feat: add row echelon matrix algorithm

Maths/RowEchelon.js

@@ -0,0 +1,138 @@
+/**
+ * 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]
+ * // ]
+ */
+
+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
+ }
+ }
+ 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++) {
+ if (matrix[i][currentCol] !== 0) {
+ 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
+ }
+}
+
+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
+ }
+ }
+}
+
+const scalarMultiplication = (currentRow, factor, matrix) => {
+ let numCols = matrix[0].length
+ for (let j = 0; j < numCols; j++) {
+ matrix[currentRow][j] *= factor
+ }
+}
+
+const subtractRow = (currentRow, fromRow, matrix) => {
+ let numCols = matrix[0].length
+ for (let j = 0; j < numCols; j++) {
+ matrix[fromRow][j] -= matrix[currentRow][j]
+ }
+}
+
+const formatResult = (matrix) => {
+ let precision = 5
+ let numRows = matrix.length
+ let numCols = matrix[0].length
+ for (let i = 0; i < numRows; i++) {
+ for (let j = 0; j < numCols; j++) {
+ matrix[i][j] = parseFloat(matrix[i][j].toFixed(precision))
+ }
+ }
+}
+
+const rowEchelon = (matrix) => {
+ if (isMatrixValid(matrix) === false) {
+ return 'Input is not a valid 2D matrix.'
+ }
+
+ let numRows = matrix.length
+ let numCols = matrix[0].length
+ let result = matrix
+
+ for (let i = 0, j = 0; i < numRows && j < numCols; ) {
+ if (checkNonZero(i, j, result) === false) {
+ j++
+ continue
+ }
+
+ selectPivot(i, j, result)
+ let factor = 1 / result[i][j]
+ scalarMultiplication(i, factor, result)
+
+ //..............make bottom elements zero...............
+ for (let x = i + 1; x < numRows; x++) {
+ factor = result[x][j]
+ if (factor === 0) {
+ continue
+ }
+ scalarMultiplication(i, factor, result)
+ subtractRow(i, x, result)
+ factor = 1 / factor
+ scalarMultiplication(i, factor, result)
+ }
+ formatResult(result)
+ i++
+ }
+ return result
+}
+
+export { rowEchelon }