Multi-Dimensional Functions
I work a lot with satellite imagery. In theory, most satellite imagery has three dimensions: (1) band, (2) row, and (3) column. However, for practical reasons, this data is often structured in a flat array, like ImageData.data or a two-dimensional array where each subarray holds all the values for a specific band in row-major order. This library was created for two main purposes: (1) to provide a unified interface for querying this data regardless of its practical structure and (2) converting this data between different array layouts.
npm install xdimMost of the functions in this library require that you specify the layout of the data using "xdim layout syntax" or "xdim syntax" for short. The format is simple with just a few main pieces:
- The straight brackets
[and]indicates an actual array or subarrays. - The comma
,appears between[and]and means dimensions are interleaved in left-to-right major order. - Dimension names can be made of any letter A to Z, lowercased or uppercased, can include underscores, and don't include spaces.
Here's a couple examples of the "xdim layout syntax":
You have an array of information about car models where the information is stored in subarrays:
[
["Fusion", "Ford", "United States", "2005", "2020"]
["Versa", "Nissan", "Japan", "2006", "2021"]
]The layout could be described as "[model][brand,maker,county,start_year,end_year]"
You have ImageData.data:
[31, 9, 71, 255, 126, 42, 53, 255, 71, 74, 71, 255, ...]The layout could be described as "[row,column,band]".
This library provides the following functions: select, prepareSelect, clip, iterClip, transform, prepareData, update, and prepareUpdate.
Select is used to get the value at a given multi-dimensional point. The point is an object where each key is the name of a dimension with an index number. Index numbers start at zero and increase until we reach the end of the length in the dimension.
import { select } from 'xdim';
// satellite imagery data broken down by band
const data = [
[0, 123, 123, 162, ...], // red band
[213, 41, 62, 124, ...], // green band
[84, 52, 124, 235, ...] // blue band
];
const result = select({
data,
// each band is a separate array
// the values in a band are in row-major order
layout: "[band][row,column]",
sizes: {
band: 3, // image has 3 bands (red, green, and blue)
column: 100 // image is 100 pixels wide
},
point: {
band: 2, // 3rd band (blue), where band index starts at zero
row: 74, // 75th row from the top
column: 63 // 64th column from the left
}
});result is an object
{
// the actual value found in the array
value: 62,
// the index in the array where the value is found
index: 7463,
// a reference to the same array in the provided data
parent: [84, 52, 124, 235, ... 62, ...]
}The prepareSelect function is use to create a supercharged select function for some data. There is some
fixed cost to creating the function, so only use it if you think you will run several to many selects.
✨ So what magic makes the prepared select statements so fast? We pre-generate select functions, so that JavaScript compilers can optimize the logical steps needed to lookup data. We then just bind the dimension names, sizes, and data to these "pre-compiled" functions.
import { prepareSelect } from 'xdim';
// satellite imagery data broken down by band
const data = [
[0, 123, 123, 162, ...], // red band
[213, 41, 62, 124, ...], // green band
[84, 52, 124, 235, ...] // blue band
];
const select = prepareSelect({
data,
// each band is a separate array
// the values in a band are in row-major order
layout: "[band][row,column]",
sizes: {
band: 3, // image has 3 bands (red, green, and blue)
column: 100 // image is 100 pixels wide
}
});
const result = select({
point: {
band: 2, // 3rd band (blue), where band index starts at zero
row: 74, // 75th row from the top
column: 63 // 64th column from the left
}
});result is an object
{
// the actual value found in the array
value: 62,
// the index in the array where the value is found
index: 7463,
// a reference to the same array in the provided data
parent: [84, 52, 124, 235, ... 62, ...]
}The clip function is used to pull out a subsection of the data within a hyperrectangle (i.e. multi-dimensional rectangle), which we call "rect". The "rect" is defined by an object with dimension name keys and a numerical range. The range is "inclusive", including the first and last numbers provided.
import { clip } from 'xdim';
// satellite imagery data broken down by band
const data = [
[0, 123, 123, 162, ...], // red band
[213, 41, 62, 124, ...], // green band
[84, 52, 124, 235, ...] // blue band
];
const result = clip({
data,
// if you don't care about the structure of the returned data
// or want to receive your results more quickly,
// you can set flat to true, and it will return a flat array
flat: false,
// each band is a separate array
// the values in a band are in row-major order
layout: "[band][row,column]",
sizes: {
band: 3, // image has 3 bands (red, green, and blue)
column: 100 // image is 100 pixels wide
},
rect: {
band: [2, 2], // 3rd band (blue), where band index starts at zero
row: [55, 74], // from the 56th to the 75th row (counting from the top)
column: [60, 62] // from the 61st to the 63rd column (counting from the left)
}
});result is an object
{
data: [
// only one band was selected, so we only have one sub-array
// because the original data combined all the rows in the same array
// the result has the same structure
// all the values in band 2 that fall within row 55 to row 74 and column 60 to 62
[64, 27, 19, 23, 45, 82 ... ]
]
}Like clip, but returns a flat iterator of values. Useful if you want to minimize memory usage and avoid creating a new array.
import { iterClip } from 'xdim';
// satellite imagery data broken down by band
const data = [
[0, 123, 123, 162, ...], // red band
[213, 41, 62, 124, ...], // green band
[84, 52, 124, 235, ...] // blue band
];
const result = iterClip({
data,
// each band is a separate array
// the values in a band are in row-major order
layout: "[band][row,column]",
sizes: {
band: 3, // image has 3 bands (red, green, and blue)
column: 100 // image is 100 pixels wide
},
rect: {
band: [2, 2], // 3rd band (blue), where band index starts at zero
row: [55, 74], // from the 56th to the 75th row (counting from the top)
column: [60, 62] // from the 61st to the 63rd column (counting from the left)
},
// optional
// order to return point values
// in left-to-right major order
order: ["band", "row", "column"]
});result is an iterator object
// call the first value
result.next();
// { done: false, next: 64}
// you can also use for of syntax
for (let n of result) {
// n is a number 27, then 19, then 23
}If your data is a one dimensional array, you can transform to another using the transform function. In the example below we transform from a flat array of ImageData.data to a truly 3-dimensional array of arrays of arrays representing bands, then rows, then columns.
import { transform } from 'multdimensional-functions';
// an array of image data red, green, blue, alpha, red, green, blue, alpha,...
const data = [0, 213, 84, 255, 123, 41, 52, 255, 123, 62, 124, 255, 162, 124, 235, 255, ...];
const result = transform({
data,
from: "[row,column,band]", // starting layout where all in one row with row-major order and interleaved bands
to: "[band][row][column]", // final layout where each dimension is represented by arrays or subarrays and there is no interleaving of numbers inside the arrays
sizes: {
band: 4, // red, green, blue and alpha
row: 768,
column: 1024
}
});result is an object
{
data: [
// red band
[
[0, 123, 123, 162, ...] // first row of the red band
[212, 124, 127, 92, ... ] // second row of the red band
],
// green band
[
[ ... ],
[ ... ]
],
// blue band
[
[ ... ],
[ ... ]
],
// alpha band
[
[ ... ],
[ ... ]
]
]
}If you just want to create the outline or skeleton of your structure without filling it in with data, you can call the prepareData function.
import { prepareData } from 'xdim';
const result = prepareData({
// the default fill value is undefined, but you can set it to zero, null, -99, an object, or really anything you want
// in this example, the default fill value is the number -99
fill: -99,
layout: "[band][row][column]",
sizes: {
band: 4,
column: 1024,
row: 768
},
arrayTypes: ["Array", "Array", "Int8Array"] // optional
});Result is an object with an empty data object and shape array. The data object holds the multi-dimensional array of arrays. The shape array is an array that describes the actual length of the arrays used to hold the data. (It is the actual practical length and not the theoretical length of the dimensions).
{
shape: [4, 768, 1024], // describes the actual length of each array
data: [
// first band
[
Int8Array[-99, -99, ... ], // band's first row of columns with length being the number of columns
Int8Array[-99, -99, ... ], // band's second row
.
.
.
],
// second band
[
Int8Array[-99, -99, ... ], // band's first row of columns with length being the number of columns
Int8Array[-99, -99, ... ], // band's second row
]
]
If you have a multi-dimensional data structure and want to change a value, use update.
import { update } from 'xdim';
// an image in RGBA Image Data Format
const data = [128, 31, 382, 255, 48, 38, 58, 255, ...];
update({
// the structure that we will be modifying with a new value
data,
// layout describing one array in major order from row to column to band
layout: "[row,column,band]",
// a point in multi-dimensional space
point: {
band: 2, // the 3rd band or blue
row: 4, // the 5th row
column: 8, // the 9th column
},
sizes: {
band: 4, // the 4 bands: red, green, blue and alpha
row: 768, // the number of rows or height of the image
column: 1024, // the number of columns or width of the image
},
// the value to insert at the specified point
// it doesn't have to be a number
value: 128
});The function prepareUpdate is to update as prepareSelect is to select. It returns an optimized update function.
import { prepareUpdate } from 'xdim';
// an image in RGBA Image Data Format
const data = [128, 31, 382, 255, 48, 38, 58, 255, ...];
const update = prepareUpdate({
// the structure that we will be modifying with update calls
data,
// layout describing one array in major order from row to column to band
layout: "[row,column,band]",
sizes: {
band: 4, // the 4 bands: red, green, blue and alpha
row: 768, // the number of rows or height of the image
column: 1024, // the number of columns or width of the image
}
});
update({
// a point in multi-dimensional space
point: {
band: 2, // the 3rd band or blue
row: 4, // the 5th row
column: 8, // the 9th column
},
// the value to insert at the specified point
// it doesn't have to be a number
value: 128
});Post an issue at https://github.com/DanielJDufour/xdim/issues.