Identity matrix in Matlab
I need to create a function in Matlab that sets a parameter to N, returns an N-by-N identity matrix. I cannot use loops and built-in functions like eye
or diag
. I've tried the following:
function I = identity( n )
I = zeros( n,n );
p = [1:n;1:n]';
I( p ) = 1;
end
But, when I call it with I = identity(3);
, I get the following result:
I =
1 0 0
1 0 0
1 0 0
And I don't understand why, because I thought Matlab could use a vector as a matrix index, and the way I did it, I have this:
p =
1 1
2 2
3 3
So, when I do I( p ) = 1
, the first step should be I( 1,1 ) = 1
, then I( 2,2 ) = 1
and so on. What can't I see?
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Without any functions, just matrix indexing
-
A(N,N) = 0;
A((N+1)*(0:N-1)+1) = 1
So the function becomes -
function A = identity( N )
A(N,N) = 0;
A((N+1)*(0:N-1)+1) = 1;
end
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The way MATLAB indices are large in column size, so fills the matrix with I
linear indices contained in p
, starting at (1,1) then going down to (2,1), etc. Therefore, he "sees" the indices as [1 2 3], and then again [1 2 3].
What you can do is change p
to a 1xn vector containing the corresponding linear indices.
For example:
p = 1:n+1:n^2
spawns those indices:
p = 1 5 9
and the following matrix I
:
I =
1 0 0
0 1 0
0 0 1
yay!
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Going with the answer on the track, we can achieve the same approach with bsxfun
, but without using any built-in functions ... except ones
. Specifically, we can use indexing to replicate the rows and columns of vectors, and then use the equality operator upon completion. Specifically, we first generated a row vector and a column vector from 1:n
, copy them so that they match matrices n x n
, and then use equality. The values in this matrix must be equal only along the diagonal elements and therefore an identity is produced.
Thus:
row = 1:n; col = row.'; row = row(ones(n,1),:); col = col(:, ones(n,1)); I = (row == col) + 0;
We need to add 0
to the output matrix to convert the matrix to precision double
as it row == col
will create a matrix logical
. I didn't use the function double
because you said you can't use any built-in functions ... but I allowed the use ones
because in your solution you are using zeros
, which is technically a built-in function.
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