def gen_leg_real(lmax, theta):
cost = np.cos(theta)
sint = np.sin(theta)
maxIndex = int( (lmax+1)*(lmax+2)/2 )
leg = np.zeros( ( maxIndex, theta.size ) )
leg_d1 = np.zeros( ( maxIndex, theta.size ) )
dp_leg = np.zeros( (maxIndex, theta.size) )
count = 0
for z in cost:
leg[:, count], leg_d1[:, count] = pleg.PlmBar_d1(lmax, z, 1, 1)
count += 1
dt_leg = leg_d1 * (-sint).reshape(1, sint.shape[0])
ellArr = np.zeros(maxIndex)
emmArr = np.zeros(maxIndex)
countm, countl = 0, 0
for i in range(maxIndex):
ellArr[i] = countl
emmArr[i] = countm
if countm==countl:
countl += 1
countm = 0
else:
countm += 1
norm = np.sqrt( ellArr * (ellArr + 1) )
norm[norm<1] = 1.0
legtemp = leg.copy()
dp_leg = emmArr.reshape(maxIndex, 1) * legtemp / sint.reshape(1, sint.shape[0])
dt_leg /= norm.reshape(maxIndex, 1)
dp_leg /= norm.reshape(maxIndex, 1)
return leg/sqrt(2)/sqrt(2*pi), dt_leg/sqrt(2)/sqrt(2*pi), dp_leg/sqrt(2)/sqrt(2*pi)
def gen_leg(lmax, theta):
"""Generates legendre polynomials and derivatives normalized to 1.0
Parameters:
-----------
lmax - int
maximum spherical harmonic degree
theta - np.ndarray(ndim=1, dtype=float)
array for theta to compute P_l(cos(theta))
Returns:
--------
leg - np.ndarray(ndim=2, dtype=float)
P_l(cos(theta))
dt_leg - np.ndarray(ndim=2, dtype=float)
d/d(theta) P_l(cos(theta))
dp_leg - np.ndarray(ndim=2, dtype=complex)
im * P_l(cos(theta)) / sin(theta)
"""
cost = np.cos(theta)
sint = np.sin(theta)
maxIndex = int((lmax + 1) * (lmax + 2) / 2)
leg = np.zeros((maxIndex, theta.size))
leg_d1 = np.zeros((maxIndex, theta.size))
dp_leg = np.zeros((maxIndex, theta.size), dtype=complex)
count = 0
for z in cost:
leg[:, count], leg_d1[:, count] = pleg.PlmBar_d1(lmax, z, 1, 1)
count += 1
dt_leg = leg_d1 * (-sint).reshape(1, sint.shape[0])
ellArr = np.zeros(maxIndex)
emmArr = np.zeros(maxIndex)
countm, countl = 0, 0
for i in range(maxIndex):
ellArr[i] = countl
emmArr[i] = countm
if countm == countl:
countl += 1
countm = 0
else:
countm += 1
norm = np.sqrt(ellArr * (ellArr + 1))
norm[norm < 1] = 1.0
legtemp = leg.copy()
dp_leg = 1j * emmArr.reshape(maxIndex, 1) \
* legtemp / sint.reshape(1, sint.shape[0])
dt_leg /= norm.reshape(maxIndex, 1)
dp_leg /= norm.reshape(maxIndex, 1)
return leg/sqrt(2)/sqrt(2*pi), \
dt_leg/sqrt(2)/sqrt(2*pi), \
dp_leg/sqrt(2)/sqrt(2*pi)