Axhline and Axvline¶

Add horizontal and vertical reference lines that span the entire axes.

Mental Model

axhline(y) draws a horizontal line at a fixed y-value, and axvline(x) draws a vertical line at a fixed x-value — both stretch edge to edge regardless of axis limits. Use them to mark thresholds, means, or baselines. They are more convenient than plot() for reference lines because they automatically span the full plot width or height.

Reference Lines Are Not Data

Unlike data lines (which come from measurements or computation), reference lines are interpretation guides — they add semantic meaning to the plot. A threshold line says "above here is critical," a mean line says "this is the center," and an event line says "this happened here." This distinction matters: reference lines should be styled differently (dashed, muted color, lower zorder) so readers do not confuse them with plotted data.

ax.axhline()¶

Add a horizontal line across the axes:

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

x = np.linspace(0, 10, 100) y = np.sin(x)

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y) ax.axhline(0, color='black', linewidth=0.5) ax.axhline(0.5, color='red', linestyle='--', label='y=0.5') ax.axhline(-0.5, color='blue', linestyle='--', label='y=-0.5') ax.legend() plt.show() ```

axhline Parameters¶

python ax.axhline( y=0, # Y position of the line xmin=0, # Starting x position (0-1, axes fraction) xmax=1, # Ending x position (0-1, axes fraction) color='black', # Line color linestyle='-', # Line style linewidth=1, # Line width alpha=1.0, # Transparency label='label' # For legend )

ax.axvline()¶

Add a vertical line across the axes:

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

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

fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(x, y) ax.axvline(0, color='black', linewidth=0.5) ax.axvline(np.pi/2, color='red', linestyle='--', label='x=π/2') ax.axvline(-np.pi/2, color='blue', linestyle='--', label='x=-π/2') ax.legend() plt.show() ```

axvline Parameters¶

python ax.axvline( x=0, # X position of the line ymin=0, # Starting y position (0-1, axes fraction) ymax=1, # Ending y position (0-1, axes fraction) color='black', # Line color linestyle='-', # Line style linewidth=1, # Line width alpha=1.0, # Transparency label='label' # For legend )

Partial Lines¶

Draw lines that don't span the entire axes:

```python import matplotlib.pyplot as plt

fig, ax = plt.subplots() ax.set_xlim(0, 10) ax.set_ylim(0, 10)

Full width horizontal line¶

ax.axhline(5, color='blue', label='Full width')

Partial horizontal line (30% to 70% of axes width)¶

ax.axhline(3, xmin=0.3, xmax=0.7, color='red', linewidth=2, label='Partial')

plt.legend() plt.show() ```

Mean and Threshold Lines¶

Common use case for statistical visualization:

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

np.random.seed(42) data = np.random.normal(100, 15, 200) x = range(len(data))

fig, ax = plt.subplots(figsize=(12, 4)) ax.plot(x, data, 'b-', alpha=0.7)

Mean line¶

mean = np.mean(data) ax.axhline(mean, color='green', linestyle='-', linewidth=2, label=f'Mean: {mean:.1f}')

Standard deviation bands¶

std = np.std(data) ax.axhline(mean + std, color='orange', linestyle='--', label=f'+1σ: {mean+std:.1f}') ax.axhline(mean - std, color='orange', linestyle='--', label=f'-1σ: {mean-std:.1f}')

ax.axhline(mean + 2std, color='red', linestyle=':', label=f'+2σ: {mean+2std:.1f}') ax.axhline(mean - 2std, color='red', linestyle=':', label=f'-2σ: {mean-2std:.1f}')

ax.legend(loc='upper right') ax.set_title('Process Control Chart') plt.show() ```

Event Markers¶

Mark specific events with vertical lines:

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

Sample stock-like data¶

np.random.seed(42) dates = pd.date_range('2024-01-01', periods=100, freq='D') prices = 100 + np.cumsum(np.random.randn(100))

fig, ax = plt.subplots(figsize=(12, 4)) ax.plot(dates, prices)

Mark earnings dates¶

earnings_dates = [dates[25], dates[55], dates[85]] for date in earnings_dates: ax.axvline(date, color='red', linestyle='--', alpha=0.7)

ax.set_title('Stock Price with Earnings Dates') plt.show() ```

ax.hlines() and ax.vlines()¶

For lines at specific data coordinates (not axes fractions):

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

x = np.linspace(0, 10, 100) y = np.sin(x)

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

Horizontal line from x=2 to x=8 at y=0.5¶

ax.hlines(y=0.5, xmin=2, xmax=8, color='red', linewidth=2)

Vertical line from y=-0.5 to y=0.5 at x=5¶

ax.vlines(x=5, ymin=-0.5, ymax=0.5, color='green', linewidth=2)

plt.show() ```

Key Takeaways¶

axhline adds horizontal lines spanning the axes
axvline adds vertical lines spanning the axes
xmin/xmax and ymin/ymax control partial line extent (0-1 range)
Use for reference lines, thresholds, and event markers
hlines and vlines use data coordinates for extent

Exercises¶

Exercise 1. Plot the function y = sin(x) for x in \([0, 4\pi]\), then add a horizontal dashed line at y = 0 in gray and two horizontal lines at y = 0.5 (green) and y = -0.5 (red). These represent upper and lower thresholds. Add a legend identifying each line.

Solution to Exercise 1

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 4 * np.pi, 500)
y = np.sin(x)

fig, ax = plt.subplots(figsize=(10, 5))
ax.plot(x, y, label='sin(x)')
ax.axhline(y=0, color='gray', linestyle='--', label='y = 0')
ax.axhline(y=0.5, color='green', linestyle='-', label='Upper threshold')
ax.axhline(y=-0.5, color='red', linestyle='-', label='Lower threshold')
ax.legend()
ax.set_title('Sine Wave with Thresholds')
plt.show()

Exercise 2. Generate 100 random samples from a standard normal distribution and plot them as a line. Add a vertical line at the index of the maximum value (red) and the minimum value (blue). Also add a horizontal line at the mean value (green, dashed). Use ax.text to label the max and min values near their respective vertical lines.

Solution to Exercise 2

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
data = np.random.randn(100)

fig, ax = plt.subplots(figsize=(10, 5))
ax.plot(data, color='steelblue')

max_idx = np.argmax(data)
min_idx = np.argmin(data)
mean_val = data.mean()

ax.axvline(x=max_idx, color='red', linestyle='-', label='Max')
ax.axvline(x=min_idx, color='blue', linestyle='-', label='Min')
ax.axhline(y=mean_val, color='green', linestyle='--', label='Mean')

ax.text(max_idx + 1, data[max_idx], f'{data[max_idx]:.2f}', color='red')
ax.text(min_idx + 1, data[min_idx], f'{data[min_idx]:.2f}', color='blue')

ax.legend()
ax.set_title('Random Data with Max, Min, and Mean')
plt.show()

Exercise 3. Create a plot of y = x^2 for x in \([-3, 3]\). Use axvspan to shade the region between x = -1 and x = 1 in light yellow, and use axhline to mark the minimum value at y = 0. Add axvline at x = -1 and x = 1 with dashed linestyle to show the boundaries of the shaded region.

Solution to Exercise 3

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-3, 3, 200)
y = x ** 2

fig, ax = plt.subplots(figsize=(8, 6))
ax.plot(x, y, color='navy', linewidth=2)

ax.axvspan(-1, 1, color='lightyellow', alpha=0.8, label='Region [-1, 1]')
ax.axhline(y=0, color='green', linestyle='-', linewidth=1)
ax.axvline(x=-1, color='gray', linestyle='--')
ax.axvline(x=1, color='gray', linestyle='--')

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title(r'$y = x^2$ with Highlighted Region')
ax.legend()
plt.show()

Exercise 4. Plot a time series of 100 random values simulating daily temperatures. Add axhline for the mean (solid green) and mean ± 1 standard deviation (dashed red). Use axhspan to shade the region between the two SD lines in light red. Explain how these reference elements help a reader interpret the data without reading values.

Solution to Exercise 4

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
temps = np.random.randn(100) * 5 + 20

fig, ax = plt.subplots()
ax.plot(temps, color='black', alpha=0.7)

mu, sigma = temps.mean(), temps.std()
ax.axhline(mu, color='green', linestyle='-', label=f'Mean ({mu:.1f})')
ax.axhline(mu + sigma, color='red', linestyle='--', label=f'+1 SD')
ax.axhline(mu - sigma, color='red', linestyle='--', label=f'-1 SD')
ax.axhspan(mu - sigma, mu + sigma, alpha=0.1, color='red')

ax.legend()
ax.set_title('Daily Temperature with Reference Lines')
plt.show()

# The reference lines act as semantic anchors: the green line says
# "this is normal," the red band says "68% of data falls here,"
# and points outside the band are unusual — readable at a glance.

Exercise 5. A colleague marks an event time on a plot using ax.plot([5, 5], [-1, 1], 'r--'). Explain why axvline(5) is better. Demonstrate the problem: change ylim after plotting and show the manual line no longer spans the full height.

Solution to Exercise 5

import matplotlib.pyplot as plt
import numpy as np

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
x = np.linspace(0, 10, 100)
y = np.sin(x)

ax1.plot(x, y)
ax1.plot([5, 5], [-1, 1], 'r--', label='manual line')
ax1.set_ylim(-2, 2)
ax1.set_title('Manual line (broken on resize)')
ax1.legend()

ax2.plot(x, y)
ax2.axvline(5, color='r', linestyle='--', label='axvline')
ax2.set_ylim(-2, 2)
ax2.set_title('axvline (always spans full height)')
ax2.legend()

plt.tight_layout()
plt.show()
# axvline uses axes-relative coordinates (0 to 1) for vertical span