how to plot the Partition list data in Mathematica?

Questions
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1

Dear all,

I am a new user of mathematica.

I have some data which got from Partition in mathematica, but I don’t know how to plot it as the picture shown below, could anyone help teach me to plot it?

{{{0., 0., 0.}, {-0.554448, 0.656188, -0.511864}}, {{0., 0., 
   1.}, {-0.559555, 0.703101, -0.438803}}, {{0., 0., 2.}, {-0.5273, 
   0.712295, -0.46324}}, {{0., 0., 3.}, {-0.465697, 
   0.744465, -0.478433}}, {{0., 0., 4.}, {-0.522768, 
   0.719231, -0.457625}}, {{0., 0., 5.}, {-0.543862, 
   0.683603, -0.486724}}, {{1., 0., 0.}, {-0.505162, 
   0.687541, -0.52163}}, {{1., 0., 1.}, {-0.535401, 
   0.695653, -0.47897}}, {{1., 0., 2.}, {-0.524684, 
   0.700169, -0.48422}}, {{1., 0., 3.}, {-0.478812, 
   0.739216, -0.473602}}, {{1., 0., 4.}, {-0.486477, 
   0.709122, -0.510378}}, {{1., 0., 5.}, {-0.474792, 
   0.723038, -0.501786}}, {{2., 0., 0.}, {-0.548709, 
   0.667078, -0.50391}}, {{2., 0., 1.}, {-0.547318, 
   0.663301, -0.510367}}, {{2., 0., 2.}, {-0.516255, 
   0.6467, -0.56148}}, {{2., 0., 3.}, {-0.494794, 
   0.706974, -0.505339}}, {{2., 0., 4.}, {-0.474068, 
   0.741548, -0.474728}}, {{2., 0., 5.}, {-0.482781, 
   0.705229, -0.519206}}, {{3., 0., 0.}, {-0.597856, 
   0.605314, -0.525513}}, {{3., 0., 1.}, {-0.6, 
   0.638907, -0.481454}}, {{3., 0., 2.}, {-0.534381, 
   0.666498, -0.519824}}, {{3., 0., 3.}, {-0.523751, 
   0.717818, -0.458719}}, {{3., 0., 4.}, {-0.543924, 
   0.719078, -0.43252}}, {{3., 0., 5.}, {-0.564297, 
   0.670404, -0.481796}}, {{4., 0., 0.}, {-0.619932, 
   0.62298, -0.477054}}, {{4., 0., 1.}, {-0.596892, 
   0.624093, -0.50421}}, {{4., 0., 2.}, {-0.587609, 
   0.664546, -0.461621}}, {{4., 0., 3.}, {-0.629204, 
   0.642922, -0.436753}}, {{4., 0., 4.}, {-0.622141, 
   0.631332, -0.462991}}, {{4., 0., 5.}, {-0.665868, 
   0.575591, -0.474673}}, {{5., 0., 0.}, {-0.66667, 
   0.618194, -0.416397}}, {{5., 0., 1.}, {-0.61844, 
   0.664754, -0.419087}}, {{5., 0., 2.}, {-0.594029, 
   0.645327, -0.480294}}, {{5., 0., 3.}, {-0.608024, 
   0.640567, -0.469021}}, {{5., 0., 4.}, {-0.667069, 
   0.58274, -0.464148}}, {{5., 0., 5.}, {-0.76775, 
   0.519976, -0.374413}}, {{6., 0., 0.}, {-0.678086, 
   0.655006, -0.333418}}, {{6., 0., 1.}, {-0.624181, 
   0.685756, -0.374348}}, {{6., 0., 2.}, {-0.628309, 
   0.613852, -0.477927}}, {{6., 0., 3.}, {-0.6771, 
   0.550492, -0.488358}}, {{6., 0., 4.}, {-0.693756, 
   0.524024, -0.494066}}, {{6., 0., 5.}, {-0.741287, 
   0.549593, -0.385281}}, {{7., 0., 0.}, {-0.619309, 
   0.659949, -0.425351}}, {{7., 0., 1.}, {-0.587752, 
   0.685348, -0.429937}}, {{7., 0., 2.}, {-0.643552, 
   0.613281, -0.45796}}, {{7., 0., 3.}, {-0.716033, 
   0.528534, -0.456014}}, {{7., 0., 4.}, {-0.717883, 
   0.516774, -0.466465}}, {{7., 0., 5.}, {-0.732864, 
   0.531756, -0.424437}}, {{8., 0., 0.}, {-0.634958, 
   0.650951, -0.416042}}, {{8., 0., 1.}, {-0.621014, 
   0.675993, -0.396706}}, {{8., 0., 2.}, {-0.652096, 
   0.643836, -0.400309}}, {{8., 0., 3.}, {-0.717357, 
   0.587399, -0.374648}}, {{8., 0., 4.}, {-0.703421, 
   0.574388, -0.418663}}, {{8., 0., 5.}, {-0.683398, 
   0.584367, -0.437586}}, {{9., 0., 0.}, {-0.60179, 
   0.579024, -0.550072}}, {{9., 0., 1.}, {-0.598156, 
   0.613293, -0.515831}}, {{9., 0., 2.}, {-0.661149, 
   0.646108, -0.381347}}, {{9., 0., 3.}, {-0.656127, 
   0.696351, -0.29085}}, {{9., 0., 4.}, {-0.695973, 
   0.644622, -0.316361}}, {{9., 0., 5.}, {-0.670292, 
   0.59991, -0.436826}}, {{10., 0., 0.}, {-0.566763, 
   0.669403, -0.480291}}, {{10., 0., 1.}, {-0.611619, 
   0.625311, -0.484674}}, {{10., 0., 2.}, {-0.704291, 
   0.627551, -0.331893}}, {{10., 0., 3.}, {-0.649539, 
   0.71374, -0.262058}}, {{10., 0., 4.}, {-0.698806, 
   0.653659, -0.290517}}, {{10., 0., 5.}, {-0.651989, 
   0.652849, -0.385615}}, {{11., 0., 0.}, {-0.669785, 
   0.589218, -0.451897}}, {{11., 0., 1.}, {-0.645654, 
   0.607927, -0.46212}}, {{11., 0., 2.}, {-0.714631, 
   0.602887, -0.354725}}, {{11., 0., 3.}, {-0.754299, 
   0.596464, -0.274342}}, {{11., 0., 4.}, {-0.737249, 
   0.605677, -0.299365}}, {{11., 0., 5.}, {-0.71901, 
   0.553676, -0.420079}}, {{12., 0., 0.}, {-0.653972, 
   0.606627, -0.452023}}, {{12., 0., 1.}, {-0.620618, 
   0.600267, -0.504492}}, {{12., 0., 2.}, {-0.699709, 
   0.573614, -0.42588}}, {{12., 0., 3.}, {-0.737488, 
   0.588048, -0.33213}}, {{12., 0., 4.}, {-0.720453, 
   0.611532, -0.32707}}, {{12., 0., 5.}, {-0.718731, 
   0.575664, -0.389918}}, {{13., 0., 0.}, {-0.60657, 
   0.607946, -0.512323}}, {{13., 0., 1.}, {-0.619851, 
   0.555794, -0.553965}}, {{13., 0., 2.}, {-0.668154, 
   0.574349, -0.472963}}, {{13., 0., 3.}, {-0.672173, 
   0.630932, -0.387439}}, {{13., 0., 4.}, {-0.692549, 
   0.612666, -0.380809}}, {{13., 0., 5.}, {-0.665822, 
   0.601195, -0.441865}}, {{14., 0., 0.}, {-0.596214, 
   0.594012, -0.540073}}, {{14., 0., 1.}, {-0.612741, 
   0.593539, -0.521786}}, {{14., 0., 2.}, {-0.609389, 
   0.56983, -0.551307}}, {{14., 0., 3.}, {-0.606619, 
   0.625419, -0.490779}}, {{14., 0., 4.}, {-0.594598, 
   0.662306, -0.455854}}, {{14., 0., 5.}, {-0.629944, 
   0.617005, -0.471673}}, {{15., 0., 0.}, {-0.537375, 
   0.618406, -0.573413}}, {{15., 0., 1.}, {-0.60263, 
   0.58684, -0.540792}}, {{15., 0., 2.}, {-0.588604, 
   0.611426, -0.52887}}, {{15., 0., 3.}, {-0.578745, 
   0.661086, -0.477514}}, {{15., 0., 4.}, {-0.578269, 
   0.667172, -0.46956}}, {{15., 0., 5.}, {-0.603734, 
   0.637977, -0.478007}}}

In fact, it is a crystal structure, in whose every atomic site, the directions of magnetic moment are plotted.

![Atomic coordinates and magnetic moment1

I

Thank you in advance!

2

One way:

vectors = <your data>

With[{scale = 2, base = First, vector = Last}, 
 Graphics3D[{Red, Thick, 
   Arrow[{base@#, base@# + scale*vector@#}] & /@ vectors},
  PlotRange -> {Automatic, {0, 5}, Automatic}, Axes -> True]
 ]

Your data has all second coordinates equal to zero. ListVectorPlot3D does not like that, but that function might be useful to you.

3

Hi, Michael,

Great thanks! It works well. Yes, the atomic second coordinates are zero because it’s a thin film model.

In addition, could you explain this line Arrow[{base@#, base@# + scalevector@#}] & /@ vectors}* for me?
I don’t understand this expression.

Thanks

4

Hi! You’re welcome.

The code snippet constructs a list of arrows, each of the form Arrow[{basepoint, tip}], one for each pair of triplets in the list vectors which pair I interpreted to be of the form {base, vector}. The tip is calculated by adding the scaled vector to the base point.

I’m not sure which parts need explaining. Here are some pointers to the documentation:

  1. # is short for Slot[1], which together with & forms a Function in which # represents the first argument.

  2. /@ is short for Map, which applies a function to each element of a list and returns the transformed list; in C/Java, one would normally do this with an array and a for-loop.

  3. @ is short for function application, e.g. f@x is the same as f[x].

So the Map makes an Arrow for each pair in the list vectors.

5

Dear Prof. Rogers, great thanks! It’s my honor that my first question could be answered by you. Your code snippet and explanation is really helpful for me. I have been able to plot my data quickly.