Contour plot of concentration of chemical species

Hi. I am releasing a chemical species CHX (N units) in a chamber. The size of the chamber is 100 X 100 X 100 cms^3. I want to plot the contour/surface plot of concentration of this chemical species in the chamber at different spatial locations.

I want to look at the concentration profiles overlapped or plotted on one plane, say X-Y plane (100 X 100 cm^2).

I am using a digital chemical analyzer which gives the X and Y vectors, X and Y which give the spatial location. Each and every (X,Y) corresponds to a spatial location at which the chemical species is present.

For example, if a given (X,Y) shows up "m" times it, means that there are "m" units of that species at that location. In my surface plot, at that particualr (X,Y), I want the value to be m/N (with some colormap). The same is with other (X,Y) locations.

Can someone help me with this?

Answer 1

[Star Strider]

Try this example:

xy = randi(9, 100, 2);                                      % Matrix Of ‘x’ and ‘y’ Positions
[Uxy,ia,ic] = unique(xy, 'rows');                           % Unique Rows
tally = accumarray(ic, 1);                                  % Tally Numbers Of Unique Row Repeats
Freq = [Uxy, tally];                                        % Concatenated Matrix

xv = min(xy(:,1)):max(xy(:,1));                             % ‘x’ Vector For Interpolation
yv = min(xy(:,2)):max(xy(:,2));                             % ‘y’ Vector For Interpolation
[X,Y] = ndgrid(xv,yv);                                      % Create Interpolation Grid
Z = griddata(Freq(:,1), Freq(:,2), Freq(:,3), X, Y);        % Interpolated Grid Of ‘tally’ Values

figure
contourf(X, Y, Z)                                           % Contour Plot
colorbar

Experiment to get the result you want.

[SS]

Thanks for the answer. Where, should I divide it by total concentration N?

[Star Strider]

My pleasure.

To normalise by total concentration (that I assume is the sum of all the concnetrations returned in ‘xy’ in my code), divide ‘tally’ by ‘sum(tally)’:

Freq = [Uxy, tally/sum(tally)];                             % Concatenated Matrix (Normalised Concentrations)

The rest of my code remains the same.

[SS]

Thank you. I have tried you code but, got stuck with something. May be, I should have mentioned it before. The dimensions of the chamber are set according to the coordinate system of the digital analyzer. The X-axis has limits [-300,300] and Y-axis has limits [0,500]. When, I tried to used the above code with modifications, it gave me the wrong result.

I want to generate the grid using these X and Y limits. I really appreciate if, you can help me with generating the grid with these limits. I want a fine grid. I have around 300,000 data points from the digital chemical analyzer.

[Star Strider]

My pleasure.

It might still be useful to have a representative sample of your data. Lacking that, this updated version of my previous code (most of it unchanged) to accomodate the new instrument results appears to me to do what you requested:

x = randi([-300 300], 1000, 1);                             % X: [-300 300]
y = randi([0 500], 1000, 1);                                % Y: [0 500]
xy = [x y];                                                 % Matrix Of ‘x’ and ‘y’ Positions
[Uxy,ia,ic] = unique(xy, 'rows');                           % Unique Rows
tally = accumarray(ic, 1);                                  % Tally Numbers Of Unique Row Repeats
Freq = [Uxy, tally/sum(tally)];                             % Concatenated Matrix (Normalised Concentrations)

xv = min(xy(:,1)):max(xy(:,1));                             % ‘x’ Vector For Interpolation
yv = min(xy(:,2)):max(xy(:,2));                             % ‘y’ Vector For Interpolation
[X,Y] = ndgrid(xv,yv);                                      % Create Interpolation Grid
Z = griddata(Freq(:,1), Freq(:,2), Freq(:,3), X, Y);        % Interpolated Grid Of ‘tally’ Values

xsf = [-300 1; 300 1] \ [0; 100];                           % X-Scale Relation
ysf = [   0 1; 500 1] \ [0; 100];                           % Y-Scale Relation

Xc = X*xsf(1) + xsf(2);                                     % Scale ‘X’ To Chamber Coordinates
Yc = Y*ysf(1) + ysf(2);                                     % Scale ‘Y’ To Chamber Coordinates

figure
contourf(Xc, Yc, Z)                                         % Contour Plot
hc = colorbar;
hc.Label.String = "[CHX]";

I created the original ‘x’ and ‘y’ vectors to match the ranges you mentioned, in order to test this. The ‘xsf’ and ‘ysf’ calculations map the [-300 300] X-coordinates and [0 500] Y-coordinates the instrument returns to the [0 100] dimensions of the chamber. (This is a simple linear regression using the \ operator.) I use them to calculate ‘Xc’ and ‘Yc’ (‘Xchamber’ and ‘Ychamber’ respectively), to use in the contourf call. I also added a title to the colorbar.

[SS]

Thank you so much. It work well. I have attached the result herein. Unlike the results, I have seen from other people in some research papers, it shows some wierd small circles and mostly the same color background through out execpt two spots. Is it some error?

The MAT file ecxeeds 5MB, I can send it to you in personal message if required.

[Star Strider]

My pleasure.

I would have to see your data in order to comment. It may be that your data simply show a more-or-less uniform distribution rather than local concentrations. (Note that the vectors I used to test this were random integers, not actual data.)

If my Answer helped you solve your problem, please Accept it!

[SS]

Hi Star Strider. I have a question. Is there any function which calculates the intensity at a grid cell based on the PDF (averaging of the Z data points in that cell) rather than interpolation scheme which griddats function does?

[Star Strider]

I am not certain that I understand what you are asking. The griddata function is necessary to create the matrices to do the contour plot. There are several different interpolation methods available in griddata, so perhaps one of them (perhaps 'nearest') is what you are looking for. (To the best of my knowledge, you cannot define your own interpolation scheme to use with griddata or the other interpolation algorithms.)