Source code for iDEA.test_EXT2
"""Tests for 2-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 EXT2
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 both ground-state non-interacting and ground-state interacting case.
Testing time-dependent interacting 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.sys.NE = 2 #: Number of electrons
pm.sys.grid = 81 #: 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 = 0.05 #: Total real time
pm.sys.imax = 51 #: 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*(0.25**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.itol = 1e-5 #: Tolerance of imaginary time propagation
pm.ext.itol_solver = 1e-12 #: Tolerance of linear solver in imaginary time propagation
pm.ext.rtol_solver = 1e-12 #: Tolerance of linear solver in real time propagation
pm.ext.itmax = 100.0 #: Total imaginary time
pm.ext.iimax = 5e3 #: Imaginary time iterations
pm.ext.ideltat = pm.ext.itmax/pm.ext.iimax #: Imaginary time step (DERIVED)
pm.ext.initial_gspsi = 'qho' #: Initial 2 electron ground-state wavefunction
self.pm = pm
[docs] def test_non_interacting_system_1(self):
"""Test non-interacting system"""
pm = self.pm
pm.sys.interaction_strength = 0.0 #: Scales the strength of the Coulomb interaction
results = EXT2.main(pm)
nt.assert_allclose(results.gs_ext_E, 0.5000, atol=5e-4)
[docs] def test_interacting_system_1(self):
"""Test interacting system"""
pm = self.pm
pm.sys.interaction_strength = 1.0 #: Scales the strength of the Coulomb interaction
results = EXT2.main(pm)
nt.assert_allclose(results.gs_ext_E, 0.7532, atol=5e-4)
[docs] def test_time_dependence(self):
"""Test real time propagation"""
pm = self.pm
pm.run.time_dependence = True #: whether to run time-dependent calculation
pm.sys.interaction_strength = 1.0 #: Scales the strength of the Coulomb interaction
results = EXT2.main(pm)
den_gs = results.gs_ext_den
den_td = results.td_ext_den
cur = results.td_ext_cur
deltan = np.sum(np.absolute(den_td[50,:]-den_gs[:]))*pm.space.delta
deltac = np.sum(np.absolute(cur[50,:]))*pm.space.delta
nt.assert_allclose(deltan, 5.43e-5, atol=1e-7)
nt.assert_allclose(deltac, 4.94e-3, atol=1e-5)
[docs]class TestDoubleWell(unittest.TestCase):
""" Tests for an asymmetric double-well potential
External potential is an asymmetric double-well potential (System 1 in Hodgson et al. 2016).
Testing ground-state interacting case.
Testing 3-, 5- and 7-point stencil for the second-derivative.
Testing initial wavefunction by starting from the non-interacting orbitals.
"""
[docs] def setUp(self):
""" Sets up double-well system """
pm = input.Input()
pm.run.name = 'unittest'
pm.run.save = False
pm.run.verbosity = 'low'
pm.sys.NE = 2 #: Number of electrons
pm.sys.grid = 41 #: Number of grid points (must be odd)
pm.sys.xmax = 15.0 #: Size of the system
pm.sys.acon = 1.0 #: Smoothing of the Coloumb interaction
pm.sys.interaction_strength = 1.0 #: Scales the strength of the Coulomb interaction
def v_ext(x):
"""Initial external potential"""
return -1.2*np.exp((-1/125)*(x-7.0)**4) - 0.9*np.exp((-1/10)*(x+6.0)**2)
pm.sys.v_ext = v_ext
pm.ext.itol = 1e-6 #: Tolerance of imaginary time propagation
pm.ext.itol_solver = 1e-12 #: Tolerance of linear solver in imaginary time propagation
pm.ext.itmax = 100.0 #: Total imaginary time
pm.ext.iimax = 1e4 #: Imaginary time iterations
pm.ext.ideltat = pm.ext.itmax/pm.ext.iimax #: Imaginary time step (DERIVED)
pm.ext.initial_gspsi = 'non' #: Initial 2 electron ground-state wavefunction
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 = EXT2.main(pm)
nt.assert_allclose(results.gs_ext_E, -1.701, atol=5e-3)
[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 = EXT2.main(pm)
nt.assert_allclose(results.gs_ext_E, -1.7006, atol=5e-4)
[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 = EXT2.main(pm)
nt.assert_allclose(results.gs_ext_E, -1.7006, atol=1e-4)
