Two-dimensional colormap

Hello everyone,

I have the following arrays: spatial_grid(30001x1 elements), physical_time_elastic (2431x1 elements), and data_set_elastic (30001x4x2431 elements). What I want to is to plot a something like the figures that appears here: https://blogs.mathworks.com/steve/2016/04/25/clim-caxis-imshow-and-imagesc/. In my case, the x-th axis will be spatial_grid, the y-th axis the physical_time_elastic array, and the magnitude that will be encoded by colors will data_set_elastic (:,2,i), where i runs over the elements of physical_time_elastic (note that length(physical_time_elastic)=2431, as the number of elements of data_set_elastic in the third dimension). For each i, therefore, I have the value that corresponds to (spatial_grid, physical_time_elastic). What I have tried to do is the following, but it does not work:

outputdir='Figures';
u1=figure(1)
for i=1:length(physical_time_elastic)
    image(spatial_grid.*(10^6),physical_time_elastic(i).*(10^(12)),data_set_elastic(:,2,i))
end
colormap jet; 
axis xy;
clr1=colorbar;
xlabel('Track position, $x \, \, \left( \mu\mathrm{m} \right)$','FontSize',14,'interpreter','latex')
ylabel('Time, $t \, \, \left( \mathrm{ps} \right)$','FontSize',14,'interpreter','latex')
ylabel(clr1,'$m_x$','Interpreter','Latex','FontSize',14);
t1=title('Elastic scattering, $w_{1,2}=1/2$','FontSize',14,'interpreter','latex')
set(t1,'interpreter','latex','FontSize',14)
set(gca,'TickLabelInterpreter','latex','FontSize',14)
set(u1,'Units','Inches');
posu1=get(u1,'Position');
set(u1,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[posu1(3),posu1(4)])
saveas(gcf,fullfile(outputdir,['In-Plane_Magnetization_Distribution_Elastic_Scattering.pdf']))

Any idea? I have attached a sample of what I get. The values that appears in the colorbar are completly wrong, because the variable that it is encoded in the color has values between -1 and +1. Also the track position begins in 0 and goes to a value like 3000, increasing its value linearly.

Answer 1

[Joseph Cheng]

I'm puzzeled by your first portion and the need for a for loop. unless you have a hold somewhere the images shouldn't be stacking and you're only doing it per item in physical_time_eleastic so you're imaging a single index at a time but without hold.... i'm not sure what is going on there.

outputdir='Figures';
u1=figure(1)
for i=1:length(physical_time_elastic)
    image(spatial_grid.*(10^6),physical_time_elastic(i).*(10^(12)),data_set_elastic(:,2,i))
end
colormap jet;

in each loop you are imaging a 1x30001 image and overwriting it. as well as axes are not set correctly as your x and y do not match column row of data_set_elastic. so something else is going on there.

why don't you image the whole 2nd dimension?

here is dummy data

spatial_grid = [0:300]';
physical_time_elastic = [0:10:1000]';
data_set_elastic = 2*rand(301,3,101)-1;
u1=figure(1)
% hold on
% for i=1:length(physical_time_elastic)
%     image(spatial_grid.*(10^6),physical_time_elastic(i).*(10^(12)),data_set_elastic(:,2,i))
% end
imagesc(spatial_grid,physical_time_elastic,squeeze(data_set_elastic(:,2,:))');
colormap jet; 
colorbar

note squeezing data_set_elastic(:,2,:) which for you is (30001 x 1 x 2431 elements) would turn out to be (30001 x 2431 elements) which then doesn't match your 30001 for x (ie columns of the image) and 2431 for y. which is why there is a transpose of squeezing data_set_elastic(:,2,:)' .

also i'm not sure image deals with negative values which you should then use imagesc or other functions which you define the color scale.

[Roderick]

Hey! Thank you very much for your answer. Definitely it allowed me to do a step further. Certainly I was completely misunderstanding working with three-dimensional array, and the for loop was nothing but a demonstration of that. I have done the following now, instead using squeeze I have isolated the data from the second element of the second dimension of my array data_set_elastic, but of course your approach is correct:

mx_elastic=zeros(length(spatial_grid),length(physical_time_elastic));
for i=1:length(physical_time_elastic)
    for j=1:length(spatial_grid)
        mx_elastic(j,i)=data_set_elastic(j,2,i);
    end
end
u1=figure(1)
imagesc(spatial_grid.*(10^6),physical_time_elastic.*(10^(12)),mx_elastic') 
clr1=colorbar;
xlabel('Track position, $x \, \, \left( \mu\mathrm{m} \right)$','FontSize',14,'interpreter','latex')
ylabel('Time, $t \, \, \left( \mathrm{ps} \right)$','FontSize',14,'interpreter','latex')
set(gca,'ydir','reverse')
ylabel(clr1,'$m_x$','Interpreter','Latex','FontSize',14);
t1=title('Elastic scattering, $w_{1,2}=1/2$','FontSize',14,'interpreter','latex')
set(t1,'interpreter','latex','FontSize',14)
set(gca,'TickLabelInterpreter','latex','FontSize',14)
set(u1,'Units','Inches');
posu1=get(u1,'Position');
set(u1,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[posu1(3),posu1(4)])
saveas(gcf,fullfile(outputdir,['In-Plane_Magnetization_Distribution_Elastic_Scattering.pdf']))

I have attached my current result, pretty the final stage. Nevertheless, I have transposed my mx_elastic, as you have told me. The problem is that now my data is turned in a strange way, because the y-th axis of my plot is flipped, the values and labels of the values. Why this happens and how I could fix that? Moreover, I have another question related to this plot. I am not very happy with the labels of my colorbar, because I want them to be [-1:0.5:1], where -1 corresponds to the lowest value of my plot and +1 to the highest. The problem is that I usually fix this referring to the problematic axis, but here I have used two times ylabel and I am not sure how to manipulate only the one related to the colorbar. My usual approach is as follows (it is an example):

set(gca,'TickLabelInterpreter','latex','FontSize',18)
set(gca,'XTick',0:vminus/5:vminus) 
set(gca,'XTickLabel',{'0','0.2','0.4','0.6','0.8','1'})

Any idea? Thank for your help!

[Joseph Cheng]

to set the y axis to be normal cartesian (ie [0,0] being lower left corner) use:

set(gca,'Ydir','normal')

for the scale you can set that as the 4th term max and min value (refer to the help portion of of imagesc) but then again if you take a look at the example Jan has in this post https://www.mathworks.com/matlabcentral/answers/58634-setting-ticks-in-a-colorbar

you'll be able to set ticks and limits of the color bar.

[Roderick]

Everything is all right. Nevertheless, concerning the change of the labels of the colorbar, I have followed the method of your recommended post. In its spirit, I have added the following to my code:

clr1=colorbar('XTickLabel',{'-1','-0.5','0','0.5','1'},'XTick',[-1:0.5:1]);

This does not display the +1 and -1 in the colorbar axis (see my figure). Any idea? Thank you very much for your instructive answers!

[Joseph Cheng]

that in itself isn't setting the limits, the line above it in Jan's post

AxesH = axes('CLim', [-12, 12]);

which can also be done using the function caxis() https://www.mathworks.com/help/matlab/ref/caxis.html. the items there are only the text values in the colorbar object.

[Roderick]

Thank you for your comment. I have tried it, and I obtain something very strange.

u1=figure(1)
imagesc(spatial_grid.*(10^6),physical_time_elastic.*(10^(12)),mx_elastic') 
AxesH=axes('CLim',[-1, 1]);
clr1=colorbar('peer',AxesH,...
    'YTickLabel',{'-1','-0.5','0','0.5','1'},'YTick',[-1:0.5:1]);
% clr1=colorbar(axes('CLim',[-1,1]),'YTickLabel',{'-1','-0.5','0','0.5','1'},'YTick',[-1:0.5:1]);
xlabel('Track position, $x \, \, \left( \mu\mathrm{m} \right)$','FontSize',14,'interpreter','latex')
ylabel('Time, $t \, \, \left( \mathrm{ps} \right)$','FontSize',14,'interpreter','latex')
ylabel(clr1,'$m_x$','Interpreter','Latex','FontSize',14);
t1=title('Elastic collision, $w_{\mathrm{overall}}=1$','FontSize',14,'interpreter','latex')
set(t1,'interpreter','latex','FontSize',14)
set(gca,'TickLabelInterpreter','latex','FontSize',14)
set(gca,'Ydir','normal')
set(u1,'Units','Inches');
posu1=get(u1,'Position');
set(u1,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[posu1(3),posu1(4)])
saveas(gcf,fullfile(outputdir,['In-Plane_Magnetization_Distribution_Elastic_Collision.pdf']))

Maybe I am still misunderstanding something from the Jan's post.

[Joseph Cheng]

you shouldn't just implement but digest what is going on. by doing axes afer imagesc you created a new axes inside the figure.

again just use caxis() function like you would xlim, ylim or zlim to set the limits in a plot if you are not familiar with matlab graphical handles.

see example:

figure(1);
dummydata = randi(10,10,10);
subplot(121),imagesc(dummydata )
caxis([0 10])
colorbar
subplot(122),imagesc(dummydata ),caxis([0 50])
colorbar

[Roderick]

I see your point about creating additional axis. The function caxis works as expected. Nothing more to ask, thank you very much for everything.