plot a surface from a three variable table

I have a 3 column table and need help with applying meshgrid to the first two columns and reshaping the third column into a matrix to use with surf(x,y,z). I tried something like:

[X,Y]=meshgrid(table.Temperature,table.StrainRate) but got an error that it is too large of a request

Error using repmat

Requested 202005x202005 (304.0GB) array exceeds maximum array size preference

(31.6GB). This might cause MATLAB to become unresponsive.

I believe that once I get the meshgrid issue sorted I can then turn the Z column 'Stress' into a matrix using

reshape(z, size(X))

Is this correct?

Thanks for any help!

[Corey]

For more context, this is a scatter3 plot of the data in the attached table, what I would like to do is make a surface plot of the maximum stress values

Answer 1

[Voss]

Load and plot the data:

T = load('table.mat','t6').t6;

figure
plot3(T.(1),T.(2),T.(3),'.')
set(gca,'XScale','log','YScale','log','YDir','reverse')
grid on
axis tight

To make the requested surface, you can try something along these lines:

T = T(all(isfinite(T{:,:}),2),:)

T = 197400x3 table
    Temperature    StrainRate    Stress
    ___________    __________    ______

        700        2.2903e-07     71.38
        700        2.2815e-07    71.311
        700        2.2738e-07     71.25
        700        2.2644e-07    71.177
        700         2.253e-07    71.086
        700        2.2388e-07     70.97
        700        2.2245e-07    70.853
        700        2.2102e-07    70.737
        700         2.196e-07    70.621
        700        2.1817e-07    70.505
        700        2.1675e-07    70.389
        700        2.1532e-07    70.272
        700         2.139e-07    70.156
        700        2.1247e-07     70.04
        700        2.1183e-07    69.987
        700        2.1179e-07    69.982

[x,~,xidx] = unique(T.(1));
NX = numel(x);

NY = 100;
[yidx,yedge] = discretize(log(T.(2)),NY);
y = (yedge(1:end-1)+yedge(2:end))/2;
y(~ismember(1:NY,unique(yidx))) = [];
y = exp(y);

z = groupsummary(T.(3),[xidx,yidx],'max','IncludeEmptyGroups',true);
z = reshape(z,[],NX);

figure
surf(x,y,z)
set(gca,'XScale','log','YScale','log','YDir','reverse')
grid on
axis tight

Answer 2

[Walter Roberson]

If not the below code, then use meshgrid instead of ndgrid

This code takes a long time to execute !! The internal triangulation that is done by scatteredInterpolant takes a long time on the 197400 data points that remain after removing the missing entries.

load('table.mat');

t7 = rmmissing(t6);
F = scatteredInterpolant(t7.Temperature, t7.StrainRate, t7.Stress);
[tmin, tmax] = bounds(t7.Temperature);
[srmin, srmax] = bounds(t7.StrainRate);
N = 100;
[tG, srG] = ndgrid(linspace(tmin, tmax, N), linspace(srmin, srmax, N+1));
stG = F(tG, srG);
surf(tG, srG, stG, 'edgecolor', 'none');

[Corey]

hey thank you! I will try this out. I can follow the code you wrote but one thing I don't understand is why is the strain rate vector (srG) one unit longer (N+1) than the tG vector? also out of curiosity why ndgrid instead of meshgrid?

[Walter Roberson]

This is the plot of the above. I think it needs a finer grain than N = 100

Notice the large flat area. Surface plots seldom adapt themselves to the shape of the data.

[Walter Roberson]

The reason that I made the srG one unit longer than the tG, is a safety check for the surf(). If you give the parameters in the wrong order to surf, then if the parameters are all square matrices, then surf() will end up plotting them the wrong way around. If you make the parameters non-square then if you give the parameters in the wrong order to surf() then surf will complain about the array sizes not properly matching.

It happens that I did give the parameters in the correct order and used the correct ndgrid() instead of meshgrid(), so everything plotted correctly in this code -- but I could easily have gotten it wrong, in which case surf() would have given me an error message about the array size not matching instead of silently plotting the data incorrectly.

[Walter Roberson]

The stG = F(tG, srG); took a pretty long time. Somewhere between half an hour and an hour on my machine.

I suspect that the bulk of the time is in performing the triangulation, so I don't think reducing N to (say) 50 would speed it up all that much.