fix: correctly ready elements in QR#orthogonalMatrix

Fixes: #96

README.md

@@ -110,7 +110,7 @@ const {
   linearDependencies,
   QrDecomposition,
   LuDecomposition,
-  CholeskyDecomposition
+  CholeskyDecomposition,
 } = require('ml-matrix');
 
 //===========================
@@ -157,15 +157,15 @@ var error = Matrix.sub(b, A.mmul(x)); // The error enables to evaluate the solut
 // QR Decomposition
 
 var A = new Matrix([[2, 3, 5], [4, 1, 6], [1, 3, 0]]);
-var QR = QrDecomposition(A);
+var QR = new QrDecomposition(A);
 var Q = QR.orthogonalMatrix;
 var R = QR.upperTriangularMatrix;
 // So you have the QR decomposition. If you multiply Q by R, you'll see that A = Q.R, with Q orthogonal and R upper triangular
 
 // LU Decomposition
 
 var A = new Matrix([[2, 3, 5], [4, 1, 6], [1, 3, 0]]);
-var LU = LuDecomposition(A);
+var LU = new LuDecomposition(A);
 var L = LU.lowerTriangularMatrix;
 var U = LU.upperTriangularMatrix;
 var P = LU.pivotPermutationVector;
@@ -174,13 +174,13 @@ var P = LU.pivotPermutationVector;
 // Cholesky Decomposition
 
 var A = new Matrix([[2, 3, 5], [4, 1, 6], [1, 3, 0]]);
-var cholesky = CholeskyDecomposition(A);
+var cholesky = new CholeskyDecomposition(A);
 var L = cholesky.lowerTriangularMatrix;
 
 // Eigenvalues & eigenvectors
 
 var A = new Matrix([[2, 3, 5], [4, 1, 6], [1, 3, 0]]);
-var e = EigenvalueDecomposition(A);
+var e = new EigenvalueDecomposition(A);
 var real = e.realEigenvalues;
 var imaginary = e.imaginaryEigenvalues;
 var vectors = e.eigenvectorMatrix;
@@ -195,7 +195,7 @@ var A = new Matrix([
   [0, 1, 6, 0],
   [0, 3, 0, 1],
   [0, 0, 1, 0],
-  [0, 1, 2, 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.
 ```

src/__tests__/decompositions/qr.js

@@ -50,4 +50,13 @@ describe('Qr decomposition', () => {
     const qr = new QR(A);
     expect(qr.solve(b).to2DArray()).toBeDeepCloseTo([[1], [0.9999]], 4);
   });
+
+  it('should work with the example in the documentation', () => {
+    const A = [[2, 3, 5], [4, 1, 6], [1, 3, 0]];
+    const dc = new QR(A);
+    const Q = dc.orthogonalMatrix;
+    const R = dc.upperTriangularMatrix;
+    const qR = Q.mmul(R);
+    expect(qR.to2DArray()).toBeDeepCloseTo(A, 4);
+  });
 });

src/dc/qr.js

@@ -136,7 +136,7 @@ export default class QrDecomposition {
             s += qr.get(i, k) * X.get(i, j);
           }
 
-          s = -s / qr[k][k];
+          s = -s / qr.get(k, k);
 
           for (i = k; i < rows; i++) {
             X.set(i, j, X.get(i, j) + s * qr.get(i, k));