Forward difference: Difference between revisions
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{{trans|Python}}
<
F difn(s, n) -> [Int]
R I n != 0 {difn(dif(s), n - 1)} E s
Line 57:
L(i) 10
print(difn(s, i))</
{{out}}
Line 74:
=={{header|Ada}}==
<
with Ada.Float_Text_Io; use Ada.Float_Text_Io;
with Ada.containers.Vectors;
Line 123:
Print(Diff(A, 10));
print(Diff(A, 0));
end Forward_Difference;</
{{out}}
<pre>
Line 138:
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}}
{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of FORMATted transput}}
<
MODE LISTREAL = [1:0]REAL;
Line 158:
printf((list fmt,s,$";"l$))
OD
)</
{{out}}
<pre>
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=={{header|ALGOL W}}==
<
% calculate forward differences %
Line 204:
for i := 1 until length do v( i ) := diff( i )
end for_order
end.</
{{out}}
<pre>
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{{works with|Dyalog APL}}{{trans|J}}
<
fd ← {⍺=0:⍵⋄(⍺-1)∇(1↓⍵)-(¯1↓⍵)}
Line 229:
2 fd list
54 ¯40 22 17 13 ¯73 100 ¯32</
=={{header|AppleScript}}==
{{Trans|JavaScript}}
<
on forwardDifference(xs)
zipWith(my subtract, xs, rest of xs)
Line 453:
return lst
end tell
end zipWith</
{{Out}}
<pre>0 -> [90, 47, 58, 29, 22, 32, 55, 5, 55, 73]
Line 465:
8 -> [1017, -1904]
9 -> [-2921]</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">; element-wise subtraction of two blocks. e.g.
; vsub [1 2 3] [1 2 3] ; [0 0 0]
vsub: function [u v][
map couple u v 'pair -> pair\0 - pair\1
]
differences: function [block][
order: attr "order"
if order = null -> order: 1
loop 1..order 'n -> block: vsub block drop block
return block
]
print differences .order: 4 [90.5 47 58 29 22 32 55 5 55 73.5]
print differences [1 2 3 4 5 6 7]</syntaxhighlight>
{{out}}
<pre>156.5 -67 1 -82 259 -304.5
-1 -1 -1 -1 -1 -1</pre>
=={{header|AutoHotkey}}==
contributed by Laszlo on the ahk [http://www.autohotkey.com/forum/post-276470.html#276470 forum]
<
MsgBox % diff("2,3,4,3",2)
MsgBox % diff("2,3,4,3",3)
Line 484 ⟶ 507:
}
Return list
}</
=={{header|AWK}}==
<
BEGIN {
if (p<1) {p = 1};
Line 507 ⟶ 530:
{
print diff($0, p);
}</
Using Pascal's triangle:
<
BEGIN {
if (p<1) {p = 1};
Line 537 ⟶ 560:
{
print diff($0, p);
}</
{{out}}
Line 561 ⟶ 584:
=={{header|BBC BASIC}}==
{{works with|BBC BASIC for Windows}}
<
A() = 90.0, 47.0, 58.0, 29.0, 22.0, 32.0, 55.0, 5.0, 55.0, 73.0
PRINT "Original array: " FNshowarray(A())
Line 590 ⟶ 613:
a$ += STR$(a(i%)) + ", "
NEXT
= LEFT$(LEFT$(a$))</
{{out}}
<pre>
Line 598 ⟶ 621:
Forward diff 9: -2921
</pre>
=={{header|BQN}}==
Left argument is the order, right argument is the array.
<syntaxhighlight lang="bqn">FDiff ← {{-˜´˘2↕𝕩}⍟𝕨 𝕩}
•Show 1 FDiff 90‿47‿58‿29‿22‿32‿55‿5‿55‿73
•Show 2 FDiff 90‿47‿58‿29‿22‿32‿55‿5‿55‿73</syntaxhighlight>
=={{header|C}}==
<
#include <string.h>
#include <stdio.h>
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return 0;
}</
Use method with Pascal triangle, binomial coefficients are pre-computed
<
int* binomCoeff(int n) {
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printf("\n");
}
</syntaxhighlight>
=={{header|C sharp|C#}}==
<
using System.Collections.Generic;
using System.Linq;
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} while ((sequence = ForwardDifference(sequence)).Any());
}
}</
{{out}}
<pre>90, 47, 58, 29, 22, 32, 55, 5, 55, 73
Line 724 ⟶ 757:
which is then called several times for calculating n-th order forward difference.
No error checking is implemented.
<
#include <iterator>
#include <algorithm>
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return 0;
}</
{{out}}
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===Using Standard Template Library===
<
#include <iostream>
#include <numeric>
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return 0;
}
</syntaxhighlight>
{{out}}
<pre>
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Usually one will not want the intermediate results,
in which case the following is sufficient:
<
#include <iostream>
#include <numeric>
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return 0;
}
</syntaxhighlight>
{{out}}
<pre>
Line 901 ⟶ 934:
===Using Pascal's Triangle===
<
#include <iostream>
#include <algorithm>
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return 0;
}
</syntaxhighlight>
{{out}}
<pre>
Line 923 ⟶ 956:
=={{header|Clojure}}==
<
(nth (iterate #(map - (next %) %) nums) order))</
=={{header|CoffeeScript}}==
<
forward_difference = (arr, n) ->
# Find the n-th order forward difference for arr using
Line 939 ⟶ 972:
for n in [0..arr.length]
console.log n, forward_difference arr, n
</syntaxhighlight>
{{out}}
<pre>> coffee forward_difference.coffee
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=={{header|Common Lisp}}==
<
(mapcar #'- (rest list) list))
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(setf list (copy-list list))
(loop repeat n do (map-into list #'- (rest list) list))
(subseq list 0 (- (length list) n)))</
=={{header|D}}==
===Basic Version===
<
in {
assert(level >= 0 && level < data.length);
Line 982 ⟶ 1,015:
foreach (immutable level; 0 .. data.length)
forwardDifference(data, level).writeln;
}</
{{out}}
<pre>[90.5, 47, 58, 29, 22, 32, 55, 5, 55, 73.5]
Line 997 ⟶ 1,030:
===Alternative Version===
Same output.
<
auto forwardDifference(Range)(Range d, in int level) pure {
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foreach (immutable level; 0 .. data.length)
forwardDifference(data, level).writeln;
}</
===Using Vector Operations===
forwardDifference mutates the array in-place (same output):
<
T[] forwardDifference(T)(T[] s, in int n) pure nothrow @nogc {
Line 1,024 ⟶ 1,057:
foreach (immutable level; 0 .. A.length)
forwardDifference(A.dup, level).writeln;
}</
===Short Functional Version===
Same output:
<
import std.stdio, std.range;
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a[n - 1][0 .. $ - 1])[0 .. $] }(D)
.take(D.length));
}</
=={{header|Dart}}==
<
for (int i = _list.length - 1; i > 0; i--) {
_list[i] = _list[i] - _list[i - 1];
Line 1,056 ⟶ 1,089:
print(_list);
}
}</
{{out}}
Line 1,072 ⟶ 1,105:
flutter: []
</pre>
=={{header|Delphi}}==
See [https://rosettacode.org/wiki/Forward_difference#Pascal Pascal].
=={{header|E}}==
<
/** Single step. */
def forwardDifference(seq :List) {
Line 1,106 ⟶ 1,141:
> require(r1 == nthForwardDifference2(sampleData, n))
> println(r1)
> }</
=={{header|EchoLisp}}==
Using the built-in function '''iterate''' which, given a function f and n, returns the function f°f°f....°f .
<
(define (Δ-1 list)
(for/list ([x (cdr list)] [y list]) (- x y)))
Line 1,118 ⟶ 1,153:
((Δ-n 9) '(90 47 58 29 22 32 55 5 55 73))
→ (-2921)
</syntaxhighlight>
=={{header|Elixir}}==
<
def forward(list,i\\1) do
forward(list,[],i)
Line 1,135 ⟶ 1,170:
Enum.each(1..9, fn i ->
Diff.forward([90, 47, 58, 29, 22, 32, 55, 5, 55, 73],i)
end)</
{{out}}
Line 1,151 ⟶ 1,186:
=={{header|Erlang}}==
<
-export([difference/1, difference/2]).
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io:format("Initial: ~p~n",[?TEST_DATA]),
[io:format("~3b: ~p~n",[N,difference(?TEST_DATA,N)]) || N <- lists:seq(0,length(?TEST_DATA))],
ok.</
{{out}}
<pre>80> forward_difference:task().
Line 1,188 ⟶ 1,223:
=={{header|F_Sharp|F#}}==
Straightforward recursive solution
<
match n with
| _ when input = [] || n < 0 -> [] // If there's no more input, just return an empty list
Line 1,196 ⟶ 1,231:
|> Seq.zip input // tupled with itself
|> Seq.map (fun (a, b) -> b-a) // Subtract the i'th element from the (i+1)'th
|> Seq.toList) (n-1) // Make into a list and do an n-1 difference on it</
=={{header|Factor}}==
<
IN: rosetacode
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dup 0 <=
[ drop ] [ [ 1-order ] times ] if ;
</syntaxhighlight>
( scratchpad ) { 90.5 47 58 29 22 32 55 5 55 73.5 } 4 n-order .
{ 156.5 -67 1 -82 259 -304.5 }
=={{header|Forth}}==
<
dup 0
?do
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: test a 10 9 forward-difference bounds ?do i ? loop ;
test</
=={{header|Fortran}}==
{{works with|Fortran|90 and later}}
<
IMPLICIT NONE
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WRITE (*,*) b(1:arraysize-n)
END SUBROUTINE Fdiff
END MODULE DIFFERENCE</
<
USE DIFFERENCE
Line 1,264 ⟶ 1,299:
END DO
END PROGRAM TEST</
{{out}}
<pre>
Line 1,277 ⟶ 1,312:
-2921
</pre>
=={{Header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">function forward_difference( a() as uinteger ) as uinteger ptr
dim as uinteger ptr b = allocate( sizeof(uinteger) * (ubound(a)-1) )
for i as uinteger = 0 to ubound(a)-1
*(b+i) = a(i+1)-a(i)
next i
return b
end function
dim as uinteger a(0 to 15) = {2, 3, 5, 7, 11, 13, 17, 19,_
23, 29, 31, 37, 41, 43, 47, 53}
dim as uinteger i
dim as uinteger ptr b = forward_difference( a() )
for i = 0 to ubound(a)-1
print *(b+i)
next i
</syntaxhighlight>
=={{header|Go}}==
<
import "fmt"
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}
return a[:len(a)-ord]
}</
{{out}}
<pre>
Line 1,305 ⟶ 1,360:
=={{header|Haskell}}==
<
forwardDifference = tail >>= zipWith (-)
Line 1,314 ⟶ 1,369:
main =
mapM_ print $
take 10 (iterate forwardDifference [90, 47, 58, 29, 22, 32, 55, 5, 55, 73])</
{{Out}}
<pre>[90,47,58,29,22,32,55,5,55,73]
Line 1,328 ⟶ 1,383:
=={{header|HicEst}}==
<
list = ( 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 )
Line 1,339 ⟶ 1,394:
ENDDO
END</
{{out}}
<pre>0 90 47 58 29 22 32 55 5 55 73
Line 1,353 ⟶ 1,408:
=={{header|Icon}} and {{header|Unicon}}==
<
every order := 1 to (*A-1) do showList(order, fdiff(A, order))
end
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every writes(!L," ")
write()
end</
{{out|A sample run}}
Line 1,389 ⟶ 1,444:
Standard IDL library function <tt>TS_diff(X,k,[/double])</tt>:
<
15.1473 58.0953 82.7465 16.8637 97.7182 59.7856 17.7699 74.9154
print,ts_diff(x,1)
Line 1,396 ⟶ 1,451:
-18.2967 -90.5341 146.737 -118.787 -4.08316 99.1613 0.000000 0.000000
print,ts_diff(x,3)
72.2374 -237.271 265.524 -114.704 -103.244 0.000000 0.000000 0.000000</
=={{header|J}}==
Of the many ways to code this in J, a particularly concise solution is:
<
Alternatively, to reduce the number of J primitives, use:
<
(which is also elegant, because the open-ended power conjunction reads like "to the power of anything").
For example:
<
1 fd list
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2 fd list
54 _40 22 17 13 _73 100 _32</
J is array oriented, so you can even ask for more than one forward difference at a time (i.e. <tt>N</tt> can be a list, instead of a single number):
<
43 _11 29 7 _10 _23 50 _50 _18
54 _40 22 17 13 _73 100 _32 0
Line 1,433 ⟶ 1,488:
1017 _1904 0 0 0 0 0 0 0 0
2921 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0</
=={{header|Java}}==
{{works with|Java|1.5+}}
<
public class FD {
public static void main(String args[]) {
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return a;
}
}</
{{out}}
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===ES6===
<
'use strict';
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// MAIN ---
return main();
})();</
{{Out}}
Line 1,650 ⟶ 1,705:
=={{header|jq}}==
{{works with|jq|1.4}}
<
# a (possibly empty) array of numbers,
# emit an array, even if the input list is too short:
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elif n == 1 then . as $in | [range(1;length) | $in[.] - $in[.-1]]
else ndiff(1) | ndiff(n-1)
end;</
'''Example''':
<
range(0;12) as $i | (s|ndiff($i))</
{{out}}
<
[90,47,58,29,22,32,55,5,55,73]
[-43,11,-29,-7,10,23,-50,50,18]
Line 1,675 ⟶ 1,730:
[-2921]
[]
[]</
=={{header|Julia}}==
Line 1,681 ⟶ 1,736:
Using the built-in <code>diff</code> function, which returns the 1st forward difference:
<
s = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73]
println.(collect(ndiff(s, i) for i in 0:9))</
{{out}}
Line 1,699 ⟶ 1,754:
=={{header|K4}}==
<syntaxhighlight lang
To compute the ''n''th forward difference, call as:
<syntaxhighlight lang
In order to obtain all intermediate results, call as:
<syntaxhighlight lang
{{out|Examples}}
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=={{header|Kotlin}}==
<
fun forwardDifference(ia: IntArray, order: Int): IntArray {
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printArray(fd)
}
}</
{{out}}
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=={{header|Lambdatalk}}==
<
{def fdiff
{lambda {:l}
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[1017,-1904]
[-2921]
</syntaxhighlight>
=={{header|Lasso}}==
<
define forwardDiff(values, order::integer=1) => {
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local(data = (:90, 47, 58, 29, 22, 32, 55, 5, 55, 73))
with x in generateSeries(0, #data->size-1)
do stdoutnl(#x + ': ' + forwardDiff(#data, #x))</
{{out}}
<pre>0: array(90, 47, 58, 29, 22, 32, 55, 5, 55, 73)
Line 1,829 ⟶ 1,884:
=={{header|Logo}}==
<
if empty? :l [output []]
if empty? bf :l [output []]
Line 1,840 ⟶ 1,895:
show nth.fwd.diff 9 [90 47 58 29 22 32 55 5 55 73]
[-2921]</
=={{header|Lua}}==
<
if(b) then return b-a, dif(b, ...) end
end
function dift(t) return {dif(unpack(t))} end
print(unpack(dift{1,3,6,10,15}))</
=={{header|M2000 Interpreter}}==
Function Diff(a()) get an array by value (a shallow copy)
<syntaxhighlight lang="m2000 interpreter">
Form 80, 40
Module Forward_difference {
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Forward_difference
</syntaxhighlight>
{{out}}
<pre style="height:30ex;overflow:scroll">
Line 1,890 ⟶ 1,945:
=={{header|Mathematica}} / {{header|Wolfram Language}}==
Built-in function:
<
Differences[i]</
{{out|gives back}}
<
The n<sup>th</sup> difference can be done as follows:
<
Differences[i,n]</
=={{header|MATLAB}} / {{header|Octave}}==
Line 1,903 ⟶ 1,958:
X is the list of numbers,
n is the order of the forward difference.
<
{{out}} 1st order forward difference.
Line 1,913 ⟶ 1,968:
=={{header|Maxima}}==
<
=={{header|NetRexx}}==
<
* Forward differences
* 18.08.2012 Walter Pachl derived from Rexx
Line 1,949 ⟶ 2,004:
Say n ol
End
End</
Output is the same as for Rexx
=={{header|Nial}}==
Define forward difference for order 1
<
{{out}} forward difference of 4th order
<
4 fold fd b
= 156 -67 1 -82 259 -305</
=={{header|Nim}}==
<
result = newSeq[int](s.len-1)
for i
result[i] =
proc difn(s
if n > 0: difn(dif(s), n-1)
else: s
const s = @[90, 47, 58, 29, 22, 32, 55, 5, 55, 73]
echo difn(s, 0)
echo difn(s, 1)
echo difn(s, 2)</
{{out}}
<pre>@[90, 47, 58, 29, 22, 32, 55, 5, 55, 73]
Line 1,982 ⟶ 2,037:
=={{header|Objeck}}==
{{trans|Java}}
<
bundle Default {
class Test {
Line 2,019 ⟶ 2,074:
}
}
</syntaxhighlight>
=={{header|OCaml}}==
<
a :: (b :: _ as xs) ->
b - a :: forward_difference xs
Line 2,033 ⟶ 2,088:
xs
else
nth_forward_difference (pred n) (forward_difference xs)</
{{out}}
Line 2,043 ⟶ 2,098:
=={{header|Oforth}}==
<
: forwardDiffN(n, l) l #[ forwardDiff dup println ] times(n) ;</
{{out}}
<pre>
Line 2,061 ⟶ 2,116:
=={{header|PARI/GP}}==
<
=={{header|Pascal}}==
<
procedure fowardDifference(list: array of integer);
Line 2,089 ⟶ 2,144:
begin
fowardDifference(a);
end.</
{{out}}
<pre>:> ./ForwardDifference
Line 2,104 ⟶ 2,159:
=={{header|Perl}}==
<
my @s = @_;
map { $s[$_+1] - $s[$_] } 0 .. $#s-1
Line 2,110 ⟶ 2,165:
@a = qw<90 47 58 29 22 32 55 5 55 73>;
while (@a) { printf('%6d', $_) for @a = dif @a; print "\n" }</
{{out}}
<pre> -43 11 -29 -7 10 23 -50 50 18
Line 2,123 ⟶ 2,178:
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">fwd_diff_n</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">order</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">order</span><span style="color: #0000FF;"><</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">order</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">90</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">47</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">58</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">32</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">55</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">55</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">73</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">fwd_diff_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 2,153 ⟶ 2,212:
=={{header|PHP}}==
<
function forwardDiff($anArray, $times = 1) {
Line 2,195 ⟶ 2,254:
}
}</
=={{header|Picat}}==
<syntaxhighlight lang="picat">go =>
L = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73],
foreach(I in 1..L.length-1)
println([d=I,diffi(L,I)])
end,
nl,
% All differences (a sublist to save space)
println(alldiffs(L[1..6])),
nl.
% Difference of the list
diff(L) = Diff =>
Diff = [L[I]-L[I-1] : I in 2..L.length].
% The i'th list difference
diffi(L,D) = Diff =>
Diff1 = L,
foreach(_I in 1..D)
Diff1 := diff(Diff1)
end,
Diff = Diff1.
% all differences
alldiffs(L) = Diffs =>
Diffs1 = [],
Diff = L,
foreach(_I in 1..L.length-1)
Diff := diff(Diff),
Diffs1 := Diffs1 ++ [Diff]
end,
Diffs = Diffs1.</syntaxhighlight>
{{out}}
<pre>[d = 1,[-43,11,-29,-7,10,23,-50,50,18]]
[d = 2,[54,-40,22,17,13,-73,100,-32]]
[d = 3,[-94,62,-5,-4,-86,173,-132]]
[d = 4,[156,-67,1,-82,259,-305]]
[d = 5,[-223,68,-83,341,-564]]
[d = 6,[291,-151,424,-905]]
[d = 7,[-442,575,-1329]]
[d = 8,[1017,-1904]]
[d = 9,[-2921]]
[[-43,11,-29,-7,10],[54,-40,22,17],[-94,62,-5],[156,-67],[-223]]</pre>
=={{header|PicoLisp}}==
<
(mapcar - (cdr Lst) Lst) )
(for (L (90 47 58 29 22 32 55 5 55 73) L (fdiff L))
(println L) )</
{{out}}
<pre>(90 47 58 29 22 32 55 5 55 73)
Line 2,216 ⟶ 2,321:
=={{header|PL/I}}==
<syntaxhighlight lang="pl/i">
/* Forward differences. */ /* 23 April 2010 */
differences: procedure options (main);
Line 2,238 ⟶ 2,343:
end differences;
</syntaxhighlight>
=={{header|Plain English}}==
<syntaxhighlight lang="plainenglish">To add a fraction to some fraction things:
Allocate memory for a fraction thing.
Put the fraction into the fraction thing's fraction.
Append the fraction thing to the fraction things.
To create some fraction things:
Add 90-1/2 to the fraction things.
Add 47/1 to the fraction things.
Add 58/1 to the fraction things.
Add 29/1 to the fraction things.
Add 22/1 to the fraction things.
Add 32/1 to the fraction things.
Add 55/1 to the fraction things.
Add 5/1 to the fraction things.
Add 55/1 to the fraction things.
Add 73-1/2 to the fraction things.
To find the difference of some fraction things:
If the fraction things' count is less than 2, exit.
Get a fraction thing from the fraction things.
Loop.
If the fraction thing's next is nil, remove the fraction thing from the fraction things; destroy the fraction thing; exit.
Put the fraction thing's next's fraction minus the fraction thing's fraction into the fraction thing's fraction.
Put the fraction thing's next into the fraction thing.
Repeat.
To find the difference of some fraction things given an order:
If a counter is past the order, exit.
Find the difference of the fraction things.
Repeat.
A fraction thing is a thing with a fraction.
An order is a number.
To run:
Start up.
Create some fraction things.
Write "Original list:" on the console.
Show the fraction things.
Find the difference of the fraction things given 4.
Write "Order 4 forward difference:" on the console.
Show the fraction things.
Destroy the fraction things.
Wait for the escape key.
Shut down.
To show some fraction things:
Get a fraction thing from the fraction things.
Loop.
If the fraction thing is nil, write "" on the console; exit.
Write "" then the fraction thing's fraction on the console without advancing.
If the fraction thing's next is not nil, write ", " on the console without advancing.
Put the fraction thing's next into the fraction thing.
Repeat.</syntaxhighlight>
{{out}}
<pre>
Original list:
90-1/2, 47, 58, 29, 22, 32, 55, 5, 55, 73-1/2
Order 4 forward difference:
156-1/2, -67, 1, -82, 259, -304-1/2
</pre>
=={{header|Pop11}}==
<
lvars res = [], prev, el;
if l = [] then
Line 2,260 ⟶ 2,429:
endfor;
res;
enddefine;</
=={{header|PowerShell}}==
<math>\Delta^n [f](x)= \sum_{k=0}^n \left ({\prod_{i=1}^k \frac{n-k+i}{i}}\right ) (-1)^{n-k} f(x+k)</math>
<
{
$flen = $f.length
Line 2,285 ⟶ 2,454:
}
Forward-Difference 2 1,2,4,5</
=={{header|PureBasic}}==
<
If ListSize(a()) <= 1
ClearList(a()): ProcedureReturn
Line 2,342 ⟶ 2,511:
EndIf
</syntaxhighlight>
{{out}}
<pre>1 [43,-11,29,7,-10,-23,50,-50,-18]
Line 2,357 ⟶ 2,526:
=={{header|Python}}==
===Python 2===
<
>>> # or, dif = lambda s: [x-y for x,y in zip(s[1:],s)]
>>> difn = lambda s, n: difn(dif(s), n-1) if n else s
Line 2,380 ⟶ 2,549:
[-442, 575, -1329],
[1017, -1904],
[-2921]]</
===Python 3===
Defining functions for first order and nth order forward difference:
{{Works with|Python|3.7}}
<
Line 2,477 ⟶ 2,646:
# MAIN ---
if __name__ == '__main__':
main()</
{{Out}}
<pre>9th order forward difference of:
Line 2,495 ⟶ 2,664:
8 -> [1017, -1904]
9 -> [-2921]</pre>
=={{header|Quackery}}==
<syntaxhighlight lang="quackery"> [ times
[ [] swap behead
swap witheach
[ tuck dip [ - join ] ]
drop ] ] is f-diff ( [ n --> [ )
' [ 90 47 58 29 22 32 55 5 55 73 ]
dup size times
[ dup i^
dup echo say ": "
f-diff echo cr ]
drop</syntaxhighlight>
{{out}}
<pre>0: [ 90 47 58 29 22 32 55 5 55 73 ]
1: [ -43 11 -29 -7 10 23 -50 50 18 ]
2: [ 54 -40 22 17 13 -73 100 -32 ]
3: [ -94 62 -5 -4 -86 173 -132 ]
4: [ 156 -67 1 -82 259 -305 ]
5: [ -223 68 -83 341 -564 ]
6: [ 291 -151 424 -905 ]
7: [ -442 575 -1329 ]
8: [ 1017 -1904 ]
9: [ -2921 ]
</pre>
=={{header|R}}==
<
if ( n == 1 )
a[2:length(a)] - a[1:length(a)-1]
Line 2,517 ⟶ 2,716:
print(forwarddif(v, 9))
print(fdiff(v, 9))</
=={{header|Racket}}==
<syntaxhighlight lang="racket">
#lang racket
Line 2,533 ⟶ 2,732:
(nth-forward-difference 9 '(90 47 58 29 22 32 55 5 55 73))
;; -> '(-2921)
</syntaxhighlight>
=={{header|Raku}}==
Line 2,541 ⟶ 2,740:
The Z- operator is a zip metaoperator with a minus to subtract the two lists pairwise.
It's almost a shame to define difn, since the series and subscript are hardly longer than the call itself would be, and arguably more self-documenting than the name of the function would be.
<syntaxhighlight lang="raku"
sub difn($array, $n) { ($array, &dif ... *)[$n] }</
=={{header|REXX}}==
Line 2,549 ⟶ 2,748:
This version allows a specification of the list of numbers and/or which ''order'' to process.
<
numeric digits 100 /*ensure enough accuracy (decimal digs)*/
parse arg e ',' N /*get a list: ε1 ε2 ε3 ε4 ··· , order */
Line 2,571 ⟶ 2,770:
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
th: procedure; x=abs(arg(1)); return word('th st nd rd',1+x//10*(x//100%10\==1)*(x//10<4))</
'''output''' when using the default input:
<pre>
Line 2,606 ⟶ 2,805:
===with error checking===
<
numeric digits 100 /*ensure enough accuracy (decimal digs)*/
parse arg e ',' N /*get a list: ε1 ε2 ε3 ε4 ··· , order */
Line 2,634 ⟶ 2,833:
/*──────────────────────────────────────────────────────────────────────────────────────*/
ser: say; say '***error***'; say arg(1); say; exit 13
th: procedure; x=abs(arg(1)); return word('th st nd rd',1+x//10*(x//100%10\==1)*(x//10<4))</
'''output''' is the same as the REXX entry above.
===with output alignment===
<
numeric digits 100 /*ensure enough accuracy (decimal digs)*/
parse arg e ',' N /*get a list: ε1 ε2 ε3 ε4 ··· , order */
Line 2,670 ⟶ 2,869:
/*──────────────────────────────────────────────────────────────────────────────────────*/
ser: say; say '***error***'; say arg(1); say; exit 13
th: procedure; x=abs(arg(1)); return word('th st nd rd',1+x//10*(x//100%10\==1)*(x//10<4))</
'''output''' when using the default input:
<pre>
Line 2,689 ⟶ 2,888:
===Version 2===
<
* Forward differences
* 18.08.2012 Walter Pachl derived from PL/I
Line 2,723 ⟶ 2,922:
End
End
Return</
{{out}} for Java's input
<pre>
Line 2,742 ⟶ 2,941:
=={{header|Ring}}==
<
# Project : Forward difference
Line 2,768 ⟶ 2,967:
see svect
see "}" + nl
</syntaxhighlight>
Output:
<pre>
Line 2,781 ⟶ 2,980:
{-2921}
</pre>
=={{header|RPL}}==
===Iterative approach===
{| class="wikitable" ≪
! RPL code
! Comment
|-
|
≪
'''IF''' OVER SIZE OVER > '''THEN'''
'''WHILE''' DUP '''REPEAT'''
SWAP { } 2 3 PICK SIZE '''FOR''' j
OVER j GET + '''NEXT'''
LIST→ →ARRY
SWAP OVER SIZE { } + RDM -
SWAP 1 - '''END'''
DROP '''END'''
≫ ‘<span style="color:blue">DIFFN</span>’ STO
|
<span style="color:blue">DIFFN</span> ''( [array] order → [nth_difference] ) ''
if order < array size
while order > 0
initialize loop
to build { array[2]...array[n] }
convert list into array
pop last item of array and substract
order -= 1
clean stack
|}
[90, 47, 58, 29, 22, 32, 55, 5, 55, 73] 1 <span style="color:blue">DIFFN</span>
[90, 47, 58, 29, 22, 32, 55, 5, 55, 73] 3 <span style="color:blue">DIFFN</span>
{{out}}
<pre>
2: [-43, 11, -29, -7, 10, 23, -50, 50, 18]
1: [-94, 62, -5, -4, -86, 173, -132]
</pre>
===Direct approach===
We use here local variables and algebraic notation to increase code readability.
{| class="wikitable" ≪
! RPL code
! Comment
|-
|
≪ → n
≪ '<span style="color:green">F</span>' STO
{ } 1 <span style="color:green">F</span> SIZE 1 - '''FOR''' j
-1 n ^ '<span style="color:green">F</span>' j GET *
1 n '''FOR''' k
'COMB(n,k)*(-1)^(n-k)*<span style="color:green">F</span>(j+k)' EVAL +
'''NEXT'''
+ '''NEXT'''
LIST→ →ARRY '<span style="color:green">F</span>' PURGE
≫ ≫ ‘<span style="color:blue">DIFFN</span>’ STO
|
<span style="color:blue">DIFFN</span> ''( [array] order → [nth_difference] ) ''
store array in global variable F
initialize output array building loop
put 1st term of sum (k=0) in stack // reverse Polish notation
loop
add terms for 0<k≤n // algebraic notation
add sum to list
convert list into array, clean memory
|}
Postfix fans can replace the following line
'COMB(n,k)*(-1)^(n-k)*<span style="color:green">F</span>(j+k)' EVAL + '''NEXT'''
by
n k COMB -1 n k - ^ * '<span style="color:green">F</span>' j k + GET * + '''NEXT'''
On HP-48G and newer models, first difference is directly returned by the <code>ΔLIST</code> instruction, so we can simplify the above code, provided that input is given as a list { } instead of an array [ ]:
≪ 1 SWAP '''START''' ΔLIST '''NEXT''' ≫ ‘<span style="color:blue">DIFFN</span>’ STO
=={{header|Ruby}}==
Line 2,789 ⟶ 3,061:
{{works with|Ruby|1.8.7}}
<
s.each_cons(2).collect { |x, y| y - x }
end
Line 2,795 ⟶ 3,067:
def difn(s, n)
n.times.inject(s) { |s, | dif(s) }
end</
{{out|Example usage}}
<
p difn([1, 23, 45, 678], 2) # => [0, 611]</
=={{header|Rust}}==
<syntaxhighlight lang="rust">
fn forward_difference(input_seq: Vec<i32>, order: u32) -> Vec<i32> {
match order {
0 => input_seq,
1 => {
let input_seq_iter = input_seq.into_iter();
let clone_of_input_seq_iter = input_seq_iter.clone();
input_seq_iter.zip(clone_of_input_seq_iter.skip(1)).map(|(current, next)| next - current).collect()
},
_ => forward_difference(forward_difference(input_seq, order - 1), 1),
}
}
fn main() {
let mut sequence = vec![90, 47, 58, 29, 22, 32, 55, 5, 55, 73];
loop {
println!("{:?}", sequence);
sequence = forward_difference(sequence, 1);
if sequence.is_empty() {
break;
}
}
}
</syntaxhighlight>
{{out}}
<pre>
[90, 47, 58, 29, 22, 32, 55, 5, 55, 73]
[-43, 11, -29, -7, 10, 23, -50, 50, 18]
[54, -40, 22, 17, 13, -73, 100, -32]
[-94, 62, -5, -4, -86, 173, -132]
[156, -67, 1, -82, 259, -305]
[-223, 68, -83, 341, -564]
[291, -151, 424, -905]
[-442, 575, -1329]
[1017, -1904]
[-2921]
</pre>
=={{header|Scala}}==
<
def fdiffn(i: Int, xs: List[Int]): List[Int] = if (i == 1) fdiff(xs) else fdiffn(i - 1, fdiff(xs))</
{{out|Example}}
<
(1 to 9)foreach(x=>println(fdiffn(x,l)))</
{{out}}
<pre>
Line 2,823 ⟶ 3,136:
=={{header|Scheme}}==
<
(if (or (null? lst) (null? (cdr lst)))
'()
Line 2,833 ⟶ 3,146:
xs
(nth-forward-diff (- n 1)
(forward-diff xs))))</
{{out}}
Line 2,842 ⟶ 3,155:
=={{header|Seed7}}==
<
const func array integer: forwardDifference (in array integer: data) is func
Line 2,874 ⟶ 3,187:
data := forwardDifference(data);
end for;
end func;</
{{out}}
Line 2,892 ⟶ 3,205:
=={{header|SequenceL}}==
Solution that keeps track of intermediate values:
<syntaxhighlight lang="sequencel">
forwardDifference(x(1), n) := forwardDifferenceHelper(x, n, [x]);
Line 2,901 ⟶ 3,214:
result when n = 0 or size(x) = 1 else
forwardDifferenceHelper(difference, n - 1, result ++ [difference]);
</syntaxhighlight>
If no intermediate values are needed, the following is sufficient:
<syntaxhighlight lang="sequencel">
forwardDifference(x(1),n) :=
x when n = 0 or size(x) = 1 else
forwardDifference(tail(x) - x[1 ... size(x) - 1], n - 1);
</syntaxhighlight>
=={{header|Sidef}}==
<
gather {
for i (0 ..^ arr.end) {
Line 2,924 ⟶ 3,237:
say dif([1, 23, 45, 678]) # => [22, 22, 633]
say difn(2, [1, 23, 45, 678]) # => [0, 611]</
=={{header|Slate}}==
<
[
s allButFirst with: s allButLast collect: #- `er
Line 2,943 ⟶ 3,256:
[
(0 below: n) inject: s into: [| :seq :_ | seq forwardDifference]
].</
{{out|Usage}}
<
data keysDo: [| :index | inform: (data forwardDifference: index) printString].</
=={{header|Smalltalk}}==
{{works with|GNU Smalltalk}}
<
difference [
^self allButFirst with: self allButLast collect: [ :a :b | a - b ]
Line 2,964 ⟶ 3,277:
s := #(90 47 58 29 22 32 55 5 55 73)
1 to: s size - 1 do: [ :i |
(s nthOrderDifference: i) printNl ]</
=={{header|SQL}}==
Line 2,970 ⟶ 3,283:
{{works with|SQLite|3.13.0}}
<
T0 (N, ITEM, LIST, NEW_LIST) AS
(
Line 3,006 ⟶ 3,319:
WHERE NEW_LIST IS NULL
AND LIST <> ''
ORDER BY N;</
=={{header|Standard ML}}==
<
fun nth_forward_difference n xs =
Line 3,016 ⟶ 3,329:
xs
else
nth_forward_difference (n-1) (forward_difference xs)</
{{out}}
Line 3,027 ⟶ 3,340:
It's possible to implement differences using row indices. For instance, first forward differences of a variable x can be defined by:
<
However, it's much more natural to use [http://www.stata.com/help.cgi?tsvarlist time-series varlists]. In order to use them, it's necessary to first set a ''time'' variable, which may be simply an index variable.
<
clear all
set obs 100
Line 3,040 ⟶ 3,353:
* Differences
display "Difference order?" _request(k)
gen y=D${k}F${k}.x</
=={{header|Swift}}==
<
return zip(arr.dropFirst(), arr).map({ $0.0 - $0.1 })
}
Line 3,063 ⟶ 3,376:
for diff in (0...9).map({ nthForwardsDifference(of: [90, 47, 58, 29, 22, 32, 55, 5, 55, 73], n: $0) }) {
print(diff)
}</
{{out}}
Line 3,079 ⟶ 3,392:
=={{header|Tcl}}==
<
set previous [lindex $list 0]
set new [list]
Line 3,101 ⟶ 3,414:
for {set order 0} {$order <= 10} {incr order} {
puts [format "%d\t%s" $order [fwd_diff $a $order]]
}</
{{out}}
<pre>0 90.5 47 58 29 22 32 55 5 55 73.5
Line 3,118 ⟶ 3,431:
This function doesn't need to be defined because it's in a library already,
but it could be defined like this:
<
#import nat
#import flo
nth_diff "n" = rep"n" minus*typ</
test program:
<
#show+
Line 3,132 ⟶ 3,445:
printf/*=*' %0.0f' <
nth_diff6 test_data,
nth_diff7 test_data></
{{out}}
<pre> 291 -151 424 -905
Line 3,139 ⟶ 3,452:
=={{header|Visual Basic .NET}}==
{{works with|Visual Basic .NET|2008+}}
<
Sub Main()
Line 3,160 ⟶ 3,473:
End Function
End Module</
{{out}}
<pre>
Line 3,176 ⟶ 3,489:
=={{header|Visual FoxPro}}==
<
#DEFINE CTAB CHR(9)
LOCAL lcList As String, i As Integer, n As Integer
Line 3,214 ⟶ 3,527:
? lcTxt
ENDPROC
</syntaxhighlight>
{{out}}
<pre>
Line 3,227 ⟶ 3,540:
Difference 8: 1017 -1904
Difference 9: -2921
</pre>
=={{header|Wren}}==
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./fmt" for Fmt
var forwardDiff = Fn.new { |a, order|
if (order < 0) Fiber.abort("Order must be a non-negative integer.")
if (a.count == 0) return
Fmt.print(" 0: $5d", a)
if (a.count == 1) return
if (order == 0) return
for (o in 1..order) {
var b = List.filled(a.count-1, 0)
for (i in 0...b.count) b[i] = a[i+1] - a[i]
Fmt.print("$2d: $5d", o, b)
if (b.count == 1) return
a = b
}
}
forwardDiff.call([90, 47, 58, 29, 22, 32, 55, 5, 55, 73], 9)</syntaxhighlight>
{{out}}
<pre>
0: 90 47 58 29 22 32 55 5 55 73
1: -43 11 -29 -7 10 23 -50 50 18
2: 54 -40 22 17 13 -73 100 -32
3: -94 62 -5 -4 -86 173 -132
4: 156 -67 1 -82 259 -305
5: -223 68 -83 341 -564
6: 291 -151 424 -905
7: -442 575 -1329
8: 1017 -1904
9: -2921
</pre>
=={{header|XPL0}}==
{{trans|ALGOL W}}
<syntaxhighlight lang "XPL0">\Calculate forward differences
\Sets elements of B to the first order forward differences of A.
\A should have bounds 1 :: N, B should have bounds 1 :: N - 1.
procedure FirstOrderFDifference ( A, B, N );
integer A, B, N, I;
for I := 2 to N do B( I - 1 ) := A( I ) - A( I - 1 );
integer V ( 1 + 10 );
integer Diff( 1 + 9 );
integer VPos, Length, List, I, Order;
begin
\construct the initial values array
VPos := 1;
List:= [90, 47, 58, 29, 22, 32, 55, 5, 55, 73];
for I := 0 to 10-1 do begin
V( VPos ) := List( I );
VPos := VPos + 1
end;
\calculate and show the differences
Format(8, 0); \set output format
Length := 10;
for Order := 1 to Length - 1 do begin
FirstOrderFDifference( V, Diff, Length );
Length := Length - 1;
IntOut(0, Order); Text(0, " : ");
for I := 1 to Length do RlOut(0, float(Diff( I ) ));
CrLf(0);
for I := 1 to Length do V( I ) := Diff( I )
end
end</syntaxhighlight>
{{out}}
<pre>
1 : -43 11 -29 -7 10 23 -50 50 18
2 : 54 -40 22 17 13 -73 100 -32
3 : -94 62 -5 -4 -86 173 -132
4 : 156 -67 1 -82 259 -305
5 : -223 68 -83 341 -564
6 : 291 -151 424 -905
7 : -442 575 -1329
8 : 1017 -1904
9 : -2921
</pre>
=={{header|zkl}}==
{{trans|Scheme}}
<
if(lst.len()<2)
return(T);
Line 3,240 ⟶ 3,635:
return(xs);
return(nthForwardDiff(n-1,forwardDiff(xs))) // tail recursion
}</
<
{{out}}
<pre>
Line 3,248 ⟶ 3,643:
=={{header|ZX Spectrum Basic}}==
<
20 LET p=1
30 READ n: DIM b(n)
Line 3,261 ⟶ 3,656:
120 FOR i=1 TO n-p
130 PRINT b(i);" ";
140 NEXT i</
|