Examples

Hankel matrix

${cal H}_{m,n}(p) := left[begin{array}{ccccc} p_1 & p_2 & p_3 & cdots & p_n p_2 & p_3 & iddots & & p_{n+1} p_3 & iddots & & & vdots vdots & & & & p_m & p_{m+1} & cdots & & p_{m+n-1} end{array}right] in mathbb{R}^{mtimes n}$

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 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 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 , 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 .

Missing elements

Missing elements of are specified by setting them to NaN:

p(I_missing) = NaN;

where I_imssing are the indeces of the missing elements of .