Axes Basics¶

The Axes object is the core component for plotting in Matplotlib. It contains most plot elements including the data, axes, ticks, labels, and title.

What is an Axes Object¶

An Axes object encapsulates all elements of an individual (sub-)plot:

• X-axis and Y-axis (Axis objects)
• Ticks and tick labels
• Plot elements (Line2D, Text, Polygon, etc.)
• Coordinate system

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100) y = np.sin(x)

fig, ax = plt.subplots() ax.plot(x, y) plt.show()

print(type(ax)) # ```

Axes vs Figure¶

```python import matplotlib.pyplot as plt

One figure, one axes¶

fig, ax = plt.subplots()

One figure, four axes¶

fig, axes = plt.subplots(2, 2) ```

Axes is a NumPy Array¶

When creating multiple subplots, plt.subplots returns a NumPy array of Axes:

```python import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 2)

print(type(axes)) # print(axes.shape) # (2, 2) print(axes.dtype) # object print(type(axes[0, 0])) # AxesSubplot ```

Accessing Individual Axes¶

Access axes using NumPy indexing:

```python import matplotlib.pyplot as plt import numpy as np

x = np.linspace(-2np.pi, 2np.pi, 100)

fig, axes = plt.subplots(2, 2)

axes[0, 0].plot(x, np.sin(x)) axes[0, 0].set_title("sin")

axes[0, 1].plot(x, np.cos(x)) axes[0, 1].set_title("cos")

axes[1, 0].plot(x, np.sinh(x)) axes[1, 0].set_title("sinh")

axes[1, 1].plot(x, np.cosh(x)) axes[1, 1].set_title("cosh")

plt.tight_layout() plt.show() ```

Key Axes Properties¶

Important attributes of an Axes object:

```python import matplotlib.pyplot as plt import numpy as np

fig, ax = plt.subplots() x = np.linspace(0, 1, 10) ax.plot(x, x**2)

Access components¶

print(ax.xaxis) # XAxis object print(ax.yaxis) # YAxis object print(ax.spines) # Dictionary of Spine objects print(ax.lines) # List of Line2D objects print(ax.patches) # List of Patch objects print(ax.texts) # List of Text objects

plt.show() ```

OOP Style Benefits¶

Using explicit Axes objects provides:

1. Clear references: Know exactly which plot you're modifying
2. Flexibility: Modify any axes at any time
3. Reusability: Pass axes to functions
4. Complex layouts: Handle multi-panel figures easily

```python import matplotlib.pyplot as plt import numpy as np

def plot_sine(ax, frequency=1): """Reusable plotting function that takes an axes.""" x = np.linspace(0, 2*np.pi, 100) ax.plot(x, np.sin(frequency * x)) ax.set_title(f"sin({frequency}x)")

fig, axes = plt.subplots(1, 3, figsize=(12, 3))

for i, ax in enumerate(axes): plot_sine(ax, frequency=i+1)

plt.tight_layout() plt.show() ```

Key Takeaways¶

• Axes is the main plotting area within a Figure
• plt.subplots returns a NumPy array of Axes objects
• Use NumPy indexing to access individual Axes
• OOP style with explicit Axes provides more control
• Each Axes contains its own coordinate system

Exercises¶

Exercise 1. Create a single Axes and plot both y = x^2 and y = x^3 for x in \([-2, 2]\). Customize the axes by setting x and y labels, a title, grid lines, and a legend. Also set the y-axis limits to \([-10, 10]\).

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-2, 2, 200)

fig, ax = plt.subplots()
ax.plot(x, x**2, label=r'$y = x^2$')
ax.plot(x, x**3, label=r'$y = x^3$')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title('Polynomial Functions')
ax.set_ylim(-10, 10)
ax.grid(True)
ax.legend()
plt.show()

Exercise 2. Create a figure with one Axes. Plot random data (50 points) as a scatter plot. Then use the axes object to access and print: the x-axis limits (get_xlim), the y-axis limits (get_ylim), and the number of lines/collections in the axes (len(ax.collections)).

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
x = np.random.rand(50) * 10
y = np.random.rand(50) * 10

fig, ax = plt.subplots()
ax.scatter(x, y, color='steelblue')

print(f"X limits: {ax.get_xlim()}")
print(f"Y limits: {ax.get_ylim()}")
print(f"Number of collections: {len(ax.collections)}")

plt.show()

Exercise 3. Create an Axes and plot y = sin(x). Then use the Axes methods to: set the background color to light gray (set_facecolor), remove the top and right spines, and set major grid lines with alpha=0.3. Show that the Axes is the central object controlling all visual elements.

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 2 * np.pi, 200)

fig, ax = plt.subplots()
ax.plot(x, np.sin(x), color='navy')

ax.set_facecolor('#f0f0f0')
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.grid(True, alpha=0.3)
ax.set_xlabel('x')
ax.set_ylabel('sin(x)')
ax.set_title('Customized Axes')
plt.show()