matlabmatrixdiagonalsymmetry

How to create a symmetric matrix where each row/column is a subset of a known vector

I have a 7*1 vector a = (1:7).'. I want to form a matrix A of size 4*4 from vector a such that the elements of a form the anti-diagonals of matrix A as follows:

A = [1 2 3 4;
     2 3 4 5;
     3 4 5 6;
     4 5 6 7]

I would like this to work for a general a, not just when the elements are consecutive integers.

I appreciate any help.

Solution

  • You can use hankel:

    n= 4;
A= hankel(a(1:n),a(n:2*n-1))

    Other solution(expansion/bsxfun):

    In MATLAB r2016b /Octave It can be created as:

    A = a((1:4)+(0:3).')

    In pre r2016b you can use bsxfun:

    A = a(bsxfun(@plus,1:4, (0:3).'))

    Example input/output

    a = [4 6 2 7 3 5 1]

A =

   4   6   2   7
   6   2   7   3
   2   7   3   5
   7   3   5   1

    Using the benchmark provided by @Wolfie tested in Octave:

     _____________________________________
|Method   |memory peak(MB)|timing(Sec)|
|=========|===============|===========|
|bsxfun   |2030           |1.50       |
|meshgrid |3556           |2.43       |
|repmat   |2411           |2.64       |
|hankel   |886            |0.43       |
|for loop |886            |0.82       |