66 lines
1.5 KiB
Python
66 lines
1.5 KiB
Python
|
#!/usr/bin/env python3
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from scipy.special import lpmv
|
||
|
|
|
||
|
|
def lgndr(mplus, lplus, thet):
|
||
|
|
"""
|
||
|
|
Calculates Legendre polynomials Plm
|
||
|
|
|
||
|
|
Parameters:
|
||
|
|
mplus : int
|
||
|
|
Number of m's > 0
|
||
|
|
lplus : int
|
||
|
|
Number of l's > 0
|
||
|
|
thet : float
|
||
|
|
Angle in degrees
|
||
|
|
|
||
|
|
Returns:
|
||
|
|
plm : list
|
||
|
|
List containing Legendre polynomials
|
||
|
|
"""
|
||
|
|
|
||
|
|
theta = np.radians(thet)
|
||
|
|
y = np.cos(theta)
|
||
|
|
z = np.sin(theta)
|
||
|
|
plm = np.zeros(459, dtype=np.float64)
|
||
|
|
|
||
|
|
ix = 0
|
||
|
|
for m in range(1, mplus + 1): # For MPLUS = 1, LPLUS = 16
|
||
|
|
lx = m - 1 # LX = 0
|
||
|
|
l2 = 0 # L2 = 0
|
||
|
|
p3 = 1.0 # P3 = 1.0
|
||
|
|
fl1 = float(lx) # FL1 = 0
|
||
|
|
|
||
|
|
if lx != 0:
|
||
|
|
for lt in range(1, lx + 1):
|
||
|
|
fl1 += 1.0
|
||
|
|
p3 *= fl1 * z / 2.0
|
||
|
|
|
||
|
|
p2 = 0.0 # P2 = 0.0
|
||
|
|
fl2 = fl1 + 1.0 # FL2 = 1.0
|
||
|
|
fl3 = 1.0 # FL3 = 1.0
|
||
|
|
|
||
|
|
for lt in range(1, lplus + 1): # Loop Lb
|
||
|
|
ix1 = ix + lt
|
||
|
|
|
||
|
|
if l2 < lx:
|
||
|
|
plm[ix1] = 0.0
|
||
|
|
else:
|
||
|
|
if l2 > lx:
|
||
|
|
p3 = (fl2 * y * p2 - fl1 * p1) / fl3
|
||
|
|
fl1 += 1.0
|
||
|
|
fl2 += 2.0
|
||
|
|
fl3 += 1.0
|
||
|
|
plm[ix1] = p3
|
||
|
|
print(f'PLM, {lx:3d}, {l2:3d}, {ix1:3d}, {plm[ix1]:15.10f}')
|
||
|
|
p1, p2 = p2, p3
|
||
|
|
|
||
|
|
l2 += 1
|
||
|
|
|
||
|
|
ix += lplus
|
||
|
|
|
||
|
|
return plm
|
||
|
|
|
||
|
|
|
||
|
|
plm = lgndr(3, 16, 1)
|