About the number format in ticks

Question

I want to LogPlot a function, but I have the trouble in the number format in the ticks.

For example,

LogPlot[Abs[BesselJ[1, x] Sin[x]^2], {x, -10, 10},
   Frame -> True, FrameTicks -> {{Automatic, None}, {None, None}}]

The output is

If I use the command

LogPlot[Abs[BesselJ[1, x] Sin[x]^2], {x, -10, 10}, Frame -> True,  
  FrameTicks -> {
    {{#, HoldForm[#]} & /@ {10^0, 10^-1, 10^-2, 10^-3, 10^-4, 10^-5}, None},
    {None, None}
   }
]

I can get

Actually, I prefer the all the ticks in the form of 10^n, and none of the commands shown above works.

Is there any simple and clever way to cope with it? I'll be grateful for your reply.

Answer 1

Perhaps this?

LogPlot[Abs[BesselJ[1, x] Sin[x]^2], {x, -10, 10}, Frame -> True, 
 FrameTicks -> {{{#, Superscript[10, Log10@#]} & /@ ({10^0, 10^-1, 
       10^-2, 10^-3, 10^-4, 10^-5}), None}, {None, None}}]

---

Here's a completely different approach, manipulating the existing tick labels in the generated graph, and preserving the unlabeled ticks. This seems much cleaner to me than Peter's approach, assuming that it works on version 8 as it does on version 7.

format = Replace[#, {p_, n_?NumericQ} :> {p, Superscript[10, Log10@n]}, {#2}] &;

ticks = MapThread[format, {Options[#, {Ticks, FrameTicks}], {3, 4}}] &;

Use:

p = LogPlot[Abs[BesselJ[1, x] Sin[x]^2], {x, -10, 10}, Frame -> True];

Show[p, ticks[p]]

Answer 2

If you want the minor ticks too, you can use the following function:

SetAttributes[dtZahl, Listable]
dtZahl[x_] := Block[{n}, If[IntegerQ[n = Rationalize[x]], n, x]]

exponentForm[x_?NumberQ] := 
  Module[{me = MantissaExponent[x], num, exp}, 
   If[MemberQ[{0, 0., 1, 1., -1, -1.}, x], Return[IntegerPart[x]]];
   exp = Superscript["\[CenterDot]10", me[[2]] - 1];
   num = NumberForm[N[me[[1]]]*10 // dtZahl, 3];
   If[me[[1]] == 0.1,(*no mantissa*)num = "";
    exp = Superscript[10, me[[2]] - 1], 
    If[me[[2]] == 1,(*range 0..10*)exp = ""]];
   Row[{num, exp}]];
exponentForm[x_] := x

Options[logTicks] = {TicksFaktor -> 1};
logTicks[von_Integer, bis_Integer, werte_List, subwerte_List, 
  OptionsPattern[]] :=
 Module[{mt, st, ticks, res, tf},
  tf = OptionValue[TicksFaktor];
  mt = {#, exponentForm[N[#]], {0.01, 0}*tf} & /@ 
    Flatten@Table[10^i*werte, {i, von, bis}];
  st = {#, Null, {0.005, 0}*tf} & /@ 
    Flatten@Table[10^i*subwerte, {i, von, bis}];
  Join[mt, st]]

logTicks takes the following Parameters:
von and bis are the lowest and highest exponent. The list werte is the list of labeled ticks in one decade and subwerte the list of unlabeled ticks in one decade.

Example:

GraphicsRow[{
  ticks = logTicks[-4, 1, {1}, {2, 3, 5, 7}];
  LogPlot[Abs[BesselJ[1, x] Sin[x]^2], {x, -10, 10}, Frame -> True, 
   FrameTicks -> {{ticks, None}, {None, None}}],
  ticks = logTicks[-4, 1, {1, 3}, {2, 5, 7}];
  LogPlot[Abs[BesselJ[1, x] Sin[x]^2], {x, -10, 10}, Frame -> True, 
   FrameTicks -> {{ticks, None}, {None, None}}]
  }]

Output: