Defining Matrix

Defining Matrix

To make it easier to create and access elements of a two-dimensional table we have created a class matrix generating objects of type Matrix. Matrix

We create a two-dimensional table by providing the type of values, the number of rows and columns, and the default value with which to initialize all slots. Thus we can create the two-dimensional list above by writing:

   def a:Matrix<Number> = matrix.size<Number>(5,3) defaultValue (0)

Type Matrix<T> is defined as follows:

type Matrix<T> = {
  at(r: Number, c: Number) -> T 
  at(r: Number, c: Number) put (value:T) -> Done
}

Thus we can access and update values by providing the row and column and, when updating, the new value.

A nested for loop is the most common way to access or update the elements of a two-dimensional list. One loop walks through the rows and the other walks through the columns. For example, if we wanted to assign a unique number to each cell of our two-dimensional list, we could do the following:

    for (1..5) do {row: Number ->
        for (1..3) do { col: Number -> 
            a.at(row,col)put(4*(row-1) + col)
        }
    }

This assigns the numbers 1 through 15 to the elements of list a. The list is filled by assigning values to the elements in the first row, then the second row, etc. and results in:

 1  2  3  
 4  5  6
 7  8  9
 10 11 12
 13 14 15

You could modify the above to be slightly more interesting by computing a multiplication table.

We could just as well process all the elements of column 1 first, then all of column 2, etc., by swapping the order of our loops:

    for (1..3) do {col: Number ->
        for (1..5) do {row: Number ->
            ...
         }
      }

For the most part, it doesn't matter which order you choose, though for large lists it is generally a good idea to traverse the list in the same order that your programming language will store the values in memory. In most languages the data is stored by rows, known as row major order. You will certainly see this again if you go on and take courses like Computer Organization or Operating Systems.

Defining Matrix