3. Software
Matrices provide a systematic approach to simultaneous equation solution. Although manual matrix computation can be lengthy, particularly matrix inversion, the process is easily programmed. Both these address the issues discussed at the end of Chapter C.
Although not as flexible as dedicated software, most spreadsheet programs have matrix functions. Table D-1 shows some functions in three different packages.
|
Table D-1 |
||
Function |
Microsoft Excel LibreOffice Calc |
Corel Quattro Pro |
| Transpose | =TRANSPOSE(array) | @TRANSPOSE(array) |
| Multiply | =MMULT(array1;array2) | @MMULT(array1,array2) |
| Inverse | =MINVERSE(array) | @MINVERSE(array) |
(inclusion of a particular program by name is not an endorsement of that particular product, although LibreOffice Calc is shareware so available at little to no cost)
The functions are similar in each but there some syntax differences.
In each, an array is designated by the cell addresses of the top left and bottom right array elements.
In Excel and Calc, the destination array's cells must be highlighted and the matrix function entered using Shift+Ctrl+Enter.
In Quatto Pro, the function is entered using Enter in the top left cell of the destination array.
As long as the spreadsheet is set to auto-recalcularion, destination arrays will update when any source array elements change. For an iterative solution, enter the initial approximations in specific cells and use them to set up the [C] and [K] arrays. After the matrix functions are set up correctly, the initial approximations can be updated using the [U] matrix values which in turn updates the rest.