Source code for iDEA.test_EXT1
"""Tests for 1-electron exact calculations in iDEA
"""
from __future__ import division
from __future__ import print_function
from __future__ import absolute_import
import numpy as np
import numpy.testing as nt
import unittest
from . import EXT1
from . import input
[docs]class TestHarmonicOscillator(unittest.TestCase):
""" Tests for the harmonic oscillator potential
External potential is the harmonic oscillator (this is the default in iDEA).
Testing ground-state and time-dependence case.
"""
[docs] def setUp(self):
""" Sets up harmonic oscillator system """
pm = input.Input()
pm.run.name = 'unittest'
pm.run.save = False
pm.run.verbosity = 'low'
pm.run.time_dependence = True
pm.sys.NE = 1 #: Number of electrons
pm.sys.grid = 151 #: Number of grid points (must be odd)
pm.sys.stencil = 3 #: Discretisation of 2nd derivative (3 or 5 or 7)
pm.sys.xmax = 7.5 #: Size of the system
pm.sys.tmax = 0.25 #: Total real time
pm.sys.imax = 251 #: Number of real time iterations (NB: deltat = tmax/(imax-1))
pm.sys.acon = 1.0 #: Smoothing of the Coloumb interaction
def v_ext(x):
"""Initial external potential"""
return 0.5*(0.4**2)*(x**2)
pm.sys.v_ext = v_ext
def v_pert(x):
"""Time-dependent perturbation potential
Switched on at t=0.
"""
return -0.05*x
pm.sys.v_pert = v_pert
pm.ext.rtol_solver = 1e-12 #: Tolerance of linear solver in real time propagation
self.pm = pm
[docs] def test_system(self):
"""Test ground-state and then real time propagation"""
pm = self.pm
results = EXT1.main(pm)
den_gs = results.gs_ext_den
den_td = results.td_ext_den
cur = results.td_ext_cur
# Ground-state
den_analytic = np.zeros(151, dtype=np.float)
for j in range(151):
x = -7.5 + j*0.1
den_analytic[j] = np.sqrt(0.4/np.pi)*np.exp(-0.4*x**2)
den_error = np.sum(np.absolute(den_gs-den_analytic))
nt.assert_allclose(results.gs_ext_E, 0.2000, atol=1e-4)
nt.assert_allclose(den_error, 2.8e-3, atol=1e-4)
# Time-dependence
deltan = np.sum(np.absolute(den_td[250,:]-den_gs[:]))
deltac = np.sum(np.absolute(cur[250,:]))
nt.assert_allclose(deltan, 1.11e-2, atol=1e-4)
nt.assert_allclose(deltac, 1.24e-1, atol=1e-3)
[docs]class TestAtom(unittest.TestCase):
""" Tests for an atomic-like potential
External potential is a softened atomic-like potential.
Testing ground-state case.
Testing 3-, 5- and 7-point stencil for the second-derivative.
"""
[docs] def setUp(self):
""" Sets up atomic system """
pm = input.Input()
pm.run.name = 'unittest'
pm.run.save = False
pm.run.verbosity = 'low'
pm.sys.NE = 1 #: Number of electrons
pm.sys.grid = 31 #: Number of grid points (must be odd)
pm.sys.xmax = 12.0 #: Size of the system
def v_ext(x):
"""Initial external potential"""
return -1.0/(abs(0.1*x)+1)
pm.sys.v_ext = v_ext
self.pm = pm
[docs] def test_stencil_three(self):
"""Test 3-point stencil"""
pm = self.pm
pm.sys.stencil = 3 #: Discretisation of 2nd derivative (3 or 5 or 7)
results = EXT1.main(pm)
nt.assert_allclose(results.gs_ext_E, -0.84927, atol=1e-5)
[docs] def test_stencil_five(self):
"""Test 5-point stencil"""
pm = self.pm
pm.sys.stencil = 5 #: Discretisation of 2nd derivative (3 or 5 or 7)
results = EXT1.main(pm)
nt.assert_allclose(results.gs_ext_E, -0.84840, atol=1e-5)
[docs] def test_stencil_seven(self):
"""Test 7-point stencil"""
pm = self.pm
pm.sys.stencil = 7 #: Discretisation of 2nd derivative (3 or 5 or 7)
results = EXT1.main(pm)
nt.assert_allclose(results.gs_ext_E, -0.84834, atol=1e-5)
