formalize the brute-force testing

ngm/__init__.py

@@ -111,3 +111,11 @@ def _ensure_positive_array(x: np.ndarray) -> np.ndarray:
         return -x
     else:
         raise RuntimeError(f"Cannot make vector all positive: {x}")
+
+def run_ngm(r: np.ndarray, x0: np.ndarray, steps: int) -> np.ndarray:
+    """Repeatedly applies the NGM r, starting with x0"""
+    x = x0
+    for _ in range(steps):
+        x = np.matmul(r, x)
+
+    return x

tests/test_ngm.py

@@ -94,3 +94,10 @@ def test_kr():
     r0 = ngm.dominant_eigen(r).value
 
     assert np.isclose(r0, 2.0013, atol=5e-5)
+
+def test_eigenvectors():
+    r = np.array([[3.1, 0.15, 1.7],[0.78, 1.5, 0.1],[0.32, 0.98, 1.1]])
+
+    brute_force = ngm.run_ngm(r, np.array([1, 0, 0]), 200)
+    brute_force = brute_force / brute_force.sum()
+    assert np.isclose(ngm.dominant_eigen(r).vector, brute_force).all()