hank
====

covariance to hankel matrix



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


::

    hk =hank(m, n, cov)




Arguments
~~~~~~~~~

:m number of bloc-rows
: :n number of bloc-columns
: :cov sequence of covariances; it must be given as :[R0 R1 R2...Rk]
: :hk computed hankel matrix
:



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

This function builds the hankel matrix of size `(m*d,n*d)` from the
covariance sequence of a vector process. More precisely:

This function builds the hankel matrix of size `(m*d,n*d)` from the
covariance sequence of a vector process. More precisely:





Examples
~~~~~~~~


::

    //Example of how to use the hank macro for 
          //building a Hankel matrix from multidimensional 
          //data (covariance or Markov parameters e.g.)
          //
          //This is used e.g. in the solution of normal equations
          //by classical identification methods (Instrumental Variables e.g.)
          //
          //1)let's generate the multidimensional data under the form :
          //  C=[c_0 c_1 c_2 .... c_n]
          //where each bloc c_k is a d-dimensional matrix (e.g. the k-th correlation 
          //of a d-dimensional stochastic process X(t) [c_k = E(X(t) X'(t+k)], ' 
          //being the transposition in scilab)
          //
          //we take here d=2 and n=64
          
          c = `rand`_(2, 2 * 64)
          
          //generate the hankel matrix H (with 4 bloc-rows and 5 bloc-columns)
          //from the data in c
          
          H = hank(4, 5, c);




See Also
~~~~~~~~


+ `toeplitz`_ Toeplitz matrix


.. _toeplitz: toeplitz.html