Source code for yadism.coefficient_functions.intrinsic.raw_cc
import numpy as np
from scipy.special import spence # pylint: disable=all
[docs]
def li2(x):
return spence(1 - x)
lnomx = -4.0
[docs]
def omx(y):
return -7.0 + 4.0 * np.log(1.0 - y)
[docs]
def f2sv(y):
return (
-0.3333333333333333
* ((-1 + y) * (15 + 4 * np.pi**2 - 12 * li2(y / (-1 + y)) - 9 * np.log(1 - y)))
/ y
)
[docs]
def flsv(y):
return (15 + 4 * np.pi**2 - 12 * li2(y / (-1 + y)) - 3 * np.log(1 - y)) / (3.0 * y)
[docs]
def f3sv(y):
return (
-5 - (4 * np.pi**2) / 3.0 + 4 * li2(y / (-1 + y)) + (3 - 2 / y) * np.log(1 - y)
)
[docs]
def f2r(y, z):
P1 = 1.0 / (1.0 - z)
P2 = np.log(1.0 - z) * P1
return (
P1
* (
y**4 * (3 + y)
- 2 * y**3 * (5 + y * (22 + y)) * z
+ 2 * y**3 * (54 + (41 - 3 * y) * y) * z**2
- 6 * y**2 * (5 + y * (30 + y)) * z**3
+ 6 * y * (5 + y * (30 + y)) * z**5
+ 2 * y * (-54 + y * (-41 + 3 * y)) * z**6
+ 2 * (5 + y * (22 + y)) * z**7
- (3 + y) * z**8
)
- 2
* P2
* (
-(z**6 * (5 + (-4 + z) * z))
+ y**5 * (1 + z**2)
+ y**4 * (-1 + z * (8 - 21 * z + 4 * z**3))
+ y**2 * z**2 * (-5 - (-2 + z) * z * (34 + 7 * z * (-10 + 3 * z)))
+ y**3 * z * (4 + z * (-47 + z * (112 - 50 * z + z**3)))
+ y * z**4 * (-20 + z * (68 + z * (-47 + z * (8 + z))))
)
+ 2
* P1
* (
-(z**6 * (5 + (-4 + z) * z))
+ y**5 * (1 + z**2)
+ y**4 * (-1 + z * (8 - 21 * z + 4 * z**3))
+ y**2 * z**2 * (-5 - (-2 + z) * z * (34 + 7 * z * (-10 + 3 * z)))
+ y**3 * z * (4 + z * (-47 + z * (112 - 50 * z + z**3)))
+ y * z**4 * (-20 + z * (68 + z * (-47 + z * (8 + z))))
)
* np.log(1 - y / z)
) / (y * (y - z) * (y - z**2) ** 3)
[docs]
def flr(y, z):
P1 = 1.0 / (1.0 - z)
P2 = np.log(1.0 - z) * P1
return (
-2
* P2
* (
y**3
- 2 * y**2 * (2 + 3 * y) * z
+ y * (5 + y * (25 + y)) * z**2
+ 2 * y * (-15 + (-8 + y) * y) * z**3
+ (5 + y * (25 + y)) * z**4
- 2 * (2 + 3 * y) * z**5
+ z**6
)
* (-(z**2) + y * (-1 + 2 * z))
+ P1
* (
-4 * y**5 * (-1 + z) * z
+ (10 - 3 * z) * z**7
+ y**4 * (3 - 4 * (-2 + z) * z * (-4 + 5 * z))
+ 2 * y * z**5 * (5 + z * (-35 + 16 * z))
+ 2 * y**3 * z * (-5 + z * (35 - 56 * z + 10 * z**3 + 2 * z**4))
- 2 * y**2 * z**3 * (5 + 2 * z**2 * (-28 + z * (14 + z)))
)
+ 2
* P1
* (
y**3
- 2 * y**2 * (2 + 3 * y) * z
+ y * (5 + y * (25 + y)) * z**2
+ 2 * y * (-15 + (-8 + y) * y) * z**3
+ (5 + y * (25 + y)) * z**4
- 2 * (2 + 3 * y) * z**5
+ z**6
)
* (-(z**2) + y * (-1 + 2 * z))
* np.log(1 - y / z)
) / (y * (y - z) * (y - z**2) ** 3)
[docs]
def f3r(y, z):
P1 = 1.0 / (1.0 - z)
P2 = np.log(1.0 - z) * P1
return (
-2
* P2
* (
y**3
+ y * (-3 + (-7 + y) * y) * z**2
+ 16 * y * z**3
+ (-3 + (-7 + y) * y) * z**4
+ z**6
)
- P1
* (y - z**2)
* (
z**3 * (6 + z)
+ 2 * y * z * (3 + (-11 + z) * z)
+ y**2 * (1 + 2 * z + 4 * z**2)
)
+ 2
* P1
* (
y**3
+ y * (-3 + (-7 + y) * y) * z**2
+ 16 * y * z**3
+ (-3 + (-7 + y) * y) * z**4
+ z**6
)
* np.log(1 - y / z)
) / ((y - z) * (y - z**2) ** 2)