feat: add linearDependencies method

Author: jajoe

README.md

@@ -35,7 +35,7 @@ const matrix = Matrix.ones(5, 5);
 
 ### Standard operations
 
-``` javascript
+``` js
 const {Matrix} = require('ml-matrix');
 
 var A = new Matrix([[1, 1], [2, 2]]);
@@ -101,8 +101,16 @@ var z = Matrix.eye(3, 4); // Matrix [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], r
 ```
 
 ### Maths :
-```javascript
-const {Matrix, inverse, solve, QrDecomposition, LuDecomposition, CholeskyDecomposition} = require('ml-matrix');
+```js
+const {
+    Matrix,
+    inverse,
+    solve,
+    linearDependencies,
+    QrDecomposition,
+    LuDecomposition,
+    CholeskyDecomposition
+} = require('ml-matrix');
 
 //===========================
 // inverse and pseudo-inverse
@@ -168,6 +176,13 @@ var A = new Matrix([[2, 3, 5], [4, 1, 6], [1, 3, 0]]);
 var cholesky = CholeskyDecomposition(A);
 var L = cholesky.lowerTriangularMatrix; 
 
+//=======
+// Others
+//=======
+
+// Linear dependencies
+var A = new Matrix([[2, 0, 0, 1], [0, 1, 6, 0], [0, 3, 0, 1], [0, 0, 1, 0], [0, 1, 2, 0]]);  
+var dependencies = linearDependencies(A); // dependencies is a matrix with the dependencies of the rows. When we look row by row, we see that the first row is [0, 0, 0, 0, 0], so it means that the first row is independent, and the second row is [ 0, 0, 0, 4, 1 ], i.e the second row = 4 times the 4th row + the 5th row.
 
 ```
 

package-lock.json

@@ -50,14 +50,14 @@
   "devDependencies": {
     "babel-plugin-transform-es2015-modules-commonjs": "^6.24.1",
     "benchmark": "^2.1.0",
-    "codecov": "^2.2.0",
+    "codecov": "^2.3.0",
     "csv-parse": "^1.0.0",
-    "eslint": "^4.2.0",
+    "eslint": "^4.4.1",
     "eslint-config-cheminfo": "^1.5.2",
     "eslint-plugin-no-only-tests": "^2.0.0",
     "jest-cli": "^20.0.4",
-    "jest-matcher-deep-close-to": "^1.0.0",
-    "mathjs": "^3.14.2",
+    "jest-matcher-deep-close-to": "^1.0.2",
+    "mathjs": "^3.16.0",
     "npm-run-all": "^4.0.1",
     "numeric": "^1.2.6",
     "pretty-hrtime": "^1.0.0",

package.json

@@ -0,0 +1,23 @@
+import {Matrix, linearDependencies} from '../..';
+import {toBeDeepCloseTo} from 'jest-matcher-deep-close-to';
+expect.extend({toBeDeepCloseTo});
+
+describe('Linear Dependencies', () => {
+    it('should compute the rows dependencies', () => {
+        const A = new Matrix([
+            [2, 0, 0, 1],
+            [0, 1, 6, 0],
+            [0, 3, 0, 1],
+            [0, 0, 1, 0],
+            [0, 1, 2, 0]
+        ]);
+        const dependencies = linearDependencies(A);
+        expect(dependencies.to2DArray()).toBeDeepCloseTo([
+            [0, 0, 0, 0, 0],
+            [0, 0, 0, 4, 1],
+            [0, 0, 0, 0, 0],
+            [0, 0.25, 0, 0, -0.25],
+            [0, 1, 0, -4, 0]
+        ], 3);
+    });
+});

src/__tests__/matrix/linearDependencies.js

@@ -6,6 +6,7 @@ export {default as WrapperMatrix2D} from './wrap/WrapperMatrix2D';
 export {default as WrapperMatrix1D} from './wrap/WrapperMatrix1D';
 
 export {solve, inverse} from './decompositions';
+export {linearDependencies} from './linearDependencies';
 export {default as SingularValueDecomposition, default as SVD} from './dc/svd.js';
 export {default as EigenvalueDecomposition, default as EVD} from './dc/evd.js';
 export {default as CholeskyDecomposition, default as CHO} from './dc/cholesky.js';