Mathematica Manipulate Plot: Scaling Axes

Question

Say I have set up the following function f[a,b,c] which I wish to plot while varying a and b

f[a_,b_,c_]:=a b c Exp[a b]

Manipulate[
Plot
[
f[a,b,c],
{c,0,1},
PlotRange->{{0,0.05},Automatic}
],
{a,0,1},
{b,0,1}
]

Is it possible to have the ordinate scaled automatically when I fix the abscissa viewing range? You'll notice with the code above that when varying a and b the ordinate does scale automatically as if I were viewing the whole range of {c,0,1}. I would like it to still handle c from 0 to 1, but if I want to view a smaller section of this plot, say c from 0 to 0.05, still have the vertical axis scaled correctly. Thank you all for your help.

Answer 1

A variant on Artes Docendo's suggestion:

Manipulate[
 Plot[f[a, b, c], {c, 0, Evaluate@d}, 
  PlotRange -> {{0, Evaluate@d}, Full}], {a, 0., 1.}, {b, 0., 1.}, {d, 
  0.05, 1.}]

Notice the Evaluate to force the machine-precision value to be fed to the Plot function before it actually tries to draw something.

I prefer Full instead of Automatic for the y-axis PlotRange in cases like this, because then you know it will never crop the plot in ways that hide parts of the curve.

Answer 2

Here is one of many possible solutions :

f[a_, b_, c_] := a b c Exp[a b]
Manipulate[ Plot[f[a, b, c], {c, 0, d}, PlotRange -> Automatic], 
            {a, 0, 1}, {b, 0, 1}, {d, 0.1, 1}, Initialization :> (d := 0.1)]

However your example is not very instructive, to see how it works better try something like this :

g[a_, b_, c_] := 3 (a - 0.5) Cos[4 Pi (a - c)] Sin[8 Pi (c - 0.5)] Cos[6 Pi (b - c)]

Manipulate[
           Plot[g[a, b, c], {c, 0, d}, PlotRange -> Automatic],
           {a, 0, 1}, {b, 0, 1}, {d, 0.1, 1}, 
           Initialization :> (a := 0.4; b := 0.4; d := 0.5)]

Answer 3

See if this does what you want. I simply use ListPlot instead of plot.

But I am not sure what you are doing, as you are plotting f for c from 0 to 1, but then setting the x-range to only be from 0 to 0.05? Why not then just plot f using {c,0,0.05}? May be I am missing something.

Anyway, here is what I have

 Manipulate[

 xmax = 0.05;
 y = Table[f[a, b, c], {c, 0, xmax, 0.01}];
 max = Max[y];
 min = Min[y];

 Plot[f[a, b, c], {c, 0, 1},
  PlotRange -> {{0, xmax}, {min, max}}, ImagePadding -> 30],

 {a, 0, 1},
 {b, 0, 1},
 Initialization :>
  (
   f[a_, b_, c_] := a b c Exp[a b]
   )

 ]

edit(1)

it just occurred to me, to make the above more efficient, is to use the first Table command, to generate the data itself as well, and not just find the max/min of the plot range. And then use ListPlot instead of Plot. This should be faster, so that sampling of the function f only happens once instead of 2 times?

So here is second version

Manipulate[xmax = 0.05;

 data = Table[{c, f[a, b, c]}, {c, 0, xmax, 0.01}];
 max = Max[data[[All, 2]]];
 min = Min[data[[All, 2]]];

 ListPlot[
  data,
  PlotRange -> {Automatic, {min, max}},
  Joined -> True,
  ImagePadding -> 30
  ],

 {a, 0, 1},
 {b, 0, 1},
 Initialization :>
  (
   f[a_, b_, c_] := a b c Exp[a b]
   )
 ]