LogLinear/LogLogPlot Point Sampling

*To*: mathgroup at smc.vnet.net*Subject*: [mg25349] LogLinear/LogLogPlot Point Sampling*From*: Anthony Foglia <afoglia at sal.physics.ucsb.edu>*Date*: Sat, 23 Sep 2000 03:36:21 -0400 (EDT)*Organization*: University of California, Santa Barbara*Sender*: owner-wri-mathgroup at wolfram.com

I seem to have come across a slight bug/problem in the way Mathematica draws LogLog and LogLinear plots. In particular, it samples the plotted function as if it were a normal linearlinear plot and then scales the results. This leads to oversampling on the right side of the plot, and undersampling on the left. For example: Plot[UnitStep[x - 1], {x, 0, 10}]; returns the correct plot, but LogLinearPlot[UnitStep[x - 1], {x, 0.01, 10}]; has a slight slope instead of a sharp discontinuity at x=1. We can worsen the plot by changing the scale LogLinearPlot[UnitStep[x - 1], {x, 0.01, 1000}]; looks even worse, starting out linearly increasing from .01 to 1. This problem is obviously caused by the sampled points, as increasing the PlotPoints option improves the plots. But, short of that (some of my plots take a long time for each point to be calculated), has anyone come up with a fix to the LogLinearPlot and LogLogPlot functions to sample the range logarithmically. (Looking through the Graphics`Graphics` library, it seems to involve the ScaledPlot function, but I'm very new to Mathematica programming and quickly find myself lost trying to understand it.) Thank you. --Anthony