Re: precision of y-axis values in plot
- To: mathgroup at smc.vnet.net
- Subject: [mg123808] Re: precision of y-axis values in plot
- From: Heike Gramberg <heike.gramberg at gmail.com>
- Date: Tue, 20 Dec 2011 03:04:21 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jccgik$min$1@smc.vnet.net> <jcf8kl$70m$1@smc.vnet.net> <201112191222.HAA14592@smc.vnet.net>
The values for min and max values used in Ticks->func are the min and max values of the total
plot range of the plot which is a combination of PlotRange and PlotRangePadding. Consider for
example
tickFunction[min_, max_] := (Table[i, {i, min, max, (max - min)/7}])
Plot[Sin[x], {x, 0, 1}, PlotRange -> Automatic,
PlotRangePadding -> 0.1, Ticks -> tickFunction]
Then the ticks along the x-axis run from -.1 to 1.1 which is the plot range in the x-direction plus
a padding of .1 on both sides. If an explicit PlotRange is given then PlotRangePadding is
ignored and min and max values are taken directly from PlotRange. Consider for example
Plot[Sin[x], {x, 0, 1}, PlotRange -> {{-.2, 1.3}, {-.2, 1}}, Ticks -> tickFunction]
Calculating the total plot range in the original case is slightly more complicated since the
default value for PlotRangePadding is Scaled[0.02], which means that 2 percent of the total
plot range in the final plot is padding, and the rest is the plot range which you would find with
AbsoluteOptions[Plot[Sin[x], {x, 0, 1}], PlotRange]
which is equal to {PlotRange -> {{0., 1.}, {0., 0.841471}}} in this case. This means that the
total plot range in the horizontal direction is 1./(1-2*.02)==1.04167. The amount of padding on
the left and right-hand side is then .02*1.04167==0.0208334. Therefore, with
tickFunction[min_, max_] := (Table[i, {i, min, max, (max - min)/7}]) we would expect tick marks
along the horizontal axis at
tickFunction[-.0208334, 1.0208334]== {-0.0208334, 0.127976, 0.276786, 0.425595,
0.574405, 0.723214, 0.872024, 1.02083}
which is exactly what we get with Plot[Sin[x], {x, 0, 1}, Ticks->tickFunction]
By the way the tick marks you found on the last line are the tick marks along the y-axis.
Apparently they were calculated after the tick marks along the x-axis were calculated
which overwrote limits in your tickFunction.
Heike.
On 19 Dec 2011, at 13:22, DrMajorBob wrote:
> The behavior of Ticks -> func is not explained in Help for Ticks -- and no
> examples are given -- so I suppose any guess is as good as another. It's
> pretty clear that Table[{i, NumberForm[i, {3, 4}]}, {i, min, max, 1/7}]
> should yield tick marks separated by about
>
> 1/7.
>
> 0.142857
>
> The question is what "min" and "max" arguments are used.
>
> When I run this code:
>
> tickFunction[min_, max_] := Table[{i, NumberForm[i, {3, 4}]}, {i, min,
> max, 1/7}]
>
> Plot[Sin[x], {x, 0, 1}, Ticks -> tickFunction]
>
> The ticks I see are {0.1220, 0.2650, 0.4081, 0.5510, .6930, .8360,
> 0.9790}, which are spaced just about right:
>
> differences =
> Subtract @@@
> Partition[
> ticks = {0.1220, 0.2650, 0.4081, 0.5510, .6930, .8360, 0.9790}, 2,
> 1]
> -7 Rationalize@Mean@%
>
> {-0.143, -0.1431, -0.1429, -0.142, -0.143, -0.143}
>
> 5999/6000
>
> xmin = 0.1220 should be the first tick mark, and xmax could be 1.12186:
>
> Through[{First, Last}@ticks] + {0, 1}/7
> (tickFunction @@ %)[[All, 1]]
>
> {0.122, 1.12186}
>
> {0.122, 0.264857, 0.407714, 0.550571, 0.693429, 0.836286, 0.979143}
>
> but those are not the plotted tick marks. (Close, but no cigar.)
>
> If we modify tickFunction to get the arguments directly, a very different
> result arises:
>
> tickFunction[min_, max_] := (limits = {min, max};
> Table[{i, NumberForm[i, {3, 4}]}, {i, min, max, 1/7}])
> Plot[Sin[x], {x, 0, 1}, Ticks -> tickFunction];
> limits
> (tickFunction @@ limits)[[All, 1]]
>
> {-0.0175306, 0.859002}
>
> {-0.0175306, 0.125326, 0.268184, 0.411041, 0.553898, 0.696755, \
> 0.839612}
>
> Those are really, REALLY not the tick marks on the plot.
>
> Don't you just love the documentation?
>
> Bobby
>
> On Sun, 18 Dec 2011 03:36:44 -0600, Armand Tamzarian
> <mike.honeychurch at gmail.com> wrote:
>
>> On Dec 17, 6:44 pm, Nathan <nhroll... at gmail.com> wrote:
>>> On Dec 16, 4:04 am, Armand Tamzarian <mike.honeychu... at gmail.com>
>>> wrote:
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>> On Dec 15, 9:01 pm, Nathan <nhroll... at gmail.com> wrote:
>>>
>>>>> Hi,
>>>
>>>>> I'm relatively new to Mathematica. I'm having a problem with the
>>>>> precision of the y-axis values of some of my plots. All of the data
>>>>> labels show up as "2422.3", which isn't very informative since
>>> they're
>>>>> all the same. I need the plot to show two more decimal point values
>>>>> (ex: "2422.305"). I've looked high and low and can't find any way
>>> to
>>>>> do this. Any ideals? Thanks!
>>>
>>>>> Nathan.
>>>
>>>> What you need to do is make a tick function and wrap NumberForm around
>>>> your labels and set the number of decimal points that you want. If you
>>>> do a search on here for tick functions and NumberForm you should find
>>>> many examples.
>>>
>>>> Mike
>>>
>>> Mike,
>>>
>>> Thank you for your help. Forgive my ignorance, but what should I put
>>> in the NumberForm function? Here's the plot command I'm using:
>>>
>>> plot2T := Plot[LT2[T, \[Lambda]], {T, min2, max2}, Frame -> True,
>>> FrameLabel -> {{"Task Execution Time (s)", ""}, {"Optimal CSCP
>>> Checkpoint Interval (s)", ""}}, FrameStyle -> {{Black, White},
>>> {Black, White}}, Axes -> {False, False}]
>>>
>>> Based on what you said, I assume I should add something like the
>>> following to the Plot function:
>>> Tick -> NumberForm[ N[?], 8]
>>>
>>> However, I'm not sure what should replace the ?. Will you please
>>> indulge a newbie with a specific example? Thanks!
>>
>>
>> tickFunction[min_, max_] := Table[{i, NumberForm[i, {3, 4}]}, {i, min,
>> max, 1/7}]
>>
>> Plot[Sin[x], {x, 0, 1}, Ticks -> tickFunction]
>>
>> You will need to read the documentation on Ticks and NumberForm to get
>> this to do exactly what you want.
>>
>> Mike
>>
>
>
> --
> DrMajorBob at yahoo.com
>
- References:
- Re: precision of y-axis values in plot
- From: DrMajorBob <btreat1@austin.rr.com>
- Re: precision of y-axis values in plot