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"""Test the module that is used to generate the response function
(qmix.respfn).
This classes in this module (based on qmix.respfn.RespFn) will:
1. Either generate the DC I-V curve using some sort of model
(from qmix.mathfn.ivcurve_models) or import the DC I-V curve from
experimental data. (The DC I-V curve is the imaginary component of the
response function.)
2. Calculate the Kramers-Kronig transform of the DC I-V curve using the
qmix.mathfn.kktrans module. The KK trans of the DC I-V curve is the real
component of the response function.
3. Sample the response function such that there are more sample points in
the 'curvier' regions of the response function.
4. Set up the spline interpolation so that the response function can be
interpolated very quickly when calculating the tunneling currents (i.e.,
in the qmix.qtcurrent module).
The most important thing to test in this module is that the response function
is interpolated correctly. (The I-V curve models and the KK transform are
tested in different pytests.)
To test these classes:
1. Generate the response function.
2. Interpolate the response function using a very high density of bias
voltages.
3. Compare these interpolated values to known values.
"""
import os
import tempfile
import matplotlib.pyplot as plt
import numpy as np
import pytest
import qmix
from qmix.mathfn.ivcurve_models import (expanded, exponential, perfect,
polynomial)
from qmix.respfn import *
MAX_INTERP_ERROR = 0.01 # 1% allowable max error when interpolating
@pytest.mark.filterwarnings("ignore::FutureWarning")
def test_RespFnFromIVData():
"""Try generating a response function using voltage and current data."""
# Use a model to genereate a DC I-V curve
voltage = np.linspace(-1, 10, 2001)
current = qmix.mathfn.ivcurve_models.polynomial(voltage, 50)
# Generate response function using the DC I-V curve from the model
resp = RespFnFromIVData(voltage, current)
print(resp)
# High-density interpolation
i_resp = resp._f_idc(voltage)
# Check interpolated values
max_diff = np.abs(i_resp - current).max()
assert max_diff < MAX_INTERP_ERROR
@pytest.mark.filterwarnings("ignore::FutureWarning")
def test_polynomial():
"""Try generating a response function using the polynomial model."""
# Order of polynomial model
order = 50
# Known values
v = np.linspace(0, 2, 501)
current = qmix.mathfn.ivcurve_models.polynomial(v, order)
# Interpolated values
resp = RespFnPolynomial(order, check_error=True)
print(resp)
i_resp = resp._f_idc(v)
# Check interpolated values
max_diff = np.abs(i_resp - current).max()
assert max_diff < MAX_INTERP_ERROR
# Check resp_swap and resp_conj
voltage = np.linspace(0, 2, 201)
resp1 = resp.resp_swap(voltage)
resp2 = 1j * resp.resp_conj(voltage)
np.testing.assert_equal(resp1, resp2)
# Check derivative of I-V curve
vb = np.linspace(0, 2, 201)
idc0 = resp.didc(vb)
assert abs(idc0[-1] - 1.) < 1e-10
assert abs(idc0[0]) < 1e-10
idx_max = idc0.argmax()
assert idx_max == 100
# Check derivative of KK transform
vb = np.linspace(0, 2, 201)
ikk0 = resp.dikk(vb)
assert ikk0[99] > 0.
assert ikk0[101] < 0.
assert ikk0[100] < ikk0[99]
assert ikk0[100] > ikk0[101]
@pytest.mark.filterwarnings("ignore::FutureWarning")
def test_exponential_interpolation():
"""Try generating a response function using the exponential model."""
# Parameters for exponential model
v_gap = 2.8e-3
r_sg = 1000
r_n = 14
a_g = 4e4
# Known values
v = np.linspace(0, 2, 501)
current = exponential(v, v_gap, r_n, r_sg, a_g)
# Interpolated values
resp = RespFnExponential(v_gap, r_n, r_sg, a_g)
print(resp)
i_resp = resp._f_idc(v)
# Check interpolated values
max_diff = np.abs(i_resp - current).max()
assert max_diff < MAX_INTERP_ERROR
def test_perfect_interpolation():
"""Test 'perfect' response function."""
# Generate response function
resp = RespFnPerfect()
print(resp)
# Check individual DC I-V values using known values
assert resp.idc(-2.0) == -2.
assert resp.idc(-1.0) == -0.5
assert resp.idc(0.00) == 0.
assert resp.idc(0.99) == 0
assert resp.idc(1.00) == 0.5
assert resp.idc(1.01) == 1.01
assert resp.idc(2.00) == 2.
# Check individual KK values using known values
assert resp._f_ikk(-1e10) < 1e-7
assert resp._f_ikk(-1.0) >= 100
assert resp._f_ikk(1.00) >= 100
assert resp._f_ikk(1e10) < 1e-7
def test_smearing_perfect_respfn():
"""Try smearing the perfect model.
The RespFn class has an option to 'smear' the DC I-V curve. This can help
to model heating. The 'smear' convolves the DC I-V curve with a Gaussian
distribution of a given std dev."""
# Generate 'smeared' response function
resp = RespFnPerfect(v_smear=0.05)
print(resp)
# Check DC I-V curve
# The smear should only affect the region around the transition
# It should NOT introduce any sort of offset (which we will check now)
x = np.array([0., 0.5, 1.5, -1.5])
y = resp.idc(x)
np.testing.assert_almost_equal(y, [0., 0., 1.5, -1.5], 5)
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