Symlog

Symlog, short for symmetric logarithmic scale, is a data visualization scaling method designed to handle data that includes both negative and positive values, as well as zero. It combines a linear region around zero with a logarithmic region for larger magnitudes, preserving the sign of each value so that negative and positive data remain distinguishable.

The transform is typically described as piecewise: within a central linear interval around zero, values are mapped linearly; outside that interval, values are mapped logarithmically while maintaining their sign. The key parameters are linthresh, which defines the width of the linear region around zero; linscale, which can adjust the slope of the linear part; and base, which sets the base of the logarithm used in the outer region. This combination allows a plot to display small absolute values with detail while still accommodating very large magnitudes.

Symlog is implemented in major plotting libraries to improve readability of data that spans several orders of magnitude. In Matplotlib, axes can be set to a symlog scale with tunable linthresh, linscale, and base. Other libraries offer similar functionality under the same concept, providing a way to visualize data that would be poorly represented on a traditional linear or pure log scale.

Common use cases include scientific measurements, financial data with both gains and losses, and any dataset containing zero and large positive or negative values. While it preserves interpretability near zero, users should be aware of the transition region where the scaling shifts from linear to logarithmic, which can affect precise interpretation of values near the threshold.