Is it possible to rotate a matrix by 45 degrees in matlab

Question

i.e. so that it appears like a diamond. (it\'s a square matrix) with each row having 1 more element than the row before up until the middle row which has the number of eleme

Answer 1

A rotation is of course not possible as the "grid" a matrix is based on is regular.

But I remember what your initially idea was, so the following will help you:

%example data
A = magic(5);

A =

    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9

---

d = length(A)-1;
diamond = zeros(2*d+1);

for jj = d:-2:-d

    ii = (d-jj)/2+1;
    kk = (d-abs(jj))/2;

    D{ii} = { [zeros( 1,kk ) A(ii,:) zeros( 1,kk ) ] };
    diamond = diamond + diag(D{ii}{1},jj);
end

will return the diamond:

diamond =

     0     0     0     0    17     0     0     0     0
     0     0     0    23     0    24     0     0     0
     0     0     4     0     5     0     1     0     0
     0    10     0     6     0     7     0     8     0
    11     0    12     0    13     0    14     0    15
     0    18     0    19     0    20     0    16     0
     0     0    25     0    21     0    22     0     0
     0     0     0     2     0     3     0     0     0
     0     0     0     0     9     0     0     0     0

Now you can again search for words or patterns row by row or column by column, just remove the zeros then:

Imagine you extract a single row:

row = diamond(5,:)

you can extract the non-zero elements with find:

rowNoZeros = row( find(row) )

rowNoZeros =

    11    12    13    14    15

---

Not a real diamond, but probably useful as well:

(Idea in the comments by @beaker. I will remove this part, if he is posting it by himself.)

B = spdiags(A)

B =

    11    10     4    23    17     0     0     0     0
     0    18    12     6     5    24     0     0     0
     0     0    25    19    13     7     1     0     0
     0     0     0     2    21    20    14     8     0
     0     0     0     0     9     3    22    16    15