def F_W(a, b, M_0, M_1, M_2, M_3):
'''
F_W function, the top level of computation.
When b=0, value is immediately phi(a).
'''
return np.where(b==0.,
hlp.psi_catnew(u=a),
F_0(a=a, b=b, M_0=M_0)-F_3(a=a, b=b, M_1=M_1, M_2=M_2, M_3=M_3))
def coef_onecubeminus_D(gam, eta):
alpha = (eta - 1) / eta
return 6 * (hlp.psi_catnew(math.sqrt(2)) * alpha + gam - gam**3 / 6)
def xhat_mult_bernoulli(x, s):
return s * np.mean(hlp.psi_catnew(x/s))
def Hfn(eta, gam):
out = np.zeros(eta.shape)
deltaval = math.fabs((gam - math.sqrt(2)))
idx_zero = np.nonzero(eta == 0)[0]
idx_one = np.nonzero(eta == 1)[0]
idx_half = np.nonzero(eta == 1 / 2)[0]
idx_small = np.setdiff1d(np.nonzero(eta < 1 / 2)[0], idx_zero)
idx_large = np.setdiff1d(np.nonzero(eta > 1 / 2)[0], idx_one)
idx_tricky = np.union1d(np.union1d(idx_half, idx_zero), idx_one)
idx_therest = np.setdiff1d(np.arange(eta.size), idx_tricky)
eta_large = eta[idx_large]
eta_small = eta[idx_small]
eta_therest = eta[idx_therest]
if (gam <= math.sqrt(2) / 2):
# In this case, only solve the double-cube condition.
Hvals = Hfn_double(gam=gam, eta=eta_therest)
out[idx_therest] = Hvals
elif (gam > math.sqrt(2)):
# In this case, only solve the single-cube condition.
# Deal with larger eta values (above 1/2).
out[idx_large] = Hfn_single_large(gam=gam, eta=eta_large)
# Deal with smaller eta values (below 1/2).
out[idx_small] = Hfn_single_small(gam=gam, eta=eta_small)
else:
# Otherwise, a bit more checking is required.
Q = hlp.psi_catnew(deltaval - gam) / hlp.psi_catnew(deltaval + gam)
tocheck = np.where((eta_therest > 1 / 2),
((eta_therest - 1) / eta_therest),
(eta_therest / (eta_therest - 1)))
Hvals = np.zeros(eta_therest.size)
for t in range(eta_therest.size):
etaval = np.take(a=eta_therest, indices=[t])
if (Q < tocheck[t]):
# Solving the single-cube condition is enough.
if (etaval > 1 / 2):
Hvals[t] = Hfn_single_large(gam=gam, eta=etaval)
else:
Hvals[t] = Hfn_single_small(gam=gam, eta=etaval)
else:
# None are relevant; solve the double-cube condition.
Hvals[t] = Hfn_double(gam=gam, eta=etaval)
out[idx_therest] = Hvals
# Deal with the edges and middle.
out = np.where((eta == 1), 0, out)
out = np.where((eta == 0), 0, out)
out = np.where((eta == 1 / 2), hlp.rho_catnew(gam), out)
return out