ListPlot3D not working for very small numbers

Question

I have defined a function

FreeEnergy[x,y],

which I want to plot in 3D. It is a function involving numerical integrals. When I make a flattened table

a = Flatten[Table[{i, j, FreeEnergy[i, j]}, {i, 10^(-11), 10^(-10), 10^(-11)}, 
{j, 0.01, 0.1, 0.01}], 1]

I get triples of numbers, like so:

a = {{1/100000000000, 0.01, 418.254}, {1/100000000000, 0.02, 332.037}, 
{1/100000000000, 0.03, 290.103}, {1/100000000000, 0.04, 263.607}, 
{1/100000000000, 0.05, 244.735}, {1/100000000000, 0.06, 230.324}, 
{1/100000000000, 0.07, 218.805}, {1/100000000000, 0.08, 209.294}, 
{1/100000000000, 0.09, 201.249}, {1/100000000000, 0.1, 194.315}, 
{1/50000000000, 0.01, 131.97}, {1/50000000000, 0.02, 104.813}, 
{1/50000000000, 0.03, 91.6048}, {1/50000000000, 0.04, 83.2588}, 
{1/50000000000, 0.05, 77.3145}, {1/50000000000, 0.06, 72.7753}, 
{1/50000000000, 0.07, 69.1469}, {1/50000000000, 0.08, 66.1511}, 
{1/50000000000, 0.09, 63.6171}, {1/50000000000, 0.1, 61.4331}, 
{3/100000000000, 0.01, 67.3045}, {3/100000000000, 0.02, 53.4881}, 
{3/100000000000, 0.03, 46.7681}, {3/100000000000, 0.04, 42.522}, 
{3/100000000000, 0.05, 39.4977}, {3/100000000000, 0.06, 37.1882}, 
{3/100000000000, 0.07, 35.3422}, {3/100000000000, 0.08, 33.818}, 
{3/100000000000, 0.09, 32.5288}, {3/100000000000, 0.1, 31.4176}, 
{1/25000000000, 0.01, 41.7954}, {1/25000000000, 0.02, 33.2413}, 
{1/25000000000, 0.03, 29.0808}, {1/25000000000, 0.04, 26.4519}, 
{1/25000000000, 0.05, 24.5794}, {1/25000000000, 0.06, 23.1496}, 
{1/25000000000, 0.07, 22.0066}, {1/25000000000, 0.08, 21.0629}, 
{1/25000000000, 0.09, 20.2647}, {1/25000000000, 0.1, 19.5767}, 
{1/20000000000, 0.01, 28.9173}, {1/20000000000, 0.02, 23.0198}, 
{1/20000000000, 0.03, 20.1513}, {1/20000000000, 0.04, 18.3388}, 
{1/20000000000, 0.05, 17.0478}, {1/20000000000, 0.06, 16.062}, 
{1/20000000000, 0.07, 15.2739}, {1/20000000000, 0.08, 14.6233}, 
{1/20000000000, 0.09, 14.0729}, {1/20000000000, 0.1, 13.5985}, 
{3/50000000000, 0.01, 21.4262}, {3/50000000000, 0.02, 17.0739}, 
{3/50000000000, 0.03, 14.9569}, {3/50000000000, 0.04, 13.6192}, 
{3/50000000000, 0.05, 12.6664}, {3/50000000000, 0.06, 11.9388},
{3/50000000000, 0.07, 11.3572}, {3/50000000000, 0.08, 10.877}, 
{3/50000000000, 0.09, 10.4708}, {3/50000000000, 0.1, 10.1206}, 
{7/100000000000, 0.01, 16.6463}, {7/100000000000, 0.02, 13.2798}, 
{7/100000000000, 0.03, 11.6423}, {7/100000000000, 0.04, 10.6075}, 
{7/100000000000, 0.05, 9.8705}, {7/100000000000, 0.06, 9.30765}, 
{7/100000000000, 0.07, 8.85772}, {7/100000000000, 0.08, 8.48621}, 
{7/100000000000, 0.09, 8.17195}, {7/100000000000, 0.1, 7.90109}, 
{1/12500000000, 0.01, 13.3903}, {1/12500000000, 0.02, 10.6953}, 
{1/12500000000, 0.03, 9.3843}, {1/12500000000, 0.04, 8.55586}, 
{1/12500000000, 0.05, 7.96575}, {1/12500000000, 0.06, 7.51509}, 
{1/12500000000, 0.07, 7.15484}, {1/12500000000, 0.08, 6.85736}, 
{1/12500000000, 0.09, 6.60572}, {1/12500000000, 0.1, 6.38882}, 
{9/100000000000, 0.01, 11.0619}, {9/100000000000, 0.02, 8.84689}, 
{9/100000000000, 0.03, 7.76938}, {9/100000000000, 0.04, 7.08843}, 
{9/100000000000, 0.05, 6.60336}, {9/100000000000, 0.06, 6.2329}, 
{9/100000000000, 0.07, 5.93675}, {9/100000000000, 0.08, 5.6922}, 
{9/100000000000, 0.09, 5.48532}, {9/100000000000, 0.1, 5.307}, 
{1/10000000000, 0.01, 9.3328}, {1/10000000000, 0.02, 7.4742}, 
{1/10000000000, 0.03, 6.56999}, {1/10000000000, 0.04, 5.99852}, 
{1/10000000000, 0.05, 5.59142}, {1/10000000000, 0.06, 5.2805}, 
{1/10000000000, 0.07, 5.03193}, {1/10000000000, 0.08, 4.82666}, 
{1/10000000000, 0.09, 4.653}, {1/10000000000, 0.1, 4.50331}}.

Trying to plot this data with ListPlot3D returns an empty graph, while ListPointPlot3D works. Why? Help much appreciated.

I haven't seen this problem before, but if you post a complete example (i.e. provide wither the function or the data) then someone will surely figure it out. Without any way to reproduce it, it's unlikely there will be an answer. — Szabolcs, Feb 20 '15 at 14:42

Zviovich · Accepted Answer · 2015-02-20T20:34:55.327

3

As Michael Stern states, the issue seems to be with the scale of the numbers. Rescaling the x axis allows to show the Plot. You can specify the ticks to show the actual numbers you had in the dataset.

a[[All, 1]] = 10^11 N[a[[All, 1]]]
labels = {#, # 10^-11} & /@ a[[All, 1]] // Union
(*{{1., 1.*10^-11}, {2., 2.*10^-11}, {3., 3.*10^-11}, {4., 
  4.*10^-11}, {5., 5.*10^-11}, {6., 6.*10^-11}, {7., 7.*10^-11}, {8., 
  8.*10^-11}, {9., 9.*10^-11}, {10., 1.*10^-10}}*)
ListPlot3D[a, Ticks -> {labels, Automatic, Automatic}]

Mathematica graphics

edited Feb 20 '15 at 20:34

answered Feb 20 '15 at 15:07

Zviovich

9,308
1
30
52

Thank you very much! Will definitely use this trick. – drabus Feb 20 '15 at 15:17
@drabus Also use PlotRange->All in this solution because some data points are not shown. Or refer to my answer which does not need rescaling. – egwene sedai Feb 20 '15 at 15:20
A similar more general solution can be found in https://mathematica.stackexchange.com/a/146120/45020. – Kvothe Oct 20 '21 at 15:28

score 2 · Answer 2 · answered Feb 20 '15 at 15:02

I have run into this before when dealing with very small numbers as you do here. One solution is to rescale your data and then, if you need to, adjust the ticks.

So if your nested list is saved under the variable name a,

ListPlot3D[a]

fails, but

a[[All, 1]] = a[[All, 1]]*10^6;
ListPlot3D[a]

works.

score 2 · Answer 3 · answered Feb 20 '15 at 15:16

2

ListPlot3D[a, DataRange -> All, PlotRange -> All] works for me.

answered Feb 20 '15 at 15:16

egwene sedai

2,355
16
24

ListPlot3D not working for very small numbers

3 Answers3

Linked