Forward difference
Provide code that produces a list of numbers which is the nth order forward difference, given a non-negative integer (specifying the order) and a list of numbers.
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
The first-order forward difference of a list of numbers A is a new list B, where Bn = An+1 - An.
List B should have one fewer element as a result.
The second-order forward difference of A will be:
tdefmodule Diff do def forward(arr,i\\1) do forward(arr,[],i) end def forward([_|[]],diffs,i) do if i == 1 do IO.inspect diffs else forward(diffs,[],i-1) end end def forward([val1|[val2|vals]],diffs,i) do forward([val2|vals],diffs++[val2-val1],i) end end
The same as the first-order forward difference of B.
That new list will have two fewer elements than A and one less than B.
The goal of this task is to repeat this process up to the desired order.
For a more formal description, see the related Mathworld article.
- Algorithmic options
- Iterate through all previous forward differences and re-calculate a new array each time.
- Use this formula (from Wikipedia):
- (Pascal's Triangle may be useful for this option.)
11l
<lang 11l>V dif = s -> enumerate(s[1..]).map2((i, x) -> x - @s[i]) F difn(s, n) -> [Int]
R I n != 0 {difn(dif(s), n - 1)} E s
V s = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73]
L(i) 10
print(difn(s, i))</lang>
- Output:
[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]
Ada
<lang ada>with Ada.Text_Io; with Ada.Float_Text_Io; use Ada.Float_Text_Io; with Ada.containers.Vectors;
procedure Forward_Difference is
package Flt_Vect is new Ada.Containers.Vectors(Positive, Float); use Flt_Vect; procedure Print(Item : Vector) is begin if not Item.Is_Empty then Ada.Text_IO.Put('['); for I in 1..Item.Length loop Put(Item => Item.Element(Positive(I)), Fore => 1, Aft => 1, Exp => 0); if Positive(I) < Positive(Item.Length) then Ada.Text_Io.Put(", "); end if; end loop; Ada.Text_Io.Put_line("]"); else Ada.Text_IO.Put_Line("Empty List"); end if; end Print; function Diff(Item : Vector; Num_Passes : Natural) return Vector is A : Vector := Item; B : Vector := Empty_Vector; begin if not A.Is_Empty then for I in 1..Num_Passes loop for I in 1..Natural(A.Length) - 1 loop B.Append(A.Element(I + 1) - A.Element(I)); end loop; Move(Target => A, Source => B); end loop; end if; return A; end Diff; Values : array(1..10) of Float := (90.0, 47.0, 58.0, 29.0, 22.0, 32.0, 55.0, 5.0, 55.0, 73.0); A : Vector;
begin
for I in Values'range loop A.Append(Values(I)); -- Fill the vector end loop; Print(Diff(A, 1)); Print(Diff(A, 2)); Print(Diff(A, 9)); Print(Diff(A, 10)); print(Diff(A, 0));
end Forward_Difference;</lang>
- Output:
[-43.0, 11.0, -29.0, -7.0, 10.0, 23.0, -50.0, 50.0, 18.0] [54.0, -40.0, 22.0, 17.0, 13.0, -73.0, 100.0, -32.0] [-2921.0] Empty List [90.0, 47.0, 58.0, 29.0, 22.0, 32.0, 55.0, 5.0, 55.0, 73.0]
ALGOL 68
<lang algol68>main:(
MODE LISTREAL = [1:0]REAL;
OP - = (LISTREAL a,b)LISTREAL: ( [UPB a]REAL out; FOR i TO UPB out DO out[i]:=a[i]-b[i] OD; out );
FORMAT real fmt=$zzz-d.d$; FORMAT repeat fmt = $n(UPB s-1)(f(real fmt)",")f(real fmt)$; FORMAT list fmt = $"("f(UPB s=1|real fmt|repeat fmt)")"$;
FLEX [1:0] REAL s := (90, 47, 58, 29, 22, 32, 55, 5, 55, 73);
printf((list fmt,s,$";"l$)); TO UPB s-1 DO s := s[2:] - s[:UPB s-1]; printf((list fmt,s,$";"l$)) OD
)</lang>
- Output:
( 90.0, 47.0, 58.0, 29.0, 22.0, 32.0, 55.0, 5.0, 55.0, 73.0); ( -43.0, 11.0, -29.0, -7.0, 10.0, 23.0, -50.0, 50.0, 18.0); ( 54.0, -40.0, 22.0, 17.0, 13.0, -73.0, 100.0, -32.0); ( -94.0, 62.0, -5.0, -4.0, -86.0, 173.0, -132.0); ( 156.0, -67.0, 1.0, -82.0, 259.0, -305.0); ( -223.0, 68.0, -83.0, 341.0, -564.0); ( 291.0, -151.0, 424.0, -905.0); ( -442.0, 575.0,-1329.0); ( 1017.0,-1904.0); (-2921.0);
ALGOL W
<lang algolw>begin
% 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 ( integer array A( * ) ; integer array B( * ) ; integer value n ) ; for i := 2 until n do B( i - 1 ) := A( i ) - A( i - 1 );
integer array v ( 1 :: 10 ); integer array diff( 1 :: 9 ); integer vPos, length;
% construct the initial values array % vPos := 1; for i := 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 do begin v( vPos ) := i; vPos := vPos + 1 end for_i ; % calculate and show the differences % i_w := 5; % set output format % length := 10; for order := 1 until length - 1 do begin FirstOrderFDifference( v, diff, length ); length := length - 1; write( order, ": " ); for i := 1 until length do writeon( diff( i ) ); for i := 1 until length do v( i ) := diff( i ) end for_order
end.</lang>
- Output:
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
APL
<lang apl> list ← 90 47 58 29 22 32 55 5 55 73
fd ← {⍺=0:⍵⋄(⍺-1)∇(1↓⍵)-(¯1↓⍵)} 1 fd list
¯43 11 ¯29 ¯7 10 23 ¯50 50 18
2 fd list
54 ¯40 22 17 13 ¯73 100 ¯32</lang>
AppleScript
<lang AppleScript>-- forwardDifference :: Num a => [a] -> [a] on forwardDifference(xs)
zipWith(my subtract, xs, rest of xs)
end forwardDifference
-- nthForwardDifference :: Num a => Int -> [a] -> [a]
on nthForwardDifference(xs, i)
|index|(iterate(forwardDifference, xs), 1 + i)
end nthForwardDifference
TEST ---------------------------
on run
script show on |λ|(xs, i) ((i - 1) as string) & " -> " & showList(xs) end |λ| end script unlines(map(show, ¬ take(10, ¬ iterate(forwardDifference, ¬ {90, 47, 58, 29, 22, 32, 55, 5, 55, 73}))))
end run
GENERIC FUNCTIONS --------------------
-- Just :: a -> Maybe a on Just(x)
-- Constructor for an inhabited Maybe (option type) value. -- Wrapper containing the result of a computation. {type:"Maybe", Nothing:false, Just:x}
end Just
-- Nothing :: Maybe a on Nothing()
-- Constructor for an empty Maybe (option type) value. -- Empty wrapper returned where a computation is not possible. {type:"Maybe", Nothing:true}
end Nothing
-- index (!!) :: [a] -> Int -> Maybe a
-- index (!!) :: Gen [a] -> Int -> Maybe a
-- index (!!) :: String -> Int -> Maybe Char
on |index|(xs, i)
if script is class of xs then repeat with j from 1 to i set v to |λ|() of xs end repeat if missing value is not v then Just(v) else Nothing() end if else if length of xs < i then Nothing() else Just(item i of xs) end if end if
end |index|
-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
set {dlm, my text item delimiters} to ¬ {my text item delimiters, delim} set str to xs as text set my text item delimiters to dlm str
end intercalate
-- iterate :: (a -> a) -> a -> Gen [a]
on iterate(f, x)
script property v : missing value property g : mReturn(f)'s |λ| on |λ|() if missing value is v then set v to x else set v to g(v) end if return v end |λ| end script
end iterate
-- length :: [a] -> Int
on |length|(xs)
set c to class of xs if list is c or string is c then length of xs else (2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite) end if
end |length|
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f -- to each element of xs. tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to |λ|(item i of xs, i, xs) end repeat return lst end tell
end map
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then y else x end if
end min
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper. if script is class of f then f else script property |λ| : f end script end if
end mReturn
-- showList :: [a] -> String
on showList(xs)
"[" & intercalate(", ", map(my str, xs)) & "]"
end showList
-- str :: a -> String
on str(x)
x as string
end str
-- subtract :: Num -> Num -> Num
on subtract(x, y)
y - x
end subtract
-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs if list is c then if 0 < n then items 1 thru min(n, length of xs) of xs else {} end if else if string is c then if 0 < n then text 1 thru min(n, length of xs) of xs else "" end if else if script is c then set ys to {} repeat with i from 1 to n set v to |λ|() of xs if missing value is v then return ys else set end of ys to v end if end repeat return ys else missing value end if
end take
-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation -- of a list of strings with the newline character. set {dlm, my text item delimiters} to ¬ {my text item delimiters, linefeed} set s to xs as text set my text item delimiters to dlm s
end unlines
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(|length|(xs), |length|(ys)) if 1 > lng then return {} set xs_ to take(lng, xs) -- Allow for non-finite set ys_ to take(lng, ys) -- generators like cycle etc set lst to {} tell mReturn(f) repeat with i from 1 to lng set end of lst to |λ|(item i of xs_, item i of ys_) end repeat return lst end tell
end zipWith</lang>
- Output:
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]
Arturo
<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 1 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]</lang>
- Output:
156.5 -67 1 -82 259 -304.5 -1 -1 -1 -1 -1 -1
AutoHotkey
contributed by Laszlo on the ahk forum <lang AutoHotkey>MsgBox % diff("2,3,4,3",1) MsgBox % diff("2,3,4,3",2) MsgBox % diff("2,3,4,3",3) MsgBox % diff("2,3,4,3",4)
diff(list,ord) { ; high order forward differences of a list
Loop %ord% { L = Loop Parse, list, `, %A_Space%%A_Tab% If (A_Index=1) p := A_LoopField Else L .= "," A_LoopField-p, p := A_LoopField list := SubStr(L,2) } Return list
}</lang>
AWK
<lang awk>#!/usr/bin/awk -f BEGIN {
if (p<1) {p = 1};
}
function diff(s, p) {
n = split(s, a, " "); for (j = 1; j <= p; j++) { for(i = 1; i <= n-j; i++) { a[i] = a[i+1] - a[i]; } } s = ""; for (i = 1; i <= n-p; i++) s = s" "a[i]; return s;
}
{
print diff($0, p);
}</lang>
Using Pascal's triangle:
<lang awk>#!/usr/bin/awk -f BEGIN {
if (p<1) {p = 1};
}
function diff(s, p) {
# pascal triangled with sign changes b[1] = (p%2) ? 1 : -1; for (j=1; j < p; j++) { b[j+1] = -b[j]*(p-j)/j; };
n = split(s, a, " "); s = ""; for (j = 1; j <= n-p+1; j++) { c = 0; for(i = 1; i <= p; i++) { c += b[i]*a[j+i-1]; } s = s" "c; } return s;
}
{
print diff($0, p);
}</lang>
- Output:
$ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=1 1 1 2 3 -3 -2 -1 -1 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=2 0 1 1 -6 1 1 0 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=3 1 0 -7 7 0 -1 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=4 -1 -7 14 -7 -1 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=5 -6 21 -21 6 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=6 27 -42 27 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=7 -69 69 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=8 138 $ echo '0 1 2 4 7 4 2 1 0' | ./diff.awk -v p=9
BBC BASIC
<lang bbcbasic> DIM A(9)
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()) PROCforward_difference(1, A(), B()) PRINT "Forward diff 1: " FNshowarray(B()) PROCforward_difference(2, A(), C()) PRINT "Forward diff 2: " FNshowarray(C()) PROCforward_difference(9, A(), D()) PRINT "Forward diff 9: " FNshowarray(D()) END DEF PROCforward_difference(n%, a(), RETURN b()) LOCAL c%, i%, j% DIM b(DIM(a(),1) - n%) FOR i% = 0 TO DIM(b(),1) b(i%) = a(i% + n%) c% = 1 FOR j% = 1 TO n% c% = -INT(c% * (n% - j% + 1) / j% + 0.5) b(i%) += c% * a(i% + n% - j%) NEXT NEXT ENDPROC DEF FNshowarray(a()) LOCAL i%, a$ FOR i% = 0 TO DIM(a(),1) a$ += STR$(a(i%)) + ", " NEXT = LEFT$(LEFT$(a$))</lang>
- Output:
Original array: 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 Forward diff 1: -43, 11, -29, -7, 10, 23, -50, 50, 18 Forward diff 2: 54, -40, 22, 17, 13, -73, 100, -32 Forward diff 9: -2921
BQN
Left argument is the order, right argument is the array.
<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</lang>
C
<lang c>#include <stdlib.h>
- include <string.h>
- include <stdio.h>
double* fwd_diff(double* x, unsigned int len, unsigned int order) { unsigned int i, j; double* y;
/* handle two special cases */ if (order >= len) return 0;
y = malloc(sizeof(double) * len); if (!order) { memcpy(y, x, sizeof(double) * len); return y; }
/* first order diff goes from x->y, later ones go from y->y */ for (j = 0; j < order; j++, x = y) for (i = 0, len--; i < len; i++) y[i] = x[i + 1] - x[i];
y = realloc(y, sizeof(double) * len); return y; }
int main(void) { double *y, x[] = {90, 47, 58, 29, 22, 32, 55, 5, 55, 73}; int i, len = sizeof(x) / sizeof(x[0]);
y = fwd_diff(x, len, 1); for (i = 0; i < len - 1; i++) printf("%g ", y[i]); putchar('\n');
return 0; }</lang>
Use method with Pascal triangle, binomial coefficients are pre-computed
<lang c>#include <stdio.h>
int* binomCoeff(int n) {
int *b = calloc(n+1,sizeof(int)); int j; b[0] = n%2 ? -1 : 1; for (j=1 ; j<=n; j++) b[j] = -b[j-1]*(n+1-j)/j;
return(b);
};
main () {
double array[] = { 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 }; size_t lenArray = sizeof(array)/sizeof(array[0]);
int p = 4; // order int *b = binomCoeff(p); // pre-compute binomial coefficients for order p
int j, k; // compute p-th difference for (k=0 ; k < lenArray; k++) for (array[k] *= b[0], j=1 ; j<=p; j++) array[k] += b[j] * array[k+j];
free(b);
// resulting series is shorter by p elements lenArray -= p; for (k=0 ; k < lenArray; k++) printf("%f ",array[k]); printf("\n");
} </lang>
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
class Program {
static IEnumerable<int> ForwardDifference(IEnumerable<int> sequence, uint order = 1u) { switch (order) { case 0u: return sequence; case 1u: return sequence.Skip(1).Zip(sequence, (next, current) => next - current); default: return ForwardDifference(ForwardDifference(sequence), order - 1u); } }
static void Main() { IEnumerable<int> sequence = new[] { 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 }; do { Console.WriteLine(string.Join(", ", sequence)); } while ((sequence = ForwardDifference(sequence)).Any()); }
}</lang>
- Output:
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
C++
This code uses a separate function to do a first-order forward difference, which is then called several times for calculating n-th order forward difference. No error checking is implemented. <lang cpp>#include <vector>
- include <iterator>
- include <algorithm>
// calculate first order forward difference // requires: // * InputIterator is an input iterator // * OutputIterator is an output iterator // * The value type of InputIterator is copy-constructible and assignable // * The value type of InputIterator supports operator - // * The result type of operator- is assignable to the value_type of OutputIterator // returns: The iterator following the output sequence template<typename InputIterator, typename OutputIterator>
OutputIterator forward_difference(InputIterator first, InputIterator last, OutputIterator dest)
{
// special case: for empty sequence, do nothing if (first == last) return dest;
typedef typename std::iterator_traits<InputIterator>::value_type value_type;
value_type temp = *first++; while (first != last) { value_type temp2 = *first++; *dest++ = temp2 - temp; temp = temp2; }
return dest;
}
// calculate n-th order forward difference. // requires: // * InputIterator is an input iterator // * OutputIterator is an output iterator // * The value type of InputIterator is copy-constructible and assignable // * The value type of InputIterator supports operator - // * The result type of operator- is assignable to the value_type of InputIterator // * The result type of operator- is assignable to the value_type of OutputIterator // * order >= 0 // returns: The iterator following the output sequence template<typename InputIterator, typename OutputIterator>
OutputIterator nth_forward_difference(int order, InputIterator first, InputIterator last, OutputIterator dest)
{
// special case: If order == 0, just copy input to output if (order == 0) return std::copy(first, last, dest);
// second special case: If order == 1, just forward to the first-order function if (order == 1) return forward_difference(first, last, dest);
// intermediate results are stored in a vector typedef typename std::iterator_traits<InputIterator>::value_type value_type; std::vector<value_type> temp_storage;
// fill the vector with the result of the first order forward difference forward_difference(first, last, std::back_inserter(temp_storage));
// the next n-2 iterations work directly on the vector typename std::vector<value_type>::iterator begin = temp_storage.begin(), end = temp_storage.end(); for (int i = 1; i < order-1; ++i) end = forward_difference(begin, end, begin);
// the final iteration writes directly to the output iterator return forward_difference(begin, end, dest);
}
// example usage code
- include <iostream>
int main() {
double array[10] = { 90.0, 47.0, 58.0, 29.0, 22.0, 32.0, 55.0, 5.0, 55.0, 73.0 };
// this stores the results in the vector dest std::vector<double> dest; nth_forward_difference(1, array, array+10, std::back_inserter(dest));
// output dest std::copy(dest.begin(), dest.end(), std::ostream_iterator<double>(std::cout, " ")); std::cout << std::endl;
// however, the results can also be output as they are calculated nth_forward_difference(2, array, array+10, std::ostream_iterator<double>(std::cout, " ")); std::cout << std::endl;
nth_forward_difference(9, array, array+10, std::ostream_iterator<double>(std::cout, " ")); std::cout << std::endl;
nth_forward_difference(10, array, array+10, std::ostream_iterator<double>(std::cout, " ")); std::cout << std::endl;
nth_forward_difference(0, array, array+10, std::ostream_iterator<double>(std::cout, " ")); std::cout << std::endl;
// finally, the results can also be written into the original array // (which of course destroys the original content) double* end = nth_forward_difference(3, array, array+10, array);
for (double* p = array; p < end; ++p) std::cout << *p << " "; std::cout << std::endl;
return 0;
}</lang>
- Output:
-43 11 -29 -7 10 23 -50 50 18 54 -40 22 17 13 -73 100 -32 -2921 90 47 58 29 22 32 55 5 55 73 -94 62 -5 -4 -86 173 -132
Note the empty line indicating the empty sequence for order 10.
Using Standard Template Library
<lang cpp>
- include <iostream>
- include <numeric>
// Calculate the Forward Difference of a series if integers showing each order // // Nigel Galloway. August 20th., 2012 // int main() {
int x[] = {NULL,-43,11,-29,-7,10,23,-50,50,18}; const int N = sizeof(x) / sizeof(int) - 1; for (int ord = 0; ord < N - 1; ord++) { std::adjacent_difference(x+1, x + N + 1 - ord, x); for (int i = 1; i < N - ord; i++) std::cout << x[i] << ' '; std::cout << std::endl; } return 0;
} </lang>
- Output:
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
Usually one will not want the intermediate results, in which case the following is sufficient: <lang cpp>
- include <iostream>
- include <numeric>
// Calculate the Forward Difference of a series if integers // // Nigel Galloway. August 20th., 2012 // int main() {
int x[] = {NULL,-43,11,-29,-7,10,23,-50,50,18}; const int N = sizeof(x) / sizeof(int) - 1; for (int ord = 0; ord < N - 1; ord++) std::adjacent_difference(x+1, x + N + 1 - ord, x); std::cout << x[1] << std::endl; return 0;
} </lang>
- Output:
-2921
Using Pascal's Triangle
<lang cpp>
- include <iostream>
- include <algorithm>
// Calculate the Forward Difference of a series if integers using Pascal's Triangle // For this example the 9th line of Pascal's Triangle is stored in P. // // Nigel Galloway. August 20th., 2012 // int main() {
const int P[] = {1,-8,28,-56,70,-56,28,-8,1}; int x[] = {-43,11,-29,-7,10,23,-50,50,18}; std::transform(x, x + sizeof(x) / sizeof(int), P, x, std::multiplies<int>()); std::cout << std::accumulate(x, x + sizeof(x) / sizeof(int), 0) << std::endl; return 0;
} </lang>
- Output:
-2921
Clojure
<lang lisp>(defn fwd-diff [nums order]
(nth (iterate #(map - (next %) %) nums) order))</lang>
CoffeeScript
<lang coffeescript> forward_difference = (arr, n) ->
# Find the n-th order forward difference for arr using # a straightforward recursive algorithm. # Assume arr is integers and n <= arr.length. return arr if n == 0 arr = forward_difference(arr, n-1) (arr[i+1] - arr[i] for i in [0...arr.length - 1])
arr = [-1, 0, 1, 8, 27, 64, 125, 216] for n in [0..arr.length]
console.log n, forward_difference arr, n
</lang>
- Output:
> coffee forward_difference.coffee 0 [ -1, 0, 1, 8, 27, 64, 125, 216 ] 1 [ 1, 1, 7, 19, 37, 61, 91 ] 2 [ 0, 6, 12, 18, 24, 30 ] 3 [ 6, 6, 6, 6, 6 ] 4 [ 0, 0, 0, 0 ] 5 [ 0, 0, 0 ] 6 [ 0, 0 ] 7 [ 0 ] 8 []
Common Lisp
<lang lisp>(defun forward-difference (list)
(mapcar #'- (rest list) list))
(defun nth-forward-difference (list n)
(setf list (copy-list list)) (loop repeat n do (map-into list #'- (rest list) list)) (subseq list 0 (- (length list) n)))</lang>
D
Basic Version
<lang d>T[] forwardDifference(T)(in T[] data, in int level) pure nothrow in {
assert(level >= 0 && level < data.length);
} body {
auto result = data.dup; foreach (immutable i; 0 .. level) foreach (immutable j, ref el; result[0 .. $ - i - 1]) el = result[j + 1] - el; result.length -= level; return result;
}
void main() {
import std.stdio;
const data = [90.5, 47, 58, 29, 22, 32, 55, 5, 55, 73.5]; foreach (immutable level; 0 .. data.length) forwardDifference(data, level).writeln;
}</lang>
- Output:
[90.5, 47, 58, 29, 22, 32, 55, 5, 55, 73.5] [-43.5, 11, -29, -7, 10, 23, -50, 50, 18.5] [54.5, -40, 22, 17, 13, -73, 100, -31.5] [-94.5, 62, -5, -4, -86, 173, -131.5] [156.5, -67, 1, -82, 259, -304.5] [-223.5, 68, -83, 341, -563.5] [291.5, -151, 424, -904.5] [-442.5, 575, -1328.5] [1017.5, -1903.5] [-2921]
Alternative Version
Same output. <lang d>import std.stdio, std.algorithm, std.range, std.array;
auto forwardDifference(Range)(Range d, in int level) pure {
foreach (immutable _; 0 .. level) d = d.zip(d.dropOne).map!(a => a[0] - a[1]).array; return d;
}
void main() {
const data = [90.5, 47, 58, 29, 22, 32, 55, 5, 55, 73.5]; foreach (immutable level; 0 .. data.length) forwardDifference(data, level).writeln;
}</lang>
Using Vector Operations
forwardDifference mutates the array in-place (same output): <lang d>import std.stdio;
T[] forwardDifference(T)(T[] s, in int n) pure nothrow @nogc {
foreach (immutable i; 0 .. n) s[0 .. $ - i - 1] = s[1 .. $ - i] - s[0 .. $ - i - 1]; return s[0 .. $ - n];
} void main() {
immutable A = [90.5, 47, 58, 29, 22, 32, 55, 5, 55, 73.5]; foreach (immutable level; 0 .. A.length) forwardDifference(A.dup, level).writeln;
}</lang>
Short Functional Version
Same output: <lang d>void main() {
import std.stdio, std.range;
auto D = [90.5, 47, 58, 29, 22, 32, 55, 5, 55, 73.5]; writefln("%(%s\n%)", recurrence!q{ (a[n - 1][0 .. $ - 1] = a[n - 1][1 .. $] - a[n - 1][0 .. $ - 1])[0 .. $] }(D) .take(D.length));
}</lang>
Dart
<lang dart>List forwardDifference(List _list) {
for (int i = _list.length - 1; i > 0; i--) { _list[i] = _list[i] - _list[i - 1]; }
_list.removeRange(0, 1); return _list;
}
void mainAlgorithms() {
List _intList = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73];
for (int i = _intList.length - 1; i >= 0; i--) { List _list = forwardDifference(_intList); print(_list); }
}</lang>
- Output:
Restarted application in 1,143ms. flutter: [-43, 11, -29, -7, 10, 23, -50, 50, 18] flutter: [54, -40, 22, 17, 13, -73, 100, -32] flutter: [-94, 62, -5, -4, -86, 173, -132] flutter: [156, -67, 1, -82, 259, -305] flutter: [-223, 68, -83, 341, -564] flutter: [291, -151, 424, -905] flutter: [-442, 575, -1329] flutter: [1017, -1904] flutter: [-2921] flutter: []
Delphi
See Pascal.
E
<lang e>pragma.enable("accumulator") /** Single step. */ def forwardDifference(seq :List) {
return accum [] for i in 0..(seq.size() - 2) { _.with(seq[i + 1] - seq[i]) }
}
/** Iterative implementation of the goal. */ def nthForwardDifference1(var seq :List, n :(int >= 0)) {
for _ in 1..n { seq := forwardDifference(seq) } return seq
}
/** Imperative implementation of the goal. */ def nthForwardDifference2(seq :List, n :(int >= 0)) {
def buf := seq.diverge() def finalSize := seq.size() - n for lim in (finalSize..!seq.size()).descending() { for i in 0..!lim { buf[i] := buf[i + 1] - buf[i] } } return buf.run(0, finalSize)
}
? def sampleData := [90, 47, 58, 29, 22, 32, 55, 5, 55, 73] > for n in 0..10 { > def r1 := nthForwardDifference1(sampleData, n) > require(r1 == nthForwardDifference2(sampleData, n)) > println(r1) > }</lang>
EchoLisp
Using the built-in function iterate which, given a function f and n, returns the function f°f°f....°f . <lang lisp> (define (Δ-1 list) (for/list ([x (cdr list)] [y list]) (- x y)))
(define (Δ-n n) (iterate Δ-1 n))
((Δ-n 9) '(90 47 58 29 22 32 55 5 55 73))
→ (-2921)
</lang>
Elixir
<lang Elixir>defmodule Diff do
def forward(list,i\\1) do forward(list,[],i) end def forward([_],diffs,1), do: IO.inspect diffs def forward([_],diffs,i), do: forward(diffs,[],i-1) def forward([val1,val2|vals],diffs,i) do forward([val2|vals],diffs++[val2-val1],i) end
end
Enum.each(1..9, fn i ->
Diff.forward([90, 47, 58, 29, 22, 32, 55, 5, 55, 73],i)
end)</lang>
- Output:
[-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]
Erlang
<lang erlang>-module(forward_difference). -export([difference/1, difference/2]).
-export([task/0]). -define(TEST_DATA,[90, 47, 58, 29, 22, 32, 55, 5, 55, 73]).
difference([X|Xs]) ->
{Result,_} = lists:mapfoldl(fun (N_2,N_1) -> {N_2 - N_1, N_2} end, X, Xs), Result.
difference([],_) -> []; difference(List,0) -> List; difference(List,Order) -> difference(difference(List),Order-1).
task() ->
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.</lang>
- Output:
80> forward_difference:task(). Initial: [90,47,58,29,22,32,55,5,55,73] 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] 10: [] ok
F#
Straightforward recursive solution <lang fsharp>let rec ForwardDifference input n =
match n with | _ when input = [] || n < 0 -> [] // If there's no more input, just return an empty list | 0 -> input // If n is zero, we're done - return the input | _ -> ForwardDifference // otherwise, recursively difference.. (input.Tail // All but the first element |> 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</lang>
Factor
<lang factor>USING: kernel math math.vectors sequences ; IN: rosetacode
- 1-order ( seq -- seq' )
[ rest-slice ] keep v- ;
- n-order ( seq n -- seq' )
dup 0 <= [ drop ] [ [ 1-order ] times ] if ;
</lang>
( scratchpad ) { 90.5 47 58 29 22 32 55 5 55 73.5 } 4 n-order . { 156.5 -67 1 -82 259 -304.5 }
Forth
<lang forth>: forward-difference
dup 0 ?do swap rot over i 1+ - 0 ?do dup i cells + dup cell+ @ over @ - swap ! loop swap rot loop -
create a
90 , 47 , 58 , 29 , 22 , 32 , 55 , 5 , 55 , 73 ,
- test a 10 9 forward-difference bounds ?do i ? loop ;
test</lang>
Fortran
<lang fortran>MODULE DIFFERENCE
IMPLICIT NONE
CONTAINS SUBROUTINE Fdiff(a, n) INTEGER, INTENT(IN) :: a(:), n INTEGER :: b(SIZE(a)) INTEGER :: i, j, arraysize b = a arraysize = SIZE(b) DO i = arraysize-1, arraysize-n, -1 DO j = 1, i b(j) = b(j+1) - b(j) END DO END DO WRITE (*,*) b(1:arraysize-n) END SUBROUTINE Fdiff
END MODULE DIFFERENCE</lang>
<lang fortran>PROGRAM TEST
USE DIFFERENCE IMPLICIT NONE
INTEGER :: array(10) = (/ 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 /) INTEGER :: i DO i = 1, 9 CALL Fdiff(array, i) END DO
END PROGRAM TEST</lang>
- Output:
-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
FreeBASIC
<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 </lang>
Go
<lang go>package main
import "fmt"
func main() {
a := []int{90, 47, 58, 29, 22, 32, 55, 5, 55, 73} fmt.Println(a) fmt.Println(fd(a, 9))
}
func fd(a []int, ord int) []int {
for i := 0; i < ord; i++ { for j := 0; j < len(a)-i-1; j++ { a[j] = a[j+1] - a[j] } } return a[:len(a)-ord]
}</lang>
- Output:
[90 47 58 29 22 32 55 5 55 73] [-2921]
Haskell
<lang haskell>forwardDifference :: Num a => [a] -> [a] forwardDifference = tail >>= zipWith (-)
nthForwardDifference :: Num a => [a] -> Int -> [a] nthForwardDifference = (!!) . iterate forwardDifference
main :: IO () main =
mapM_ print $ take 10 (iterate forwardDifference [90, 47, 58, 29, 22, 32, 55, 5, 55, 73])</lang>
- Output:
[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]
HicEst
<lang hicest>REAL :: n=10, list(n)
list = ( 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 ) WRITE(Format='i1, (i6)') 0, list
DO i = 1, n-1
ALIAS(list,1, diff,n-i) ! rename list(1 ... n-i) with diff diff = list($+1) - diff ! $ is the running left hand array index WRITE(Format='i1, (i6)') i, diff
ENDDO
END</lang>
- Output:
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
Icon and Unicon
<lang icon>procedure main(A) # Compute all forward difference orders for argument list
every order := 1 to (*A-1) do showList(order, fdiff(A, order))
end
procedure fdiff(A, order)
every 1 to order do { every put(B := [], A[i := 2 to *A] - A[i-1]) A := B } return A
end
procedure showList(order, L)
writes(right(order,3),": ") every writes(!L," ") write()
end</lang>
- A sample run:
->fdiff 3 1 4 1 5 9 2 6 3 1: -2 3 -3 4 4 -7 4 -3 2: 5 -6 7 0 -11 11 -7 3: -11 13 -7 -11 22 -18 4: 24 -20 -4 33 -40 5: -44 16 37 -73 6: 60 21 -110 7: -39 -131 8: -92 ->
IDL
Standard IDL library function TS_diff(X,k,[/double]):
<lang idl>print,(x = randomu(seed,8)*100)
15.1473 58.0953 82.7465 16.8637 97.7182 59.7856 17.7699 74.9154
print,ts_diff(x,1)
-42.9479 -24.6513 65.8828 -80.8545 37.9326 42.0157 -57.1455 0.000000
print,ts_diff(x,2)
-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</lang>
J
Of the many ways to code this in J, a particularly concise solution is: <lang j>fd=: 2&(-~/\)</lang>
Alternatively, to reduce the number of J primitives, use: <lang j>fd=: }. - }: ^:</lang>
(which is also elegant, because the open-ended power conjunction reads like "to the power of anything").
For example: <lang j> list=: 90 47 58 29 22 32 55 5 55 73 NB. Some numbers
1 fd list
_43 11 _29 _7 10 23 _50 50 18
2 fd list
54 _40 22 17 13 _73 100 _32</lang>
J is array oriented, so you can even ask for more than one forward difference at a time (i.e. N can be a list, instead of a single number): <lang j> 1 2 3 fd list NB. First, second, and third forward differences (simultaneously) 43 _11 29 7 _10 _23 50 _50 _18 54 _40 22 17 13 _73 100 _32 0 94 _62 5 4 86 _173 132 0 0
a: fd list NB. All forward differences 90 47 58 29 22 32 55 5 55 73 43 _11 29 7 _10 _23 50 _50 _18 0 54 _40 22 17 13 _73 100 _32 0 0 94 _62 5 4 86 _173 132 0 0 0 156 _67 1 _82 259 _305 0 0 0 0 223 _68 83 _341 564 0 0 0 0 0 291 _151 424 _905 0 0 0 0 0 0 442 _575 1329 0 0 0 0 0 0 0
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</lang>
Java
<lang java>import java.util.Arrays; public class FD {
public static void main(String args[]) { double[] a = {90, 47, 58, 29, 22, 32, 55, 5, 55, 73}; System.out.println(Arrays.toString(dif(a, 1))); System.out.println(Arrays.toString(dif(a, 2))); System.out.println(Arrays.toString(dif(a, 9))); System.out.println(Arrays.toString(dif(a, 10))); //let's test System.out.println(Arrays.toString(dif(a, 11))); System.out.println(Arrays.toString(dif(a, -1))); System.out.println(Arrays.toString(dif(a, 0))); }
public static double[] dif(double[] a, int n) { if (n < 0) return null; // if the programmer was dumb
for (int i = 0; i < n && a.length > 0; i++) { double[] b = new double[a.length - 1]; for (int j = 0; j < b.length; j++){ b[j] = a[j+1] - a[j]; } a = b; //"recurse" } return a; }
}</lang>
- Output:
[-43.0, 11.0, -29.0, -7.0, 10.0, 23.0, -50.0, 50.0, 18.0] [54.0, -40.0, 22.0, 17.0, 13.0, -73.0, 100.0, -32.0] [-2921.0] [] [] null [90.0, 47.0, 58.0, 29.0, 22.0, 32.0, 55.0, 5.0, 55.0, 73.0]
JavaScript
ES6
<lang JavaScript>(() => {
'use strict';
// forwardDifference :: Num a => [a] -> [a] const forwardDifference = xs => zipWith(subtract)(xs)(tail(xs));
// nthForwardDifference :: Num a => [a] -> Int -> [a] const nthForwardDifference = xs => index(iterate(forwardDifference)(xs)).Just;
//----------------------- TEST ------------------------ // main :: IO () const main = () => unlines( take(10)( iterate(forwardDifference)( [90, 47, 58, 29, 22, 32, 55, 5, 55, 73] ) ).map((x, i) => justifyRight(2)('x')(i) + ( ' -> ' ) + JSON.stringify(x)) );
//----------------- GENERIC FUNCTIONS -----------------
// Just :: a -> Maybe a const Just = x => ({ type: 'Maybe', Nothing: false, Just: x });
// Nothing :: Maybe a const Nothing = () => ({ type: 'Maybe', Nothing: true, });
// Tuple (,) :: a -> b -> (a, b) const Tuple = a => b => ({ type: 'Tuple', '0': a, '1': b, length: 2 });
// index (!!) :: [a] -> Int -> Maybe a // index (!!) :: Generator (Int, a) -> Int -> Maybe a // index (!!) :: String -> Int -> Maybe Char const index = xs => i => { const s = xs.constructor.constructor.name; return 'GeneratorFunction' !== s ? (() => { const v = xs[i]; return undefined !== v ? Just(v) : Nothing(); })() : Just(take(i)(xs), xs.next().value); };
// iterate :: (a -> a) -> a -> Gen [a] const iterate = f => function*(x) { let v = x; while (true) { yield(v); v = f(v); } };
// justifyRight :: Int -> Char -> String -> String const justifyRight = n => // The string s, preceded by enough padding (with // the character c) to reach the string length n. c => s => n > s.length ? ( s.padStart(n, c) ) : s;
// length :: [a] -> Int const length = xs => // Returns Infinity over objects without finite // length. This enables zip and zipWith to choose // the shorter argument when one is non-finite, // like cycle, repeat etc (Array.isArray(xs) || 'string' === typeof xs) ? ( xs.length ) : Infinity;
// map :: (a -> b) -> [a] -> [b] const map = f => // The list obtained by applying f // to each element of xs. // (The image of xs under f). xs => ( Array.isArray(xs) ? ( xs ) : xs.split() ).map(f);
// subtract :: Num -> Num -> Num const subtract = x => y => y - x;
// tail :: [a] -> [a] const tail = xs => // A new list consisting of all // items of xs except the first. 0 < xs.length ? xs.slice(1) : [];
// take :: Int -> [a] -> [a] // take :: Int -> String -> String const take = n => // The first n elements of a list, // string of characters, or stream. xs => 'GeneratorFunction' !== xs .constructor.constructor.name ? ( xs.slice(0, n) ) : [].concat.apply([], Array.from({ length: n }, () => { const x = xs.next(); return x.done ? [] : [x.value]; }));
// unlines :: [String] -> String const unlines = xs => // A single string formed by the intercalation // of a list of strings with the newline character. xs.join('\n');
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] const zipWith = f => xs => ys => { const lng = Math.min(length(xs), length(ys)), [as, bs] = [xs, ys].map(take(lng)); return Array.from({ length: lng }, (_, i) => f(as[i])( bs[i] )); };
// MAIN --- return main();
})();</lang>
- Output:
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]
jq
<lang jq># If n is a non-negative number and if input is
- a (possibly empty) array of numbers,
- emit an array, even if the input list is too short:
def ndiff(n):
if n==0 then . elif n == 1 then . as $in | [range(1;length) | $in[.] - $in[.-1]] else ndiff(1) | ndiff(n-1) end;</lang>
Example: <lang jq>def s: [90, 47, 58, 29, 22, 32, 55, 5, 55, 73];
range(0;12) as $i | (s|ndiff($i))</lang>
- Output:
<lang sh>$ jq -c -n -f forward-difference.jq [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] [] []</lang>
Julia
Using the built-in diff
function, which returns the 1st forward difference:
<lang julia>ndiff(A::Array, n::Integer) = n < 1 ? A : diff(ndiff(A, n-1))
s = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73] println.(collect(ndiff(s, i) for i in 0:9))</lang>
- Output:
[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]
K4
<lang k4>fd:1_-':</lang>
To compute the nth forward difference, call as: <lang k4>n fd/</lang>
In order to obtain all intermediate results, call as: <lang k4>n fd\</lang>
- Examples:
fd 1 2 4 7 11 16 1 2 3 4 5 2 fd/1 2 4 7 11 16 1 1 1 1 3 fd\1 2 4 7 11 16 (1 2 4 7 11 16;1 2 3 4 5;1 1 1 1;0 0 0)
Kotlin
<lang scala>// version 1.1.2
fun forwardDifference(ia: IntArray, order: Int): IntArray {
if (order < 0) throw IllegalArgumentException("Order must be non-negative") if (order == 0) return ia val size = ia.size if (size == 0) return ia // same empty array if (order >= size) return intArrayOf() // new empty array var old = ia var new = old var count = order while (count-- >= 1) { new = IntArray(old.size - 1) for (i in 0 until new.size) new[i] = old[i + 1] - old[i] old = new } return new
}
fun printArray(ia: IntArray) {
print("[") for (i in 0 until ia.size) { print("%5d".format(ia[i])) if (i < ia .size - 1) print(", ") } println("]")
}
fun main(args: Array<String>) {
val ia = intArrayOf(90, 47, 58, 29, 22, 32, 55, 5, 55, 73) for (order in 0..ia.size) { val fd = forwardDifference(ia, order) print("%2d".format(order) + ": ") printArray(fd) }
}</lang>
- Output:
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] 10: []
Lambdatalk
<lang scheme> {def fdiff
{lambda {:l} {A.new {S.map {{lambda {:l :i} {- {A.get {+ :i 1} :l} {A.get :i :l}} } :l} {S.serie 0 {- {A.length :l} 2}}}}}}
-> fdiff
{def disp
{lambda {:l} {if {A.empty? {A.rest :l}} then else {let { {:l {fdiff :l}} } {br}:l {disp :l}}}}}
-> disp
{def L {A.new 90 47 58 29 22 32 55 5 55 73}} -> L
{disp {L}} -> [-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] </lang>
Lasso
<lang lasso>#!/usr/bin/lasso9
define forwardDiff(values, order::integer=1) => {
!#order ? return #values->asArray local(result = array) iterate(#values) => { loop_count < #values->size ? #result->insert(#values->get(loop_count+1) - #values->get(loop_count)) } #order > 1 ? #result = forwardDiff(#result, #order-1) return #result
}
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))</lang>
- Output:
0: array(90, 47, 58, 29, 22, 32, 55, 5, 55, 73) 1: array(-43, 11, -29, -7, 10, 23, -50, 50, 18) 2: array(54, -40, 22, 17, 13, -73, 100, -32) 3: array(-94, 62, -5, -4, -86, 173, -132) 4: array(156, -67, 1, -82, 259, -305) 5: array(-223, 68, -83, 341, -564) 6: array(291, -151, 424, -905) 7: array(-442, 575, -1329) 8: array(1017, -1904) 9: array(-2921)
Logo
<lang logo>to fwd.diff :l
if empty? :l [output []] if empty? bf :l [output []] output fput (first bf :l)-(first :l) fwd.diff bf :l
end to nth.fwd.diff :n :l
if :n = 0 [output :l] output nth.fwd.diff :n-1 fwd.diff :l
end
show nth.fwd.diff 9 [90 47 58 29 22 32 55 5 55 73] [-2921]</lang>
Lua
<lang lua>function dif(a, b, ...)
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}))</lang>
M2000 Interpreter
Function Diff(a()) get an array by value (a shallow copy) <lang M2000 Interpreter> Form 80, 40 Module Forward_difference {
Print $(0,6) ' 6 characters column Dim a(), b() a()=(90,47,58,29,22,32,55,5,55,73) Function Diff(a()) { for i=0 to len(a())-2: a(i)=a(i+1)-a(i):Next i Dim a(len(a())-1) ' redim one less =a() } Print "Original:","",a() b()=a() ' copy a() to b() k=1 While len(b())>1 { b()=Diff(b()) ' copy returned array to b() Print "Difference ";k;":",b() k++ }
} Forward_difference
</lang>
- Output:
Original: 90 47 58 29 22 32 55 5 55 73 Difference 1: -43 11 -29 -7 10 23 -50 50 18 Difference 2: 54 -40 22 17 13 -73 100 -32 Difference 3: -94 62 -5 -4 -86 173 -132 Difference 4: 156 -67 1 -82 259 -305 Difference 5: -223 68 -83 341 -564 Difference 6: 291 -151 424 -905 Difference 7: -442 575 -1329 Difference 8: 1017 -1904 Difference 9: -2921
Mathematica / Wolfram Language
Built-in function: <lang Mathematica>i={3,5,12,1,6,19,6,2,4,9}; Differences[i]</lang>
- gives back:
<lang Mathematica>{2, 7, -11, 5, 13, -13, -4, 2, 5}</lang> The nth difference can be done as follows: <lang Mathematica>i={3,5,12,1,6,19,6,2,4,9}; Differences[i,n]</lang>
MATLAB / Octave
This is a built-in function. X is the list of numbers, n is the order of the forward difference. <lang MATLAB>Y = diff(X,n);</lang>
- Output:
1st order forward difference.
diff([1 2 3 4 5]) ans = 1 1 1 1
Maxima
<lang maxima>ldiff(u, n) := block([m: length(u)], for j thru n do u: makelist(u[i + 1] - u[i], i, 1, m - j), u);</lang>
NetRexx
<lang NetRexx>/* NetRexx*************************************************************
- Forward differences
- 18.08.2012 Walter Pachl derived from Rexx
- /
Loop n=-1 To 11 differences('90 47 58 29 22 32 55 5 55 73',n) End
method differences(a,n) public static --arr=Rexx[11] -- array must be declared (zero based) arr= -- alternative: indexed string m=a.words Select When n<0 Then Say 'n is negative:' n '<' 0 When n>m Then Say 'n is too large:' n '>' m Otherwise Do Loop i=1 To m arr[i]=a.word(i) End Loop i = 1 to n t = arr[i] Loop j = i+1 to m u = arr[j] arr[j] = arr[j]-t t = u end end ol= Loop i=n+1 to m ol=ol arr[i] End Say n ol End End</lang>
Output is the same as for Rexx
Nial
Define forward difference for order 1 <lang nial>fd is - [rest, front]</lang>
- Output:
forward difference of 4th order
<lang nial>b := 90 47 58 29 22 32 55 5 55 73 4 fold fd b = 156 -67 1 -82 259 -305</lang>
Nim
<lang nim>proc dif(s: seq[int]): seq[int] =
result = newSeq[int](s.len-1) for i in 0..<s.high: result[i] = s[i+1] - s[i]
proc difn(s: seq[int]; n: int): seq[int] =
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)</lang>
- Output:
@[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]
Objeck
<lang objeck> bundle Default {
class Test { function : Main(args : String[]) ~ Nil { a := [90.0, 47.0, 58.0, 29.0, 22.0, 32.0, 55.0, 5.0, 55.0, 73.0]; Print(Diff(a, 1)); Print(Diff(a, 2)); Print(Diff(a, 9)); }
function : Print(a : Float[]) ~ Nil { if(a <> Nil) { '['->Print(); each(i : a) { a[i]->Print(); ','->Print(); }; ']'->PrintLine(); }; }
function : Diff(a : Float[], n : Int) ~ Float[] { if (n < 0) { return Nil; };
for(i := 0; i < n & a->Size() > 0; i += 1;) { b := Float->New[a->Size() - 1]; for(j := 0; j < b->Size(); j += 1;){ b[j] := a[j+1] - a[j]; }; a := b; };
return a; } }
} </lang>
OCaml
<lang ocaml>let rec forward_difference = function
a :: (b :: _ as xs) -> b - a :: forward_difference xs | _ -> []
let rec nth_forward_difference n xs =
if n = 0 then xs else nth_forward_difference (pred n) (forward_difference xs)</lang>
- Output:
# nth_forward_difference 9 [90; 47; 58; 29; 22; 32; 55; 5; 55; 73];; - : int list = [-2921]
Oforth
<lang Oforth>: forwardDiff(l) l right(l size 1 -) l zipWith(#-) ;
- forwardDiffN(n, l) l #[ forwardDiff dup println ] times(n) ;</lang>
- Output:
10 [ 90, 47, 58, 29, 22, 32, 55, 5, 55, 73] forwardDiffN [-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] []
PARI/GP
<lang parigp>fd(v)=vector(#v-1,i,v[i+1]-v[i]);</lang>
Pascal
<lang pascal>Program ForwardDifferenceDemo(output);
procedure fowardDifference(list: array of integer);
var b: array of integer; i, newlength: integer; begin newlength := length(list) - 1; if newlength > 0 then begin setlength(b, newlength); for i := low(b) to high(b) do begin b[i] := list[i+1] - list[i]; write (b[i]:6); end; writeln; fowardDifference(b); end; end;
var
a: array [1..10] of integer = (90, 47, 58, 29, 22, 32, 55, 5, 55, 73);
begin
fowardDifference(a);
end.</lang>
- Output:
:> ./ForwardDifference -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
Perl
<lang perl>sub dif {
my @s = @_; map { $s[$_+1] - $s[$_] } 0 .. $#s-1
}
@a = qw<90 47 58 29 22 32 55 5 55 73>; while (@a) { printf('%6d', $_) for @a = dif @a; print "\n" }</lang>
- Output:
-43 11 -29 -7 10 23 -50 50 18 54 -40 22 17 13 -73 100 -32 -94 62 -5 -4 -86 173 -132 156 -67 1 -82 259 -305 -223 68 -83 341 -564 291 -151 424 -905 -442 575 -1329 1017 -1904 -2921
Phix
with javascript_semantics function fwd_diff_n(sequence s, integer order) assert(order<length(s)) s = deep_copy(s) for i=1 to order do for j=1 to length(s)-1 do s[j] = s[j+1]-s[j] end for s = s[1..-2] end for return s end function constant s = {90, 47, 58, 29, 22, 32, 55, 5, 55, 73} for i=1 to 9 do ?fwd_diff_n(s,i) end for
- Output:
{-43,11,-29,-7,10,23,-50,50,18} {54,-40,22,17,13,-73,100,-32} {-94,62,-5,-4,-86,173,-132} {156,-67,1,-82,259,-305} {-223,68,-83,341,-564} {291,-151,424,-905} {-442,575,-1329} {1017,-1904} {-2921}
PHP
<lang php><?php
function forwardDiff($anArray, $times = 1) {
if ($times <= 0) { return $anArray; } for ($accumilation = array(), $i = 1, $j = count($anArray); $i < $j; ++$i) { $accumilation[] = $anArray[$i] - $anArray[$i - 1]; } if ($times === 1) { return $accumilation; } return forwardDiff($accumilation, $times - 1);
}
class ForwardDiffExample extends PweExample {
function _should_run_empty_array_for_single_elem() { $expected = array($this->rand()->int()); $this->spec(forwardDiff($expected))->shouldEqual(array()); } function _should_give_diff_of_two_elem_as_single_elem() { $twoNums = array($this->rand()->int(), $this->rand()->int()); $expected = array($twoNums[1] - $twoNums[0]); $this->spec(forwardDiff($twoNums))->shouldEqual($expected); } function _should_compute_correct_forward_diff_for_longer_arrays() { $diffInput = array(10, 2, 9, 6, 5); $expected = array(-8, 7, -3, -1); $this->spec(forwardDiff($diffInput))->shouldEqual($expected); } function _should_apply_more_than_once_if_specified() { $diffInput = array(4, 6, 9, 3, 4); $expectedAfter1 = array(2, 3, -6, 1); $expectedAfter2 = array(1, -9, 7); $this->spec(forwardDiff($diffInput, 1))->shouldEqual($expectedAfter1); $this->spec(forwardDiff($diffInput, 2))->shouldEqual($expectedAfter2); } function _should_return_array_unaltered_if_no_times() { $this->spec(forwardDiff($expected = array(1,2,3), 0))->shouldEqual($expected); }
}</lang>
Picat
<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.</lang>
Output:
[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]]
PicoLisp
<lang PicoLisp>(de fdiff (Lst)
(mapcar - (cdr Lst) Lst) )
(for (L (90 47 58 29 22 32 55 5 55 73) L (fdiff L))
(println L) )</lang>
- Output:
(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)
PL/I
<lang PL/I> /* Forward differences. */ /* 23 April 2010 */ differences: procedure options (main);
declare a(10) fixed(10) static initial (7, 3, 9, 250, 300, 4, 68, 72, 154, 601); declare (i, j, m, n, t, u) fixed binary;
m = hbound(a,1); get (n); if n > m then signal error; put skip edit (a) (F(7)); do i = 1 to n; t = a(i); do j = i+1 to m; u = a(j); a(j) = a(j) - t; t = u; end; put skip edit (a) (F(7)); end; put skip edit ((a(i) do i = n+1 to m)) (F(9));
end differences; </lang>
Plain English
<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.</lang>
- Output:
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
Pop11
<lang pop11>define forward_difference(l);
lvars res = [], prev, el; if l = [] then return([]); endif; front(l) -> prev; for el in back(l) do cons(el - prev, res) -> res; el -> prev; endfor; rev(res);
enddefine;
define nth_difference(l, n);
lvars res = l, i; for i from 1 to n do forward_difference(res) -> res; endfor; res;
enddefine;</lang>
PowerShell
<lang PowerShell>function Forward-Difference( [UInt64] $n, [Array] $f ) { $flen = $f.length if( $flen -gt [Math]::Max( 1, $n ) ) { 0..( $flen - $n - 1 ) | ForEach-Object { $l=0; for( $k = 0; $k -le $n; $k++ ) { $j = 1 for( $i = 1; $i -le $k; $i++ ) { $j *= ( ( $n - $k + $i ) / $i ) } $l += $j * ( 1 - 2 * ( ( $n - $k ) % 2 ) ) * $f[ $_ + $k ] } $l } } }
Forward-Difference 2 1,2,4,5</lang>
PureBasic
<lang PureBasic>Procedure forward_difference(List a())
If ListSize(a()) <= 1 ClearList(a()): ProcedureReturn EndIf Protected NewList b() CopyList(a(), b()) LastElement(a()): DeleteElement(a()) SelectElement(b(), 1) ForEach a() a() - b(): NextElement(b()) Next
EndProcedure
Procedure nth_difference(List a(), List b(), n)
Protected i CopyList(a(), b()) For i = 1 To n forward_difference(b()) Next
EndProcedure
Procedure.s display(List a())
Protected output.s ForEach a() output + Str(a()) + "," Next ProcedureReturn RTrim(output,",")
EndProcedure
DataSection
;list data Data.i 10 ;element count Data.i 90, 47, 58, 29, 22, 32, 55, 5, 55, 73
EndDataSection
- create and fill list
Define i NewList a() Read.i i While i > 0
AddElement(a()): Read.i a(): i - 1
Wend
If OpenConsole()
NewList b() For i = 1 To 10 nth_difference(a(), b(), i) PrintN(Str(i) + " [" + display(b()) + "]") Next Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input() CloseConsole()
EndIf
</lang>
- Output:
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] 10 []
Python
Python 2
<lang python>>>> dif = lambda s: [x-s[i] for i,x in enumerate(s[1:])] >>> # 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
>>> s = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73] >>> difn(s, 0) [90, 47, 58, 29, 22, 32, 55, 5, 55, 73] >>> difn(s, 1) [-43, 11, -29, -7, 10, 23, -50, 50, 18] >>> difn(s, 2) [54, -40, 22, 17, 13, -73, 100, -32]
>>> from pprint import pprint >>> pprint( [difn(s, i) for i in xrange(10)] ) [[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]]</lang>
Python 3
Defining functions for first order and nth order forward difference:
<lang python>Forward difference
from itertools import islice
from operator import sub
- forwardDifference :: Num a => [a] -> [a]
def forwardDifference(xs):
1st order forward difference of xs. return [sub(*x) for x in zip(xs[1:], xs)]
- nthForwardDifference :: Num a => [a] -> Int -> [a]
def nthForwardDifference(xs):
Nth order forward difference of xs. return index(iterate(forwardDifference)(xs))
- ------------------------- TEST --------------------------
- main :: IO ()
def main():
Nth order forward difference.
xs = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73]
print('9th order forward difference of:') print(xs) print() print( ' -> ' + repr(nthForwardDifference(xs)(9)) )
print('\nSuccessive orders of forward difference:') print(unlines([ str(i) + ' -> ' + repr(x) for i, x in enumerate(take(10)( iterate(forwardDifference)(xs) )) ]))
- ------------------- GENERIC FUNCTIONS -------------------
- index (!!) :: [a] -> Int -> a
def index(xs):
Item at given (zero-based) index. return lambda n: None if 0 > n else ( xs[n] if ( hasattr(xs, "__getitem__") ) else next(islice(xs, n, None)) )
- iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
An infinite list of repeated applications of f to x. def go(x): v = x while True: yield v v = f(v) return go
- take :: Int -> [a] -> [a]
- take :: Int -> String -> String
def take(n):
The prefix of xs of length n, or xs itself if n > length xs. return lambda xs: ( xs[0:n] if isinstance(xs, (list, tuple)) else list(islice(xs, n)) )
- unlines :: [String] -> String
def unlines(xs):
A single string formed by the intercalation of a list of strings with the newline character. return '\n'.join(xs)
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
9th order forward difference of: [90, 47, 58, 29, 22, 32, 55, 5, 55, 73] -> [-2921] Successive orders of forward difference: 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]
Quackery
<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</lang>
- Output:
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 ]
R
<lang R>forwarddif <- function(a, n) {
if ( n == 1 ) a[2:length(a)] - a[1:length(a)-1] else { r <- forwarddif(a, 1) forwarddif(r, n-1) }
}
fdiff <- function(a, n) {
r <- a for(i in 1:n) { r <- r[2:length(r)] - r[1:length(r)-1] } r
}
v <- c(90, 47, 58, 29, 22, 32, 55, 5, 55, 73)
print(forwarddif(v, 9)) print(fdiff(v, 9))</lang>
Racket
<lang Racket>
- lang racket
(define (forward-difference list)
(for/list ([x (cdr list)] [y list]) (- x y)))
(define (nth-forward-difference n list)
(for/fold ([list list]) ([n n]) (forward-difference list)))
(nth-forward-difference 9 '(90 47 58 29 22 32 55 5 55 73))
- -> '(-2921)
</lang>
Raku
(formerly Perl 6)
Here we use signature matching to bind both an entire array and a version missing the head. 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. <lang perl6>sub dif(@array [$, *@tail]) { @tail Z- @array } sub difn($array, $n) { ($array, &dif ... *)[$n] }</lang>
REXX
no error checking
The REXX version uses the same (input) numbers (for the default) as the Ada example.
This version allows a specification of the list of numbers and/or which order to process. <lang rexx>/*REXX program computes the forward difference of a list of numbers. */ numeric digits 100 /*ensure enough accuracy (decimal digs)*/ parse arg e ',' N /*get a list: ε1 ε2 ε3 ε4 ··· , order */ if e== then e=90 47 58 29 22 32 55 5 55 73 /*Not specified? Then use the default.*/
- =words(e) /*# is the number of elements in list.*/
/* [↓] assign list numbers to @ array.*/ do i=1 for #; @.i=word(e, i)/1; end /*i*/ /*process each number one at a time. */ /* [↓] process the optional order. */
if N== then parse value 0 # # with bot top N /*define the default order range. */
else parse var N bot 1 top /*Not specified? Then use only 1 order*/
say right(# 'numbers:', 44) e /*display the header title and ··· */ say left(, 44)copies('─', length(e)+2) /* " " " fence. */
/* [↓] where da rubber meets da road. */ do o=bot to top; do r=1 for #; !.r=@.r; end /*r*/; $= do j=1 for o; d=!.j; do k=j+1 to #; parse value !.k !.k-d with d !.k; end /*k*/ end /*j*/ do i=o+1 to #; $=$ !.i/1; end /*i*/ if $== then $=' [null]' say right(o, 7)th(o)'─order forward difference vector =' $ end /*o*/
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))</lang> output when using the default input:
10 numbers: 90 47 58 29 22 32 55 5 55 73 ────────────────────────────── 0th-order forward difference vector = 90 47 58 29 22 32 55 5 55 73 1st-order forward difference vector = -43 11 -29 -7 10 23 -50 50 18 2nd-order forward difference vector = 54 -40 22 17 13 -73 100 -32 3rd-order forward difference vector = -94 62 -5 -4 -86 173 -132 4th-order forward difference vector = 156 -67 1 -82 259 -305 5th-order forward difference vector = -223 68 -83 341 -564 6th-order forward difference vector = 291 -151 424 -905 7th-order forward difference vector = -442 575 -1329 8th-order forward difference vector = 1017 -1904 9th-order forward difference vector = -2921 10th-order forward difference vector = [null]
output when the Tcl's input was used: 90.5 47 58 29 22 32 55 5 55 73.5
10 numbers: 90.5 47 58 29 22 32 55 5 55 73.5 ────────────────────────────────── 0th-order forward difference vector = 90.5 47 58 29 22 32 55 5 55 73.5 1st-order forward difference vector = -43.5 11 -29 -7 10 23 -50 50 18.5 2nd-order forward difference vector = 54.5 -40 22 17 13 -73 100 -31.5 3rd-order forward difference vector = -94.5 62 -5 -4 -86 173 -131.5 4th-order forward difference vector = 156.5 -67 1 -82 259 -304.5 5th-order forward difference vector = -223.5 68 -83 341 -563.5 6th-order forward difference vector = 291.5 -151 424 -904.5 7th-order forward difference vector = -442.5 575 -1328.5 8th-order forward difference vector = 1017.5 -1903.5 9th-order forward difference vector = -2921 10th-order forward difference vector = [null]
with error checking
<lang rexx>/*REXX program computes the forward difference of a list of numbers. */ numeric digits 100 /*ensure enough accuracy (decimal digs)*/ parse arg e ',' N /*get a list: ε1 ε2 ε3 ε4 ··· , order */ if e== then e=90 47 58 29 22 32 55 5 55 73 /*Not specified? Then use the default.*/
- =words(e) /*# is the number of elements in list.*/
/* [↓] verify list items are numeric. */ do i=1 for #; _=word(e, i) /*process each number one at a time. */ if \datatype(_, 'N') then call ser _ "isn't a valid number"; @.i=_/1 end /*i*/ /* [↑] removes superfluous stuff. */ /* [↓] process the optional order. */
if N== then parse value 0 # # with bot top N /*define the default order range. */
else parse var N bot 1 top /*Not specified? Then use only 1 order*/
if #==0 then call ser "no numbers were specified." if N<0 then call ser N "(order) can't be negative." if N># then call ser N "(order) can't be greater than" # say right(# 'numbers:', 44) e /*display the header (title) and ··· */ say left(, 44)copies('─', length(e)+2) /*display the header fence. */
/* [↓] where da rubber meets da road. */ do o=bot to top; do r=1 for #; !.r=@.r; end /*r*/; $= do j=1 for o; d=!.j; do k=j+1 to #; parse value !.k !.k-d with d !.k; end /*k*/ end /*j*/ do i=o+1 to #; $=$ !.i/1; end /*i*/ if $== then $=' [null]' say right(o, 7)th(o)'─order forward difference vector =' $ end /*o*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ 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))</lang> output is the same as the REXX entry above.
with output alignment
<lang rexx>/*REXX program computes the forward difference of a list of numbers. */ numeric digits 100 /*ensure enough accuracy (decimal digs)*/ parse arg e ',' N /*get a list: ε1 ε2 ε3 ε4 ··· , order */ if e== then e=90 47 58 29 22 32 55 5 55 73 /*Not specified? Then use the default.*/
- =words(e); w=5 /*# is the number of elements in list.*/
/* [↓] verify list items are numeric. */ do i=1 for #; _=word(e, i) /*process each number one at a time. */ if \datatype(_, 'N') then call ser _ "isn't a valid number"; @.i=_/1 w=max(w, length(@.i)) /*use the maximum length of an element.*/ end /*i*/ /* [↑] removes superfluous stuff. */ /* [↓] process the optional order. */
if N== then parse value 0 # # with bot top N /*define the default order range. */
else parse var N bot 1 top /*Not specified? Then use only 1 order*/
if #==0 then call ser "no numbers were specified." if N<0 then call ser N "(order) can't be negative." if N># then call ser N "(order) can't be greater than" # _=; do k=1 for #; _=_ right(@.k, w); end /*k*/; _=substr(_, 2) say right(# 'numbers:', 44) _ /*display the header title and ··· */ say left(, 44)copies('─', w*#+#) /* " " " fence. */
/* [↓] where da rubber meets da road. */ do o=bot to top; do r=1 for #; !.r=@.r; end /*r*/; $= do j=1 for o; d=!.j; do k=j+1 to #; parse value !.k !.k-d with d !.k w=max(w, length(!.k)) end /*k*/ end /*j*/ do i=o+1 to #; $=$ right(!.i/1, w); end /*i*/ if $== then $=' [null]' say right(o, 7)th(o)'─order forward difference vector =' $ end /*o*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ 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))</lang> output when using the default input:
10 numbers: 90 47 58 29 22 32 55 5 55 73 ──────────────────────────────────────────────────────────── 0th─order forward difference vector = 90 47 58 29 22 32 55 5 55 73 1st─order forward difference vector = -43 11 -29 -7 10 23 -50 50 18 2nd─order forward difference vector = 54 -40 22 17 13 -73 100 -32 3rd─order forward difference vector = -94 62 -5 -4 -86 173 -132 4th─order forward difference vector = 156 -67 1 -82 259 -305 5th─order forward difference vector = -223 68 -83 341 -564 6th─order forward difference vector = 291 -151 424 -905 7th─order forward difference vector = -442 575 -1329 8th─order forward difference vector = 1017 -1904 9th─order forward difference vector = -2921 10th─order forward difference vector = [null]
Version 2
<lang rexx>/* REXX ***************************************************************
- Forward differences
- 18.08.2012 Walter Pachl derived from PL/I
- /
Do n=-1 To 11
Call differences '90 47 58 29 22 32 55 5 55 73',n End
Exit
differences: Procedure
Parse Arg a,n m=words(a) Select When n<0 Then Say 'n is negative:' n '<' 0 When n>m Then Say 'n is too large:' n '>' m Otherwise Do Do i=1 By 1 while a<> Parse Var a a.i a End Do i = 1 to n; t = a.i; Do j = i+1 to m; u = a.j a.j = a.j-t; t = u; end; end; ol= Do k=n+1 to m ol=ol a.k End Say n ol End End Return</lang>
- Output:
for Java's input
n is negative: -1 < 0 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 10 n is too large: 11 > 10
Ring
<lang ring>
- Project : Forward difference
s = [90, 47, 58, 29, 22, 32, 55, 5, 55, 73] for p = 1 to 9
s = fwddiff(s) showarray(s)
next
func fwddiff(s)
for j=1 to len(s)-1 s[j] = s[j+1]-s[j] next n = len(s) del(s, n) return s
func showarray(vect)
see "{" svect = "" for n = 1 to len(vect) svect = svect + vect[n] + ", " next svect = left(svect, len(svect) - 2) see svect see "}" + nl
</lang> Output:
{-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}
Ruby
This code uses new features from Ruby 1.8.7:
- Enumerable#each_cons is a new method.
- Integer#times, without a block, returns an enumerator.
<lang ruby>def dif(s)
s.each_cons(2).collect { |x, y| y - x }
end
def difn(s, n)
n.times.inject(s) { |s, | dif(s) }
end</lang>
- Example usage:
<lang ruby>p dif([1, 23, 45, 678]) # => [22, 22, 633] p difn([1, 23, 45, 678], 2) # => [0, 611]</lang>
Scala
<lang scala>def fdiff(xs: List[Int]) = (xs.tail, xs).zipped.map(_ - _)
def fdiffn(i: Int, xs: List[Int]): List[Int] = if (i == 1) fdiff(xs) else fdiffn(i - 1, fdiff(xs))</lang>
- Example:
<lang scala>val l=List(90,47,58,29,22,32,55,5,55,73) (1 to 9)foreach(x=>println(fdiffn(x,l)))</lang>
- Output:
List(-43, 11, -29, -7, 10, 23, -50, 50, 18) List(54, -40, 22, 17, 13, -73, 100, -32) List(-94, 62, -5, -4, -86, 173, -132) List(156, -67, 1, -82, 259, -305) List(-223, 68, -83, 341, -564) List(291, -151, 424, -905) List(-442, 575, -1329) List(1017, -1904) List(-2921)
Scheme
<lang scheme>(define (forward-diff lst)
(if (or (null? lst) (null? (cdr lst))) '() (cons (- (cadr lst) (car lst)) (forward-diff (cdr lst)))))
(define (nth-forward-diff n xs)
(if (= n 0) xs (nth-forward-diff (- n 1) (forward-diff xs))))</lang>
- Output:
> (nth-forward-diff 9 '(90 47 58 29 22 32 55 5 55 73)) (-2921)
Seed7
<lang seed7>$ include "seed7_05.s7i";
const func array integer: forwardDifference (in array integer: data) is func
result var array integer: diffResult is 0 times 0; local var integer: index is 0; begin for index range 1 to pred(length(data)) do diffResult &:= -data[index] + data[succ(index)]; end for; end func;
const proc: main is func
local var array integer: data is [] (90, 47, 58, 29, 22, 32, 55, 5, 55, 73); var integer: level is 0; var integer: number is 0; var boolean: firstElement is TRUE; begin for level range 0 to length(data) do firstElement := TRUE; for number range data do if not firstElement then write(", "); end if; firstElement := FALSE; write(number); end for; writeln; data := forwardDifference(data); end for; end func;</lang>
- Output:
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
SequenceL
Solution that keeps track of intermediate values: <lang sequenceL> forwardDifference(x(1), n) := forwardDifferenceHelper(x, n, [x]);
forwardDifferenceHelper(x(1), n, result(2)) := let difference := tail(x) - x[1 ... size(x) - 1]; in result when n = 0 or size(x) = 1 else forwardDifferenceHelper(difference, n - 1, result ++ [difference]); </lang> If no intermediate values are needed, the following is sufficient: <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); </lang>
Sidef
<lang ruby>func dif(arr) {
gather { for i (0 ..^ arr.end) { take(arr[i+1] - arr[i]) } }
}
func difn(n, arr) {
{ arr = dif(arr) } * n arr
}
say dif([1, 23, 45, 678]) # => [22, 22, 633] say difn(2, [1, 23, 45, 678]) # => [0, 611]</lang>
Slate
<lang slate>s@(Sequence traits) forwardDifference [
s allButFirst with: s allButLast collect: #- `er
].
s@(Sequence traits) forwardDifference "Without creating two intermediate throwaway Sequences." [
result ::= s allButFirst. result doWithIndex: [| :nextValue :index | result at: index infect: [| :oldValue | oldValue - (s at: index)]. result
].
s@(Sequence traits) forwardDifference: n [
(0 below: n) inject: s into: [| :seq :_ | seq forwardDifference]
].</lang>
- Usage:
<lang slate>#data := ##(90 47 58 29 22 32 55 5 55 73). data keysDo: [| :index | inform: (data forwardDifference: index) printString].</lang>
Smalltalk
<lang smalltalk>Array extend [
difference [ ^self allButFirst with: self allButLast collect: [ :a :b | a - b ] ]
nthOrderDifference: n [ ^(1 to: n) inject: self into: [ :old :unused | old difference ] ]
]
s := #(90 47 58 29 22 32 55 5 55 73) 1 to: s size - 1 do: [ :i |
(s nthOrderDifference: i) printNl ]</lang>
SQL
<lang sql>WITH RECURSIVE T0 (N, ITEM, LIST, NEW_LIST) AS (
SELECT 1, NULL, '90,47,58,29,22,32,55,5,55,73' || ',', NULL UNION ALL SELECT CASE WHEN SUBSTR(LIST, INSTR(LIST, ',') + 1, LENGTH(LIST)) = THEN N + 1 ELSE N END, CASE WHEN SUBSTR(LIST, INSTR(LIST, ',') + 1, LENGTH(LIST)) <> THEN SUBSTR(LIST, 1, INSTR(LIST, ',') - 1) ELSE NULL END, CASE WHEN SUBSTR(LIST, INSTR(LIST, ',') + 1, LENGTH(LIST)) = THEN IFNULL(NEW_LIST || (SUBSTR(LIST, 1, INSTR(LIST, ',') - 1) - ITEM) || ',', ) ELSE SUBSTR(LIST, INSTR(LIST, ',') + 1, LENGTH(LIST)) END, CASE WHEN SUBSTR(LIST, INSTR(LIST, ',') + 1, LENGTH(LIST)) <> THEN IFNULL(NEW_LIST, ) || IFNULL((SUBSTR(LIST, 1, INSTR(LIST, ',') - 1) - ITEM) || ',', ) ELSE NULL END FROM T0 WHERE INSTR(LIST, ',') > 0
) SELECT N,
TRIM(LIST, ',') LIST FROM T0 WHERE NEW_LIST IS NULL AND LIST <> ORDER BY N;</lang>
Standard ML
<lang sml>fun forward_difference xs = ListPair.map op- (tl xs, xs)
fun nth_forward_difference n xs =
if n = 0 then xs else nth_forward_difference (n-1) (forward_difference xs)</lang>
- Output:
- nth_forward_difference 9 [90, 47, 58, 29, 22, 32, 55, 5, 55, 73]; val it = [~2921] : int list
Stata
It's possible to implement differences using row indices. For instance, first forward differences of a variable x can be defined by:
<lang stata>gen y=x[_n+1]-x[_n]</lang>
However, it's much more natural to use time-series varlists. In order to use them, it's necessary to first set a time variable, which may be simply an index variable.
<lang stata>* First create a dataset clear all set obs 100 gen i=_n tsset i gen x=rnormal()
- Differences
display "Difference order?" _request(k) gen y=D${k}F${k}.x</lang>
Swift
<lang swift>func forwardsDifference<T: SignedNumeric>(of arr: [T]) -> [T] {
return zip(arr.dropFirst(), arr).map({ $0.0 - $0.1 })
}
func nthForwardsDifference<T: SignedNumeric>(of arr: [T], n: Int) -> [T] {
assert(n >= 0)
switch (arr, n) { case ([], _): return [] case let (arr, 0): return arr case let (arr, i): return nthForwardsDifference(of: forwardsDifference(of: arr), n: i - 1) }
}
for diff in (0...9).map({ nthForwardsDifference(of: [90, 47, 58, 29, 22, 32, 55, 5, 55, 73], n: $0) }) {
print(diff)
}</lang>
- Output:
[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]
Tcl
<lang tcl>proc do_fwd_diff {list} {
set previous [lindex $list 0] set new [list] foreach current [lrange $list 1 end] { lappend new [expr {$current - $previous}] set previous $current } return $new
}
proc fwd_diff {list order} {
while {$order >= 1} { set list [do_fwd_diff $list] incr order -1 } return $list
}
set a {90.5 47 58 29 22 32 55 5 55 73.5}
for {set order 0} {$order <= 10} {incr order} {
puts [format "%d\t%s" $order [fwd_diff $a $order]]
}</lang>
- Output:
0 90.5 47 58 29 22 32 55 5 55 73.5 1 -43.5 11 -29 -7 10 23 -50 50 18.5 2 54.5 -40 22 17 13 -73 100 -31.5 3 -94.5 62 -5 -4 -86 173 -131.5 4 156.5 -67 1 -82 259 -304.5 5 -223.5 68 -83 341 -563.5 6 291.5 -151 424 -904.5 7 -442.5 575 -1328.5 8 1017.5 -1903.5 9 -2921.0 10
Ursala
This function doesn't need to be defined because it's in a library already, but it could be defined like this: <lang Ursala>#import std
- import nat
- import flo
nth_diff "n" = rep"n" minus*typ</lang> test program: <lang Ursala>test_data = <90.,47.,58.,29.,22.,32.,55.,5.,55.,73.>
- show+
examples =
printf/*=*' %0.0f' <
nth_diff6 test_data, nth_diff7 test_data></lang>
- Output:
291 -151 424 -905 -442 575 -1329
Visual Basic .NET
<lang vbnet>Module ForwardDifference
Sub Main() Dim lNum As New List(Of Integer)(New Integer() {90, 47, 58, 29, 22, 32, 55, 5, 55, 73}) For i As UInteger = 0 To 9 Console.WriteLine(String.Join(" ", (From n In Difference(i, lNum) Select String.Format("{0,5}", n)).ToArray())) Next Console.ReadKey() End Sub
Private Function Difference(ByVal Level As UInteger, ByVal Numbers As List(Of Integer)) As List(Of Integer) If Level >= Numbers.Count Then Throw New ArgumentOutOfRangeException("Level", "Level must be less than number of items in Numbers")
For i As Integer = 1 To Level Numbers = (From n In Enumerable.Range(0, Numbers.Count - 1) _ Select Numbers(n + 1) - Numbers(n)).ToList() Next
Return Numbers End Function
End Module</lang>
- Output:
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
Visual FoxPro
<lang vfp>
- DEFINE CTAB CHR(9)
LOCAL lcList As String, i As Integer, n As Integer n = 10 LOCAL ARRAY aa[n] CLEAR lcList = "90,47,58,29,22,32,55,5,55,73" FOR i = 1 TO n
aa[i] = VAL(GETWORDNUM(lcList, i, ","))
ENDFOR ShowOutput("Original", @aa) k = n - 1 FOR i = 1 TO n - 1
ForwardDiff(@aa) ShowOutput("Difference " + TRANSFORM(i), @aa)
ENDFOR
PROCEDURE ForwardDiff(a) LOCAL i As Integer, n As Integer n = ALEN(a) LOCAL ARRAY b[n-1] FOR i = 1 TO n - 1
b[i] = a[i+1] - a[i]
ENDFOR DIMENSION a[n-1] ACOPY(b, a) ENDPROC
PROCEDURE ShowOutput(lcLabel, zz) LOCAL i As Integer, n As Integer, lcTxt As String n = ALEN(zz) lcTxt = lcLabel + ":" + CTAB FOR i = 1 TO n
lcTxt = lcTxt + TRANSFORM(zz[i]) + CTAB
ENDFOR lcTxt = LEFT(lcTxt, LEN(lcTxt) - 1) ? lcTxt ENDPROC </lang>
- Output:
Original: 90 47 58 29 22 32 55 5 55 73 Difference 1: -43 11 -29 -7 10 23 -50 50 18 Difference 2: 54 -40 22 17 13 -73 100 -32 Difference 3: -94 62 -5 -4 -86 173 -132 Difference 4: 156 -67 1 -82 259 -305 Difference 5: -223 68 -83 341 -564 Difference 6: 291 -151 424 -905 Difference 7: -442 575 -1329 Difference 8: 1017 -1904 Difference 9: -2921
Wren
<lang ecmascript>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)</lang>
- Output:
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
zkl
<lang zkl>fcn forwardDiff(lst){
if(lst.len()<2) return(T); return(T(lst[1]-lst[0]).extend(forwardDiff(lst[1,*])))
} fcn nthForwardDiff(n,xs){
if(n==0) return(xs); return(nthForwardDiff(n-1,forwardDiff(xs))) // tail recursion
}</lang> <lang zkl>nthForwardDiff(9,T(90, 47, 58, 29, 22, 32, 55, 5, 55, 73)).println();</lang>
- Output:
L(-2921)
ZX Spectrum Basic
<lang zxbasic>10 DATA 9,0,1,2,4,7,4,2,1,0 20 LET p=1 30 READ n: DIM b(n) 40 FOR i=1 TO n 50 READ b(i) 60 NEXT i 70 FOR j=1 TO p 80 FOR i=1 TO n-j 90 LET b(i)=b(i+1)-b(i) 100 NEXT i 110 NEXT j 120 FOR i=1 TO n-p 130 PRINT b(i);" "; 140 NEXT i</lang>