generate 11x11x11 symmetric matrix from 6x6x6 matrix

Hello,

I'm slowly going mad trying to accomplish something I feel is actually rather simple.

I've got a 6x6x6 matrix which I would like to be symmetric around all the principal axes about the point (1,1,1), thus making me an 11x11x11 matrix. Rather than having to do this the long way (and I have quite a few arrays to do this on), is there a quick command that would do this for me, perhaps some combination of fliplr/flipud?

Thanks,

Jim

[José-Luis]

I am not sure I understand what you mean. For instance, in two dimensions, what result would you expect from:

 a=[1 2; 3 4];

[Jan]

[6x6x6] is not a "matrix", but an array. Matrices are 2 dimensional. The term "symmetric" is not defined for 3D arrays. What is a "principal axes about a point"? Axes are lines, therefore "about" a point is not clear to me. What is "the long way"? Do we have a chance to guess this?

[Jim O'Doherty]

Apologies, yes I meant an array rather than matrix.

The "long way" would be me manually copying the array values into their correct positions.

Maybe its best shown with a 2-D example (I've shortened the array from 6x6 for space):

t=[788404.4  122836.9  2857.7  
   122836.9  32833.4          994.4       
   2857.7  994.4           31.9  
   7.3           5.4                3.9  
   3.2           3.0            2.6  
   2.1           2.0            1.8
];

should result in:

t_r = [2857.7  122836.9  788404.4  122836.9  2857.7
        994.4  32833.4          122836.9  32833.4           994.4
         31.9  994.4          2857.7          994.4           31.9
          3.9  5.4          7.3           5.4           3.9
          2.6  3.0          3.2           3.0           2.6
          1.8  2.0          2.1           2.0           1.8
];

For a 2D matrix, this "flip" in matrix "t" would happen to the left and upwards, so that the value 788404.4 located at (1,1) would become the value at the centre of the new matrix

EDIT: the new matrix would now be of dimensions 11x5

[Jan]

And Jose-Luis' question would result in:

 a = [1 2;
      3 4];
 b = [4 3 4;
      2 1 2;
      4 3 4];

You example handles the columns only. But "[6x6x6]->[11x11x11]" implies, that the rows should be handled also. Am I right?

Answer 1

[Jan]

n = 6;
A = rand(n, n, n);
v = [n:-1:2, 1:n];
B = A(v, :, :);
C = B(:, v, :);
D = C(:, :, v);

[Jim O'Doherty]

Thank you so much, this is exactly what I was looking to achieve!

Jim

[Jan]

There must be a one-liner also. Unfortunately I cannot run Matlab currently to test this.