how to manipulate dense 4D data ?

hi,

I have a 4-D array. I plot it as using the code below(You need the function 'plotgrid' below as well). Based on the plot the spacing of the cube is very dense, I want to make the inter-spacing in the cube plot sparser than it currently is. But I dont know how to resample 4D data (or skip rows). Can anyone help ?

clc;clear all;close all;
%%%%%Test script
[x,y,z] = meshgrid(-2:.2:2,-2:.25:2,-2:.16:2);
v = x.*exp(-x.^2-y.^2-z.^2);

xslice = [-1.2,.8,2]; yslice = 2; zslice = [-2,0];
slice(x,y,z,v,xslice,yslice,zslice)
colormap hsv
% I work with NDGRID rather than MESHGRID
[x,y,z] = ndgrid(-2:0.1:2,-2:.1:2,-2:.1:2);
xyz = cat(4, x, y, z);
plotgrid(gca, xyz, 'color', [0 0.5 0]);

%----------------------------------------%
function h = plotgrid(ax, xyz, varargin)
% function h = plotgrid(ax, xyz, varargin)
% Plot the 4D position array xyz(nx,ny,nz,3) in a grid-like plot

if isempty(ax)
    ax = gca();
end

hold(ax, 'on');
h = [];
for dim=1:3
    p = 1:4;
    p([1 dim]) = [dim 1];
    a = permute(xyz, p);
    m = size(a,1);
    a = reshape(a, m, [], 3);
    if m > 1
        hd = plot3(ax, a(:,:,1), a(:,:,2), a(:,:,3), '.-', varargin{:});
    else
        hd = plot3(ax, a(:,:,1), a(:,:,2), a(:,:,3), '.', varargin{:});
    end
    h = [h; hd];
end
hold(ax, 'off');

end % plotgrid

Answer 1

[Walter Roberson]

You can resample using interpn

You can also use every [p, q, r]'th point along the first three dimensions using reducevolume(). It is not documented clearly but the code for reducevolume is set up so that any higher dimensions are kept intact.

[Kate]

hi walter,

I tried using interpn, but get an error when I try to plot. Please see code below if you get a chance (PS: it uses the 'plotgrid' function above in original post). thanks.

%%%%%Test script
[x,y,z] = meshgrid(-2:.2:2,-2:.25:2,-2:.16:2);
v = x.*exp(-x.^2-y.^2-z.^2);

xslice = [-1.2,.8,2]; yslice = 2; zslice = [-2,0];
slice(x,y,z,v,xslice,yslice,zslice)
colormap hsv
% I work with NDGRID rather than MESHGRID
[x,y,z] = ndgrid(-2:0.1:2,-2:.1:2,-2:.1:2);
xyz = cat(4, x, y, z);
plotgrid(gca, xyz, 'color', [0 0.5 0]);

[xq,yq,zq,tq] = ndgrid(-2:0.1:2,-2:0.1:2,-2:0.1:2,-2:0.1:2);

Vq = interpn(xyz,xq,yq,zq,tq);
figure, 
plotgrid(gca, Vq, 'color', [0 0.5 0]);

[Walter Roberson]

What error do you get? What does size(Vq) indicate ?

[Kate]

hi Walter,

the error is :

Error using reshape
Product of known dimensions, 123, not divisible
into total number of elements, 2825761.

The size of my original 4-D array named 'xyz' is [41 41 41 3]. After applying interpn, the new array named 'Vq' is [41 41 41 41].

I am not sure if I am applying the interpn correctly to resample. thanks

[Walter Roberson]

The gridplot documentation does say,

   % Plot the 4D position array xyz(nx,ny,nz,3) in a grid-like plot

I suspect now that what you want is your original code, except with

[x,y,z] = ndgrid(-2:0.1:2,-2:.1:2,-2:.1:2);

replaced with something like

[x,y,z] = ndgrid(-2:0.2:2,-2:0.2:2,-2:0.2:2);

or for finer control,

numlines = 11;   %for example
[x,y,z] = ndgrid(linspace(-2,2,numlines), linspace(-2,2,numlines), linspace(-2,2,numlines));

In this special case of wanting the same grid in each of the dimensions you can abbreviate this to

[x,y,z] = ndgrid(linspace(-2,2,numlines));

[Kate]

Walter,

thanks, but, the issue is that I am given the dense 4-D matrix (I do not generate it) and want to reduce to a sparser form.

In my original test code above, I generated a dense 4D array only for testing purposes.

thanks again

[Walter Roberson]

If you have an xyzv matrix and you want every P'th point in the x, y, z dimensions, leaving v (because it is only 3 wide), then

newmatrix = xyzv(1:P:end, 1:P:end, 1:P:end, :);

This simply drops points. If your matrix varies quickly enough in value then you might prefer to interpolate instead of simply dropping points. If you want to be left with N points along each of x, y, z, keeping 3 along v, then:

SZ = size(xyzv);
[xq,yq,zq,tq] = ndgrid(linspace(1,SZ(1),N), linspace(1,SZ(2),N), linspace(1,SZ(3),N), 1:SZ(4));
newmatrix = interpn(xyzv, xq, yq, zq, tq);

[Kate]

thanks walter