11422 allow x to the n scaling in plots #13367
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…caling_in_plots 11422 allow x to the n scaling in plots
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Closes #11422
A "power" option is added to the "Scale" tab of the "General Plot Options" window. Selecting it enables entry of exponent value "n". For example, n=2 corresponds to a quadratic axis scale, whilst n=-1 corresponds to a reciprocal scale. Both negative and non-integer values of n are permitted.
It is mostly left to the user to choose a sensible combination of axis limits, data to plot, and value of n. Some situations which may be more commonly met, such as having an axis limit at 0 but having a diverging scale length at 0, are resolved automatically by plotting only to near 0 (0.01 times the other axis limit). However, other situations may lead to apparently blank plots, which is consistent with what happens if you try to plot negative data on a logarithmic scale.
A warning is visible to the user in the GUI when "power" is selected, alerting them to ensure axis scaling and ranges are compatible. I believe this is preferable to reducing the versatility of the "power" option by restricting possible values of n.
For tester:
One method to test that scales are correct is to plot, for example, data with y = x^0.5 and then set the scale to quadratic and see that the curve now looks like a straight line.
When "power" is selected as scale type: