💡 Problem Formulation: In data visualization, it is often necessary to highlight the area under a curve to emphasize the integral part of the dataset. This becomes slightly more complex when working with logarithmic scales. Within the context of Python’s Matplotlib library, this article demonstrates how to fill the area under a curve when the axes are on a log scale, enabling clearer data presentations where scale matters. An input example would be a series of data points and the desired output would be a plotted curve with the area underneath shaded on a log-scaled plot.
Method 1: Use Basic fill_between with Logarithmic Scale
This method involves the use of Matplotlib’s fill_between function combined with setting the y-axis to a logarithmic scale using set_yscale('log'). It’s simple and straightforward for filling areas on plots with log-scaled axes.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(1, 10, 100)
y = np.log(x)
plt.plot(x, y, label='Log Curve')
plt.fill_between(x, y, color='skyblue', alpha=0.4)
plt.yscale('log')
plt.legend()
plt.show()Output: A plot with a logarithmic y-axis and the area under the log curve filled with a semi-transparent sky blue color.
This code snippet creates a series of data points using np.linspace and calculates their logarithms. The plt.plot and plt.fill_between functions are used to draw and fill the curve respectively. Finally, plt.yscale('log') applies the logarithmic scale to the y-axis, rendering the filled area accurately in log scale context.
Method 2: Combine fill_between with Logarithmic Scale on Both Axes
To fill the area under a curve on a plot where both the x-axis and y-axis are on a log scale, we employ the same fill_between function as in Method 1, but also apply set_xscale('log') to set the x-axis to a logarithmic scale.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
x = np.logspace(0.1, 1, 100)
y = np.exp(x)
plt.plot(x, y, label='Exp Curve')
plt.fill_between(x, y, color='lightgreen', alpha=0.5)
plt.xscale('log')
plt.yscale('log')
plt.legend()
plt.show()Output: A plot where both x and y axes are log-scaled with the area under an exponential curve filled with light green color.
Here, np.logspace generates points in a logarithmic space, suitable for the log-scaled x-axis. The curve is filled using plt.fill_between after which both axes are set to log scale using plt.xscale('log') and plt.yscale('log'). This is particularly useful when the range of both axes spans several orders of magnitude.
Method 3: Fill Between with Log Scale and Custom Y-Limits
It’s possible to control the limits of the filled area, especially when working with log scales. This method allows you to specify the minimum bound for the fill, which is crucial for log scales since they cannot handle values less than or equal to 0.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0.1, 10, 100)
y = np.power(x, 2)
plt.plot(x, y, label='Power Curve')
plt.fill_between(x, y, where=(y>1), color='orange', alpha=0.3)
plt.yscale('log')
plt.legend()
plt.show()Output: A plot with the area under the power curve filled with orange color above y=1 on a logarithmic y-axis.
This code snippet demonstrates filling the area above a certain threshold—only sections of the curve where y is greater than 1 are filled. The where parameter in plt.fill_between is crucial when paired with log scale as it helps to avoid the region where log(0) would be undefined.
Method 4: Use Stackplot for Filling Multiple Regions
For multiple curves, Matplotlib’s stackplot can be used to fill areas between stacked lines on a log-scaled plot. This is useful for plotting cumulative distributions or summative data series.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(1, 10, 100)
y1 = np.log(x)
y2 = np.log2(x)
plt.stackplot(x, y1, y2, colors=['lightblue', 'lightgreen'], alpha=0.5)
plt.yscale('log')
plt.show()Output: A stack plot with logarithmic y-axis, showing two cumulative areas filled, representing log and log2 curves.
In this snippet, plt.stackplot is used with logarithmic data to create a stacked area chart. After plotting, plt.yscale('log') makes the y-axis logarithmic. This method neatly illustrates how data series overlap and can distinguish multiple datasets with different fill colors and transparency levels.
Bonus One-Liner Method 5: Inline Filling with Plotting
The plt.plot command accepts a format string that can specify both line style and color. By using a special plot format (‘–‘), you can create a plot with a filled line in a single command. While not specifically designed for log scales, it’s a fast and effective method suitable for simple cases.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(1, 10, 100)
y = np.log10(x)
plt.plot(x, y, '--', color='plum', linewidth=2, alpha=0.6)
plt.fill_between(x, y, color='plum', alpha=0.3)
plt.yscale('log')
plt.show()Output: A plot with a dashed line indicating the curve and the area beneath it filled in a matching color on a logarithmic y-axis.
By using the dashed line format (‘–‘) and a matching color for both the line and the fill, this code achieves the effect of filling the area under the curve in a single step. It’s a quick and elegant solution suitable for log-scaled axes when you want both the curve and its filled area to be plotted in tandem with matching styles.
Summary/Discussion
- Method 1: Basic fill_between with Logarithmic Scale. Simple to implement and effective for single y-log scale. Limited to handling one axis in log scale.
- Method 2: Fill_between with Logarithmic Scale on Both Axes. Ideal for data that spans several orders of magnitude on both axes. More complicated setup with additional scale setting.
- Method 3: Fill Between with Log Scale and Custom Y-Limits. Provides control over the fill region, essential for log scales to avoid undefined areas. Requires additional logic to set the fill limits.
- Method 4: Stackplot for Filling Multiple Regions. Good for cumulative or summative data and differentiating multiple datasets. Not as straightforward for simple single-curve fills.
- Bonus Method 5: Inline Filling with Plotting. Quick and clean for simple plots, but not specifically designed for log scales; less flexibility for complex filling scenarios.