diff --git a/Maths/RowEchelon.js b/Maths/RowEchelon.js new file mode 100644 index 0000000000..c773bb80a9 --- /dev/null +++ b/Maths/RowEchelon.js @@ -0,0 +1,150 @@ +/** + * Given a two dimensional matrix, find its row echelon form. + * + * For more info: https://en.wikipedia.org/wiki/Row_echelon_form + * + * @param {number[[]]} matrix - Two dimensional array of rational numbers. + * @returns {number[[]]} - Two dimensional array of rational numbers (row echelon form). + * + * @example + * const matrix = [ + * [2,3,4,5,7], + * [9,8,4,0,9], + * [5,7,4,3,9], + * [3,4,0,2,1] + * ] + * + * const result = rowEchelon(matrix) + * + * // The function returns the corresponding row echelon form: + * // result: + * // [ + * // [1, 1.5, 2, 2.5, 3.5], + * // [0, 1, 2.54545, 4.09091, 4.09091], + * // [0, 0, 1, 1.57692, 1.36539], + * // [0, 0, 0, 1, -0.25] + * // ] + */ + +// Set a tolerance value for floating-point comparisons +const tolerance = 0.000001 + +// Check if all the rows have same length of elements +const isMatrixValid = (matrix) => { + let numRows = matrix.length + let numCols = matrix[0].length + for (let i = 0; i < numRows; i++) { + if (numCols !== matrix[i].length) { + return false + } + } + + // Check for input other than a 2D matrix + if ( + !Array.isArray(matrix) || + matrix.length === 0 || + !Array.isArray(matrix[0]) + ) { + return false + } + return true +} + +const checkNonZero = (currentRow, currentCol, matrix) => { + let numRows = matrix.length + for (let i = currentRow; i < numRows; i++) { + // Checks if the current element is not very near to zero. + if (!isTolerant(0, matrix[i][currentCol], tolerance)) { + return true + } + } + return false +} + +const swapRows = (currentRow, withRow, matrix) => { + let numCols = matrix[0].length + let tempValue = 0 + for (let j = 0; j < numCols; j++) { + tempValue = matrix[currentRow][j] + matrix[currentRow][j] = matrix[withRow][j] + matrix[withRow][j] = tempValue + } +} + +// Select a pivot element in the current column to facilitate row operations. +// Pivot element is the first non-zero element found from the current row +// down to the last row. +const selectPivot = (currentRow, currentCol, matrix) => { + let numRows = matrix.length + for (let i = currentRow; i < numRows; i++) { + if (matrix[i][currentCol] !== 0) { + swapRows(currentRow, i, matrix) + return + } + } +} + +// Multiply each element of the given row with a factor. +const scalarMultiplication = (currentRow, factor, matrix) => { + let numCols = matrix[0].length + for (let j = 0; j < numCols; j++) { + matrix[currentRow][j] *= factor + } +} + +// Subtract one row from another row +const subtractRow = (currentRow, fromRow, matrix) => { + let numCols = matrix[0].length + for (let j = 0; j < numCols; j++) { + matrix[fromRow][j] -= matrix[currentRow][j] + } +} + +// Check if two numbers are equal within a given tolerance +const isTolerant = (a, b, tolerance) => { + const absoluteDifference = Math.abs(a - b) + return absoluteDifference <= tolerance +} + +const rowEchelon = (matrix) => { + // Check if the input matrix is valid; if not, throw an error. + if (!isMatrixValid(matrix)) { + throw new Error('Input is not a valid 2D matrix.') + } + + let numRows = matrix.length + let numCols = matrix[0].length + let result = matrix + + // Iterate through the rows (i) and columns (j) of the matrix. + for (let i = 0, j = 0; i < numRows && j < numCols; ) { + // If the current column has all zero elements below the current row, + // move to the next column. + if (!checkNonZero(i, j, result)) { + j++ + continue + } + + // Select a pivot element and normalize the current row. + selectPivot(i, j, result) + let factor = 1 / result[i][j] + scalarMultiplication(i, factor, result) + + // Make elements below the pivot element zero by performing + // row operations on subsequent rows. + for (let x = i + 1; x < numRows; x++) { + factor = result[x][j] + if (isTolerant(0, factor, tolerance)) { + continue + } + scalarMultiplication(i, factor, result) + subtractRow(i, x, result) + factor = 1 / factor + scalarMultiplication(i, factor, result) + } + i++ + } + return result +} + +export { rowEchelon } diff --git a/Maths/test/RowEchelon.test.js b/Maths/test/RowEchelon.test.js new file mode 100644 index 0000000000..5575bc6d39 --- /dev/null +++ b/Maths/test/RowEchelon.test.js @@ -0,0 +1,89 @@ +import { rowEchelon } from '../RowEchelon' +describe('Determinant', () => { + const tolerance = 0.000001 + test.each([ + [ + [ + [8, 1, 3, 5], + [4, 6, 8, 2], + [3, 5, 6, 8] + ], + [ + [1, 0.125, 0.375, 0.625], + [0, 1, 1.18182, -0.09091], + [0, 0, 1, -11.0769] + ] + ], + [ + [ + [6, 8, 1, 3, 5], + [1, 4, 6, 8, 2], + [0, 3, 5, 6, 8], + [2, 5, 9, 7, 8], + [5, 5, 7, 0, 1] + ], + [ + [1, 1.33333, 0.16667, 0.5, 0.83333], + [0, 1, 2.1875, 2.8125, 0.4375], + [0, 0, 1, 1.56, -4.28003], + [0, 0, 0, 1, -3.3595], + [0, 0, 0, 0, 1] + ] + ], + [ + [ + [1, 3, 5], + [6, 8, 2], + [5, 6, 8], + [7, 9, 9], + [5, 0, 6] + ], + [ + [1, 3, 5], + [0, 1, 2.8], + [0, 0, 1], + [0, 0, 0], + [0, 0, 0] + ] + ], + [ + [ + [0, 7, 8, 1, 3, 5], + [0, 6, 4, 6, 8, 2], + [0, 7, 3, 5, 6, 8], + [6, 8, 1, 0, 0, 4], + [3, 3, 5, 7, 3, 1], + [1, 2, 1, 0, 9, 7], + [8, 8, 0, 2, 3, 1] + ], + [ + [1, 1.33333, 0.16667, 0, 0, 0.66667], + [0, 1, 0.66667, 1, 1.33333, 0.33333], + [0, 0, 1, 1.2, 1.99999, -3.4], + [0, 0, 0, 1, 1.3, -1.4], + [0, 0, 0, 0, 1, -2.32854], + [0, 0, 0, 0, 0, 1], + [0, 0, 0, 0, 0, 0] + ] + ] + ])('Should return the matrix in row echelon form.', (matrix, expected) => { + for (let i = 0; i < matrix.length; i++) { + for (let j = 0; j < matrix[i].length; j++) { + expect(rowEchelon(matrix)[i][j]).toBeCloseTo(expected[i][j], tolerance) + } + } + }) + + test.each([ + [ + [ + [8, 1, 3, 5], + [4, 6, 8, 2, 7], + [3, 5, 6, 8] + ], + 'Input is not a valid 2D matrix.' + ] + ])('Should return the error message.', (matrix, expected) => { + expect(() => rowEchelon(matrix)).toThrowError(expected) + }) +})