3-dimensional matrix

I have a program that is in 2-dimensions and now I am trying to convert it to 3-dimensions. In the original program I have created a search grid with the syntax:

xg = xl:delta_x:xu;
yg = yl:delta_y:yu;

where

      xl is the lowest value of the x plane
      xu is the highest value of the x plane
      delta_x is the gridline spacing in the x direction
      yl is the lowest value of the y plane
      yu is the highest value of the y plane
      delta_y is the gridline spacing in the y direction

From these values I create a matrix [x,y] calculating distance from each grid point to 10 random points.

If I define a zl, zu, and delta_z...How do I create the 3-dimensional object/matrix holding these distances?

Answer 1

[Sean de Wolski]

some possibilities:

doc ndgrid
doc reshape
doc permute

Answer 2

[Walter Roberson]

Is that "average" or "median" distance or some other kind of aggregate distance that you were calculating? If not then you would not have been able to store 10 distances at each (x,y), not unless you were using a cell array.

Anyhow, if you do have a single value per location, then

D = zeros(length(xg), length(yg), length(zg));

Depending on your calculations, you might not need to create this array in advance. For example,

[X,Y,Z] = ndgrid(xg, yg, zg);
D = sqrt((X - x0).^2 + (Y - y0).^2 + (Z - z0).^2);

Note here the use of ndgrid rather than meshgrid. meshgrid can only handle 2 dimensions. Be careful in changing from meshgrid to ndgrid as the first two outputs are not quite the same between the two.

[Kylie]

All of the distances from each grid point to the random points are calculated using a loop:

distances = zeros(1,n); % allocate storage vector for distances

for ii = 1:length(xg); % create index values for x

for jj = 1:length(yg); % create index values for y

for kk = 1:n; % create index values for observables

distances(kk) = norm([xg(ii),yg(jj)]-xy(kk,:),2);

Then they were put into a matrix called "Dist" to find the maximum distance at each grid point..

Dist(ii,jj)= max(distances);

[Walter Roberson]

[X,Y,Z] = ndgrid(xg, yg, zg);

for K = 1 : 10

D(:,:,:,K) = sqrt((X - xyz(K,1)).^2 + (Y - xyz(K,2)).^2 + (Z - xyz(K,3)).^2);

end

Dist = max(D,4);