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Commit adda5c5

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Add Euclidean Distance formula (trekhleb#602)
* Add Matrices section with basic Matrix operations (multiplication, transposition, etc.) * Add Euclidean Distance algorithm.
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‎README.md‎

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@@ -78,6 +78,7 @@ a set of rules that precisely define a sequence of operations.
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* `B` [Fast Powering](src/algorithms/math/fast-powering)
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* `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation
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* `B` [Matrices](src/algorithms/math/matrix) - matrices and basic matrix operations (multiplication, transposition, etc.)
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* `B` [Euclidean Distance](src/algorithms/math/euclidean-distance) - distance between two points/vectors/matrices
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* `A` [Integer Partition](src/algorithms/math/integer-partition)
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* `A` [Square Root](src/algorithms/math/square-root) - Newton's method
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* `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
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# Euclidean Distance
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In mathematics, the **Euclidean distance** between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.
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![Euclidean distance between two points](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
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## Distance formulas
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### One dimension
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The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates
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![One dimension formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d75418dbec9482dbcb70f9063ad66e9cf7b5db9)
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### Two dimensions
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![Two dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c0157084fd89f5f3d462efeedc47d3d7aa0b773)
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### Higher dimensions
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In three dimensions, for points given by their Cartesian coordinates, the distance is
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![Three dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1d13a40a7b203b455ae6d4be8b3cce898bda625)
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Example: the distance between the two points `(8,2,6)` and `(3,5,7)`:
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![3-dimension example](https://www.mathsisfun.com/algebra/images/dist-2-points-3d.svg)
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In general, for points given by Cartesian coordinates in `n`-dimensional Euclidean space, the distance is
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![n-dimensional formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0ef4fe055b2a51b4cca43a05e5d1cd93f758dcc)
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## References
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- [Euclidean Distance on MathIsFun](https://www.mathsisfun.com/algebra/distance-2-points.html)
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- [Euclidean Distance on Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)
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import euclideanDistance from '../euclideanDistance';
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describe('euclideanDistance', () => {
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it('should calculate euclidean distance between vectors', () => {
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expect(euclideanDistance([[1]], [[2]])).toEqual(1);
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expect(euclideanDistance([[2]], [[1]])).toEqual(1);
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expect(euclideanDistance([[5, 8]], [[7, 3]])).toEqual(5.39);
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expect(euclideanDistance([[5], [8]], [[7], [3]])).toEqual(5.39);
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expect(euclideanDistance([[8, 2, 6]], [[3, 5, 7]])).toEqual(5.92);
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expect(euclideanDistance([[8], [2], [6]], [[3], [5], [7]])).toEqual(5.92);
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expect(euclideanDistance([[[8]], [[2]], [[6]]], [[[3]], [[5]], [[7]]])).toEqual(5.92);
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});
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it('should throw an error in case if two matrices are of different shapes', () => {
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expect(() => euclideanDistance([[1]], [[[2]]])).toThrowError(
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'Matrices have different dimensions',
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);
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expect(() => euclideanDistance([[1]], [[2, 3]])).toThrowError(
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'Matrices have different shapes',
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);
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});
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});
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/**
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* @typedef {import('../matrix/Matrix.js').Matrix} Matrix
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*/
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import * as mtrx from '../matrix/Matrix';
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/**
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* Calculates the euclidean distance between 2 matrices.
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*
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* @param {Matrix} a
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* @param {Matrix} b
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* @returns {number}
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* @trows {Error}
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*/
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const euclideanDistance = (a, b) => {
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mtrx.validateSameShape(a, b);
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let squaresTotal = 0;
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mtrx.walk(a, (indices, aCellValue) => {
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const bCellValue = mtrx.getCellAtIndex(b, indices);
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squaresTotal += (aCellValue - bCellValue) ** 2;
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});
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return Number(Math.sqrt(squaresTotal).toFixed(2));
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};
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export default euclideanDistance;

‎src/algorithms/math/matrix/Matrix.js‎

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* @param {Matrix} b
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* @trows {Error}
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*/
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const validateSameShape = (a, b) => {
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exportconst validateSameShape = (a, b) => {
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validateType(a);
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validateType(b);
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* @param {Matrix} m
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* @param {function(indices: CellIndices, c: Cell)} visit
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*/
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const walk = (m, visit) => {
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exportconst walk = (m, visit) => {
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/**
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* Traverses the matrix recursively.
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*
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* @param {CellIndices} cellIndices - Array of cell indices
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* @return {Cell}
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*/
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const getCellAtIndex = (m, cellIndices) => {
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exportconst getCellAtIndex = (m, cellIndices) => {
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// We start from the row at specific index.
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let cell = m[cellIndices[0]];
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// Going deeper into the next dimensions but not to the last one to preserve
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* @param {CellIndices} cellIndices - Array of cell indices
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* @param {Cell} cellValue - New cell value
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*/
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const updateCellAtIndex = (m, cellIndices, cellValue) => {
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exportconst updateCellAtIndex = (m, cellIndices, cellValue) => {
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// We start from the row at specific index.
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let cell = m[cellIndices[0]];
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// Going deeper into the next dimensions but not to the last one to preserve

‎src/algorithms/ml/knn/__test__/knn.test.js‎

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const inconsistent = () => {
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kNN([[1, 1]], [1], [1]);
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};
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expect(inconsistent).toThrowError('Inconsistent vector lengths');
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expect(inconsistent).toThrowError('Matrices have different shapes');
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});
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it('should find the nearest neighbour', () => {

‎src/algorithms/ml/knn/kNN.js‎

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/**
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* Calculates calculate the euclidean distance between 2 vectors.
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*
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* @param {number[]} x1
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* @param {number[]} x2
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* @returns {number}
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*/
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function euclideanDistance(x1, x2) {
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// Checking for errors.
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if (x1.length !== x2.length) {
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throw new Error('Inconsistent vector lengths');
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}
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// Calculate the euclidean distance between 2 vectors and return.
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let squaresTotal = 0;
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for (let i = 0; i < x1.length; i += 1) {
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squaresTotal += (x1[i] - x2[i]) ** 2;
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}
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return Number(Math.sqrt(squaresTotal).toFixed(2));
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}
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/**
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* Classifies the point in space based on k-nearest neighbors algorithm.
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*
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* @param {number} k - number of nearest neighbors which will be taken into account (preferably odd)
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* @return {number} - the class of the point
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*/
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import euclideanDistance from '../../math/euclidean-distance/euclideanDistance';
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export default function kNN(
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dataSet,
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labels,
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const distances = [];
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for (let i = 0; i < dataSet.length; i += 1) {
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distances.push({
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dist: euclideanDistance(dataSet[i],toClassify),
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dist: euclideanDistance([dataSet[i]],[toClassify]),
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label: labels[i],
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});
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}

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