Section9.82

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## 9.82 TwoDimensionalArray

The TwoDimensionalArray domain is used for storing data in a two dimensional data structure indexed by row and by column. Such an array is a homogeneous data structure in that all the entries of the array must belong to the same Axiom domain (although see ugTypesAnyNonePage in Section ugTypesAnyNoneNumber ). Each array has a fixed number of rows and columns specified by the user and arrays are not extensible. In Axiom, the indexing of two-dimensional arrays is one-based. This means that both the ``first'' row of an array and the ``first'' column of an array are given the index 1. Thus, the entry in the upper left corner of an array is in position (1,1).

The operation newnewTwoDimensionalArray creates an array with a specified number of rows and columns and fills the components of that array with a specified entry. The arguments of this operation specify the number of rows, the number of columns, and the entry.

This creates a five-by-four array of integers, all of whose entries are zero.

arr : ARRAY2 INT := new(5,4,0)

[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer

The entries of this array can be set to other integers using the operation seteltseteltTwoDimensionalArray.

Issue this to set the element in the upper left corner of this array to 17.

setelt(arr,1,1,17)

17

Type: PositiveInteger

Now the first element of the array is 17.

arr

[17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer

Likewise, elements of an array are extracted using the operation elteltTwoDimensionalArray.

elt(arr,1,1)

17

Type: PositiveInteger

Another way to use these two operations is as follows. This sets the element in position (3,2) of the array to 15.

arr(3,2) := 15

15

Type: PositiveInteger

This extracts the element in position (3,2) of the array.

arr(3,2)

15

Type: PositiveInteger

The operations elteltTwoDimensionalArray and seteltseteltTwoDimensionalArray come equipped with an error check which verifies that the indices are in the proper ranges. For example, the above array has five rows and four columns, so if you ask for the entry in position (6,2) with arr(6,2) Axiom displays an error message. If there is no need for an error check, you can call the operations qeltqeltTwoDimensionalArray and qseteltqseteltTwoDimensionalArray which provide the same functionality but without the error check. Typically, these operations are called in well-tested programs.

The operations rowrowTwoDimensionalArray and columncolumnTwoDimensionalArray extract rows and columns, respectively, and return objects of OneDimensionalArray with the same underlying element type.

row(arr,1)

[17, 0, 0, 0]

Type: OneDimensionalArray Integer
column(arr,1)

[17, 0, 0, 0, 0]

Type: OneDimensionalArray Integer

You can determine the dimensions of an array by calling the operations nrowsnrowsTwoDimensionalArray and ncolsncolsTwoDimensionalArray, which return the number of rows and columns, respectively.

nrows(arr)

5

Type: PositiveInteger
ncols(arr)

4

Type: PositiveInteger

To apply an operation to every element of an array, use mapmapTwoDimensionalArray. This creates a new array. This expression negates every element.

map(-,arr)

[-17 0 0 0 0 0 0 0 0-15 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer

This creates an array where all the elements are doubled.

map((x +-> x + x),arr)

[34 0 0 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer

To change the array destructively, use mapmapTwoDimensionalArray instead of mapmapTwoDimensionalArray. If you need to make a copy of any array, use copycopyTwoDimensionalArray.

arrc := copy(arr)

[17 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer
map!(-,arrc)

[-17 0 0 0 0 0 0 0 0-15 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer
arrc

[-17 0 0 0 0 0 0 0 0-15 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer
arr

[17 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0]

Type: TwoDimensionalArray Integer

Use member? member? TwoDimensionalArray to see if a given element is in an array.

member?(17,arr)

true

Type: Boolean
member?(10317,arr)

false

Type: Boolean

To see how many times an element appears in an array, use countcountTwoDimensionalArray.

count(17,arr)

1

Type: PositiveInteger
count(0,arr)

18

Type: PositiveInteger

For more information about the operations available for TwoDimensionalArray, issue )show TwoDimensionalArray. For information on related topics, see MatrixXmpPage and OneDimensionalArrayXmpPage .

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