diag
====

diagonal including or extracting



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [y]=diag(vm, [k])




Arguments
~~~~~~~~~

:vm vector or matrix (full or sparse storage)
: :k integer (default value 0)
: :y vector or matrix
:



Description
~~~~~~~~~~~

for `vm` a (row or column) n-vector `diag(vm)` returns a diagonal
matrix with entries of `vm` along the main diagonal.

`diag(vm,k)` is a `(n+abs(k))x(n+abs(k))` matrix with the entries of
`vm` along the kth diagonal. `k=0` is the main diagonal `k>0` is for
upper diagonals and `k<0` for lower diagonals.

For a matrix `vm`, `diag(vm,k)` is the column vector made of entries
of the kth diagonal of `vm`. `diag(vm)` is the main diagonal of `vm`.
`diag(diag(x))` is a diagonal matrix.

If `vm` is a sparse matrix `diag(vm,k)` returns a sparse matrix.

To construct a diagonal linear system, use `sysdiag`.

Note that `eye(A).*A` returns a diagonal matrix made with the diagonal
entries of `A`. This is valid for any matrix (constant, polynomial,
rational, state-space linear system,...).



Examples
~~~~~~~~


::

    diag([1,2])
    
    A=[1,2;3,4];
    diag(A)  // main diagonal
    diag(A,1) 
    
    diag(`sparse`_(1:10))  // sparse diagonal matrix
    
    // form a tridiagonal matrix of size 2*m+1
    m=5;diag(-m:m) +  diag(`ones`_(2*m,1),1) +diag(`ones`_(2*m,1),-1)




See Also
~~~~~~~~


+ `sysdiag`_ block diagonal system connection
+ `sparse`_ sparse matrix definition


.. _sparse: sparse.html
.. _sysdiag: sysdiag.html