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}^{mtimes 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 mtimes 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.