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hank

covariance to hankel matrix

Syntax

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:

\mathrm{hank}(m, n, [R_0, R_1, R_2, \ldots])=m\mbox{ blocks}\left\{\vphantom{\begin{matrix}R_0\cr R_1\cr R_2\cr\vdots\end{matrix}}\right.\left(\vphantom{\begin{matrix}R_0\cr R_1\cr R_2\cr\vdots\end{matrix}}\right.\overbrace{\begin{matrix}R_0 & R_1 & R_2 & \cdots\cr R_1 & R_2 & \cdots &\cr R_2 & \cdots &&\cr \vdots&&&\cr\end{matrix}}^{n \mbox{ blocks}}\left.\vphantom{\begin{matrix}R_0\cr R_1\cr R_2\cr\vdots\end{matrix}}\right)

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 (chosen constant diagonal bands)
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Last updated:
Mon Jun 17 17:55:06 CEST 2024