Composite vectors

Simple vectors can often be combined to build more complicated ones. The Isf implementation above is a composite vector since it is basically an array of vectors, but that implementation is hidden from the programmer.

On the other hand, the compositional character of a ProductVector, ${\bf x = (x_1, x_2)}$, is not hidden from a programmer. A programmer can address the ProductVector as a single vector, ${\bf x}$ or he can address each individual vector ${\bf x_i}$ by itself. A ProductVector object contains the Cartesian product of the vector ${\bf x_1}$ and ${\bf x_2}$ and is handy when we need to formulate a minimization problem, such as

$$\left[ \begin{array} {cc} {\bf A_{11}} & {\bf A_{21}} \\ {\b... ...eft[ \begin{array} {c} {\bf b_1} \\ {\bf b_2}\end{array}\right]$$

in the canonical form ${\bf A x \approx b}$. We will talk about composite operators such as ${\bf A}$ in the next section.