next up previous contents index
Next: The root-element Up: Elements of the Fib Previous: Set-element   Contents   Index


Matrix element


The matrix element represents a matrix. The matrix element works similar to the set element, except that a number of counter variables is generated automatically.


Syntax:

\begin{eqnarray*}
Obj &=& matrix( (Variable_1, \ldots, Variable_d, Variable_{d+1...
..., \ldots, W_{i.1}), \ldots, (W_{1.k}, \ldots, W_{i.k}) ), Obj_1)
\end{eqnarray*}


Description of the elements:

The matrix element represents a matrix with $d$ dimensions, which elements are sets of $i$ values.

In the matrix element each dimension / counter / index variable $Variable_c$ (with $c=1 \ldots d$) goes through all integers of the corresponding area $Startvalue_h$ to $Endvalue_h$. For each integer value of the $Variable_h$ all integer values of the variable $Variable_{h-1}$ will be set. For each value allocation of the dimension variables $(Variable_1, \ldots, Variable_d)$ the value variables $(Variable_{d+1}, \ldots,$ $Variable_{d+i})$ will be set to the next set of values $(W_{1.b}, \ldots, W_{i.b})$. This continues until either the dimension variables $(Variable_1, \ldots, Variable_d)$ have gone through all of their values or there is no next set of values $(W_{1.k+1}, \ldots, W_{i.k+1})$. If an element $W_{a.b}$ is a variable, so the $Variable_{d+a}$ will be assigned according to the value of the variable $W_{a.b}$.

If there are no value variables ($i=0$), just all the values of the dimension variables $(Variable_1, \ldots, Variable_d)$ will be set and the sets of values will be ignored.

In listing 1 the operation of the matrix element is shown with C-pseudo code.


\begin{lstlisting}[language=C, numbers=left, frame=single, caption={Pseudo algor...
...
\par
a++;
if ( (k < a) && (0 < i) ){
return;
}
}
...
}
}
\end{lstlisting}


Example:


Note: Matrices and vectors (one-dimensional matrices) are often used in mathematics, computer science, image processing. With the matrix element for example subimages can directly be specified as a raster image or the values of a flow chart can be given directly.


next up previous contents index
Next: The root-element Up: Elements of the Fib Previous: Set-element   Contents   Index
Betti Österholz 2013-02-13