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mbtrack2
Commits
b74830df
Commit
b74830df
authored
10 months ago
by
Keon Hee KIM
Browse files
Options
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Patches
Plain Diff
bug fix, refactor nested loops and optimize performance in misc.py
parent
80e7ba6a
No related branches found
No related tags found
2 merge requests
!14
Faster CircularResistiveWall
,
!3
Yokoya elliptic (reopened)
Changes
1
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mbtrack2/utilities/misc.py
+107
-319
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mbtrack2/utilities/misc.py
with
107 additions
and
319 deletions
mbtrack2/utilities/misc.py
+
107
−
319
View file @
b74830df
...
...
@@ -202,13 +202,13 @@ def yokoya_elliptic(x_radius, y_radius):
elif
x_radius
==
np
.
inf
and
y_radius
==
np
.
inf
:
raise
ValueError
(
"
Both radii have infinite values.
"
)
elif
x_radius
==
np
.
inf
:
yoklong
=
1
yoklong
=
1
.0
yokxdip
=
np
.
pi
**
2
/
24
yokydip
=
np
.
pi
**
2
/
12
yokxquad
=
-
np
.
pi
**
2
/
24
yokyquad
=
np
.
pi
**
2
/
24
elif
y_radius
==
np
.
inf
:
yoklong
=
1
yoklong
=
1
.0
yokxdip
=
np
.
pi
**
2
/
12
yokydip
=
np
.
pi
**
2
/
24
yokxquad
=
np
.
pi
**
2
/
24
...
...
@@ -227,185 +227,98 @@ def yokoya_elliptic(x_radius, y_radius):
mu_b
=
np
.
arccosh
(
large_semiaxis
/
F
)
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
:
yoklong
=
1
yokxdip
=
1
yokydip
=
1
yokxquad
=
0
yokyquad
=
0
yoklong
=
1
.0
yokxdip
=
1
.0
yokydip
=
1
.0
yokxquad
=
0
.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.
# Fortunately, beyond this threshold, they should show asymptotic behavior,
# so we perform linear interpolation.
elif
qr
>
qr_th
:
if
y_radius
<
x_radius
:
yoklong_pp
=
1
yokxdip_pp
=
np
.
pi
**
2
/
24
yokydip_pp
=
np
.
pi
**
2
/
12
yokxquad_pp
=
-
np
.
pi
**
2
/
24
yokyquad_pp
=
np
.
pi
**
2
/
24
else
:
yoklong_pp
=
1
yokxdip_pp
=
np
.
pi
**
2
/
12
yokydip_pp
=
np
.
pi
**
2
/
24
yokxquad_pp
=
np
.
pi
**
2
/
24
yokyquad_pp
=
-
np
.
pi
**
2
/
24
yoklong_pp
=
1.0
yokxdip_pp
=
np
.
pi
**
2
/
24
yokydip_pp
=
np
.
pi
**
2
/
12
yokxquad_pp
=
-
np
.
pi
**
2
/
24
yokyquad_pp
=
np
.
pi
**
2
/
24
if
y_radius
>
x_radius
:
yokxdip_pp
,
yokydip_pp
=
yokydip_pp
,
yokxdip_pp
yokxquad_pp
,
yokyquad_pp
=
yokyquad_pp
,
yokxquad_pp
small_semiaxis_th
=
large_semiaxis
*
(
1
-
qr_th
)
/
(
1
+
qr_th
)
F_th
=
np
.
sqrt
(
large_semiaxis
**
2
-
small_semiaxis_th
**
2
)
mu_b_th
=
np
.
arccosh
(
large_semiaxis
/
F_th
)
yoklong_th
=
0
yokxdip_th
=
0
yokydip_th
=
0
yokxquad_th
=
0
if
y_radius
<
x_radius
:
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
))
)
)
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
])
yoklong_th
=
0.0
yokxdip_th
=
0.0
yokydip_th
=
0.0
yokxquad_th
=
0.0
ip_range
=
np
.
arange
(
50
)
il_range
=
np
.
arange
(
50
)
ip
,
il
=
np
.
meshgrid
(
ip_range
,
il_range
,
indexing
=
'
ij
'
)
ff_values
=
np
.
array
(
function_ff
(
small_semiaxis_th
,
F_th
,
mu_b_th
,
ip
,
il
))
L_values
=
np
.
array
(
function_L
(
mu_b_th
,
ip
,
il
))
coeff_long
=
np
.
where
((
ip
==
0
)
&
(
il
==
0
),
0.25
,
np
.
where
((
ip
==
0
)
|
(
il
==
0
),
0.5
,
1.0
))
coeff_quad
=
np
.
where
(
il
==
0
,
0.5
,
1.0
)
yoklong
=
np
.
sum
(
coeff_long
*
ff_values
[
0
]
*
L_values
[
0
])
yokxdip
=
np
.
sum
(
ff_values
[
1
]
*
L_values
[
1
])
yokydip
=
np
.
sum
(
ff_values
[
2
]
*
L_values
[
2
])
yokxquad
=
-
np
.
sum
(
coeff_quad
*
ff_values
[
3
]
*
L_values
[
0
])
yokyquad
=
-
yokxquad
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
])
yokxdip_array
=
np
.
array
([
yokxdip_th
,
yokxdip_pp
])
yokydip_array
=
np
.
array
([
yokydip_th
,
yokydip_pp
])
...
...
@@ -419,155 +332,30 @@ def yokoya_elliptic(x_radius, y_radius):
yokyquad
=
np
.
interp
(
qr
,
qr_array
,
yokyquad_array
)
else
:
yoklong
=
0
yokxdip
=
0
yokydip
=
0
yokxquad
=
0
if
y_radius
<
x_radius
:
for
ip
in
range
(
50
):
for
il
in
range
(
50
):
if
(
ip
==
0
)
and
(
il
==
0
):
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
))
)
)
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
else
:
for
ip
in
range
(
50
):
for
il
in
range
(
50
):
if
(
ip
==
0
)
and
(
il
==
0
):
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
yoklong
=
0.0
yokxdip
=
0.0
yokydip
=
0.0
yokxquad
=
0.0
ip_range
=
np
.
arange
(
50
)
il_range
=
np
.
arange
(
50
)
ip
,
il
=
np
.
meshgrid
(
ip_range
,
il_range
,
indexing
=
'
ij
'
)
ff_values
=
np
.
array
(
function_ff
(
small_semiaxis
,
F
,
mu_b
,
ip
,
il
))
L_values
=
np
.
array
(
function_L
(
mu_b
,
ip
,
il
))
coeff_long
=
np
.
where
((
ip
==
0
)
&
(
il
==
0
),
0.25
,
np
.
where
((
ip
==
0
)
|
(
il
==
0
),
0.5
,
1.0
))
coeff_quad
=
np
.
where
(
il
==
0
,
0.5
,
1.0
)
yoklong
=
np
.
sum
(
coeff_long
*
ff_values
[
0
]
*
L_values
[
0
])
yokxdip
=
np
.
sum
(
ff_values
[
1
]
*
L_values
[
1
])
yokydip
=
np
.
sum
(
ff_values
[
2
]
*
L_values
[
2
])
yokxquad
=
-
np
.
sum
(
coeff_quad
*
ff_values
[
3
]
*
L_values
[
0
])
yokyquad
=
-
yokxquad
if
y_radius
>
x_radius
:
yokxdip
,
yokydip
=
yokydip
,
yokxdip
yokxquad
,
yokyquad
=
yokyquad
,
yokxquad
return
(
yoklong
,
yokxdip
,
yokydip
,
yokxquad
,
yokyquad
)
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