fix: improves SVD

Author: Volodymyr Orlov

src/linalg/svd.rs

@@ -53,6 +53,19 @@ pub struct SVD<T: RealNumber, M: SVDDecomposableMatrix<T>> {
     tol: T,
 }
 
+impl<T: RealNumber, M: SVDDecomposableMatrix<T>> SVD<T, M> {
+    /// Diagonal matrix with singular values
+    pub fn S(&self) -> M {
+        let mut s = M::zeros(self.U.shape().1, self.V.shape().0);
+
+        for i in 0..self.s.len() {
+            s.set(i, i, self.s[i]);
+        }
+
+        s
+    }
+}
+
 /// Trait that implements SVD decomposition routine for any matrix.
 pub trait SVDDecomposableMatrix<T: RealNumber>: BaseMatrix<T> {
     /// Solves Ax = b. Overrides original matrix in the process.
@@ -711,4 +724,19 @@ mod tests {
         let w = a.svd_solve_mut(b).unwrap();
         assert!(w.approximate_eq(&expected_w, 1e-2));
     }
+
+    #[test]
+    fn decompose_restore() {
+        let a = DenseMatrix::from_2d_array(&[&[1.0, 2.0, 3.0, 4.0], &[5.0, 6.0, 7.0, 8.0]]);
+        let svd = a.svd().unwrap();
+        let u: &DenseMatrix<f32> = &svd.U; //U
+        let v: &DenseMatrix<f32> = &svd.V; // V
+        let s: &DenseMatrix<f32> = &svd.S(); // Sigma
+
+        let a_hat = u.matmul(s).matmul(&v.transpose());
+
+        for (a, a_hat) in a.iter().zip(a_hat.iter()) {
+            assert!((a - a_hat).abs() < 1e-3)
+        }
+    }
 }