def plot_runge_different_nodes():
"""Plot runge function at different nodes."""
get_interpolator = partial(get_interpolator_monomial_flexible_nodes,
problem_runge, 11)
interp_unif = get_interpolator(nodes="uniform")
interp_cheby = get_interpolator(nodes="chebychev")
xvalues = np.linspace(-1, 1, 10000)
fig, ax = plt.subplots()
ax.plot(xvalues, problem_runge(xvalues), label="True")
ax.plot(xvalues, interp_unif(xvalues), label="Uniform")
ax.plot(xvalues, interp_cheby(xvalues), label="Chebychev")
ax.legend()
ax.set_title("Runge function")
fig, ax = plt.subplots()
ax.plot(
xvalues,
interp_unif(xvalues) - problem_runge(xvalues),
label="Uniform",
)
ax.plot(
xvalues,
interp_cheby(xvalues) - problem_runge(xvalues),
label="Chebychev",
)
ax.legend()
ax.set_title("Approximation error")
def plot_runge_function_cubic():
"""Plot cubic runge function."""
xvalues = get_uniform_nodes(10000, -1, 1)
for degree in [5, 10, 15]:
x_fit = get_uniform_nodes(degree, -1, 1)
interp = interp1d(x_fit, problem_runge(x_fit), kind="cubic")
yfit = interp(xvalues)
fig, ax = plt.subplots()
ax.plot(xvalues, problem_runge(xvalues), label="True")
ax.plot(xvalues, yfit, label="Approximation")
ax.legend()
ax.set_title(f"Degree {degree}")
def plot_runge_multiple():
"""Plot multiple runge functions."""
a, b = -1, 1
xvals = np.linspace(a, b, 1000)
yvals = problem_runge(xvals)
fig, ax = plt.subplots()
ax.plot(xvals, yvals, label="Function")
for degree in [5, 9]:
xnodes = np.linspace(a, b, degree)
poly = np.polynomial.Polynomial.fit(xnodes, problem_runge(xnodes),
degree)
yfit = poly(xvals)
ax.plot(xvals, yfit, label=" 9th-order")
ax.legend()
def test_exercise_1():
"""Run test exercise 1."""
index = product([10, 20, 30, 40, 50], np.linspace(-1, 1, 1000))
index = pd.MultiIndex.from_tuples(index, names=("Degree", "Point"))
df = pd.DataFrame(columns=["Value", "Approximation"], index=index)
df["Value"] = problem_runge(df.index.get_level_values("Point"))
for degree in [10, 20, 30, 40, 50]:
xnodes = get_uniform_nodes(degree, -1, 1)
poly = np.polynomial.Polynomial.fit(xnodes, problem_runge(xnodes),
degree)
xvalues = df.index.get_level_values("Point").unique()
yvalues = poly(xvalues)
df.loc[(degree, slice(None)), "Approximation"] = yvalues
df["Error"] = df["Value"] - df["Approximation"]
df.groupby("Degree").apply(compute_interpolation_error_df).plot()
def plot_problem_runge():
"""Plot runge function."""
fig, ax = plt.subplots()
xvals = np.linspace(-1, 1, 1000)
yvals = problem_runge(xvals)
ax.plot(xvals, yvals, label="Function")