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Questions on applying common nonlinear scalings to functions or data--useful for making sense of data which varies over a large range.

4 votes

Control plot range of logarithmic histogram

Maybe this?: y0 = 10^-4; Histogram[data, {0, 15, 0.1}, {"Log", "PDF"}] // Show[ #, ReplacePart[AbsoluteOptions[#, AxesOrigin], {1, 2, 2} -> Log[y0]], PlotRange -> Log@{y0, 1}, PlotRangeCl …
Michael E2's user avatar
  • 245k
5 votes
Accepted

Plot[Zeta[x], {x, 2, 20}, ScalingFunctions -> "Log"] is not logarithmic

Maybe worth showing this: Verification of log scaling, although with a significant but small error in the first point: plot = Plot[Zeta[x], {x, 2, 20}, ScalingFunctions -> "Log"]; {xvals, logzvals} = …
Michael E2's user avatar
  • 245k
3 votes

How to ask Mathematica to show NumberLinePlot of a function in logarithmic scale?

Here's a manual way to do the scaling (you have to scale the domain and ticks one way and the input arguments the inverse way): NumberLinePlot[ {Sin[Pi*x] < 0, Sin[Pi*x] >= 0} /. x -> Exp@x // Evalua …
Michael E2's user avatar
  • 245k
6 votes

How to correctly show the slope of a linear part on LogPlot

LogPlot plots $\log y$ vs. $x$, so the slope in the plot is given by $$m = {d \over dx} \log y = {dy/dx \over y} \,.$$ If you let f be your function, whether that is an InterpolatingFucntion[...][x] …
Michael E2's user avatar
  • 245k
1 vote

Interpolate on log scale

[Just noticed this was @Quantum_Oil's idea in a comment above. Probably why I didn't answer before.] Often one interpolates to avoid transcendental functions, but the OP's objective cannot be achieve …
Michael E2's user avatar
  • 245k
4 votes
Accepted

Transformation of values on $x$ and $y$ axis for a LogLogPlot

A couple of ways: Log-parametric plot: ParametricPlot[Log10@{x, x^2}, {x, 0.1, 10}, AspectRatio -> 0.6] Redefining the ticks (note that LogLogPlot transforms the coordinates by the natural logar …
Michael E2's user avatar
  • 245k
8 votes

How can I get exactly 5 logarithmic divisions of an interval?

Here's a mathematically simple approach, assuming that exactly n divisions are sought, no matter how nice or not. This produces exactly n intervals: Clear[logDiv]; logDiv[{x_?Positive, y_?Positive}, …
J. M.'s missing motivation's user avatar
5 votes
Accepted

Half Plot - half LogLinearPlot

ScalingFunctions works for Plot, but I had to tweak the ticks by hand: ClearAll[sfn, isfn]; SetAttributes[sfn, Listable]; SetAttributes[isfn, Listable]; sfn[x_] := Piecewise[{{x, x < 30}, {30 + Log[x …
Michael E2's user avatar
  • 245k
7 votes
Accepted

How to change the scale of a ListContourPlot to logarithmic and combine it with a LogLinearPlot

For the first question, you can do this: ListContourPlot[MapAt[Log, data, {All, ;; 2}], Mesh -> None, PlotRange -> All, InterpolationOrder -> 3, ColorFunction -> ColorData[{"LakeColors", "Reverse …
Community's user avatar
  • 1
3 votes

LogPlot does not show all points

Plot does not use open sampling on regions, so with the following we get the whole range: Plot[1/x, {x} ∈ Line[{{10^-12}, {1}}], PlotRange -> All, Frame -> True] Unfortunately, there's a bug in Log …
Michael E2's user avatar
  • 245k
8 votes
Accepted

Use different markers/colors in logarithmic plot depending on sign

You can use VertexColors to color the individual points, since the points are all in a single Point in order. ListLogPlot[Transpose[{xData, Abs[yData - 1]}], Joined -> True, Mesh -> All] /. Point[p …
Michael E2's user avatar
  • 245k