feat: add echelonForm method

Author: Goneiross

src/__tests__/matrix/utility.js

@@ -286,19 +286,25 @@ describe('utility methods', () => {
   });
 
   it('isEchelonForm', () => {
-    var matrix = new Matrix([[1, 0], [0, 1]]);
-    var matrix2 = new Matrix([[2, 1], [1, 1]]);
+    const matrix = new Matrix([[1, 0], [0, 1]]);
+    const matrix2 = new Matrix([[2, 1], [1, 1]]);
     expect(matrix.isEchelonForm()).toStrictEqual(true);
     expect(matrix2.isEchelonForm()).toStrictEqual(false);
   });
 
   it('isReducedEchelonForm', () => {
-    var matrix = new Matrix([[1, 0], [0, 1]]);
-    var matrix2 = new Matrix([[1, 1], [0, 1]]);
+    const matrix = new Matrix([[1, 0], [0, 1]]);
+    const matrix2 = new Matrix([[1, 1], [0, 1]]);
     expect(matrix.isReducedEchelonForm()).toStrictEqual(true);
     expect(matrix2.isReducedEchelonForm()).toStrictEqual(false);
   });
 
+  it('echelonForm', () => {
+    const matrix = new Matrix([[1, 3], [4, 8]]);
+    const result = [[1, 2], [0, 1]];
+    expect(matrix.echelonForm().to2DArray()).toStrictEqual(result);
+  });
+
   it('isRowVector', () => {
     var m = new Matrix(1, 3);
     expect(m.isRowVector()).toBe(true);

src/matrix.js

@@ -399,6 +399,42 @@ export class AbstractMatrix {
     return isReducedEchelonForm;
   }
 
+  /**
+   * @return the row echelon form of a matrix, using Gaussian elimination
+   */
+  echelonForm() {
+    let result = this.clone();
+    let h = 0;
+    let k = 0;
+    while ((h < result.rows) && (k < result.columns)) {
+      let iMax = h;
+      for (let i = h; i < result.rows; i++) {
+        if (result.get(i, k) > result.get(iMax, k)) {
+          iMax = i;
+        }
+      }
+      if (result.get(iMax, k) === 0) {
+        k++;
+      } else {
+        result.swapRows(h, iMax);
+        let tmp = result.get(h, k);
+        for (let j = k; j < result.columns; j++) {
+          result.set(h, j, result.get(h, j) / tmp);
+        }
+        for (let i = h + 1; i < result.rows; i++) {
+          let factor = result.get(i, k) / result.get(h, k);
+          result.set(i, k, 0);
+          for (let j = k + 1; j < result.columns; j++) {
+            result.set(i, j, result.get(i, j) - result.get(h, j) * factor);
+          }
+        }
+        h++;
+        k++;
+      }
+    }
+    return result;
+  }
+
   /**
    * Sets a given element of the matrix.
    * @abstract