def condition_array_xyz(thetav, phiv, order=13):
mv,lv=newleg.degrees(order, start=1)
leg,dleg=newleg.legendre(scipy.cos(thetav), order)
cossin = numpy.zeros((len(phiv),order*(order+2)))
cossin[:, mv >= 0] = numpy.cos(phiv[:, numpy.newaxis] @ abs(mv[numpy.newaxis, :]))[:, mv >= 0]
cossin[:, mv < 0] = numpy.sin(phiv[:, numpy.newaxis] @ abs(mv[numpy.newaxis, :]))[:, mv < 0]
sinmcos=numpy.zeros((len(phiv),order*(order+2)))
sinmcos[:, mv >= 0] = numpy.sin(phiv[:, numpy.newaxis] @ abs(mv[numpy.newaxis, :]))[:, mv >= 0]
sinmcos[:, mv < 0] = -numpy.cos(phiv[:, numpy.newaxis] @ abs(mv[numpy.newaxis, :]))[:, mv < 0]
costhetav = numpy.cos(thetav)
sinthetav = numpy.sin(thetav)
Ax = cossin.transpose() * dleg * (-sinthetav)
Ay = abs(mv[:, numpy.newaxis]) * leg * sinmcos.transpose() / sinthetav
Az = -(lv + 1)[:, numpy.newaxis] * leg * cossin.transpose()
return Ax, Ay, Az
def xyzfieldv2(gcoefs, phi, theta, rparam=1.0, order=13, regular=False):
mv, lv = newleg.degrees(order, start=1)
legv, dlegv = newleg.legendre(scipy.cos(theta), order)
x = numpy.zeros_like(theta)
y = x.copy()
z = x.copy()
for m, l, g, leg, dleg in zip(mv, lv, gcoefs, legv, dlegv):
rparamexp = rparam ** (l + 2)
m_abs = abs(m)
cossin = scipy.cos(m_abs * phi) if m >= 0 else scipy.sin(m_abs * phi)
sinmcos = scipy.sin(m_abs * phi) if m >= 0 else -scipy.cos(m_abs * phi)
x += rparamexp * (g * cossin) * dleg * (-scipy.sin(theta))
y += rparamexp * (g * sinmcos) * m_abs * leg / (scipy.sin(theta))
z -= rparamexp * (l + 1) * (g * cossin) * leg
return x, y, z
