How can I make a contour plot from two lists?

Question

I have a matrix called sigmaelement

sigmaelement[[All, a, e]] = Ce.Belement[[All, All, e]].ELd[[All, e]];

sigmaelement[[1,All,1]] will have values I want to contour plot

I also have a matrix called

coordinates = {{x1,y1}, {x2,y2}} 

When I look at the documentation, I find an example like

ListContourPlot[Table[Sin[i + j^2], {i, 0, 3, 0.1}, {j, 0, 3, 0.1}]]

but in my case, instead of Sin[i+j^2], I want to use sigmaelement[[1, All, 1]]. and instead of i and j, I want to use coordinates.

Could you tell me what could be the answer?

Answer 1

You have to get your data into the form

{{x1, y1, sigmaelement1},{x2, y2, sigmaelement2}, ..., {xn, yn, sigmaelementn}}

ListContourPlot doesn't require the coordinates to be a rectangular array, but it gives better results when they are.

Since you don't supply any usable data, I will contrive some.

coordinates = Catenate @ CoordinateBoundsArray[{{0, 9}, {0, 9}}];
coordinates // Short

{{0, 0}, {0, 1}, {0, 2}, {0, 3}, <<92>>, {9, 6}, {9, 7}, {9, 8}, {9, 9}}

SeedRandom[42]; sigmaelement = RandomReal[1., 100];
sigmaelement // Short

{0.425905, <<98>>, 0.0792812}

Now I put the two lists, coordinates and sigmaelement into the form needed. I show two ways to do this.

data = MapThread[{#1[[1]], #1[[2]], #2} &, {coordinates, sigmaelement}];
data = {#1[[1]], #1[[2]], #2} & @@@ Transpose[{coordinates, sigmaelement}];
data // Short

{{0, 0, 0.425905}, <<98>>, {9, 9, 0.0792812}}

Now the contour plot is very simple.

ListContourPlot[data]

Answer 2

The second form of ListContourPlot expects a list of triplets: {{x1,y1,f1},{x2,y2,f2},...}. So your question is how to combine two lists coordinates and values=sigmaelement[[1,All,1]] in one list of correct form. There are many possible ways to do this.

Straightforward using Table:

tab[coordinates_, values_]:= Table[{coordinates[[i, 1]], coordinates[[i, 2]], values[[i]]}, {i, 1, Length@values}]

Using Transpose and mapping transformation function over the list:

map[coordinates_, values_]:={#1[[1, 1]], #1[[1, 2]], #[[2]]} & /@Transpose@{coordinates, values};

or using replacement rules (in my opinion this one is the most clear):

repl[coordinates_, values_]:=Transpose@{coordinates, values} /. {{x_, y_}, z_} -> {x, y, z}

or using Flatten (thanks to @corey979):

cor1[coordinates_, values_]:=Flatten[#, 1] & /@ Transpose[{coordinates, values}]

or using ArrayReshape (thanks to @corey979 again):

cor2[coordinates_, values_]:=ArrayReshape[Transpose@{coordinates, values}, {Length@values, 3}]

Using MapThread to avoid transposing

mapTr[coordinates_, values_]:=MapThread[#1~Join~{#2} &, {coordinates, values}]

Since we have many options let's run quick performance benchmark for $10^6$ elements. I added two other functions from @m_goldberg's answer.

genData[n_] := {RandomReal[1.0, {n, 2}], RandomReal[1.0, {n}]};
funList = {tab, map, mapTr, cor1, cor2, repl, mg1, mg2};    
timingFun[funList_, {c_, v_}] := First@AbsoluteTiming[#[c, v]] & /@ funList;
timings = timingFun[funList, genData[10^6]]    
BarChart[{timings}, ChartElementFunction -> "GlassRectangle", 
 ChartStyle -> "Pastel", ChartLabels -> funList]

So Table is a clear winner.