## Tip 80. Three-dimension matrix

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There are two types of union the variables in
Mathcad – vector and matrix. Their analogues
are one-dimensional and two-dimensional arrays in traditional computer
languages. It is possible to create three-dimensional (and more) arrays in
computer languages but we can not do the same in Mathcad. Point is that there
are no problems to reflect on display or
paper of a printer a vector («line») or matrix («square»). But it is
(visualization of output) advantage of Mathcad. Three-dimensional matrix is a
«volume». So the reflection of it on a display is problematical. But in Mathcad
three-dimensional matrix may be deprived of its volume and presented as the
vector, which elements are matrixes. Such vector (array) is possible and it has
the name Nested Array in Mathcad: embedded (packaged) array.

Soft formation of such array is showed in the fig. 80. If for formation a vector or matrix is required
one or two cycles with parameter then for formation our three-dimensional array
(*tensor*) is required already three cycles with parameter. They are
reflected in the fig. 80. As a result of scan the
program the array with the name A is formed (it was better to write 3D-M –
three-dimensional array (3D-array), but a name of a variable can not start with
a number – see tip 15).
This array is the three-dimension matrix with lines, columns and *layers*. This matrix was «stretched»
so that it was reflected on a surface.
As well it is showed in the fig. 80how it is
possible to extract necessary element with coordinates i-j-k from the embedded array and to
award it to the variable A_{i, j, k}. This variable is not the element
of the three-dimensional array but the simple variable with textual index i, j, k: A.i, j, k.

Packaged array of the structure A can be the element of new array
(four-dimensional matrix) and etc. The main thing is a computer has enough
memory.

Too all tips >>>>>>>