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Commit b74830df authored by Keon Hee KIM's avatar Keon Hee KIM
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bug fix, refactor nested loops and optimize performance in misc.py

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2 merge requests!14Faster CircularResistiveWall,!3Yokoya elliptic (reopened)
This commit is part of merge request !14. Comments created here will be created in the context of that merge request.
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mbtrack2/utilities/misc.py
+ 107
− 319
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...@@ -202,13 +202,13 @@ def yokoya_elliptic(x_radius, y_radius): ...@@ -202,13 +202,13 @@ def yokoya_elliptic(x_radius, y_radius):
elif x_radius==np.inf and y_radius==np.inf: elif x_radius==np.inf and y_radius==np.inf:
raise ValueError("Both radii have infinite values.") raise ValueError("Both radii have infinite values.")
elif x_radius==np.inf: elif x_radius==np.inf:
yoklong = 1 yoklong = 1.0
yokxdip = np.pi**2/24 yokxdip = np.pi**2/24
yokydip = np.pi**2/12 yokydip = np.pi**2/12
yokxquad = -np.pi**2/24 yokxquad = -np.pi**2/24
yokyquad = np.pi**2/24 yokyquad = np.pi**2/24
elif y_radius==np.inf: elif y_radius==np.inf:
yoklong = 1 yoklong = 1.0
yokxdip = np.pi**2/12 yokxdip = np.pi**2/12
yokydip = np.pi**2/24 yokydip = np.pi**2/24
yokxquad = np.pi**2/24 yokxquad = np.pi**2/24
...@@ -227,185 +227,98 @@ def yokoya_elliptic(x_radius, y_radius): ...@@ -227,185 +227,98 @@ def yokoya_elliptic(x_radius, y_radius):
mu_b = np.arccosh(large_semiaxis/F) mu_b = np.arccosh(large_semiaxis/F)
qr = (large_semiaxis - small_semiaxis) / (large_semiaxis + small_semiaxis) qr = (large_semiaxis - small_semiaxis) / (large_semiaxis + small_semiaxis)
def function_ff(small_semiaxis, F, mu_b, ip, il):
fflong = ( 2*np.sqrt(2)*small_semiaxis/(np.pi*F)
* (-1)**ip/np.cosh(2*ip*mu_b)
* (-1)**il/np.cosh(2*il*mu_b) )
ffdx = ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
* (-1)**ip*(2*ip+1)/np.cosh((2*ip+1)*mu_b)
* (-1)**il*(2*il+1)/np.cosh((2*il+1)*mu_b) )
ffdy = ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
* (-1)**ip*(2*ip+1)/np.sinh((2*ip+1)*mu_b)
* (-1)**il*(2*il+1)/np.sinh((2*il+1)*mu_b) )
ffquad = ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
* (-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b)
* (-1)**il/np.cosh(2*il*mu_b) )
return (fflong, ffdx, ffdy, ffquad)
def function_L(mu_b, ip, il):
Lm = ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
* gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
* hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
* gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
* hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) )
Ldx = ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
* gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
* hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b)
* gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
* hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b)) )
Ldy = ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
* gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
* hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
- np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b)
* gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
* hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b)) )
return (Lm, Ldx, Ldy)
if qr == 0: if qr == 0:
yoklong = 1 yoklong = 1.0
yokxdip = 1 yokxdip = 1.0
yokydip = 1 yokydip = 1.0
yokxquad = 0 yokxquad = 0.0
yokyquad = 0 yokyquad = 0.0
# Beyond this threshold, they are not valid (they can even diverge), # Beyond this threshold (qr_th), they are not valid (they can even diverge),
# but should converge to Yokoya form factors of parallel plates. # but should converge to Yokoya form factors of parallel plates.
# Fortunately, beyond this threshold, they should show asymptotic behavior, # Fortunately, beyond this threshold, they should show asymptotic behavior,
# so we perform linear interpolation. # so we perform linear interpolation.
elif qr > qr_th: elif qr > qr_th:
if y_radius < x_radius: yoklong_pp = 1.0
yoklong_pp = 1
yokxdip_pp = np.pi**2/24 yokxdip_pp = np.pi**2/24
yokydip_pp = np.pi**2/12 yokydip_pp = np.pi**2/12
yokxquad_pp = -np.pi**2/24 yokxquad_pp = -np.pi**2/24
yokyquad_pp = np.pi**2/24 yokyquad_pp = np.pi**2/24
else: if y_radius > x_radius:
yoklong_pp = 1 yokxdip_pp, yokydip_pp = yokydip_pp, yokxdip_pp
yokxdip_pp = np.pi**2/12 yokxquad_pp, yokyquad_pp = yokyquad_pp, yokxquad_pp
yokydip_pp = np.pi**2/24
yokxquad_pp = np.pi**2/24
yokyquad_pp = -np.pi**2/24
small_semiaxis_th = large_semiaxis*(1-qr_th)/(1+qr_th) small_semiaxis_th = large_semiaxis*(1-qr_th)/(1+qr_th)
F_th = np.sqrt(large_semiaxis**2 - small_semiaxis_th**2) F_th = np.sqrt(large_semiaxis**2 - small_semiaxis_th**2)
mu_b_th = np.arccosh(large_semiaxis/F_th) mu_b_th = np.arccosh(large_semiaxis/F_th)
yoklong_th = 0 yoklong_th = 0.0
yokxdip_th = 0 yokxdip_th = 0.0
yokydip_th = 0 yokydip_th = 0.0
yokxquad_th = 0 yokxquad_th = 0.0
if y_radius < x_radius: ip_range = np.arange(50)
for ip in range(50): il_range = np.arange(50)
for il in range(50): ip, il = np.meshgrid(ip_range, il_range, indexing='ij')
if (ip==0) and (il==0):
yoklong_th += ( np.sqrt(2)*small_semiaxis_th/(2*np.pi*F_th) ff_values = np.array(function_ff(small_semiaxis_th, F_th, mu_b_th, ip, il))
*(-1)**ip/np.cosh(2*ip*mu_b_th) L_values = np.array(function_L(mu_b_th, ip, il))
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th) coeff_long = np.where((ip == 0) & (il == 0), 0.25, np.where((ip == 0) | (il == 0), 0.5, 1.0))
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il))) coeff_quad = np.where(il == 0, 0.5, 1.0)
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th) yoklong = np.sum(coeff_long * ff_values[0] * L_values[0])
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il)) yokxdip = np.sum(ff_values[1] * L_values[1])
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) ) yokydip = np.sum(ff_values[2] * L_values[2])
elif (ip==0 and il!=0) or (ip!=0 and il==0): yokxquad = -np.sum(coeff_quad * ff_values[3] * L_values[0])
yoklong_th += ( np.sqrt(2)*small_semiaxis_th/(np.pi*F_th) yokyquad = -yokxquad
*(-1)**ip/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
else:
yoklong_th += ( 2*np.sqrt(2)*small_semiaxis_th/(np.pi*F_th)
*(-1)**ip/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
yokxdip_th += ( np.sqrt(2)*small_semiaxis_th**3/(np.pi*F_th**3)
*(-1)**ip*(2*ip+1)/np.cosh((2*ip+1)*mu_b_th)
*(-1)**il*(2*il+1)/np.cosh((2*il+1)*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b_th)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b_th)) ) )
yokydip_th += ( np.sqrt(2)*small_semiaxis_th**3/(np.pi*F_th**3)
*(-1)**ip*(2*ip+1)/np.sinh((2*ip+1)*mu_b_th)
*(-1)**il*(2*il+1)/np.sinh((2*il+1)*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
- np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b_th)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b_th)) ) )
if (il==0):
yokxquad_th -= ( np.sqrt(2)*small_semiaxis_th**3/(2*np.pi*F_th**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
else:
yokxquad_th -= ( np.sqrt(2)*small_semiaxis_th**3/(np.pi*F_th**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
yokyquad_th = -yokxquad_th
else:
for ip in range(50):
for il in range(50):
if (ip==0) and (il==0):
yoklong_th += ( np.sqrt(2)*small_semiaxis_th/(2*np.pi*F_th)
*(-1)**ip/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
elif (ip==0 and il!=0) or (ip!=0 and il==0):
yoklong_th += ( np.sqrt(2)*small_semiaxis_th/(np.pi*F_th)
*(-1)**ip/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
else:
yoklong_th += ( 2*np.sqrt(2)*small_semiaxis_th/(np.pi*F_th)
*(-1)**ip/np.cosh(2*ip*mu_b_th)*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
yokydip_th += ( np.sqrt(2)*small_semiaxis_th**3/(np.pi*F_th**3)
*(-1)**ip*(2*ip+1)/np.cosh((2*ip+1)*mu_b_th)
*(-1)**il*(2*il+1)/np.cosh((2*il+1)*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b_th)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b_th)) ) )
yokxdip_th += ( np.sqrt(2)*small_semiaxis_th**3/(np.pi*F_th**3)
*(-1)**ip*(2*ip+1)/np.sinh((2*ip+1)*mu_b_th)
*(-1)**il*(2*il+1)/np.sinh((2*il+1)*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
- np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b_th)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b_th)) ) )
if (il==0):
yokyquad_th -= ( np.sqrt(2)*small_semiaxis_th**3/(2*np.pi*F_th**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
else:
yokyquad_th -= ( np.sqrt(2)*small_semiaxis_th**3/(np.pi*F_th**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b_th)
*(-1)**il/np.cosh(2*il*mu_b_th)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b_th)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b_th))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b_th)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b_th)) ) )
yokxquad_th = -yokyquad_th
qr_array = np.array([qr_th, 1]) if y_radius > x_radius:
yokxdip_th, yokydip_th = yokydip_th, yokxdip_th
yokxquad_th, yokyquad_th = yokyquad_th, yokxquad_th
qr_array = np.array([qr_th, 1.0])
yoklong_array = np.array([yoklong_th, yoklong_pp]) yoklong_array = np.array([yoklong_th, yoklong_pp])
yokxdip_array = np.array([yokxdip_th, yokxdip_pp]) yokxdip_array = np.array([yokxdip_th, yokxdip_pp])
yokydip_array = np.array([yokydip_th, yokydip_pp]) yokydip_array = np.array([yokydip_th, yokydip_pp])
...@@ -419,155 +332,30 @@ def yokoya_elliptic(x_radius, y_radius): ...@@ -419,155 +332,30 @@ def yokoya_elliptic(x_radius, y_radius):
yokyquad = np.interp(qr, qr_array, yokyquad_array) yokyquad = np.interp(qr, qr_array, yokyquad_array)
else: else:
yoklong = 0 yoklong = 0.0
yokxdip = 0 yokxdip = 0.0
yokydip = 0 yokydip = 0.0
yokxquad = 0 yokxquad = 0.0
if y_radius < x_radius: ip_range = np.arange(50)
for ip in range(50): il_range = np.arange(50)
for il in range(50): ip, il = np.meshgrid(ip_range, il_range, indexing='ij')
if (ip==0) and (il==0):
yoklong += ( np.sqrt(2)*small_semiaxis/(2*np.pi*F) ff_values = np.array(function_ff(small_semiaxis, F, mu_b, ip, il))
*(-1)**ip/np.cosh(2*ip*mu_b) L_values = np.array(function_L(mu_b, ip, il))
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b) coeff_long = np.where((ip == 0) & (il == 0), 0.25, np.where((ip == 0) | (il == 0), 0.5, 1.0))
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il))) coeff_quad = np.where(il == 0, 0.5, 1.0)
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b) yoklong = np.sum(coeff_long * ff_values[0] * L_values[0])
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il)) yokxdip = np.sum(ff_values[1] * L_values[1])
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) ) yokydip = np.sum(ff_values[2] * L_values[2])
elif (ip==0 and il!=0) or (ip!=0 and il==0): yokxquad = -np.sum(coeff_quad * ff_values[3] * L_values[0])
yoklong += ( np.sqrt(2)*small_semiaxis/(np.pi*F)
*(-1)**ip/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
else:
yoklong += ( 2*np.sqrt(2)*small_semiaxis/(np.pi*F)
*(-1)**ip/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
yokxdip += ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
*(-1)**ip*(2*ip+1)/np.cosh((2*ip+1)*mu_b)
*(-1)**il*(2*il+1)/np.cosh((2*il+1)*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b)) ) )
yokydip += ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
*(-1)**ip*(2*ip+1)/np.sinh((2*ip+1)*mu_b)
*(-1)**il*(2*il+1)/np.sinh((2*il+1)*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
- np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b)) ) )
if (il==0):
yokxquad -= ( np.sqrt(2)*small_semiaxis**3/(2*np.pi*F**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
else:
yokxquad -= ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
yokyquad = -yokxquad yokyquad = -yokxquad
else:
for ip in range(50): if y_radius > x_radius:
for il in range(50): yokxdip, yokydip = yokydip, yokxdip
if (ip==0) and (il==0): yokxquad, yokyquad = yokyquad, yokxquad
yoklong += ( np.sqrt(2)*small_semiaxis/(2*np.pi*F)
*(-1)**ip/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
elif (ip==0 and il!=0) or (ip!=0 and il==0):
yoklong += ( np.sqrt(2)*small_semiaxis/(np.pi*F)
*(-1)**ip/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
else:
yoklong += ( 2*np.sqrt(2)*small_semiaxis/(np.pi*F)
*(-1)**ip/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
yokydip += ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
*(-1)**ip*(2*ip+1)/np.cosh((2*ip+1)*mu_b)
*(-1)**il*(2*il+1)/np.cosh((2*il+1)*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b)) ) )
yokxdip += ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
*(-1)**ip*(2*ip+1)/np.sinh((2*ip+1)*mu_b)
*(-1)**il*(2*il+1)/np.sinh((2*il+1)*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
- np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+3)*mu_b)
*gamma(1.5+ip+il)/(gamma(0.5)*factorial(ip+il+1))
*hyp2f1(0.5, ip+il+1.5, ip+il+2, np.exp(-4*mu_b)) ) )
if (il==0):
yokyquad -= ( np.sqrt(2)*small_semiaxis**3/(2*np.pi*F**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
else:
yokyquad -= ( np.sqrt(2)*small_semiaxis**3/(np.pi*F**3)
*(-1)**ip*(2*ip)**2/np.cosh(2*ip*mu_b)
*(-1)**il/np.cosh(2*il*mu_b)
* ( np.sqrt(2)*np.pi*np.exp(-(2*abs(ip-il)+1)*mu_b)
*gamma(0.5+abs(ip-il))/(gamma(0.5)*factorial(abs(ip-il)))
*hyp2f1(0.5, abs(ip-il)+0.5, abs(ip-il)+1, np.exp(-4*mu_b))
+ np.sqrt(2)*np.pi*np.exp(-(2*ip+2*il+1)*mu_b)
*gamma(0.5+ip+il)/(gamma(0.5)*factorial(ip+il))
*hyp2f1(0.5, ip+il+0.5, ip+il+1, np.exp(-4*mu_b)) ) )
yokxquad = -yokyquad
return (yoklong, yokxdip, yokydip, yokxquad, yokyquad) return (yoklong, yokxdip, yokydip, yokxquad, yokyquad)
......
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