text: # Copyright 2021 DeepMind Technologies Limited.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  """Tests for compute_hfx_density."""
  
  from absl.testing import absltest
  from absl.testing import parameterized
  import numpy as np
  from pyscf import dft
  from pyscf import gto
  from pyscf import lib
  from pyscf import scf
  import scipy
  from density_functional_approximation_dm21 import compute_hfx_density
  
  
  class ComputeHfxDensityTest(parameterized.TestCase):
  
    def setUp(self):
      super().setUp()
      lib.param.TMPDIR = None
      lib.num_threads(1)
  
    @parameterized.named_parameters(
        {'testcase_name': 'local_hf', 'omega': 0.},
        {'testcase_name': 'range_separated_local_hf_0.5', 'omega': 0.5},
        {'testcase_name': 'range_separated_local_hf_1.0', 'omega': 1.0},
        {'testcase_name': 'range_separated_local_hf_2.0', 'omega': 2.0},
    )
    def test_closed_shell(self, omega):
      mol = gto.M(atom='He 0. 0. 0.', basis='3-21g')
      solver = dft.RKS(mol)
      solver.grids.level = 2
      solver.grids.build()
      solver.kernel()
      dm = solver.make_rdm1()
      with mol.with_range_coulomb(omega=omega):
        target_j, target_k = scf.hf.get_jk(mol, dm)
      target_hf = -0.25 * np.einsum('ij,ji', dm, target_k)
      target_coulomb = np.einsum('ij,ji', dm, target_j)
  
      coords = solver.grids.coords
      weights = solver.grids.weights
  
      results = compute_hfx_density.get_hf_density(
          mol, dm, coords, omega=omega, weights=weights)
      coulomb = np.einsum('ij,ji', dm, results.coulomb)
      hf = -0.25 * np.einsum('ij,ji', dm, results.exchange)
      predicted_hf = np.sum((results.exx[0] + results.exx[1]) * weights)
  
      with self.subTest('test_hf_density'):
        self.assertAlmostEqual(target_hf, predicted_hf)
  
      with self.subTest('test_get_jk'):
        np.testing.assert_allclose(results.coulomb, target_j)
        np.testing.assert_allclose(results.exchange, target_k)
        self.assertAlmostEqual(coulomb, target_coulomb)
        self.assertAlmostEqual(hf, target_hf)
  
    @parameterized.named_parameters(
        {'testcase_name': 'local_hf', 'omega': 0.},
        {'testcase_name': 'range_separated_local_hf_0.5', 'omega': 0.5},
        {'testcase_name': 'range_separated_local_hf_1.0', 'omega': 1.0},
        {'testcase_name': 'range_separated_local_hf_2.0', 'omega': 2.0},
    )
    def test_hf_density_on_open_shell(self, omega):
      mol = gto.M(atom='He 0. 0. 0.', basis='3-21g', charge=1, spin=1)
      solver = dft.UKS(mol)
      solver.grids.level = 2
      solver.grids.build()
      solver.kernel()
      dm = solver.make_rdm1()
      with mol.with_range_coulomb(omega=omega):
        target_j, target_k = scf.hf.get_jk(mol, dm)
      target_hf = -0.5 * (
          np.einsum('ij,ji', dm[0], target_k[0]) +
          np.einsum('ij,ji', dm[1], target_k[1]))
      target_coulomb = np.einsum('ij,ji', dm[0], target_j[0]) + np.einsum(
          'ij,ji', dm[1], target_j[1])
  
      coords = solver.grids.coords
      weights = solver.grids.weights
  
      results = compute_hfx_density.get_hf_density(
          mol, dm, coords, omega=omega, weights=weights)
  
      predicted_hf = np.sum((results.exx[0] + results.exx[1]) * weights)
      coulomb = (
          np.einsum('ij,ji', dm[0], results.coulomb[0]) +
          np.einsum('ij,ji', dm[1], results.coulomb[1]))
      hf = -0.5 * (
          np.einsum('ij,ji', dm[0], results.exchange[0]) +
          np.einsum('ij,ji', dm[1], results.exchange[1]))
  
      with self.subTest('test_hf_density'):
        self.assertAlmostEqual(target_hf, predicted_hf, places=3)
  
      with self.subTest('test_get_jk'):
        np.testing.assert_allclose(results.coulomb[0], target_j[0])
        np.testing.assert_allclose(results.coulomb[1], target_j[1])
        np.testing.assert_allclose(results.exchange[0], target_k[0])
        np.testing.assert_allclose(results.exchange[1], target_k[1])
        self.assertAlmostEqual(coulomb, target_coulomb)
        self.assertAlmostEqual(hf, target_hf)
  
  
  def _nu_test_systems():
    systems = [
        {
            'atom': 'N 0 0 0; N 0 0 2.4',
            'charge': 0,
            'spin': 0,
            'basis': 'cc-pVDZ',
            'num_grids': -1
        },
        {
            'atom': 'N 0 0 0; N 0 0 2.4',
            'charge': 0,
            'spin': 0,
            'basis': 'cc-pVDZ',
            'num_grids': 1
        },
        {
            'atom': 'N 0 0 0; N 0 0 2.4',
            'charge': 0,
            'spin': 0,
            'basis': 'cc-pVDZ',
            'num_grids': 2
        },
        {
            'atom': 'N 0 0 0; N 0 0 2.4',
            'charge': 0,
            'spin': 0,
            'basis': 'cc-pVDZ',
            'num_grids': 10
        },
        {
            'atom': 'N 0 0 0; N 0 0 2.4',
            'charge': 0,
            'spin': 0,
            'basis': 'cc-pVDZ',
            'num_grids': 32
        },
        {
            'atom': 'N 0 0 0; N 0 0 2.4',
            'charge': 0,
            'spin': 0,
            'basis': 'cc-pVDZ',
            'num_grids': 33
        },
        {
            'atom': 'Li 0 0 0',
            'charge': 0,
            'spin': 1,
            'basis': 'cc-pVTZ',
            'num_grids': -1
        },
        {
            'atom': 'H 0 0 0',
            'charge': 0,
            'spin': 1,
            'basis': 'cc-pVQZ',
            'num_grids': -1
        },
    ]
    system_names = ['N2', 'N2_1', 'N2_2', 'N2_10', 'N2_32', 'N2_33', 'Li', 'H']
    for name, system in zip(system_names, systems):
      yield {'testcase_name': f'{name}_hermitian', 'hermi': 0, **system}
      yield {'testcase_name': f'{name}_non_hermitian', 'hermi': 1, **system}
  
  
  class NuTest(parameterized.TestCase):
  
    def setUp(self):
      super(NuTest, self).setUp()
      lib.param.TMPDIR = None
      lib.num_threads(1)
  
    @parameterized.named_parameters(_nu_test_systems())
    def test_nu_integrals(self, atom, charge, spin, basis, num_grids, hermi):
      mol = gto.M(atom=atom, charge=charge, spin=spin, basis=basis)
      mf = dft.UKS(mol)
      mf.grids.build()
      if num_grids == -1:
        test_coords = mf.grids.coords
      else:
        test_coords = mf.grids.coords[0:num_grids]
      nu_slow = compute_hfx_density._evaluate_nu_slow(
          mol, test_coords, omega=0.0, hermi=hermi)
      nu_fast = compute_hfx_density._evaluate_nu(
          mol, test_coords, omega=0.0, hermi=hermi)
      np.testing.assert_allclose(nu_slow, nu_fast, atol=1E-13)
  
    def test_range_separated_nu(self):
      mol = gto.M(atom='He 0 0 0', basis='cc-pVDZ')
      r0 = np.array([[0.1, 0.2, 1.]])
      omega = 1.
      result = np.squeeze(compute_hfx_density._evaluate_nu(mol, r0, omega=omega))
  
      solver = dft.RKS(mol)
      solver.grids.level = 2
      solver.grids.build()
      coords = solver.grids.coords
      weights = solver.grids.weights
      ao_value = dft.numint.eval_ao(mol, coords, deriv=0)
      dist = np.linalg.norm(coords - r0, axis=1)
      erf = scipy.special.erf(omega * dist) / dist
      expected_result = np.squeeze(
          np.einsum('g,ga,gb->ab', weights * erf, ao_value, ao_value))
  
      np.testing.assert_allclose(result, expected_result)
  
  
  if __name__ == '__main__':
    absltest.main()
  