ndarray

Multidimensional arrays for JavaScript.

This is a fork which removes the refernece to node buffer types. This makes inclusion of this code in the browser via browserify rather smaller.

Introduction

ndarrays provide higher dimensional views of 1D arrays. For example, here is how you can turn a length 4 typed array into an nd-array:

var mat = ndarray(new Float64Array([1, 0, 0, 1]), [2,2])

//Now:
//
// mat = 1 0
//       0 1
//

Once you have an nd-array you can access elements using .set and .get. For example, here is an implementation of Conway's game of life using ndarrays:

function stepLife(next_state, cur_state) {

  //Get array shape
  var nx = cur_state.shape[0], 
      ny = cur_state.shape[1]

  //Loop over all cells
  for(var i=1; i<nx-1; ++i) {
    for(var j=1; j<ny-1; ++j) {

      //Count neighbors
      var n = 0
      for(var dx=-1; dx<=1; ++dx) {
        for(var dy=-1; dy<=1; ++dy) {
          if(dx === 0 && dy === 0) {
            continue
          }
          n += cur_state.get(i+dx, j+dy)
        }
      }
      
      //Update state according to rule
      if(n === 3 || n === 3 + cur_state.get(i,j)) {
        next_state.set(i,j,1)
      } else {
        next_state.set(i,j,0)
      }
    }
  }
}

You can also pull out views of ndarrays without copying the underlying elements. Here is an example showing how to update part of a subarray:

var x = ndarray(new Float32Array(25), [5, 5])
var y = x.hi(4,4).lo(1,1)

for(var i=0; i<y.shape[0]; ++i) {
  for(var j=0; j<y.shape[1]; ++j) {
    y.set(i,j,1)
  }
}

//Now:
//    x = 0 0 0 0 0
//        0 1 1 1 0
//        0 1 1 1 0
//        0 1 1 1 0
//        0 0 0 0 0

ndarrays can be transposed, flipped, sheared and sliced in constant time per operation. They are useful for representing images, audio, volume graphics, matrices, strings and much more. They work both in node.js and with browserify.

Install

Install the library using npm:

npm install ndarray

You can also use ndarrays in a browser with any tool that follows the CommonJS/node module conventions. The most direct way to do this is to use browserify. If you want live-reloading for faster debugging, check out beefy.

API

Once you have ndarray installed, you can use it in your project as follows:

var ndarray = require("ndarray")

Constructor

ndarray(data[, shape, stride, offset])

The default module.exports method is the constructor for ndarrays. It creates an n-dimensional array view wrapping an underlying storage type

• data is a 1D array storage. It is either an instance of Array, a typed array, or an object that implements get(), set(), .length
• shape is the shape of the view (Default: data.length)
• stride is the resulting stride of the new array. (Default: row major)
• offset is the offset to start the view (Default: 0)

Returns an n-dimensional array view of the buffer

Members

The central concept in ndarray is the idea of a view. The way these work is very similar to SciPy's array slices. Views are affine projections to 1D storage types. To better understand what this means, let's first look at the properties of the view object. It has exactly 4 variables:

• array.data - The underlying 1D storage for the multidimensional array
• array.shape - The shape of the typed array
• array.stride - The layout of the typed array in memory
• array.offset - The starting offset of the array in memory

Keeping a separate stride means that we can use the same data structure to support both row major and column major storage

Element Access

To access elements of the array, you can use the set/get methods:

array.get(i,j,...)

Retrieves element i,j,... from the array. In psuedocode, this is implemented as follows:

function get(i,j,...) {
  return this.data[this.offset + this.stride[0] * i + this.stride[1] * j + ... ]
}

array.set(i,j,...,v)

Sets element i,j,... to v. Again, in psuedocode this works like this:

function set(i,j,...,v) {
  return this.data[this.offset + this.stride[0] * i + this.stride[1] * j + ... ] = v
}

array.index(i,j, ...)

Retrieves the index of the cell in the underlying ndarray. In JS,

function index(i,j, ...) {
  return this.offset + this.stride[0] * i + this.stride[1] * j + ...
}

Properties

The following properties are created using Object.defineProperty and do not take up any physical memory. They can be useful in calculations involving ndarrays

array.dtype

Returns a string representing the undelying data type of the ndarray. Excluding generic data stores these types are compatible with typedarray-pool. This is mapped according to the following rules:

Data type | String --------: | :----- Int8Array | "int8" Int16Array | "int16" Int32Array | "int32" Uint8Array | "uint8" Uint16Array | "uint16" Uint32Array | "uint32" Float32Array | "float32" Float64Array | "float64" Array | "array" Uint8ArrayClamped | "uint8_clamped" Buffer | "buffer" Other | "generic"

Generic arrays access elements of the underlying 1D store using get()/set() instead of array accessors.

array.size

Returns the size of the array in logical elements.

array.order

Returns the order of the stride of the array, sorted in ascending length. The first element is the first index of the shortest stride and the last is the index the longest stride.

array.dimension

Returns the dimension of the array.

Slicing

Given a view, we can change the indexing by shifting, truncating or permuting the strides. This lets us perform operations like array reversals or matrix transpose in constant time (well, technically O(shape.length), but since shape.length is typically less than 4, it might as well be). To make life simpler, the following interfaces are exposed:

array.lo(i,j,k,...)

This creates a shifted view of the array. Think of it as taking the upper left corner of the image and dragging it inward by an amount equal to (i,j,k...).

array.hi(i,j,k,...)

This does the dual of array.lo(). Instead of shifting from the top-left, it truncates from the bottom-right of the array, returning a smaller array object. Using hi and lo in combination lets you select ranges in the middle of an array.

Note: hi and lo do not commute. In general:

a.hi(3,3).lo(3,3)  !=  a.lo(3,3).hi(3,3)

array.step(i,j,k...)

Changes the stride length by rescaling. Negative indices flip axes. For example, here is how you create a reversed view of a 1D array:

var reversed = a.step(-1)

You can also change the step size to be greater than 1 if you like, letting you skip entries of a list. For example, here is how to split an array into even and odd components:

var evens = a.step(2)
var odds = a.lo(1).step(2)

array.transpose(p0, p1, ...)

Finally, for higher dimensional arrays you can transpose the indices in place. This has the effect of permuting the shape and stride values. For example, in a 2D array you can calculate the matrix transpose by:

M.transpose(1, 0)

Or if you have a 3D volume image, you can shift the axes using more generic transformations:

volume.transpose(2, 0, 1)

array.pick(p0, p1, ...)

You can also pull out a subarray from an ndarray by fixing a particular axis. The way this works is you specify the direction you are picking by giving a list of values. For example, if you have an image stored as an nxmx3 array you can pull out the channel as follows:

var red   = image.pick(null, null, 0)
var green = image.pick(null, null, 1)
var blue  = image.pick(null, null, 2)

As the above example illustrates, passing a negative or non-numeric value to a coordinate in pick skips that index.

More information

For more discussion regarding the technical details see the following blog posts:

• ndarray presentation
• Interactive slice demo
• ndarray tutorial (Work in progress)
• Implementing multidimensional arrays in JavaScript
• Cache oblivious array operations
• ndarray modules
• ndarray benchmarks

Credits

(c) 2013 Mikola Lysenko. MIT License