offsets = np.linspace(0, 20, 10)
in_mesh = np.linspace(0, 1, 100)
test_mesh = np.linspace(np.min(in_mesh), np.max(in_mesh), 2000)
rescale = False
m = 4
bf = basisfunctions.ThinPlateSplines()
df = pd.DataFrame()
df.index.name = "y0"
for y0 in offsets:
f = functools.partial(func, y0=y0)
in_vals = f(in_mesh)
separated = rbf.SeparatedConsistent(bf, in_mesh, in_vals, rescale)
integrated = rbf.IntegratedConsistent(bf, in_mesh, in_vals)
no_poly = rbf.NoneConsistent(bf, in_mesh, in_vals, rescale)
s = pd.Series(
data={
"RMSE_NoPoly": no_poly.RMSE(f, test_mesh),
"RMSE_Integrated": integrated.RMSE(f, test_mesh),
"RMSE_Separated": separated.RMSE(f, test_mesh)
})
# Condition remains unchanged, input function as generally no effect on condition
s.name = y0
df = df.append(s)
for tf in tfs:
in_vals = tf(in_mesh)
sepfit = rbf.SeparatedConsistentFitted(bf,
in_mesh,
in_vals,
degree=deg)
err0 = norm(sepfit(test_mesh0) - tf(test_mesh0))
err1 = norm(sepfit(test_mesh1) - tf(test_mesh1))
df.loc[deg][str(tf) + "_InfError"] = err0
df.loc[deg][str(tf) + "_InfErrorLargerMesh"] = err1
print("Degree =", deg, ", TF =", str(tf))
print("deg1 - e0 =", df.loc[1][str(tf) + "_InfError"] - err0)
print("deg1 - e1 =", df.loc[1][str(tf) + "_InfErrorLargerMesh"] - err1)
sep = rbf.SeparatedConsistent(bf, in_mesh, in_vals)
sepfit = rbf.SeparatedConsistentFitted(bf, in_mesh, in_vals, degree=8)
print()
print("Sep Inf Error =", norm(sep(test_mesh0) - tf(test_mesh0)))
print("Sep FitInf Error =", norm(sepfit(test_mesh0) - tf(test_mesh0)))
for c in df:
print(c, df[c].idxmin())
# plt.plot(test_mesh1, tf(test_mesh1), label = "TF")
# plt.plot(test_mesh1, sep(test_mesh1), label = "Sep")
# plt.plot(test_mesh1, sepfit(test_mesh1), label = "SepFit")
# plt.plot(test_mesh, sep(test_mesh) - tf(test_mesh), label ="Error Sep")
# plt.plot(test_mesh, sepfit(test_mesh) - tf(test_mesh), label ="Error SepFit")
# plt.legend()
plt.plot(plot_mesh, func(plot_mesh), "-", label="Testfunction")
df["f"] = func(plot_mesh)
none_consistent = rbf.NoneConsistent(bf, in_mesh, in_vals, rescale=False)
plt.plot(plot_mesh,
none_consistent(plot_mesh),
"-",
label="No Polynomial Interpolant")
df["NoneConsistent"] = none_consistent(plot_mesh)
for i, gamma, vertex in zip(range(len(in_mesh)), none_consistent.gamma,
in_mesh):
plt.plot(plot_mesh, bf(plot_mesh - vertex) * gamma, "--")
df["None_BF_" + str(i)] = bf(plot_mesh - vertex) * gamma
sep_consistent = rbf.SeparatedConsistent(bf, in_mesh, in_vals, rescale=False)
plt.plot(plot_mesh,
sep_consistent(plot_mesh),
"-",
label="Polynomial Interpolant")
df["SeparatedConsistent"] = sep_consistent(plot_mesh)
plt.plot(plot_mesh,
sep_consistent.polynomial(plot_mesh),
"-",
label="Polynomial")
df["Polynomial"] = sep_consistent.polynomial(plot_mesh)
for i, gamma, vertex in zip(range(len(in_mesh)), sep_consistent.gamma,
in_mesh):
plt.plot(plot_mesh, bf(plot_mesh - vertex) * gamma, "--")
df["Separated_BF_" + str(i)] = bf(plot_mesh - vertex) * gamma