how to manipulate dense 4D data ?

2014 1 3
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更新时间：2014 1 3
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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

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Walter Roberson
Walter Roberson 2014-1-3

0 个投票

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.

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Kate
Kate 2014-1-3
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
Walter Roberson 2014-1-3
What error do you get? What does size(Vq) indicate ?
Kate
Kate 2014-1-3
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
Walter Roberson 2014-1-3
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
Kate 2014-1-3
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
Walter Roberson 2014-1-3
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
Kate 2014-1-3
thanks walter

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