hank

Scilab Function
Last update : 12/01/2004

hank - covariance to hankel matrix

### Calling Sequence

  `[hk]=hank(m,n,cov)`

### Parameters

- `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

### 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` ,

### Author

G. Le Vey