fix the bug for dsdx

Author: qzhu2017

pyxtal/lego/SO3.py

@@ -272,6 +272,7 @@ def compute_dpdr_5d(self, atoms):
             pair_ids = neigh_ids[self.neighbor_indices[:, 0] == i]
             if len(pair_ids) > 0:
                 ctot = cs[pair_ids].sum(axis=0) #(n, l, m)
+                dctot = dcs[pair_ids].sum(axis=0)
                 # power spectrum P = c*c_conj
                 # eq_3 (n, n', l) eliminate m
                 P = np.einsum('ijk, ljk->ilj', ctot, np.conj(ctot)).real
@@ -287,12 +288,16 @@ def compute_dpdr_5d(self, atoms):
                     # (N_ijs, n, n', l, 3)
                     # dc * c_conj + c * dc_conj
                     dP = np.einsum('ijkn, ljk->iljn', dcs[pair_id], np.conj(ctot))
-                    dP += np.conj(np.transpose(dP, axes=[1, 0, 2, 3]))
+                    dP += np.einsum('ijkn, ljk->iljn', np.conj(dcs[pair_id]), ctot)
+                    #dP += np.conj(np.transpose(dP, axes=[1, 0, 2, 3]))
+                    #dP += np.einsum('ijkn, ljk->iljn', np.conj(dctot), cs[pair_id])
+                    #dP += np.einsum('ijkn, ljk->iljn', dctot, np.conj(cs[pair_id]))
+
                     dP = dP.real[self.tril_indices].flatten().reshape(self.ncoefs, 3)
                     #print(cs[pair_id].shape, dcs[pair_id].shape, dP.shape)
 
                     dp_list[i, j, :, :, cell_id] += dP
-                    dp_list[i, i, :, :, cell_id] -= dP
+                    dp_list[i, i, :, :, 13] -= dP
 
         return dp_list, p_list
 

tests/test_SO3.py

@@ -6,6 +6,75 @@
 from ase import Atoms
 from ase.build import bulk, sort
 
+def calculate_S(atoms, P_ref):
+    P = calculator.compute_p(atoms)
+    S = np.sum((P - P_ref)**2)
+    return S
+
+
+def numerical_dSdx(x, xtal,  P_ref, eps=1e-4):
+    if type(x) == list: x = np.array(x)
+
+    xtal.update_from_1d_rep(x)
+    atoms = xtal.to_ase() #* 2
+    S0 = calculate_S(atoms, P_ref)
+    dSdx = np.zeros(len(x))
+    for i in range(len(x)):
+        x0 = x.copy()
+        x0[i] += eps
+        xtal.update_from_1d_rep(x0)
+        atoms = xtal.to_ase() #* 2
+        S1 = calculate_S(atoms, P_ref)
+
+        x0 = x.copy()
+        x0[i] -= eps
+        xtal.update_from_1d_rep(x0)
+        atoms = xtal.to_ase() #* 2
+        S2 = calculate_S(atoms, P_ref)
+
+        dSdx[i] = 0.5*(S1-S2)/eps
+    return dSdx
+
+
+def calculate_dSdx_supercell(x, xtal, P_ref, eps=1e-4):
+
+    xtal.update_from_1d_rep(x)
+    atoms = xtal.to_ase() #* 2
+
+    dPdr, P = calculator.compute_dpdr_5d(atoms)
+
+    # Compute dSdr [N, M] [N, N, M, 3, 27] => [N, 3, 27]
+    dSdr = np.einsum("ik, ijklm -> jlm", 2*(P - P_ref), dPdr)
+
+    # Get supercell positions
+    ref_pos = np.repeat(atoms.positions[:, :, np.newaxis], 27, axis=2)
+    for cell in range(27):
+        x1, y1, z1 = cell // 9 - 1, (cell // 3) % 3 - 1, cell % 3 - 1
+        ref_pos[:, :, cell] += np.array([x1, y1, z1]) @ atoms.cell
+
+    # Compute drdx via numerical func
+    drdx = np.zeros([len(atoms), 3, 27, len(x)])
+
+    xtal0 = xtal.copy()
+    for i in range(len(x)):
+        x0 = x.copy()
+        x0[i] += eps
+        xtal0.update_from_1d_rep(x0)
+        atoms = xtal0.to_ase()
+
+        # Get supercell positions
+        pos = np.repeat(atoms.positions[:, :, np.newaxis], 27, axis=2)
+        for cell in range(27):
+            x1, y1, z1 = cell // 9 - 1, (cell // 3) % 3 - 1, cell % 3 - 1
+            pos[:, :, cell] += np.array([x1, y1, z1]) @ atoms.cell
+
+        drdx[:, :, :, i] += (pos - ref_pos)/eps
+
+    # [N, 3, 27] [N, 3, 27, H] => H
+    dSdx = np.einsum("ijk, ijkl -> l", dSdr, drdx)
+    return dSdx
+
+
 def get_rotated_cluster(struc, angle=0, axis='x'):
     s_new = struc.copy()
     s_new.rotate(angle, axis)
@@ -28,15 +97,15 @@ def get_perturbed_xtal(struc, p0, p1, eps):
     p_struc.set_positions(pos)
     return p_struc
 
-def get_dPdR_xtal(xtal, nmax, lmax, rc, eps):
-    p0 = SO3(nmax=nmax, lmax=lmax, rcut=rc).calculate(xtal, derivative=True)
+def get_dPdR_xtal(xtal, eps):
+    p0 = calculator.calculate(xtal, derivative=True)
     shp = p0['x'].shape
     array1 = p0['dxdr']
 
     for j in range(shp[0]):
         for k in range(3):
             struc = get_perturbed_xtal(xtal, j, k, eps)
-            p1 = SO3(nmax=nmax, lmax=lmax, rcut=rc).calculate(struc)
+            p1 = calculator.calculate(struc)
             array2 = (p1['x'] - p0['x'])/eps
             #if np.linalg.norm(array2) > 1e-2: print(j, k, array2)
             if not np.allclose(array1[:, j, :, k], array2, atol=1e-4):
@@ -45,21 +114,29 @@ def get_dPdR_xtal(xtal, nmax, lmax, rc, eps):
 
 # Descriptors Parameters
 eps = 1e-8
-rc = 2.80
+rc1 = 1.8
+rc2 = 3.5
 nmax, lmax = 2, 2
+calculator = SO3(nmax=nmax, lmax=lmax, rcut=rc1)
+calculator0 = SO3(nmax=nmax, lmax=lmax, rcut=rc2)
 
 # NaCl cluster
 cluster = bulk('NaCl', crystalstructure='rocksalt', a=5.691694, cubic=True)
 cluster = sort(cluster, tags=[0, 4, 1, 5, 2, 6, 3, 7])
 cluster.set_pbc((0,0,0))
 cluster = get_rotated_cluster(cluster, angle=0.1) # Must rotate
 
+xtal = pyxtal()
+xtal.from_prototype('graphite')
+atoms = xtal.to_ase()
+P_ref = calculator.compute_p(atoms)[0]
+
 # Diamond
 class TestCluster(unittest.TestCase):
     struc = get_rotated_cluster(cluster)
-    p0 = SO3(nmax=nmax, lmax=lmax, rcut=rc).calculate(struc, derivative=True)
+    p0 = calculator0.calculate(struc, derivative=True)
     struc = get_rotated_cluster(cluster, 10, 'x')
-    p1 = SO3(nmax=nmax, lmax=lmax, rcut=rc).calculate(struc)
+    p1 = calculator0.calculate(struc)
 
     def test_SO3_rotation_variance(self):
         array1 = self.p0['x']
@@ -73,7 +150,7 @@ def test_dPdR_vs_numerical(self):
         for j in range(shp[0]):
             for k in range(3):
                 struc = get_perturbed_cluster(cluster, j, k, eps)
-                p2 = SO3(nmax=nmax, lmax=lmax, rcut=rc).calculate(struc)
+                p2 = calculator0.calculate(struc)
                 array2 = (p2['x'] - self.p0['x'])/eps
                 assert(np.allclose(array1[:,j,:,k], array2, atol=1e-3))
 
@@ -82,30 +159,53 @@ class TestXtal(unittest.TestCase):
     def test_dPdR_diamond(self):
         c = pyxtal()
         c.from_prototype('diamond')
-        get_dPdR_xtal(c.to_ase(), nmax, lmax, rc, eps)
+        get_dPdR_xtal(c.to_ase(), eps)
 
     def test_dPdR_graphite(self):
         c = pyxtal()
         c.from_prototype('graphite')
-        get_dPdR_xtal(c.to_ase(), nmax, lmax, rc, eps)
+        get_dPdR_xtal(c.to_ase(), eps)
 
     def test_dPdR_random(self):
         x = [ 7.952, 2.606, 0.592, 0.926, 0.608, 0.307]
         c = pyxtal()
         c.from_spg_wps_rep(179, ['6a', '6a', '6a', '6a'], x)
-        get_dPdR_xtal(c.to_ase(), nmax, lmax, rc, eps)
+        get_dPdR_xtal(c.to_ase(), eps)
 
     def test_dPdR_random_P(self):
         x = [ 7.952, 2.606, 0.592, 0.926, 0.608, 0.307]
         c = pyxtal()
         c.from_spg_wps_rep(179, ['6a', '6a', '6a', '6a'], x)
         atoms = c.to_ase()
-        f = SO3(nmax=nmax, lmax=lmax, rcut=rc)
-        p0 = f.compute_p(atoms)
-        _, p1 = f.compute_dpdr(atoms)
-        _, p2 = f.compute_dpdr_5d(atoms)
+        p0 = calculator.compute_p(atoms)
+        _, p1 = calculator.compute_dpdr(atoms)
+        _, p2 = calculator.compute_dpdr_5d(atoms)
         assert(np.allclose(p0, p1, atol=1e-3))
         assert(np.allclose(p0, p2, atol=1e-3))
 
+class TestSimilarity(unittest.TestCase):
+
+    def test_sim_diamond(self):
+        x = [3.0]
+        c = pyxtal()
+        c.from_spg_wps_rep(227, ['8a'], x, ['C'])
+        atoms = c.to_ase()
+        x = c.get_1d_rep_x()
+        dSdx1 = numerical_dSdx(x, c, P_ref)
+        dSdx2 = calculate_dSdx_supercell(x, c, P_ref)
+        #print(dSdx1, dSdx2)
+        assert(np.allclose(dSdx1, dSdx2, rtol=1e-1, atol=1e+1))
+
+    def test_dPdR_random(self):
+        #x = [ 7.952, 2.606, 0.592, 0.926, 0.608, 0.307]
+        x = [9.55,  2.60,  0.48,  0.88,  0.76,   0.36]
+        c = pyxtal()
+        c.from_spg_wps_rep(179, ['6a', '6a', '6a', '6a'], x)
+        atoms = c.to_ase()
+        dSdx1 = numerical_dSdx(x, c, P_ref)
+        dSdx2 = calculate_dSdx_supercell(x, c, P_ref)
+        #print(dSdx1, dSdx2)
+        assert(np.allclose(dSdx1, dSdx2, rtol=1e-1, atol=1e+1))
+
 if __name__ == "__main__":
     unittest.main()

tests/test_lego.py

@@ -43,6 +43,7 @@ def test_opt_xtal(self):
             xtal = pyxtal()
             xtal.from_spg_wps_rep(spg, wps, x, ['C']*len(wps))
             xtal, sim, _ = builder1.optimize_xtal(xtal, add_db=False)
+            #print(xtal.get_1d_rep_x())
             assert sim < 1e-2
 
     def test_opt_xtal2(self):