Editing Array slicing (section)

==Timeline of slicing in various programming languages==

===1964: [[PL/I]]===
PL/I provides two facilities for array slicing.
* Using ''iSub DEFINING'', an array slice can be declared using ''iSUB'' variables to map specific elements in a "base array" onto elements of the "defined array". iSUBs can define rows, columns, diagonals, or many-to-one mappings.<ref name=PLI>{{cite book |last1=IBM Corporation |title=PL/I for MVS & VM Language Reference |date=1995}}</ref>{{rp|pp.212–213}} The following example defines <code>Y</code> as a one-dimensional slice consisting of the diagonal elements of the two-dimensional array <code>X</code>. 
 DECLARE X(5,5);
 DECLARE Y(5) DEFINED(X(1SUB,1SUB));

A reference to <code>Y(2)</code> is a reference to <code>X(2,2)</code>, and so on.
* A slice, called a ''cross-section'', of an array can be referred to by using asterisk as the subscript for one or more dimensions. The following code sets all the elements in the first column of <code>X</code> to zero. One or more subscripts can be specified by asterisks in an expression.<ref name=PLI />{{rp|p.43}} 
 DECLARE X(5,5);
 X(*,1)=0;

===1966: [[Fortran#FORTRAN 66|Fortran 66]]===
The Fortran 66 programmers were only able to take advantage of slicing matrices by row, and then only when passing that row to a [[subroutine]]:
<syntaxhighlight lang="fortranfixed">
      SUBROUTINE PRINT V(VEC, LEN)
        REAL VEC(*)
        PRINT *, (VEC(I), I = 1, LEN)
      END

      PROGRAM MAIN
        PARAMETER(LEN = 3)
        REAL MATRIX(LEN, LEN)
        DATA MATRIX/1, 1, 1, 2, 4, 8, 3, 9, 27/
        CALL PRINT V(MATRIX(1, 2), LEN)
      END
</syntaxhighlight>
<!-- BTW: I suspect that PARAMETER and PRINT *, were not part of F66 too. -->

Result:
<syntaxhighlight lang="output">
   2.000000       4.000000       8.000000
</syntaxhighlight>
Note that there is no [[dope vector]] in FORTRAN 66 hence the length of the slice must also be passed as an argument - or some other means - to the <code>SUBROUTINE</code>. 1970s [[Pascal (programming language)|Pascal]] and [[C (programming language)|C]] had similar restrictions.

===1968: [[Algol 68]]===
Algol68 final report contains an early example of slicing, slices are specified in the form:

 [lower bound:upper bound] ''¢ for computers with extended character sets ¢''
or:
 (LOWER BOUND..UPPER BOUND) ''# FOR COMPUTERS WITH ONLY 6 BIT CHARACTERS. #''
Both bounds are inclusive and can be omitted, in which case they default to the declared array bounds. Neither the stride facility, nor diagonal slice aliases are part of the revised report.

Examples:

 [3, 3]real a := ((1, 1, 1), (2, 4, 8), (3, 9, 27)); ''# declaration of a variable matrix #''
 [,]  real c = ((1, 1, 1), (2, 4, 8), (3, 9, 27));   ''# constant matrix, the size is implied #''

 ref[]real row := a[2,];                    ''# alias/<u>ref</u> to a row slice #''
 ref[]real col2 = a[, 2];                   ''# permanent alias/<u>ref</u> to second column #''

 print ((a[:, 2], newline));                ''# second column slice #''
 print ((a[1⌈a, :], newline));              ''# last row slice #''
 print ((a[:, 2⌈a], newline));              ''# last column slice #''
 print ((a[:2, :2], newline));              ''# leading 2-by-2 submatrix "slice" #''

 +1.0000<sub>10</sub>+0 +4.0000<sub>10</sub>+0 +9.0000<sub>10</sub>+0
 +3.0000<sub>10</sub>+0 +9.0000<sub>10</sub>+0 +2.7000<sub>10</sub>+1
 +1.0000<sub>10</sub>+0 +8.0000<sub>10</sub>+0 +2.7000<sub>10</sub>+1
 +1.0000<sub>10</sub>+0 +1.0000<sub>10</sub>+0 +2.0000<sub>10</sub>+0 +4.0000<sub>10</sub>+0

===1968: [[BASIC programming language|BASIC]]===
HP's [[HP 2000]] systems, introduced in November 1968, used [[HP Time-Shared BASIC]] as their primary interface and programming language. This version of BASIC used slicing for most string manipulation operations. One oddity of the language was that it allowed round or square braces interchangeably, and which was used in practice was typically a function of the [[computer terminal]] being used.

Example:

<syntaxhighlight lang="basic">
10 A$="HELLO, WORLD"
20 PRINT A$(1,5)
30 PRINT A$[7,11]
</syntaxhighlight>

Will produce:
<syntaxhighlight lang="output">
HELLO
WORLD
</syntaxhighlight>
The HP systems were widely used in the early 1970s, especially in technical [[high school]]s and many small industrial and scientific settings.<ref>{{Cite magazine |url=http://hpmemoryproject.org/news/tenyears_comp/measure_page_00.htm |title= Passing the 10-year mark |magazine= MEASURE Magazine |date= October 1976 |publisher= Hewlett Packard}}</ref> As the first [[microcomputer]]s emerged in the mid-1970s, HP was often used as the pattern for their BASIC dialects as well. Notable examples include 1977's [[Integer BASIC|Apple BASIC]], 1978's [[Atari BASIC]], and 1979's [[Sinclair BASIC]]. This style of manipulation generally offers advantages in terms of memory use, and was often chosen on systems that shipped with small amounts of memory. Only Sinclair's dialect differed in any meaningful way, using the {{code|TO}} keyword instead of a comma-separated list:

<syntaxhighlight lang="basic">
10 LET a$="ABCDE"(2 to 4)
20 PRINT a$
</syntaxhighlight>

Slicing was also selected as the basis for the [[ANSI]] [[Full BASIC]] standard, using the colon as the separator and thus differentiating between slicing and array access:

<syntaxhighlight lang="basic">
10 DIM A$(5)
20 LET A$(2)="HELLO, WORLD"
30 PRINT A$(2)(1:5)
</syntaxhighlight>

While this style of access offered a number of advantages, especially for the small machines of the era, sometime after 1970 [[Digital Equipment Corporation]] introduced their own variation of BASIC that used the {{code|LEFT$}}, {{code|RIGHT$}} and {{code|MID$}} string functions. [[Microsoft BASIC]] was written on the [[PDP-10]] and its BASIC was used as the pattern. Through the late 1970s the two styles were both widely used, but by the early 1980s the DEC-style functions were the ''de facto'' standard.

===1970s: [[MATLAB]] ===
<syntaxhighlight lang="matlabsession">
>> A = round(rand(3, 4, 5)*10) % 3x4x5 three-dimensional or cubic array
>> A(:, :, 3) % 3x4 two-dimensional array along first and second dimensions

ans =

  8  3  5  7
  8  9  1  4
  4  4  2  5

>> A(:, 2:3, 3) % 3x2 two-dimensional array along first and second dimensions

ans =

  3 5
  9 1
  4 2

>> A(2:end, :, 3) % 2x4 two-dimensional array using the 'end' keyword; works with GNU Octave 3.2.4

ans =

   6    1    4    6
  10    1    3    1

>> A(1, :, 3) % single-dimension array along second dimension

ans =

  8  3  5  7

>> A(1, 2, 3) % single value
ans = 3
</syntaxhighlight>

The <code>:</code> operator implements the stride syntax (<code>lower_bound:upper_bound[:stride]</code>) by generating a vector. <code>1:5</code> evaluates as <code>[1, 2, 3, 4, 5]</code>. <code>1:9:2</code> evaluates as <code>[1, 3, 5, 7, 9]</code>. A bare <code>:</code> evaluates the same as <code>1:end</code>, with <code>end</code> determined by context.

===1976<!--197?-->: [[S programming language|S]]/[[R programming language|R]]===
Arrays in [[S programming language|S]] and [[R programming language|GNU R]] are always one-based, thus the indices of a new slice will begin with ''one'' for each dimension, regardless of the previous indices. Dimensions with length of ''one'' will be dropped (unless drop = FALSE). Dimension names (where present) will be preserved.
<syntaxhighlight lang="rout">
> A <- array(1:60, dim = c(3, 4, 5)) # 3x4x5 three-dimensional or cubic array
> A[, , 3] # 3x4 two-dimensional array along first and second dimensions
     [, 1] [, 2] [, 3] [, 4]
[1,]   25   28   31   34
[2,]   26   29   32   35
[3,]   27   30   33   36
> A[, 2:3, 3, drop = FALSE] # 3x2x1 cubic array subset (preserved dimensions)
, , 1

     [, 1] [, 2]
[1,]   28   31
[2,]   29   32
[3,]   30   33
> A[, 2, 3]  # single-dimension array along first dimension
[1] 28 29 30
> A[1, 2, 3] # single value
[1] 28
</syntaxhighlight>

===1977: [[Fortran#FORTRAN 77|Fortran 77]]===
The Fortran 77 standard introduced the ability to slice and [[concatenation|concatenate]] strings:

<syntaxhighlight lang="fortran">
PROGRAM MAIN
  PRINT *, 'ABCDE'(2:4)
END
</syntaxhighlight>

Produces:
<syntaxhighlight lang="output">
BCD
</syntaxhighlight>
Such strings could be passed by <u>reference</u> to another subroutine, the length would also be passed transparently to the subroutine as a kind of '''short''' dope vector.

<syntaxhighlight lang="fortran">
SUBROUTINE PRINT S(STR)
  CHARACTER *(*)STR
  PRINT *, STR
END

PROGRAM MAIN
  CALL PRINT S('ABCDE'(2:4))
END
</syntaxhighlight>

Again produces:
<syntaxhighlight lang="output">
BCD
</syntaxhighlight>

===1983: [[Ada (programming language)|Ada 83]] and above===
{{Wikibooks|Ada Programming|Types/array}}
Ada 83 supports slices for all array types. Like [[Fortran#FORTRAN 77|Fortran 77]] such arrays could be passed by <u>reference</u> to another subroutine, the length would also be passed transparently to the subroutine as a kind of '''short''' dope vector.

<syntaxhighlight lang="ada">
with Text_IO;
 
procedure Main is
   Text : String := "ABCDE";
begin
   Text_IO.Put_Line (Text (2 .. 4));
end Main;
</syntaxhighlight>

Produces:
<syntaxhighlight lang="output">
BCD
</syntaxhighlight>

'''Note:''' Since in Ada indices are n-based the term <code>Text (2 .. 4)</code> will result in an Array with the base index of 2.

The definition for <code>Text_IO.Put_Line</code> is:

<syntaxhighlight lang="ada">
package Ada.Text_IO is
   
   procedure Put_Line(Item : in  String);
</syntaxhighlight>

The definition for <code>String</code> is:

<syntaxhighlight lang="ada">
package Standard is

   subtype Positive is Integer range 1 .. Integer'Last;

   type String is array(Positive range <>) of Character;
   pragma Pack(String);
</syntaxhighlight>

As Ada supports true negative indices as in {{code|type History_Data_Array is array (-6000 .. 2010) of History_Data;|ada}} it places no special meaning on negative indices. In the example above the term <code> Some_History_Data (-30 .. 30)</code> would slice the <code>History_Data</code> from 31 [[Before Christ|BC]] to 30 [[Anno Domini|AD]] (since there was no year zero, the year number 0 actually refers to 1 [[Before Christ|BC]]).

===1987: [[Perl]]===
If we have
<syntaxhighlight lang="perl">@a = (2, 5, 7, 3, 8, 6, 4);</syntaxhighlight>
as above, then the first 3 elements, middle 3 elements and last 3 elements would be:

<syntaxhighlight lang="perl">
@a[0..2];   # (2, 5, 7)
@a[2..4];   # (7, 3, 8)
@a[-3..-1]; # (8, 6, 4)
</syntaxhighlight>

Perl supports negative list indices. The -1 index is the last element, -2 the penultimate element, etc.
In addition, Perl supports slicing based on expressions, for example:

<syntaxhighlight lang="perl">
@a[ 3.. $#a ];   # 4th element until the end (3, 8, 6, 4)
@a[ grep { !($_ % 3) } (0...$#a) ];    # 1st, 4th and 7th element (2,3,4)
@a[ grep { !(($_+1) % 3) } (0..$#a) ]; # every 3rd element (7,6)
</syntaxhighlight>

===1991: [[Python (programming language)|Python]]===
If you have the following list:

<syntaxhighlight lang="pycon">
>>> nums = [1, 3, 5, 7, 8, 13, 20]
</syntaxhighlight>

Then it is possible to slice by using a notation similar to element retrieval:

<syntaxhighlight lang="pycon">
>>> nums[3]   # no slicing
7
>>> nums[:3]  # from index 0 (inclusive) until index 3 (exclusive)
[1, 3, 5]
>>> nums[1:5]
[3, 5, 7, 8]
>>> nums[-3:]
[8, 13, 20]
</syntaxhighlight>
Note that Python allows negative list indices. The index -1 represents the last element, -2 the penultimate element, etc.
Python also allows a step property by appending an extra colon and a value. For example:
<syntaxhighlight lang="pycon">
>>> nums[3:]
[7, 8, 13, 20]
>>> nums[3::] # == nums[3:]
[7, 8, 13, 20]
>>> nums[::3] # starting at index 0 and getting every third element
[1, 7, 20]
>>> nums[1:5:2] # from index 1 until index 5 and getting every second element
[3, 7]
</syntaxhighlight>

The stride syntax (<code>nums[1:5:2]</code>) was introduced in the second half of the 1990s, as a result of requests put forward by scientific users in the Python "matrix-SIG" (special interest group).<ref name="millman">{{cite journal |first1=K. Jarrod |last1=Millman |first2=Michael |last2=Aivazis |title=Python for Scientists and Engineers |journal=Computing in Science and Engineering |volume=13 |number=2 |pages=9–12 |year=2011 |doi=10.1109/MCSE.2011.36 |bibcode=2011CSE....13b...9M |url=http://www.computer.org/csdl/mags/cs/2011/02/mcs2011020009.html}}</ref>

Slice semantics potentially differ per object; new semantics can be introduced when [[operator overloading]] the indexing operator. With Python standard lists (which are [[dynamic array]]s), every slice is a copy. Slices of [[NumPy]] arrays, by contrast, are views onto the same underlying buffer.

===1992: [[Fortran#Fortran_90|Fortran 90]] and above===
In Fortran 90, slices are specified in the form

<syntaxhighlight lang="fortran">
lower_bound:upper_bound[:stride]
</syntaxhighlight>

Both bounds are inclusive and can be omitted, in which case they default to the declared
array bounds. Stride defaults to 1. Example:

<syntaxhighlight lang="fortran">
real, dimension(m, n):: a  ! declaration of a matrix
  
print *, a(:, 2) ! second column
print *, a(m, :) ! last row
print *, a(:10, :10) ! leading 10-by-10 submatrix
</syntaxhighlight>

===1994: [[Analytica (software)|Analytica]]===
Each dimension of an array value in Analytica is identified by an Index variable. When slicing or subscripting, the syntax identifies the dimension(s) over which you are slicing or subscripting by naming the dimension. Such as:

<syntaxhighlight lang="pascal">
Index I := 1..5   { Definition of a numerical Index }
Index J := ['A', 'B', 'C'] { Definition of a text-valued Index }
Variable X := Array(I, J, [[10, 20, 30], [1, 2, 3], ....]) { Definition of a 2D value }
X[I = 1, J = 'B']  -> 20  { Subscript to obtain a single value }
X[I = 1] ->  Array(J, [10, 20, 30])  { Slice out a 1D array. }
X[J = 2] -> Array(I, [20, 2, ....]) { Slice out a 1D array over the other dimension. }
X[I = 1..3]  {Slice out first four elements over I with all elements over J}
</syntaxhighlight>

Naming indexes in slicing and subscripting is similar to naming parameters in function calls instead of relying on a fixed sequence of parameters. One advantage of naming indexes in slicing is that the programmer does not have to remember the sequence of Indexes, in a multidimensional array. A deeper advantage is that expressions generalize automatically and safely without requiring a rewrite when the number of dimensions of X changes.

===1998: [[S-Lang]]===
Array slicing was introduced in version 1.0. Earlier versions did not
support this feature.

Suppose that A is a 1-d array such as
<pre>
    A = [1:50];           % A = [1, 2, 3, ...49, 50]
</pre>
Then an array B of first 5 elements of A may be created using
<pre>
    B = A[[:4]];
</pre>
Similarly, B may be assigned to an array of the last 5 elements of A via:
<pre>
    B = A[[-5:]];
</pre>
Other examples of 1-d slicing include:
<pre>
    A[-1]                 % The last element of A
    A[*]                  % All elements of A
    A[[::2]]              % All even elements of A
    A[[1::2]]             % All odd elements of A
    A[[-1::-2]]           % All even elements in the reversed order
    A[[[0:3], [10:14]]]   % Elements 0-3 and 10-14
</pre>

Slicing of higher-dimensional arrays works similarly:
<pre>
    A[-1, *]              % The last row of A
    A[[1:5], [2:7]]       % 2d array using rows 1-5 and columns 2-7
    A[[5:1:-1], [2:7]]    % Same as above except the rows are reversed
</pre>

Array indices can also be arrays of integers. For example, suppose
that <code>I = [0:9]</code> is an array of 10 integers. Then
<code>A[I]</code> is equivalent to an array of the first 10 elements
of <code>A</code>. A practical example of this is a sorting
operation such as:
<pre>
    I = array_sort(A);    % Obtain a list of sort indices
    B = A[I];             % B is the sorted version of A
    C = A[array_sort(A)]; % Same as above but more concise.
</pre>

===1999: [[D programming language|D]]===
Consider the array:

<syntaxhighlight lang="d">
int[] a = [2, 5, 7, 3, 8, 6, 4, 1];
</syntaxhighlight>

Take a slice out of it:

<syntaxhighlight lang="d">
int[] b = a[2 .. 5];
</syntaxhighlight>

and the contents of <code>b</code> will be <code>[7, 3, 8]</code>. The first index of the slice is inclusive, the second is exclusive.

<syntaxhighlight lang="d">
auto c = a[$ - 4 .. $ - 2];
</syntaxhighlight>

means that the dynamic array <code>c</code> now contains <code>[8, 6]</code> because inside the [] the <code>$</code> symbol refers to the length of the array.

D array slices are aliased to the original array, so:

<syntaxhighlight lang="d">
b[2] = 10;
</syntaxhighlight>

means that <code>a</code> now has the contents <code>[2, 5, 7, 3, 10, 6, 4, 1]</code>. To create a copy of the array data, instead of only an alias, do:

<syntaxhighlight lang="d">
auto b = a[2 .. 5].dup;
</syntaxhighlight>

Unlike Python, D slice bounds don't saturate, so code equivalent to this Python code is an error in D:

<syntaxhighlight lang="pycon">
>>> d = [10, 20, 30]
>>> d[1 : 5]
[20, 30]
</syntaxhighlight>

===2004: [[SuperCollider]]===
The programming language [[SuperCollider]] implements some concepts from [[J (programming language)|J]]/[[APL (programming language)|APL]]. Slicing looks as follows:

<syntaxhighlight lang="sc">
a = [3, 1, 5, 7]           // assign an array to the variable a
a[0..1]                    // return the first two elements of a
a[..1]                     // return the first two elements of a: the zero can be omitted
a[2..]                     // return the element 3 till last one
a[[0, 3]]                  // return the first and the fourth element of a

a[[0, 3]] = [100, 200]     // replace the first and the fourth element of a
a[2..] = [100, 200]        // replace the two last elements of a

// assign a multidimensional array to the variable a
a = [[0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]]; 
a.slice(2, 3);             // take a slice with coordinates 2 and 3 (returns 13)
a.slice(nil, 3);           // take an orthogonal slice (returns [3, 8, 13, 18])
</syntaxhighlight>

===2005: [[Friendly interactive shell|fish]]===
Arrays in [[Friendly interactive shell|fish]] are always one-based, thus the indices of a new slice will begin with ''one'', regardless of the previous indices.
<syntaxhighlight lang="fishshell">
> set A (seq 3 2 11)       # $A is an array with the values 3, 5, 7, 9, 11
 
> echo $A[(seq 2)]         # Print the first two elements of $A 
3 5
 
> set B $A[1 2]            # $B contains the first and second element of $A, i.e. 3, 5
 
> set -e A[$B]; echo $A    # Erase the third and fifth elements of $A, print $A
3 5 9
</syntaxhighlight>

===2006: [[Cobra (programming language)|Cobra]]===
Cobra supports Python-style slicing. If you have a list

<syntaxhighlight lang="python">
nums = [1, 3, 5, 7, 8, 13, 20]
</syntaxhighlight>

then the first 3 elements, middle 3 elements, and last 3 elements would be:

<syntaxhighlight lang="python">
nums[:3]   # equals [1, 3, 5]
nums[2:5]  # equals [5, 7, 8]
nums[-3:]  # equals [8, 13, 20]
</syntaxhighlight>

Cobra also supports slicing-style syntax for 'numeric for loops':
<syntaxhighlight lang="python">
for i in 2 : 5
    print i
# prints 2, 3, 4

for j in 3
    print j
# prints 0, 1, 2
</syntaxhighlight>

===2006: [[Windows PowerShell]]===
Arrays are zero-based in PowerShell and can be defined using the comma operator:
<!-- lang="ps1con" after pygment 2.1 upgrade -->
<syntaxhighlight lang="ps1con">
PS> $a = 2, 5, 7, 3, 8, 6, 4, 1
PS> # Print the first two elements of $a:
PS> Write-Host -NoNewline $a[0, 1]
2 5
PS> # Take a slice out of it using the range operator:
PS> Write-Host -NoNewline $a[2..5]
7 3 8 6
PS> # Get the last 3 elements:
PS> Write-Host -NoNewline $a[-3..-1]
6 4 1
PS> # Return the content of the array in reverse order:
PS> Write-Host -NoNewline $a[($a.Length - 1)..0] # Length is a property of System.Object[]
1 4 6 8 3 7 5 2
</syntaxhighlight>

===2009: [[Go (programming language)|Go]]===
Go supports Python-style syntax for slicing (except negative indices are not supported). Arrays and slices can be sliced. If you have a slice

<syntaxhighlight lang="go">
nums := []int{1, 3, 5, 7, 8, 13, 20}
</syntaxhighlight>

then the first 3 elements, middle 3 elements, last 3 elements, and a copy of the entire slice would be:

<syntaxhighlight lang="go">
nums[:3]  // equals []int{1, 3, 5}
nums[2:5] // equals []int{5, 7, 8}
nums[4:]  // equals []int{8, 13, 20}
nums[:]   // equals []int{1, 3, 5, 7, 8, 13, 20}
</syntaxhighlight>

Slices in Go are reference types, which means that different slices may refer to the same underlying array.

===2010: [[Cilk Plus]]===
Cilk Plus supports syntax for array slicing as an extension to C and C++.

<syntaxhighlight lang="c">
array_base [lower_bound:length[:stride]]*
</syntaxhighlight>
Cilk Plus slicing looks as follows:
<syntaxhighlight lang="c">
A[:]     // All of vector A
B[2:6]   // Elements 2 to 7 of vector B
C[:][5]  // Column 5 of matrix C
D[0:3:2] // Elements 0, 2, 4 of vector D
</syntaxhighlight>

Cilk Plus's array slicing differs from Fortran's in two ways:

* the second parameter is the length (number of elements in the slice) instead of the upper bound, in order to be consistent with standard C libraries;
* slicing never produces a temporary, and thus never needs to allocate memory. Assignments are required to be either non-overlapping or perfectly overlapping, otherwise the result is undefined.

===2012: [[Julia_(programming language)|Julia]]===
[https://docs.julialang.org/en/v1/manual/arrays/ Julia array slicing] is like that of [[MATLAB]], but uses square brackets.  Example:

<syntaxhighlight lang="jlcon">
julia> x = rand(4, 3)
4x3 Array{Float64,2}:
 0.323877  0.186253  0.600605
 0.404664  0.894781  0.0955007
 0.223562  0.18859   0.120011
 0.149316  0.779823  0.0690126

julia> x[:, 2]                # get the second column.
4-element Array{Float64,1}:
 0.186253
 0.894781
 0.18859
 0.779823

julia> x[1, :]                # get the first row.
1x3 Array{Float64,2}:
 0.323877  0.186253  0.600605

julia> x[1:2,2:3]             # get the submatrix spanning rows 1,2 and columns 2,3
2x2 Array{Float64,2}:
 0.186253  0.600605
 0.894781  0.0955007
</syntaxhighlight>