How to create a pyramid shaped 3D matrix ?

I have 3D matrix (in a pyramid shape) which has (1x1) element in it's first matrix frame. This will increase (i.e,the number of elements = 3x3,5x5,9x9,11x11,...etc) in upcoming frames using a for loop. A small demonstration has given below. Please recommend suitable way to build without using cell technique.

LorM = 5;
for l=0:LorM+1
 Dlkm(:,:,l+1)=ones((2*l)+1);
end

The output should be get like following way (if its possible):

Dlkm(:,:,1)=    1
Dlkm(:,:,2)=  1 1 1
              1 1 1
              1 1 1 
Dlkm(:,:,3)=1 1 1 1 1 
            1 1 1 1 1 
            1 1 1 1 1
            1 1 1 1 1 
            1 1 1 1 1  and so on: Dlkm(:,:,4)=
                                Dlkm(:,:,5)=
                                Dlkm(:,:,6)=

[David Young]

It's not possible. What's wrong with using cell arrays?

Answer 1

[Stephen23]

Either:

1. use a cell array, or
2. fill the other positions with some value such as 0 or NaN:

x = 3;
for k = x:-1:0 % Reverse sequence to preallocate array.
    y = 2*k+1;
    M(1:y,1:y,k+1) = 1;
end

>> M
M(:,:,1) =
   1   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
M(:,:,2) =
   1   1   1   0   0   0   0
   1   1   1   0   0   0   0
   1   1   1   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
M(:,:,3) =
   1   1   1   1   1   0   0
   1   1   1   1   1   0   0
   1   1   1   1   1   0   0
   1   1   1   1   1   0   0
   1   1   1   1   1   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
M(:,:,4) =
   1   1   1   1   1   1   1
   1   1   1   1   1   1   1
   1   1   1   1   1   1   1
   1   1   1   1   1   1   1
   1   1   1   1   1   1   1
   1   1   1   1   1   1   1
   1   1   1   1   1   1   1

[Jacky Jo]

Hi, thanks for the reply.

But, is there any option to create the same matrix without pre-allocation of zeros? It should not be also a cell. Please share your idea.

[Stephen23]

What would you prefer to prealloate with, if not with zeros? If you want a different values, simply replace the zeros with that value (e.g. NaN):

M(M==0) = val

[Jacky Jo]

Yea... that is a good idea... Thanks a lot.

Answer 2

[John D'Errico]

You cannot have a non-rectangular matrix in MATLAB. Period. This applies to 2 dimensions, it applies to n dimensions. So a purely triangular matrix, that is not filled with zeros (or something) to fill out the rectangle cannot happen.

So every plane of a 3 dimensional matrix has the same number of rows and columns as every other plane.

You can do it using cell arrays of course, since any cell can contain essentially anything. Or you can fill the remainder with zeros, or perhaps NaNs as you desire. Or, you can use a struct to store each plane.

The only other possibility is that you can create an object of your own, where you define array indexing yourself. Even in this case, you would probably end up storing internally the various planes of the object in a cell array or a struct.

[Jacky Jo]

okay.... I will keep this in my mind... thanks for your suggestion...