Bug summary

Thelinscale parameter tomatplotlib.scale.SymmetricalLogScale does not behave as described in itsdocumentation.

Code for reproduction

importmatplotlibasmplimportmatplotlib.pyplotaspltimportnumpyasnpbase=10linthresh=2linscale=5symlog=mpl.scale.SymmetricalLogTransform(base=base,linthresh=linthresh,linscale=linscale,).transform_non_affinedefexpected_transform_a(a):abs_a=np.abs(a)withnp.errstate(divide="ignore",invalid="ignore"):out=np.sign(a)* (linscale+np.log(abs_a/linthresh)/np.log(base))inside=abs_a<=linthreshout[inside]=a[inside]/linthresh*linscalereturnoutdefexpected_transform_b(a):abs_a=np.abs(a)withnp.errstate(divide="ignore",invalid="ignore"):out= (np.sign(a)*linthresh* (linscale+np.log(abs_a/linthresh)/np.log(base))        )inside=abs_a<=linthreshout[inside]=a[inside]*linscalereturnoutxvals=np.linspace(0,30,150)fig, (ax0,ax1,ax2)=plt.subplots(3,1)fig.tight_layout()forax,transformin [    (ax0,symlog),    (ax1,expected_transform_a),    (ax2,expected_transform_b),]:ax.set_title(transform.__name__)ax.plot(xvals,transform(xvals))checkpoints=np.array([linthresh*base**iforiinrange(2)])checky=transform(checkpoints)ax.scatter(checkpoints,checky)forx,yinzip(checkpoints,checky):ax.annotate(f"({x},{y:.2f})",            (x,y),xytext=(10,-10),textcoords="offset points",        )plt.savefig("symlog_example.png")plt.show()

Actual outcome

Expected outcome

The value ofsymlog(linthresh) should be equal tolinscale*(symlog(base*linthresh) - symlog(linthresh)) , as is the case in the lower two subplots.

Additional information

The documentation states

linscale: float, optional

This allows the linear range(-linthresh, linthresh) to be stretched relative to the logarithmic range. Its value is the number of decades to use for each half of the linear range. For example, when linscale == 1.0 (the default), the space used for the positive and negative halves of the linear range will be equal to one decade in the logarithmic range.

The behavior is incorrect for any value ofbase,linthresh andlinscale, including the default valuesbase=10, linthresh=2, linscale=1.

The bug is in the definition of thetransform_non_affine method ofmatplotlib.scale.SymmetricalLogTransform:https://github.com/matplotlib/matplotlib/blob/v3.7.2/lib/matplotlib/scale.py#L363
Replacing that definition with eitherexpected_transform_a orexpected_transform_b fixes the bug.
expected_transform_a is preferable, as it makes the parameterbase have the mathematically correct meaning: whenever the argumentx is multiplied by a factor ofbase,expected_transform_a(x) increases by 1.
The variantexpected_transform_b is closer to the current, in my opinion unintuitive, behavior ofSymmetricalLogTransform, in thatexpected_transform_b(x) increases bylinthresh whenx is multiplied bybase.

Operating system

Arch

Matplotlib Version

3.7.2

Matplotlib Backend

TkAgg

Python version

3.11.3

Jupyter version

No response

Installation

pip