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= Examples

== Hankel matrix
\(
{\cal H}_{m,n}(p) :=
\left[\begin{array}{ccccc} 
p_1 & p_2 & p_3 & \cdots &  p_n \\
p_2 & p_3 &    \iddots          & & p_{n+1} \\
p_3 &  \iddots            &       &              &  \vdots\\
\vdots              &               &      &        &  \\
p_m & p_{m+1}             &  \cdots                  &  & p_{m+n-1}
\end{array}\right]  \in \mathbb{R}^{m\times n}
\)
is specified in MATLAB/Octave by a structure variable with fields +m+ (number of rows) and, optionally, +n+ (number of columns):
~~~
{}{}
s.m = m; s.n = n;
~~~
If +s.n+ is missing, the number of columns is determined from the length $n_p$ of $p$ as $n = n_p - m  + 1$.

== Mosaic Hankel matrix

A mosaic Hankel matrix
\(
{\cal H}_{\mathbf{m},\mathbf{n}} := 
\left[\begin{array}{ccc}
{\cal H}_{m_1,n_1}(p^{(11)})     & \cdots & {\cal H}_{m_1,n_N}(p^{(1N)}) \\ 
\vdots                    &        & \vdots \\ 
{\cal H}_{m_q,n_1}(p^{(q1)})     & \cdots & {\cal H}_{m_q,n_N}(p^{(qN)}) 
\end{array}\right] 
\)
is specified by the vectors 
\(
\mathbf{m} = \begin{bmatrix} m_1& \cdots & m_q \end{bmatrix}, \qquad
\mathbf{n} = \begin{bmatrix} n_1& \cdots& n_N \end{bmatrix}.
\)
For example, with $q = N = 2$,
~~~
{}{}
s.m = [m1; m2]; s.n = [n1; n2];
~~~

== Unstructured matrix

An $m\times n$ unstructured matrix is a special case of a mosaic Hankel matrix and is specified by
~~~
{}{}
s.m = ones(m, 1); s.n = ones(n, 1); 
~~~

== Weight vector

The vector $w$ of weights is considered part of the structure and is specified by a filed +w+ of +s+:
~~~
{}{}
s.w = w;
~~~

== Exact elements

Exact elements of $p$, i.e., constraints $\widehat p_i = p_i$, are specifies by infinite weights:
~~~
{}{}
s.w(I_exact) = inf;
~~~
where +I_exct+ are the indeces of the exact elements of $p$.

== Missing elements

Missing elements of $p$ are specified by setting them to +NaN+:
~~~
{}{}
p(I_missing) = NaN;
~~~
where +I_imssing+ are the indeces of the missing elements of $p$.