Split eigenvalue test and eigenvector tests

ndarray-linalg/src/eig.rs

@@ -11,6 +11,29 @@ pub trait Eig {
     type EigVal;
     type EigVec;
     /// Calculate eigenvalues with the right eigenvector
+    ///
+    /// $$ A u_i = \lambda_i u_i $$
+    ///
+    /// ```
+    /// use ndarray::*;
+    /// use ndarray_linalg::*;
+    ///
+    /// let a: Array2<f64> = array![
+    ///     [-1.01,  0.86, -4.60,  3.31, -4.81],
+    ///     [ 3.98,  0.53, -7.04,  5.29,  3.55],
+    ///     [ 3.30,  8.26, -3.89,  8.20, -1.51],
+    ///     [ 4.43,  4.96, -7.66, -7.33,  6.18],
+    ///     [ 7.31, -6.43, -6.16,  2.47,  5.58],
+    /// ];
+    /// let (eigs, vecs) = a.eig().unwrap();
+    ///
+    /// let a: Array2<c64> = a.map(|v| v.into());
+    /// for (&e, vec) in eigs.iter().zip(vecs.axis_iter(Axis(1))) {
+    ///     let ev = e * vec.into_owned();
+    ///     let av = a.dot(&vec);
+    ///     assert_close_l2!(&av, &ev, 1e-5);
+    /// }
+    /// ```
     fn eig(&self) -> Result<(Self::EigVal, Self::EigVec)>;
 }