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adding zeta stuff

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This commit is contained in:
Deepak Mallubhotla 2020-07-14 08:22:18 -05:00
parent 8b8a06490a
commit ab61ba5713
7 changed files with 51 additions and 21 deletions
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6
pynam/dielectric/low_k_nam.py
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@ -1,7 +1,7 @@
import numpy as np import numpy as np
from numpy.lib.scimath import sqrt as csqrt from numpy.lib.scimath import sqrt as csqrt
import pynam.util.complex_quad import pynam.util
def g(w, wp): def g(w, wp):
@ -35,7 +35,7 @@ def i2(w, wp, k, v):
def a(w, k, v, t): def a(w, k, v, t):
return pynam.util.complex_quad.complex_quad( return pynam.util.complex_quad(
lambda wp: np.tanh((w + wp) / (2 * t)) * (i1(w, wp, k, v)), lambda wp: np.tanh((w + wp) / (2 * t)) * (i1(w, wp, k, v)),
1 - w, 1 1 - w, 1
)[0] )[0]
@ -46,7 +46,7 @@ def b_int(wp, w, k, v, t):
def b(w, k, v, t, b_max=np.inf): def b(w, k, v, t, b_max=np.inf):
return pynam.util.complex_quad.complex_quad( return pynam.util.complex_quad(
lambda wp: b_int(wp, w, k, v, t), 1, b_max lambda wp: b_int(wp, w, k, v, t), 1, b_max
)[0] )[0]

2
pynam/dielectric/sigma_nam.py
View File

@ -41,7 +41,7 @@ def i2(w, wp, k, v):
def a(w, k, v, t): def a(w, k, v, t):
result = pynam.util.complex_quad.complex_quad( result = pynam.util.complex_quad(
lambda wp: np.tanh((w + wp) / (2 * t)) * (i1(w, wp, k, v)), lambda wp: np.tanh((w + wp) / (2 * t)) * (i1(w, wp, k, v)),
1 - w, 1, 1 - w, 1,
epsabs=1e-10 epsabs=1e-10

26
pynam/noise/zeta.py
View File

@ -12,7 +12,7 @@ def get_zeta_p_integrand(eps: Callable[[float], complex]) -> Callable[[float, fl
:param eps: :param eps:
:return: :return:
""" """
def zeta_p_integrand(u: float, y: float) -> complex: def zeta_p_integrand(y: float, u: float) -> complex:
""" """
Here y and u are in units of vacuum wavelength, coming from Ford-Weber / from the EWJN noise expressions. Here y and u are in units of vacuum wavelength, coming from Ford-Weber / from the EWJN noise expressions.
:param u: :param u:
@ -31,15 +31,15 @@ def get_zeta_p_integrand(eps: Callable[[float], complex]) -> Callable[[float, fl
return zeta_p_integrand return zeta_p_integrand
# def get_zeta_p_function(eps: Callable[[float], complex]): def get_zeta_p_function(eps: Callable[[float], complex]):
# def zeta_p(u: float) -> complex: def zeta_p(u: float) -> complex:
# zeta_p_integrand = get_zeta_integrand(eps) zeta_p_integrand = get_zeta_p_integrand(eps)
#
# integral_result = pynam.util.complex_quad(zeta_p_integrand, 0, np.inf) integral_result = pynam.util.complex_quad(lambda y: zeta_p_integrand(y, u), 0, np.inf)
#
# print(integral_result) print(integral_result)
# integral = integral_result[0] integral = integral_result[0]
#
# return integral * 2j return integral * 2j
#
# return zeta_p return zeta_p

2
pynam/util/__init__.py
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@ -1 +1 @@
from pynam.util.complex_quad import complex_quad, complex_quadrature from pynam.util.complex_integrate import complex_quad, complex_quadrature

1
pynam/util/complex_integrate.py
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@ -15,6 +15,7 @@ def complex_quad(func, a, b, **kwargs):
return real_integral[0] + 1j * imag_integral[0], real_integral[1:], imag_integral[1:] return real_integral[0] + 1j * imag_integral[0], real_integral[1:], imag_integral[1:]
def complex_quadrature(func, a, b, **kwargs): def complex_quadrature(func, a, b, **kwargs):
def real_func(x): def real_func(x):

26
tests/noise/test_zeta.py
View File

@ -14,10 +14,10 @@ def zeta_p_integrand_lindhard():
@pytest.mark.parametrize("test_input,expected", [ @pytest.mark.parametrize("test_input,expected", [
# u y zeta_p_i(u, y) # y u zeta_p_i(u, y)
((100, 100), -6.891930153028566e-13 - 7.957747045025948e-9j), ((100, 100), -6.891930153028566e-13 - 7.957747045025948e-9j),
((100, 1e5), -1.0057257267146669e-10 - 4.0591966623027983e-13j), ((1e5, 100), -1.0057257267146669e-10 - 4.0591966623027983e-13j),
((1e5, 100), 1.1789175285399862e-8 - 7.957833322596519e-9j) ((100, 1e5), 1.1789175285399862e-8 - 7.957833322596519e-9j)
]) ])
def test_zeta_p_integrand_lindhard(zeta_p_integrand_lindhard, test_input, expected): def test_zeta_p_integrand_lindhard(zeta_p_integrand_lindhard, test_input, expected):
actual = zeta_p_integrand_lindhard(*test_input) actual = zeta_p_integrand_lindhard(*test_input)
@ -26,3 +26,23 @@ def test_zeta_p_integrand_lindhard(zeta_p_integrand_lindhard, test_input, expect
actual, expected, actual, expected,
rtol=1e-7, err_msg='Zeta_p is inaccurate for Lindhard case', verbose=True rtol=1e-7, err_msg='Zeta_p is inaccurate for Lindhard case', verbose=True
) )
@pytest.fixture
def zeta_p_lindhard():
params = CalculationParams(omega=1e9, v_f=2e6, omega_p=3.544907701811032e15, tau=1e-14)
eps_l = pynam.dielectric.get_lindhard_dielectric(params)
return pynam.noise.zeta.get_zeta_p_function(eps_l)
@pytest.mark.parametrize("test_input,expected", [
# u zeta_p(u)
(1, 0.000199609 - 0.000199608j),
])
def test_zeta_p(zeta_p_lindhard, test_input, expected):
actual = zeta_p_lindhard(test_input)
np.testing.assert_allclose(
actual, expected,
rtol=1e-7, err_msg='Zeta_p is inaccurate for Lindhard case', verbose=True
)

9
tests/util/test_complex_integrate.py
View File

@ -9,3 +9,12 @@ def test_complex_quad():
actual, (6**3)/3 + 1j*(6**4)/4, actual, (6**3)/3 + 1j*(6**4)/4,
decimal=7, err_msg='complex quadrature is broken', verbose=True decimal=7, err_msg='complex quadrature is broken', verbose=True
) )
def test_complex_quadrature():
actual = pynam.util.complex_integrate.complex_quadrature(lambda x: x ** 2 + 1j * x ** 3, 0, 6)[0]
# int_1^6 dx x^2 + i x^3 should equal (1/3)6^3 + (i/4)6^4
np.testing.assert_almost_equal(
actual, (6**3)/3 + 1j*(6**4)/4,
decimal=7, err_msg='complex quadrature is broken', verbose=True
)