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 FriCAS domain.. Each array has a fixed number of rows and columns specified by the user and arrays are not extensible. In FriCAS, 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 new 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+
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|0 0 0 0|
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|0 0 0 0|
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|0 0 0 0|
| |
+0 0 0 0+
Type: TwoDimensionalArray Integer
The entries of this array can be set to other integers using setelt.
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+
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|0 0 0 0|
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|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 elt.
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 elt and setelt 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) FriCAS displays an error message. If there is no need for an error check, you can call the operations qelt and qsetelt which provide the same functionality but without the error check. Typically, these operations are called in well-tested programs.
The operations row and column 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 nrows and ncols, 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 map. This creates a new array. This expression negates every element.
map(-,arr)
+- 17 0 0 0+
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| 0 0 0 0|
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| 0 - 15 0 0|
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| 0 0 0 0|
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+ 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+
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|0 0 0 0|
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|0 30 0 0|
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|0 0 0 0|
| |
+0 0 0 0+
Type: TwoDimensionalArray Integer
To change the array destructively, use map instead of map. If you need to make a copy of any array, use copy.
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+
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| 0 0 0 0|
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| 0 - 15 0 0|
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| 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? 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 count.
count(17,arr)
1
Type: PositiveInteger
count(0,arr)
18
Type: PositiveInteger
See Also: