DOC: remove discrete SINDy examples from feature overview

Author: yb6599

examples/1_feature_overview/example.ipynb

@@ -114,7 +114,7 @@ def ignore_specific_warnings():
 x_dot_test_predicted = model.predict(x_test)
 
 # Compute derivatives with a finite difference method, for comparison
-x_dot_test_computed = model.differentiation_method._differentiate(x_test, t=dt)
+x_dot_test_computed = model.differentiation_method(x_test, t=dt)
 
 fig, axs = plt.subplots(x_test.shape[1], 1, sharex=True, figsize=(7, 9))
 for i in range(x_test.shape[1]):
@@ -149,30 +149,6 @@ def ignore_specific_warnings():
 
 fig.show()
 
-# %% [markdown]
-# ## Discrete time dynamical system (map)
-
-# %%
-
-
-def f(x):
-    return 3.6 * x * (1 - x)
-
-
-if __name__ != "testing":
-    n_steps = 1000
-else:
-    n_steps = 10
-eps = 0.001  # Noise level
-x_train_map = np.zeros((n_steps))
-x_train_map[0] = 0.5
-for i in range(1, n_steps):
-    x_train_map[i] = f(x_train_map[i - 1]) + eps * np.random.randn()
-model = ps.DiscreteSINDy()
-model.fit(x_train_map, t=1)
-
-model.print()
-
 # %% [markdown]
 # ## Optimization options
 # In this section we provide examples of different parameters accepted by the built-in sparse regression optimizers `STLSQ`, `SR3`, `ConstrainedSR3`, `MIOSR`, `SSR`, and `FROLS`. The `Trapping` optimizer is not straightforward to use; please check out Example 8 for some examples. We also show how to use a scikit-learn sparse regressor with PySINDy.
@@ -782,7 +758,7 @@ def f(x):
 x_dot_test_predicted = model.predict(x_test)
 
 # Compute derivatives with a finite difference method, for comparison
-x_dot_test_computed = model.differentiation_method._differentiate(x_test, t=dt)
+x_dot_test_computed = model.differentiation_method(x_test, t=dt)
 
 fig, axs = plt.subplots(x_test.shape[1], 1, sharex=True, figsize=(7, 9))
 for i in range(x_test.shape[1]):
@@ -905,7 +881,7 @@ def u_fun(t):
 x_dot_test_predicted = model.predict(x_test, u=u_test)
 
 # Compute derivatives with a finite difference method, for comparison
-x_dot_test_computed = model.differentiation_method._differentiate(x_test, t=dt)
+x_dot_test_computed = model.differentiation_method(x_test, t=dt)
 
 fig, axs = plt.subplots(x_test.shape[1], 1, sharex=True, figsize=(7, 9))
 for i in range(x_test.shape[1]):
@@ -1053,62 +1029,6 @@ def u_fun(t):
     model.fit(x_train, t=t)
     model.print()
 
-# %% [markdown]
-# ## SINDy with control parameters (SINDyCP)
-# The control input in PySINDy can be used to discover equations parameterized by control parameters in conjunction with the `ParameterizedLibrary`. We demonstrate on the logistic map
-# $$ x_{n+1} = r x_n(1-x_n)$$
-# which depends on a single parameter $r$.
-
-# %%
-# Iterate the map and drop the initial 500-step transient. The behavior is chaotic for r>3.6.
-if __name__ != "testing":
-    num = 1000
-    N = 1000
-    N_drop = 500
-else:
-    num = 20
-    N = 20
-    N_drop = 10
-r0 = 3.5
-rs = r0 + np.arange(num) / num * (4 - r0)
-xss = []
-for r in rs:
-    xs = []
-    x = 0.5
-    for n in range(N + N_drop):
-        if n >= N_drop:
-            xs = xs + [x]
-        x = r * x * (1 - x)
-    xss = xss + [xs]
-
-plt.figure(figsize=(4, 4), dpi=100)
-for ind in range(num):
-    plt.plot(np.ones(N) * rs[ind], xss[ind], ",", alpha=0.1, c="black", rasterized=True)
-plt.xlabel("$r$")
-plt.ylabel("$x_n$")
-plt.show()
-
-# %% [markdown]
-# We construct a `parameter_library` and a `feature_library` to act on the input data `x` and the control input `u` independently. The `ParameterizedLibrary` is composed of products of the two libraries output features. This enables fine control over the library features, which is especially useful in the case of PDEs like those arising in pattern formation modeling. See this [notebook](https://github.com/dynamicslab/pysindy/blob/master/examples/17_parameterized_pattern_formation/17_parameterized_pattern_formation.ipynb) for examples.
-
-# %%
-# use four parameter values as training data
-rs_train = [3.6, 3.7, 3.8, 3.9]
-xs_train = [np.array(xss[np.where(np.array(rs) == r)[0][0]]) for r in rs_train]
-
-feature_lib = ps.PolynomialLibrary(degree=3, include_bias=True)
-parameter_lib = ps.PolynomialLibrary(degree=1, include_bias=True)
-lib = ps.ParameterizedLibrary(
-    feature_library=feature_lib,
-    parameter_library=parameter_lib,
-    num_features=1,
-    num_parameters=1,
-)
-opt = ps.STLSQ(threshold=1e-1, normalize_columns=False)
-model = ps.DiscreteSINDy(feature_library=lib, optimizer=opt)
-model.fit(xs_train, u=rs_train, t=1, feature_names=["x", "r"])
-model.print()
-
 # %% [markdown]
 # ## PDEFIND Feature Overview
 # PySINDy now supports SINDy for PDE identification (PDE-FIND) (Rudy, Samuel H., Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz. "Data-driven discovery of partial differential equations." Science Advances 3, no. 4 (2017): e1602614.). We illustrate a basic example on Burgers' equation: