# NumberForm in logarithmic plot (with LevelScheme package)

I am trying to plot some data using the LevelScheme package, but changing the logarithmic scale to display values in NumberForm instead of ScientificForm. I.e. I want to see the axes displaying values as 1, 10, 100 and 1000 instead of 10^0, 10^1 etc. Do you have any tips on how I can achieve this?

I was trying to play with TickLabelFunction but I guess this is not meant to be used as I want.

Here's a minimal working example:

randomdata = Sort@Transpose@{
Log[10, RandomReal[{1*^-7, 1*^-5}, 1000]],
Log[10, RandomReal[{0.1, 1000}, 1000]]
};

ListPlot[randomdata, PlotRange -> {{-7, -5}, {-1, 3}}, Joined -> False,
Axes -> False, Frame -> {{True, False}, {True, False}},
FrameStyle -> {{Automatic, None}, {Automatic, None}},
FrameTicks -> {{LogTicks[10, -1, 3,TickLabelFunction -> (ScientificForm[#] &)],None},
{LogTicks[10, -7, -5], None}}
];


(Interestingly, this pseudo-data is not so randomly distributed at all ;) edit: nevermind, I didn't remember the data was in logspace)

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Have you tried AccountingForm in place of ScientificForm? – bill s Jun 5 '13 at 11:04
Yes, doesn't work either – Sosi Jun 5 '13 at 11:09
It is randomly distributed, just Log isn't. – Kuba Jun 5 '13 at 11:53
When I look at the data generated for the above plot, it has points at places like {-6.96923, 2.56757}, {-6.96601, 1.27653}. How can these points be plotted in a log axis where the numbers (from 10^-7 to 10^-5) are all positive? – bill s Jun 5 '13 at 12:06
@bills I'm not sure I am understanding your question. Those numbers are the base 10 logarithm of the original number. I.e. {-6.96923, 2.56757} correspond to {x,y}={10^-6.96601, 10^1.27653}. None of them are negative. What the package LevelScheme does is to make this correspondence – Sosi Jun 5 '13 at 12:38

here is a little hack to post-process the FrameTicks as provided by LevelScheme:

cleanTicks=Rule[FrameTicks, List[List[a_, None], List[b_, None]]] :> Rule[FrameTicks,
List[List[a /. DisplayForm[SuperscriptBox[x_, y_]] :>
AccountingForm[Power[x, y]], None], List[b, None]
]
]

ListPlot[randomdata, PlotRange -> {{-7, -5}, {-1, 3}},
Joined -> False, Axes -> False,
Frame -> {{True, False}, {True, False}},
FrameStyle -> {{Automatic, None}, {Automatic, None}},
FrameTicks -> {
{LogTicks[10, -1, 3, TickLabelFunction -> (AccountingForm[#] &)],
None},
{LogTicks[10, -7, -5], None}}] /. cleanTicks /. Rational[a_, b_] :> N[a/b]


The /. Rational[a_, b_] :> N[a/b] cleans up any ratios invented by the AccountingForm.

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This isn't exactly what you want, but you can get close using

ListLogLogPlot[10^randomdata,
Ticks -> {{0.0000001, 0.000001, 0.00001}, {1, 10, 100, 1000}}]


Here I"m using the built in ListLogLogPlot rather than the LevelScheme package - that's why I'm plotting 10^randomdata so that it plots the same data.

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