def compare_approxiation(x,
y,
x_approx,
y_approx,
error=None,
name="1",
title=""):
"""
Compare the input data with the fitted function
"""
_, ax = plt.subplots(2, 1)
ax[0].plot(x, y, "o", label="Original data", markersize=2)
ax[0].plot(x_approx, y_approx, label="Fitted line")
ax[0].set_xlabel("$x$")
ax[0].set_ylabel("$y$")
ax[0].legend()
ax[0].set_title(title)
if y.shape == y_approx.shape:
error = y - y_approx
if error is not None:
ax[1].plot(x, error, "o", label="Error", markersize=2)
ax[1].plot(x_approx, np.zeros(y_approx.shape), label="Fitted line")
ax[1].set_title("Error")
ax[1].set_xlabel("$x$")
ax[1].set_ylabel("$\Delta y$")
else:
print("Cannot compare difference, x and x_approx need to be equal")
plt.tight_layout()
show_and_save("task1_approx_{}".format(name))
def plot_phase_portrait(A,
range=[[-10, 10], [-10, 10]],
resolution=[100, 100],
trajectory=None,
name="phaseportrait",
title=""):
"""
Create a phase portrait for matrix A in the given range with a given resolution.
Optionally add a trajectory to plot in the phase portrait. Includes a filename and plot-title.
"""
x = np.linspace(range[0][0], range[0][1], num=resolution[0])
y = np.linspace(range[1][0], range[1][1], num=resolution[1])
xv, yv = np.meshgrid(x, y)
xy = np.stack((np.ravel(xv), np.ravel(yv)), axis=-1)
uv = xy @ A
u = uv[:, 0].reshape(resolution)
v = uv[:, 1].reshape(resolution)
plt.figure()
ax = plt.subplot(1, 1, 1)
ax.set_aspect('equal')
ax.set_xlim([-10, 10])
ax.set_ylim([-10, 10])
ax.set_title(title)
ax.streamplot(x, y, u, v)
if trajectory is not None:
ax.plot(trajectory[:, 0], trajectory[:, 1])
show_and_save("task2_{}".format(name))
def plot_3d_data(x, y, z, name="", labels=["x", "y", "z"], title=""):
"""
Plot and save 3-D data.
Parameters
----------
x : (N, 1) array-like
x coordinates of the data.
y : (N, 1) array-like
y coordinates of the data.
z : (N, 1) array-like
z coordinates of the data.
name : string, optional
Filename addition. Default: ""
labels : list, optional
Labels of axes. Default: ["x", "y", "z"]
title : string, optional
Title of the plot. Default: ""
"""
# Create the figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
# Plot the values
ax.plot(x, y, z, linewidth=0.4)
ax.set_xlabel(labels[0])
ax.set_ylabel(labels[1])
ax.set_zlabel(labels[2])
show_and_save("task4_{}".format(name))
def plot_data(x, y, name="", labels=["x", "y"], title=""):
"""
Plot and save 2-D data.
Parameters
----------
x : (N, 1) array-like
x coordinates of the data.
y : (N, 1) array-like
y coordinates of the data.
name : string, optional
Filename addition. Default: ""
labels : list, optional
Labels of axes. Default: ["x", "y"]
title : string, optional
Title of the plot. Default: ""
"""
plt.figure()
plt.plot(x, y, label=title)
plt.title(title)
plt.legend()
plt.xlabel(labels[0])
plt.ylabel(labels[1])
ax = plt.gca()
ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
show_and_save("task5_{}".format(name))
def nonlinear_vf(x0, x1, yi):
plt.figure()
plt.quiver(x0[:, 0], x0[:, 1], x1[:, 0], yi)
plt.title("Vector field generated with RBF")
plt.xlabel("$x$")
plt.ylabel("$y$")
show_and_save("task3_{}".format("nonlinear_vf"))
# Compute the mean squared error
mse = ((np.array(list(zip(x1[:, 0], yi))) - x1)**2).mean(axis=0)
print("Mean squared error: {}".format(mse))
def linear_vf(x0, x1, dt, A, t_end=0.1):
# Solve x_dot=A*x with all x_0^(k) as initial points until
x = task2.create_trajectory(x0, A, dt, t_end)
# The resulting points are estimates for x_1^(k).
plt.figure()
plt.quiver(x0[:, 0], x0[:, 1], x[-1][:, 0], x[-1][:, 1])
plt.title("Vector field generated with linear operator")
plt.xlabel("$x$")
plt.ylabel("$y$")
show_and_save("task3_{}".format("linear_vf"))
# Compute the mean squared error to x1
mse = ((x[-1] - x1)**2).mean(axis=0)
print("Mean squared error: {}".format(mse))
def scatter_3d_data(x,
y,
z,
name="",
labels=["x", "y", "z"],
title="",
c=None,
cmap=None,
norm=None):
"""
Scatter and save 3-D data.
Parameters
----------
x : (N, 1) array-like
x coordinates of the data.
y : (N, 1) array-like
y coordinates of the data.
z : (N, 1) array-like
z coordinates of the data.
name : string, optional
Filename addition. Default: ""
labels : list, optional
Labels of axes. Default: ["x", "y", "z"]
title : string, optional
Title of the plot. Default: ""
"""
# Create the figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
# Scatter the values
sc = ax.scatter(x, y, z, s=1, c=c, cmap=cmap, norm=norm)
ax.set_title(title)
ax.set_xlabel(labels[0])
ax.set_ylabel(labels[1])
ax.set_zlabel(labels[2])
cb = plt.colorbar(sc, pad=0.1)
cb.set_ticks([0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200])
show_and_save("task5_{}".format(name))
def plot_vectorfields(*args, labels=[], name="", title=""):
"""
Plot multiple vectorfields (len(args)). Include optional labels, a filename and plot-title
"""
marker = ["o", "x"]
plt.figure()
for idx, arg in enumerate(args):
if idx < len(labels):
plt.plot(arg[:, 0],
arg[:, 1],
marker[idx % len(marker)],
label=labels[idx],
markersize=3)
else:
plt.plot(arg[:, 0],
arg[:, 1],
marker[idx % len(marker)],
markersize=3)
plt.title(title)
plt.legend()
plt.xlabel("$x$")
plt.ylabel("$y$")
show_and_save("task2_{}".format(name))
def scatter_data(x, y, name="", labels=["x", "y"], title=""):
"""
Scatter and save 2-D data.
Parameters
----------
x : (N, 1) array-like
x coordinates of the data.
y : (N, 1) array-like
y coordinates of the data.
name : string, optional
Filename addition. Default: ""
labels : list, optional
Labels of axes. Default: ["x", "y"]
title : string, optional
Title of the plot. Default: ""
"""
plt.figure()
plt.scatter(x, y, label=title)
plt.title(title)
plt.legend()
plt.xlabel(labels[0])
plt.ylabel(labels[1])
show_and_save("task3_{}".format(name))