Add test that compares density eval with horton

There already is a test that compares density evaluation with horton, but the
density matrix used was an identity matrix. Just in case, the density
evaluations are compared for both spherical and cartesian contractions for
random symmetric density matrix.

Author: kimt33

tests/data_horton_hhe_cart_density_rand.npy

@@ -297,6 +297,38 @@ def test_evaluate_density_horton():
     )
 
 
+def test_evaluate_density_horton_nonidentity_dm():
+    """Test gbasis.evals.density.evaluate_density against result from HORTON.
+
+    The test case is diatomic with H and He separated by 0.8 angstroms with basis set ANO-RCC.
+    Density matrix here is not an identity matrix and is instead a random symmetric matrix.
+
+    """
+    basis_dict = parse_nwchem(find_datafile("data_anorcc.nwchem"))
+    points = np.array([[0, 0, 0], [0.8, 0, 0]])
+    basis = make_contractions(basis_dict, ["H", "He"], points)
+    basis = [HortonContractions(i.angmom, i.coord, i.coeffs, i.exps) for i in basis]
+
+    grid_1d = np.linspace(-2, 2, num=5)
+    grid_x, grid_y, grid_z = np.meshgrid(grid_1d, grid_1d, grid_1d)
+    grid_3d = np.vstack([grid_x.ravel(), grid_y.ravel(), grid_z.ravel()]).T
+    grid_3d = np.ascontiguousarray(grid_3d)
+
+    horton_density = np.load(find_datafile("data_horton_hhe_cart_density_rand.npy"))
+    density_matrix = np.load(find_datafile("data_horton_hhe_cart_dm_rand.npy"))
+
+    assert np.allclose(
+        evaluate_density(density_matrix, basis, grid_3d, coord_type="cartesian"), horton_density
+    )
+
+    horton_density = np.load(find_datafile("data_horton_hhe_sph_density_rand.npy"))
+    density_matrix = np.load(find_datafile("data_horton_hhe_sph_dm_rand.npy"))
+
+    assert np.allclose(
+        evaluate_density(density_matrix, basis, grid_3d, coord_type="spherical"), horton_density
+    )
+
+
 def test_evaluate_density_gradient_horton():
     """Test gbasis.evals.density.evaluate_density_gradient against result from HORTON.