  24, 114, 221, 253, 253, 253, 253, 201,  78,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,  23,  66, 213, 253, 253, 253, 253, 198,  81,   2,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,  18, 171, 219, 253, 253, 253, 253, 195,  80,   9,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,  55, 172, 226, 253, 253, 253, 253, 244, 133,  11,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0, 136, 253, 253, 253, 212, 135, 132,  16,   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,   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,   0,   0,   0,   0]], dtype=uint8)
> var resized = nj.images.resize(img, 14, 12)
>
> resized.shape
[ 14, 12 ]
>
> resized
array([[   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,   6,   9,  66,  51, 106,  94,   0],
       [   0,   0,  13, 140, 189, 233, 253, 253, 143, 159,  75,   0],
       [   0,   0,   5, 178, 217, 241,  98, 172,   0,   0,   0,   0],
       [   0,   0,   0,   4,  74, 197,   1,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   3, 180, 114,  28,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,  21, 182, 220,  51,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   4, 149, 236,  16,   0,   0],
       [   0,   0,   0,   0,   0,  47, 165, 236, 224,   1,   0,   0],
       [   0,   0,   0,  23, 152, 245, 240, 135,  20,   0,   0,   0],
       [   0,  57, 167, 245, 251, 148,  23,   0,   0,   0,   0,   0],
       [   0,  98, 127,  87,  37,   0,   0,   0,   0,   0,   0,   0],
       [   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0]], dtype=uint8)

See also this jsfiddle for more details on what is possible from the browser.

More ?

See documentation on numjs globals and NdArray methods.

Credits

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

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