Add fitting to atomdb example

Author: Ali-Tehrani

examples/atomdb_db.py

@@ -0,0 +1,103 @@
+r"""
+This files generates the results for Table (1) and (2) in the BFit paper.
+
+Specifically, it optimizes the Kullback-Leibler Divergence using the fixed
+ point iteration method. A normalized Gaussian model is used whose initial
+ guess is the universal Gaussian basis-set multipled by two.  The constraint
+ that the integral of the model should equal the atomic number is added, via
+ the attribute `integral_dens`. The attribute `disp` displays the results
+ at each iteration.
+"""
+import numpy as np
+
+from bfit.density import SlaterAtoms
+from bfit.fit import ScipyFit,KLDivergenceFPI
+from bfit.grid import ClenshawRadialGrid
+from bfit.model import AtomicGaussianDensity
+from bfit.measure import KLDivergence
+from bfit.parse_ugbs import get_ugbs_exponents
+from atomdb import load
+
+results_final = {}
+atoms = ["H",  "C", "N", "O", "F", "P", "S", "Cl"]
+atomic_numbs = [1, 6, 7, 8, 9, 15, 16, 17] #[1 + i for i in range(0, len(atoms))]
+mult = [2, 3, 4, 3, 2, 4, 3, 2]
+for k, element in enumerate(atoms):
+    print("Start Atom %s" % element)
+
+    # Construct a integration grid
+    atomic_numb = atomic_numbs[k]
+    grid = ClenshawRadialGrid(
+        atomic_numb, num_core_pts=10000, num_diffuse_pts=899, include_origin=True#, extra_pts=[50,75,100],
+    )
+
+    # Initial Guess constructed from UGBS
+    ugbs = get_ugbs_exponents(element)
+    exps_s = ugbs["S"]
+    num_s = len(exps_s)
+    exps_p = ugbs["P"]
+    num_p = len(exps_p)
+    coeffs = np.array([atomic_numb / (num_s + num_p)] * (num_s + num_p))
+    e_0 = np.array(exps_s + exps_p) * 2.0
+
+    # Construct Atomic Density and Fitting Object
+    #density = SlaterAtoms(element=element).atomic_density(grid.points)
+    # Use AtomDB to calculate the density
+    atom = load(elem=element, charge=0, mult=mult[k], dataset="hci", datapath="/home/ali-tehrani/SoftwareProjects/AtomDBdata")
+
+    dens = atom.dens_func()
+    density = dens(grid.points)
+
+    import matplotlib.pyplot as plt
+    # plt.plot(grid.points, density, "bo-")
+    # plt.show()
+    print(density[-1], grid.points[-1], grid.points[0:3])
+    density[density < 0.0] = 0.0
+    # continue
+    # assert 1 == 0
+    model = AtomicGaussianDensity(grid.points, num_s=num_s, num_p=num_p, normalize=True)
+    fit = KLDivergenceFPI(grid, density, model, mask_value=1e-18, spherical=True,
+                          integral_dens=atomic_numb)
+
+    # Run the Kullback-Leibler FPI Method
+    results = fit.run(
+        coeffs, e_0, maxiter=10000, c_threshold=1e-6, e_threshold=1e-6, d_threshold=1e-14,
+        disp=True
+    )
+    # Construct Fitting Object using SLSQP and optimizing KL
+    # measure = KLDivergence(mask_value=1e-18)
+    # fit_KL_slsqp = ScipyFit(grid, density, model, measure=measure, method="SLSQP", spherical=True)
+    # # Run the SLSQP optimization algorithm
+    # results = fit_KL_slsqp.run(coeffs, e_0, maxiter=10000, disp=True, with_constraint=True, tol=1e-14)
+
+    print("KL-FPI INFO")
+    print("-----------")
+    print("Success %s" % results["success"])
+    print("Final Coeffs")
+    print(results["coeffs"])
+    print("Final Exponents")
+    print(results["exps"])
+    print("Integration Value & L1 & L_infinity & LS & KL (With 4 pi r^2 included)")
+    p = results["performance"][-1]
+    print(p)
+    # Calculate the relative errors
+    spherical = 4.0 * np.pi * grid.points**2.0
+    l1 = results["performance"][-1][1] / grid.integrate(density * spherical)
+    linf = results["performance"][-1][2] / np.max(density)
+    ls = results["performance"][-1][3] / grid.integrate(density**2.0 * spherical)
+    kl = results["performance"][-1][4] / grid.integrate(
+        density * np.log(density) * spherical
+    )
+    print("Relative Errors L1 & L_infinity & LS & KL (With 4 pi r^2 included)")
+    print([l1, linf, ls, kl])
+
+    # Store the results
+    results_final[element + "_coeffs_s"] = results["coeffs"][:num_s]
+    results_final[element + "_exps_s"] = results["exps"][:num_s]
+    results_final[element + "_coeffs_p"] = results["coeffs"][num_s:]
+    results_final[element + "_exps_p"] = results["exps"][num_s:]
+    results_final[element + "_errors_4pir2"] = results["performance"][-1]
+    results_final[element + "_sucess"] = results["success"]
+    results_final[element + "_errors"] = [l1, linf, ls, kl]
+
+    np.savez("./result_kl_fpi_method_cugbasis_atomdb_hci.npz", **results_final)