3d plot - 4 dimensional array

Hello!

I just completed a large simulation task, whose output is a 4 dimensional array, say A, with 1 (conditions satisfied) and 0 (conditions not satisfied) elements only. The dimensions are as follows:

dimension 1: simulation number, here 10000
dimension 2: input variable 1
dimension 3: input variable 2
dimension 4: input variable 3

I am interested in knowing in how many % of cases the conditions are satisfied. For given input variables I can do the following:

mean(A(:,1,1,1))

and I will get one number, say 0.75. If I use another input varaible 1, then

mean(A(:,2,1,1))

which will also give me a number, say 0.81.

What I want to do is to make a 3d plot where:

• input variable 1 is frozen. Say I only want my plot to be based on A(:,1,:,:). Hence one dimension disappears.
• input variable 2 and 3 are the explanatory variables
• mean of the elements for different input variables is the dependent variable.

I would to make a plot both with points in the 3d space only and as a "carpet" in the 3d space.

Could you please help me with this problem?

Thank you very much in advance!

Alex

Answer 1

[Walter Roberson]

surf( squeeze( mean( A(:,V1,:,:), 1 ) ) )

[Alex]

Thanks! What do you mean by "V1"? You mean "1", right?

[Walter Roberson]

V1 is "the current value of variable 1". 1 for the first layer, 2 for the second layer, etc.

[Alex]

Thank you! Could you please help with one more detail:

When I use "mesh", it uses the array indices, so for example if the 3rd dimension has length 10 (input variable 2), the axis gets indices from 1 to 10. However, in my case each index refers to different values of an input variable: alpha = 1%, 3%, 5%, ... , 19%. My question is how I can get matlab to print "1%, 3%", etc. and give then axis label "alpha"? Right now there is no label and the axis has indices 1 to 10. Thanks in advance!

[Walter Roberson]

set(gca, 'ZTickLabel', {'1%', '3%', '5%', ... '19%'} ) zlabel('alpha');

Answer 2

[Image Analyst]

You can get a 3D array by doing

array3D = squeeze(A(:,1,:,:));

Now each slice in this 3D array is the #1 slice of the 3D array at different simulation numbers. Then you can average over all simulation numbers like this:

meanXYView = squeeze(mean(array3D , 1));

Now you have a 2D image which is the average view of "input variable 1" at a value of 1 averaged over all simulation runs. You can then view this with imshow(), image(), surf() or whatever. Is that what you're after?