def xyzfieldt(k, m, n, knots, gcoefs, thetav, phiv, t):
lpmv = scipy.special.lpmv
x = numpy.zeros_like(thetav)
y = x.copy()
z = x.copy()
schmidt = schmidt_real(m, n, grid=False)
#1. calcular los splines
#base = bspline.deboor_base(knots, t, 3).T[:-4]
base = bspline.condition_array(knots, t).T
#3. for q...
for q, spline in enumerate(base):
for ki, mi, ni, g, sch in zip(k, m, n, gcoefs[q,:], schmidt):
m_abs = abs(mi)
cossin = numpy.cos(m_abs*phiv) if mi >= 0 else numpy.sin(m_abs*phiv)
sinmcos = numpy.sin(m_abs*phiv) if mi >= 0 else -numpy.cos(m_abs*phiv)
leg = lpmv(m_abs, ni, numpy.cos(thetav))*sch
dleg = dlpmv(m_abs, ni, numpy.cos(thetav))*(-numpy.sin(thetav))*sch
x += g*cossin*dleg*spline
y += g*sinmcos*m_abs*leg/numpy.sin(thetav)*spline
z -= (ni+1)*(g*cossin)*leg*spline
return x, y, z
def invert_dift(thetav, phiv, t, D, I, F, degrees, knots, g0=None,
reg_coef_spatial = 0, reg_coef_time = 0, theta_0 = None, steps=5):
k, m, n = degrees
#n_knots, n_degrees = len(knots)-4, len(k)
#knots = bspline.fix_knots(kn, 3)
n_knots, n_degrees = len(knots), len(k)
n_coefs = n_knots*n_degrees
#base = bspline.deboor_base(knots, t, 3)[:, :-4]
Ax, Ay, Az = condition_matrix_xyz(thetav, phiv, degrees)
D_0, I_0, F_0 = D, I, F
base = numpy.concatenate((bspline.condition_array(knots, t[~numpy.isnan(D)]),
bspline.condition_array(knots, t[~numpy.isnan(I)]),
bspline.condition_array(knots, t[~numpy.isnan(F)])), axis=0)
D_0 = D_0[~numpy.isnan(D)]
I_0 = I_0[~numpy.isnan(I)]
F_0 = F_0[~numpy.isnan(F)]
if g0 is None:
g0 = numpy.zeros((n_knots, n_degrees))
can_get_z = ((~numpy.isnan(I)) & (~numpy.isnan(F)))
avg_z = numpy.average(F[can_get_z] * sin(I[can_get_z]))
g0[:, 0] = -avg_z
g = g0.copy()
di_0 = numpy.concatenate((D_0, I_0))
if (reg_coef_spatial != 0) or (reg_coef_time != 0):
reg_matrix = full_reg(spatial_reg(k, m, n, theta_0), time_reg(knots),
coef_L=reg_coef_spatial, coef_S=reg_coef_time)
else:
reg_matrix = 0.0
for iteration in range(steps):
#como poner la dependencia del tiempo aquí?
#con magia
Bx, By, Bz = xyzfieldt(k, m, n, knots, g, thetav, phiv, t)
D_model, I_model, F_model, H_model = xyz.xyz2difh(Bx, By, Bz)
Ad, Ai, Af = condition_matrix_dif(Bx, By, Bz, F_model, H_model, Ax, Ay, Az)
Af = Af / F_model[:, numpy.newaxis]
Adif = numpy.concatenate((Ad[~numpy.isnan(D), :],
Ai[~numpy.isnan(I), :],
Af[~numpy.isnan(F), :]), axis=0)
Adif = numpy.concatenate([Adif*spline[:, numpy.newaxis] for spline in base.T], axis=1)
D_model = D_model[~numpy.isnan(D)]
I_model = I_model[~numpy.isnan(I)]
F_model = F_model[~numpy.isnan(F)]
di = numpy.concatenate((D_model, I_model), axis=0)
di_delta = numpy.arctan2(numpy.sin(di-di_0), numpy.cos(di-di_0))
f_delta = (F_model - F_0)/F_model
delta = numpy.concatenate((di_delta, f_delta), axis=0)
#solution = numpy.linalg.lstsq(Adif, delta)
#g = g - solution[0].reshape((n_knots, n_degrees))
g = g - ((numpy.linalg.pinv(Adif.T @ Adif + reg_matrix) @ Adif.T) @ delta).reshape((n_knots, n_degrees))
sys.stdout.write("\r")
sys.stdout.write("[{: <20}] ".format("#"*int((iteration/steps)*20+1)))
sys.stdout.write("iteration {0} : rms = ".format(iteration+1))
sys.stdout.write(str(numpy.sqrt(sum(delta**2)/len(delta))))
#debuge
#ax.scatter(t, di_delta[:len(di_delta)//2], color="green")
#ax.scatter(t, di_delta[len(di_delta)//2:], color="red")
#ax.scatter(t, f_delta, color="blue")
#ax.scatter(t, D_model - D_0, color="green")
#ax.scatter(t, I_model - I_0, color="red")
#ax.scatter(t, F_model - F_0, color="blue")
#pyplot.show(fig)
if (sum(abs(delta**2)) > 10000): warnings.warn("a bad thing is happening ヽ( `д´*)ノ")
return g