Library Documentation

Signature `ARRAY2` `(basis)`

Polymorphic 2-dimensional arrays.

The ARRAY2 signature is a polymorphic interface to mutable 2-dimensional arrays. Two arrays are equal only if they are the same array, i.e., created by the same call to a primitive array constructor such as array, fromList, etc.; otherwise they are not equal. This also holds for arrays of zero length. The elements of 2-dimensional arrays are indexed by pair of integers (i,j) where i gives the row index, and i gives the column index. As usual, indices start at 0, with increasing indices going from left to right and, in the case of rows, from top to bottom.

structure Array2 : ARRAY2 (basis)

signature ARRAY2 = sig
  eqtype 'a array
  type 'a region = {base : 'a array,
                    row : int,
                    col : int,
                    nrows : int option,
                    ncols : int option}

  datatype traversal = RowMajor | ColMajor

  val array      : int * int * 'a -> 'a array
  val fromList   : 'a list list -> 'a array
  val tabulate   : traversal -> int * int * (int * int -> 'a) -> 'a array

  val sub        : 'a array * int * int -> 'a
  val update     : 'a array * int * int * 'a -> unit

  val dimensions : 'a array -> int * int
  val nCols      : 'a array -> int
  val nRows      : 'a array -> int

  val row        : 'a array * int -> 'a Vector.vector
  val column     : 'a array * int -> 'a Vector.vector

  val copy       : {src : 'a region,
                    dst : 'a array,
                    dst_row : int,
                    dst_col : int} -> unit

  val appi       : traversal -> (int * int * 'a -> unit) -> 'a region -> unit
  val app        : traversal -> ('a -> unit) -> 'a array -> unit
  val foldi      : traversal -> (int * int * 'a * 'b -> 'b) -> 'b -> 'a region -> 'b
  val fold       : traversal -> ('a * 'b -> 'b) -> 'b -> 'a array -> 'b
  val modifyi    : traversal -> (int * int * 'a -> 'a) -> 'a region -> unit
  val modify     : traversal -> ('a -> 'a) -> 'a array -> unit
end

[eqtype 'a array]

Type constructor for polyrmophic 2-dimensional arrays.

[type 'a region]

This type specifies a rectangular subregion of a 2-dimensional array. If ncols equals SOME(w), with 0 <= w, the region includes only those elements in columns with indices in the range from col to col + (w - 1), inclusively. If ncols is NONE, the region includes only those elements lying on or to the right of column col. A similar interpretation holds for the row and nrows fields. Thus, the region corresponds to all those elements with position (i,j) such that i lies in the specified range of rows and j lies in the specified range of columns. A region reg is said to be valid if it denotes a legal subarray of its base array. More specifically, reg is valid if

        0 <= #row reg <= nRows (#base reg)

when #nrows reg = NONE, or

        0 <= #row reg <= (#row reg)+nr <= nRows (#base reg)

when #nrows reg = SOME(nr), and the analogous conditions hold for columns.

[datatype traversal = RowMajor | ColMajor]

This type specifies a way of traversing a region. Specifically, RowMajor indicates that, given a region, the rows are traversed from left to right (smallest column index to largest column index), starting with the first row in the region, then the second, and so on until the last row is traversed. ColMajor reverses the roles of row and column, traversing the columns from top down (smallest row index to largest row index), starting with the first column, then the second, and so on until the last column is traversed.

[array (r, c, init)]

creates a new array with r rows and c columns, with each element initialized to the value init. If r < 0, c < 0 or the resulting array would be too large, the Size exception is raised.

[fromList l]

creates a new array from a list of a list of elements. The elements should be presented in row major form, i.e., hd l gives the first row, hd (tl l) gives the second row, etc. This raises the Size exception if the resulting array would be too large or if the lists in l do not all have the same length.

[tabulate trv (r, c, f)]

creates a new array with r rows and c columns, with the (i,j)(th) element initialized to f (i,j). The elements are initialized in the traversal order specified by trv. If r < 0, c < 0 or the resulting array would be too large, the Size exception is raised.

[sub (arr, i, j)]

returns the (i,j)(th) element of the array arr. If i < 0, j < 0, nRows arr <= i, or nCols arr <= j, then the Subscript exception is raised.

[update (arr, i, j, a)]

sets the (i,j)(th) element of the array arr to a. If i < 0, j < 0, nRows arr <= i, or nCols arr <= j, then the Subscript exception is raised.

[val dimensions : 'a array -> int * int]

[val nCols : 'a array -> int]

[val nRows : 'a array -> int]

These functions return size information concerning an array. nCols returns the number of columns, nRows returns the number of rows, and dimension returns a pair containing the number of rows and the number of columns of the array. The functions nRows and nCols are respectively equivalent to #1 o dimensions and #2 o dimensions

[row (arr, i)]

returns row i of arr. If (nRows arr) <= i or i < 0, this raises Subscript.

[column (arr, j)]

returns column j of arr. This raises Subscript if j < 0 or nCols arr <= j.

[copy {src, dst, dst_row, dst_col}]

copies the region src into the array dst, with the element at position (#row src, #col src) copied into the destination array at position (dst_row,dst_col). If the source region is not valid, then the Subscript exception is raised. Similarly, if the derived destination region (the source region src translated to (dst_row,dst_col)) is not valid in dst, then the Subscript exception is raised. Implementation note: The copy function must correctly handle the case in which the #base src and the dst arrays are equal, and the source and destination regions overlap.

[appi tr f reg]

[app tr f arr]

These functions apply the function f to the elements of an array in the order specified by tr. The more general appi function applies f to the elements of the region reg and supplies both the element and the element's coordinates in the base array to the function f. If reg is not valid, then the exception Subscript is raised. The function app applies f to the whole array and does not supply the element's coordinates to f. Thus, the expression app tr f arr is equivalent to:

       let
	 val range = {base=arr,row=0,col=0,nrows=NONE,ncols=NONE}
       in
	 appi tr (f o #3) range
       end

[foldi tr f init reg]

[fold tr f init arr]

These functions fold the function f over the elements of an array arr, traversing the elements in tr order, and using the value init as the initial value. The more general foldi function applies f to the elements of the region reg and supplies both the element and the element's coordinates in the base array to the function f. If reg is not valid, then the exception Subscript is raised. The function fold applies f to the whole array and does not supply the element's coordinates to f. Thus, the expression fold tr f init arr is equivalent to:

       foldi tr (fn (_,_,a,b) => f (a,b)) init
		  {base=arr, row=0, col=0, nrows=NONE, ncols=NONE}

[modifyi tr f reg]

[modify tr f arr]

These functions apply the function f to the elements of an array in the order specified by tr, and replace each element with the result of f. The more general modifyi function applies f to the elements of the region reg and supplies both the element and the element's coordinates in the base array to the function f. If reg is not valid, then the exception Subscript is raised. The function modify applies f to the whole array and does not supply the element's coordinates to f. Thus, the expression modify tr f arr is equivalent to:

	let
	  val range = {base=arr,row=0,col=0,nrows=NONE,ncols=NONE}
	in
	  modifyi tr (f o #3)
	end

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Signature ARRAY2 (basis)

Signature `ARRAY2` `(basis)`