def test_expi_complex():
dataset = []
for r in np.logspace(-99, 2, 10):
for p in np.linspace(0, 2*np.pi, 30):
z = r*np.exp(1j*p)
dataset.append((z, complex(mpmath.ei(z))))
dataset = np.array(dataset, dtype=np.complex_)
FuncData(sc.expi, dataset, 0, 1).check()
def test_expi_complex():
dataset = []
for r in np.logspace(-99, 2, 10):
for p in np.linspace(0, 2 * np.pi, 30):
z = r * np.exp(1j * p)
dataset.append((z, complex(mpmath.ei(z))))
dataset = np.array(dataset, dtype=np.complex_)
FuncData(sc.expi, dataset, 0, 1).check()
def product_term(
n,
electron_charge,
positron_charge,
vacuum_permativity,
electron_number_density,
ionisation_potential,
initial_energy,
):
a = (electron_number_density * (positron_charge ** 2) * (electron_charge ** 4)) / \
(8 * mpmath.pi * (vacuum_permativity ** 2))
b = 4 / ionisation_potential
constant_of_integration = mpmath.ei(
2 * mpmath.ln(b * initial_energy)) / (a * (b**2))
exp_integral_inv = exponential_integral_inverse(
a * (b**2) * (constant_of_integration - n))
denominator = mpmath.e**(exp_integral_inv / 2)
energy_proportionality_correction = mpmath.sqrt(
ELECTRON_MASS / (2 * (electron_number_density**2)))
return 1 - (mpmath.sqrt(
b / denominator)) / energy_proportionality_correction
def f59(x):
# expint_Ei_scaled
return mpmath.ei(x) * mpmath.exp(-x)
def f58(x):
# expint_Ei
return mpmath.ei(x)
def test_negative_values():
# For negative values `ei` is simply implemented using `e1`, which
# is tested elsewhere. Just check a single value to make sure we
# got the connection formula correct.
assert_allclose(sc.ei(-1), float(mpmath.ei(-1)), atol=0, rtol=_ε)
x_str = mpm.nstr(x_mpm, n=n)
v_str = x_str.split('e')
try:
l_m = np.log(np.float(v_str[0]))
e = np.log(10) * np.float(v_str[1]) if len(v_str) == 2 else 0.0
mpm.mp.prec, mpm.mp.dps = prec_def, dps_def # reset
return l_m + e
except: # ValueError:
s_ut.my_print('pid: ' + str(os.getpid()) +
' ERROR:::erlang_utils::log_gammainc:: a: ' + str(a) +
' lwr: ' + str(lwr) + ' upr: ' + str(upr) + ' dps: ' +
str(mpm.mp.dps))
return None
expi = np.frompyfunc(lambda x: float(mpm.ei(x)), 1, 1)
# #########################################################################
# ########## Framework for recursions and log sums ########################
# #########################################################################
def trampoline(gen, *args, **kwargs):
g = gen(*args, **kwargs)
while isinstance(g, types.GeneratorType):
g = next(g)
return g
def log_trick(arr):
# 1. if Y = a1 + a2 + ... , then the log_trick input is an array of the form arr = [[log(|a1|), sign(a1)], [log(|a2|), sign(a2)]], ] ...
