def power(gcomp, lmin, lmax, rparam=1.0, separated=False):
m,l=newleg.degrees(lmax,start=1)
powers=rparam**(2*l[l >= lmin]+4)*(l[l >= lmin] + 1)*gcomp[:, numpy.where(l >= lmin)]**2
if separated:
return powers.sum(axis=1)
else:
return powers.sum(axis=2).sum(axis=1)
def magnetic_north(gcoefs, order, south=True, debug=False):
northlons = []
northlats = []
startingpoint_north = (numpy.pi, numpy.pi / 2)
if south:
southlons = []
southlats = []
startingpoint_south = (numpy.pi, numpy.pi / 2)
m, l = newleg.degrees(order, start=1)
max_index = len(m)
def inc_value(coords, gcomp):
x, y, z = xyzfieldv2(
gcomp[:max_index], numpy.array([coords[0]]), numpy.array([coords[1]]), regular=False, order=order
)
inc = numpy.arctan2(z, numpy.sqrt(x ** 2 + y ** 2))
return -inc
for gcomp in gcoefs:
sol_north = scipy.optimize.minimize(inc_value, startingpoint_north, args=(gcomp), method="Powell")
startingpoint_north = sol_north.x
north_lon, north_lat = numpy.rad2deg(sol_north.x[0]), 90 - numpy.rad2deg(sol_north.x[1])
northlons.append(north_lon)
northlats.append(north_lat)
if south:
sol_south = scipy.optimize.minimize(
lambda x, g: -inc_value(x, g), startingpoint_south, args=(gcomp), method="Powell", options={disp: debug}
)
startingpoint_south = sol_south.x
south_lon, south_lat = numpy.rad2deg(sol_south.x[0]), 90 - numpy.rad2deg(sol_south.x[1])
southlons.append(south_lon)
southlats.append(south_lat)
if debug:
print(north_lon, north_lat)
if south:
return northlons, northlats, southlons, southlats
else:
return northlons, northlats
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