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)](/docs/2025.0.0/fr_FR/_LaTeX_hank.xml_1.png)
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 — matrice de Toeplitz, à bandes diagonales constantes choisies
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