Averages/Root mean square
Compute the Root mean square of the numbers 1..10.
You are encouraged to solve this task according to the task description, using any language you may know.
The root mean square is also known by its initials RMS (or rms), and as the quadratic mean.
The RMS is calculated as the mean of the squares of the numbers, square-rooted:
Ada
<lang Ada>with Ada.Float_Text_IO; use Ada.Float_Text_IO; with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; procedure calcrms is type float_arr is array(1..10) of Float;
function rms(nums : float_arr) return Float is sum : Float := 0.0; begin for p in nums'Range loop sum := sum + nums(p)**2; end loop; return sqrt(sum/Float(nums'Length)); end rms;
list : float_arr; begin list := (1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0); put( rms(list) , Exp=>0); end calcrms;</lang>
- Output:
6.20484
ALGOL 68
<lang algol68># Define the rms PROCedure & ABS OPerators for LONG... REAL # MODE RMSFIELD = #LONG...# REAL; PROC (RMSFIELD)RMSFIELD rms field sqrt = #long...# sqrt; INT rms field width = #long...# real width;
PROC crude rms = ([]RMSFIELD v)RMSFIELD: (
RMSFIELD sum := 0; FOR i FROM LWB v TO UPB v DO sum +:= v[i]**2 OD; rms field sqrt(sum / (UPB v - LWB v + 1))
);
PROC rms = ([]RMSFIELD v)RMSFIELD: (
- round off error accumulated at standard precision #
RMSFIELD sum := 0, round off error:= 0; FOR i FROM LWB v TO UPB v DO RMSFIELD org = sum, prod = v[i]**2; sum +:= prod; round off error +:= sum - org - prod OD; rms field sqrt((sum - round off error)/(UPB v - LWB v + 1))
);
main: (
[]RMSFIELD one to ten = (1,2,3,4,5,6,7,8,9,10);
print(("crude rms(one to ten): ", crude rms(one to ten), new line)); print(("rms(one to ten): ", rms(one to ten), new line))
)</lang>
- Output:
crude rms(one to ten): +6.20483682299543e +0 rms(one to ten): +6.20483682299543e +0
ALGOL W
<lang algolw>begin
% computes the root-mean-square of an array of numbers with % % the specified lower bound (lb) and upper bound (ub) % real procedure rms( real array numbers ( * ) ; integer value lb ; integer value ub ) ; begin real sum; sum := 0; for i := lb until ub do sum := sum + ( numbers(i) * numbers(i) ); sqrt( sum / ( ( ub - lb ) + 1 ) ) end rms ;
% test the rms procedure with the numbers 1 to 10 % real array testNumbers( 1 :: 10 ); for i := 1 until 10 do testNumbers(i) := i; r_format := "A"; r_w := 10; r_d := 4; % set fixed point output % write( "rms of 1 .. 10: ", rms( testNumbers, 1, 10 ) );
end.</lang>
- Output:
rms of 1 .. 10: 6.2048
APL
<lang APL> rms←{((+/⍵*2)÷⍴⍵)*0.5}
x←⍳10
rms x
6.204836823</lang>
AppleScript
( ES6 version )
<lang AppleScript>-- rootMeanSquare :: [Num] -> Real on rootMeanSquare(xs)
script plusSquare on lambda(a, x) a + x * x end lambda end script (foldl(plusSquare, 0, xs) / (length of xs)) ^ (1 / 2)
end rootMeanSquare
-- TEST
on run
rootMeanSquare({1, 2, 3, 4, 5, 6, 7, 8, 9, 10}) -- > 6.204836822995
end run
-- GENERIC FUNCTIONS
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f) set v to startValue set lng to length of xs repeat with i from 1 to lng set v to lambda(v, item i of xs, i, xs) end repeat return v end tell
end foldl
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then f else script property lambda : f end script end if
end mReturn</lang>
- Output:
6.204836822995
AutoHotkey
Using a loop
<lang autohotkey>MsgBox, % RMS(1, 10)
- ---------------------------------------------------------------------------
RMS(a, b) { ; Root Mean Square of integers a through b
- ---------------------------------------------------------------------------
n := b - a + 1 Loop, %n% Sum += (a + A_Index - 1) ** 2 Return, Sqrt(Sum / n)
}</lang> Message box shows:
6.204837
Avoiding a loop
Using these equations:
See wp:List of mathematical series
for :
We can show that:
<lang autohotkey>MsgBox, % RMS(1, 10)
- ---------------------------------------------------------------------------
RMS(a, b) { ; Root Mean Square of integers a through b
- ---------------------------------------------------------------------------
Return, Sqrt((b*(b+1)*(2*b+1)-a*(a-1)*(2*a-1))/6/(b-a+1))
}</lang> Message box shows:
6.204837
AWK
<lang awk>#!/usr/bin/awk -f
- computes RMS of the 1st column of a data file
{
x = $1; # value of 1st column S += x*x; N++;
}
END {
print "RMS: ",sqrt(S/N);
}</lang>
BASIC
Note that this will work in Visual Basic and the Windows versions of PowerBASIC by simply wrapping the module-level code into the MAIN
function, and changing PRINT
to MSGBOX
.
<lang qbasic>DIM i(1 TO 10) AS DOUBLE, L0 AS LONG FOR L0 = 1 TO 10
i(L0) = L0
NEXT PRINT STR$(rms#(i()))
FUNCTION rms# (what() AS DOUBLE)
DIM L0 AS LONG, tmp AS DOUBLE, rt AS DOUBLE FOR L0 = LBOUND(what) TO UBOUND(what) rt = rt + (what(L0) ^ 2) NEXT tmp = UBOUND(what) - LBOUND(what) + 1 rms# = SQR(rt / tmp)
END FUNCTION</lang>
See also: BBC BASIC, Liberty BASIC, PureBasic, Run BASIC
Applesoft BASIC
<lang ApplesoftBasic> 10 N = 10
20 FOR I = 1 TO N 30 S = S + I * I 40 NEXT 50 X = SQR (S / N) 60 PRINT X</lang>
- Output:
6.20483683
BBC BASIC
<lang bbcbasic> DIM array(9)
array() = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 PRINT FNrms(array()) END DEF FNrms(a()) = MOD(a()) / SQR(DIM(a(),1)+1)</lang>
C
<lang c>#include <stdio.h>
- include <math.h>
double rms(double *v, int n) {
int i; double sum = 0.0; for(i = 0; i < n; i++) sum += v[i] * v[i]; return sqrt(sum / n);
}
int main(void) {
double v[] = {1., 2., 3., 4., 5., 6., 7., 8., 9., 10.}; printf("%f\n", rms(v, sizeof(v)/sizeof(double))); return 0;
}</lang>
C#
<lang csharp>using System;
namespace rms {
class Program { static void Main(string[] args) { int[] x = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }; Console.WriteLine(rootMeanSquare(x)); }
private static double rootMeanSquare(int[] x) { double sum = 0; for (int i = 0; i < x.Length; i++) { sum += (x[i]*x[i]); } return Math.Sqrt(sum / x.Length); } }
}</lang> An alternative method demonstrating the more functional style introduced by LINQ and lambda expressions in C# 3.
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
namespace rms {
class Program { static void Main(string[] args) { Console.WriteLine(rootMeanSquare(Enumerable.Range(1, 10))); }
private static double rootMeanSquare(IEnumerable<int> x) { return Math.Sqrt((double)x.Sum(n => n * n) / x.Count()); } }
}</lang>
C++
<lang Cpp>#include <iostream>
- include <vector>
- include <cmath>
- include <numeric>
int main( ) {
std::vector<int> numbers ; for ( int i = 1 ; i < 11 ; i++ ) numbers.push_back( i ) ; double meansquare = sqrt( ( std::inner_product( numbers.begin(), numbers.end(), numbers.begin(), 0 ) ) / static_cast<double>( numbers.size() ) ); std::cout << "The quadratic mean of the numbers 1 .. " << numbers.size() << " is " << meansquare << " !\n" ; return 0 ;
}</lang>
- Output:
The quadratic mean of the numbers 1 .. 10 is 6.20484 !
Clojure
<lang clojure>(use '[clojure.contrib.math :only (sqrt)])
(defn rms [xs]
(sqrt (/ (reduce + (map #(* % %) xs))
(count xs))))
(println (rms (range 1 11)))</lang>
- Output:
6.2048368229954285
COBOL
Could be written more succinctly, with an inline loop and more COMPUTE statements; but that wouldn't be very COBOLic. <lang cobol>IDENTIFICATION DIVISION. PROGRAM-ID. QUADRATIC-MEAN-PROGRAM. DATA DIVISION. WORKING-STORAGE SECTION. 01 QUADRATIC-MEAN-VARS.
05 N PIC 99 VALUE 0. 05 N-SQUARED PIC 999. 05 RUNNING-TOTAL PIC 999 VALUE 0. 05 MEAN-OF-SQUARES PIC 99V9(16). 05 QUADRATIC-MEAN PIC 9V9(15).
PROCEDURE DIVISION. CONTROL-PARAGRAPH.
PERFORM MULTIPLICATION-PARAGRAPH 10 TIMES. DIVIDE RUNNING-TOTAL BY 10 GIVING MEAN-OF-SQUARES. COMPUTE QUADRATIC-MEAN = FUNCTION SQRT(MEAN-OF-SQUARES). DISPLAY QUADRATIC-MEAN UPON CONSOLE. STOP RUN.
MULTIPLICATION-PARAGRAPH.
ADD 1 TO N. MULTIPLY N BY N GIVING N-SQUARED. ADD N-SQUARED TO RUNNING-TOTAL.</lang>
- Output:
6.204836822995428
CoffeeScript
<lang coffeescript> root_mean_square = (ary) ->
sum_of_squares = ary.reduce ((s,x) -> s + x*x), 0 return Math.sqrt(sum_of_squares / ary.length) alert root_mean_square([1..10])</lang>
Common Lisp
<lang lisp>(loop for x from 1 to 10
for xx = (* x x) for n from 1 summing xx into xx-sum finally (return (sqrt (/ xx-sum n))))</lang>
Here's a non-iterative solution.
<lang lisp> (defun root-mean-square (numbers)
"Takes a list of numbers, returns their quadratic mean." (sqrt (/ (apply #'+ (mapcar #'(lambda (x) (* x x)) numbers)) (length numbers))))
(root-mean-square (loop for i from 1 to 10 collect i)) </lang>
D
<lang d>import std.stdio, std.math, std.algorithm, std.range;
real rms(R)(R d) pure {
return sqrt(d.reduce!((a, b) => a + b * b) / real(d.length));
}
void main() {
writefln("%.19f", iota(1, 11).rms);
}</lang>
- Output:
6.2048368229954282979
Delphi/Pascal
<lang Delphi>program AveragesMeanSquare;
{$APPTYPE CONSOLE}
uses Types;
function MeanSquare(aArray: TDoubleDynArray): Double; var
lValue: Double;
begin
Result := 0;
for lValue in aArray do Result := Result + (lValue * lValue); if Result > 0 then Result := Sqrt(Result / Length(aArray));
end;
begin
Writeln(MeanSquare(TDoubleDynArray.Create())); Writeln(MeanSquare(TDoubleDynArray.Create(1,2,3,4,5,6,7,8,9,10)));
end.</lang>
E
Using the same generic mean function as used in pythagorean means: <lang e>def makeMean(base, include, finish) {
return def mean(numbers) { var count := 0 var acc := base for x in numbers { acc := include(acc, x) count += 1 } return finish(acc, count) }
}
def RMS := makeMean(0, fn b,x { b+x**2 }, fn acc,n { (acc/n).sqrt() })</lang>
<lang e>? RMS(1..10)
- value: 6.2048368229954285</lang>
EchoLisp
<lang scheme> (define (rms xs)
(sqrt (// (for/sum ((x xs)) (* x x)) (length xs))))
(rms (range 1 11))
→ 6.2048368229954285
</lang>
Elixir
<lang elixir> defmodule RC do
def root_mean_square(enum) do enum |> square |> mean |> :math.sqrt end
defp mean(enum), do: Enum.sum(enum) / Enum.count(enum)
defp square(enum), do: (for x <- enum, do: x * x)
end
IO.puts RC.root_mean_square(1..10) </lang>
- Output:
6.2048368229954285
Emacs Lisp
<Lang lisp> (defun rms (nums)
;; `/' returns a float only when given floats (setq nums (mapcar 'float nums)) (sqrt (/ (apply '+ (mapcar (lambda (x) (* x x)) nums))
(length nums)))) </lang>
or, if using Emacs's Common Lisp library cl-lib.el
to use cl-map
:
<Lang lisp>
(defun rms (nums)
(setq nums (mapcar 'float nums)) (sqrt (/ (apply '+ (cl-map 'list '* nums nums))
(length nums))))
(rms (number-sequence 1 10)) </lang>
6.2048368229954285
Erlang
<lang erlang>rms(Nums) ->
math:sqrt(lists:foldl(fun(E,S) -> S+E*E end, 0, Nums) / length(Nums)).
rms([1,2,3,4,5,6,7,8,9,10]).</lang>
- Output:
6.2048368229954285
ERRE
<lang> PROGRAM ROOT_MEAN_SQUARE BEGIN
N=10 FOR I=1 TO N DO S=S+I*I END FOR X=SQR(S/N) PRINT("Root mean square is";X)
END PROGRAM </lang> You can, obviously, generalize reading data from a DATA line or from a file.
Euphoria
<lang euphoria>function rms(sequence s)
atom sum if length(s) = 0 then return 0 end if sum = 0 for i = 1 to length(s) do sum += power(s[i],2) end for return sqrt(sum/length(s))
end function
constant s = {1,2,3,4,5,6,7,8,9,10} ? rms(s)</lang>
- Output:
6.204836823
Excel
If values are entered in the cells A1 to A10, the below expression will give the RMS value <lang excel> =SQRT(SUMSQ($A1:$A10)/COUNT($A1:$A10)) </lang>
The RMS of [1,10] is then : 6.204836823 ( Actual displayed value 6.204837)
F#
Uses a lambda expression and function piping. <lang Fsharp>let RMS (x:float list) : float = List.map (fun y -> y**2.0) x |> List.average |> System.Math.Sqrt
let res = RMS [1.0..10.0]</lang> Answer (in F# Interactive window):
val res : float = 6.204836823
Fantom
<lang fantom>class Main {
static Float averageRms (Float[] nums) { if (nums.size == 0) return 0.0f Float sum := 0f nums.each { sum += it * it } return (sum / nums.size.toFloat).sqrt }
public static Void main () { a := [1f,2f,3f,4f,5f,6f,7f,8f,9f,10f] echo ("RMS Average of $a is: " + averageRms(a)) }
}</lang>
Factor
<lang factor>: root-mean-square ( seq -- mean )
[ [ sq ] map-sum ] [ length ] bi / sqrt ;</lang>
( scratchpad ) 10 [1,b] root-mean-square . 6.204836822995428
Forth
<lang forth>: rms ( faddr len -- frms )
dup >r 0e floats bounds do i f@ fdup f* f+ float +loop r> s>f f/ fsqrt ;
create test 1e f, 2e f, 3e f, 4e f, 5e f, 6e f, 7e f, 8e f, 9e f, 10e f, test 10 rms f. \ 6.20483682299543</lang>
Fortran
Assume stored in array x. <lang Fortran>print *,sqrt( sum(x**2)/size(x) )</lang>
FreeBASIC
<lang freebasic> ' FB 1.05.0 Win64
Function QuadraticMean(array() As Double) As Double
Dim length As Integer = Ubound(array) - Lbound(array) + 1 Dim As Double sum = 0.0 For i As Integer = LBound(array) To UBound(array) sum += array(i) * array(i) Next Return Sqr(sum/length)
End Function
Dim vector(1 To 10) As Double For i As Integer = 1 To 10
vector(i) = i
Next
Print "Quadratic mean (or RMS) is :"; QuadraticMean(vector()) Print Print "Press any key to quit the program" Sleep </lang>
- Output:
Quadratic mean (or RMS) is : 6.204836822995429
Futhark
<lang Futhark> fun main(as: [n]f64): f64 =
sqrt64 ((reduce (+) 0.0 (map (**2.0) as)) / f64(n))
</lang>
GEORGE
<lang GEORGE> 1, 10 rep (i)
i i | (v) ;
0
1, 10 rep (i) i dup mult + ]
10 div
sqrt print
</lang>
6.204836822995428
Go
<lang go>package main
import (
"fmt" "math"
)
func main() {
const n = 10 sum := 0. for x := 1.; x <= n; x++ { sum += x * x } fmt.Println(math.Sqrt(sum / n))
}</lang>
- Output:
6.2048368229954285
Groovy
Solution: <lang groovy>def quadMean = { list ->
list == null \ ? null \ : list.empty \ ? 0 \ : ((list.collect { it*it }.sum()) / list.size()) ** 0.5
}</lang> Test: <lang groovy>def list = 1..10 def Q = quadMean(list) println """ list: ${list}
Q: ${Q}
"""</lang>
- Output:
list: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] Q: 6.2048368229954285
Haskell
Given the mean
function defined in Averages/Pythagorean means:
<lang haskell>main = print $ mean 2 [1 .. 10]</lang>
Or, naively, (but see https://donsbot.wordpress.com/2008/06/04/haskell-as-fast-as-c-working-at-a-high-altitude-for-low-level-performance/):
<lang haskell>rootMeanSquare :: [Double] -> Double rootMeanSquare xs =
sqrt (foldl (\a x -> a + (x * x)) 0 xs / fromIntegral (length xs))
main :: IO () main = print $ rootMeanSquare [1 .. 10]</lang>
- Output:
6.2048368229954285
HicEst
<lang HicEst>sum = 0 DO i = 1, 10
sum = sum + i^2
ENDDO WRITE(ClipBoard) "RMS(1..10) = ", (sum/10)^0.5 </lang> RMS(1..10) = 6.204836823
Icon and Unicon
<lang Icon>procedure main() every put(x := [], 1 to 10) writes("x := [ "); every writes(!x," "); write("]") write("Quadratic mean:",q := qmean!x) end</lang>
<lang Icon>procedure qmean(L[]) #: quadratic mean
local m if *L = 0 then fail every (m := 0.0) +:= !L^2 return sqrt(m / *L)
end</lang>
Io
<lang Io>rms := method (figs, (figs map(** 2) reduce(+) / figs size) sqrt)
rms( Range 1 to(10) asList ) println</lang>
J
Solution: <lang j>rms=: (+/ % #)&.:*:</lang>
Example Usage:
<lang j> rms 1 + i. 10
6.20484</lang>
*:
means square
(+/ % #)
is an idiom for mean.
&.:
means under -- in other words, we square numbers, take their average and then use the inverse of square on the result. (see also the page on &. which does basically the same thing but with different granularity -- item at a time instead of everything at once.
Java
<lang java>public class RMS {
public static double rms(double[] nums){ double ms = 0; for (int i = 0; i < nums.length; i++) ms += nums[i] * nums[i]; ms /= nums.length; return Math.sqrt(ms); }
public static void main(String[] args){ double[] nums = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0}; System.out.println("The RMS of the numbers from 1 to 10 is " + rms(nums)); }
}</lang>
- Output:
The RMS of the numbers from 1 to 10 is 6.2048368229954285
JavaScript
ES5
<lang javascript>function root_mean_square(ary) {
var sum_of_squares = ary.reduce(function(s,x) {return (s + x*x)}, 0); return Math.sqrt(sum_of_squares / ary.length);
}
print( root_mean_square([1,2,3,4,5,6,7,8,9,10]) ); // ==> 6.2048368229954285</lang>
ES6
<lang JavaScript>(() => {
'use strict'; // rootMeanSquare :: [Num] -> Real const rootMeanSquare = xs => Math.sqrt( xs.reduce( (a, x) => (a + x * x), 0 ) / xs.length ); return rootMeanSquare([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]); // -> 6.2048368229954285
})();</lang>
- Output:
6.2048368229954285
jq
The following filter returns null if given an empty array: <lang jq>def rms: length as $length
| if $length == 0 then null else map(. * .) | add | sqrt / $length end ;</lang>With this definition, the following program would compute the rms of each array in a file or stream of numeric arrays:<lang jq>rms</lang>
Julia
There are a variety of ways to do this via built-in functions in Julia, given an array A = [1:10]
of values. The formula can be implemented directly as:
<lang julia>sqrt(sum(A.^2.) / length(A))</lang>
or shorter (and as spoken: root-mean-square)
<lang julia>sqrt(mean(A.^2.))</lang>
or the implicit allocation of a new array by A.^2.
can be avoided by using sum
as a higher-order function: <lang julia>sqrt(sum(x -> x*x, A) / length(A))</lang>
One can also use an explicit loop for near-C performance
<lang julia>
function rms(A)
s = 0.0 for a in A s += a*a end return sqrt(s / length(A))
end
</lang>
Potentially even better is to use the built-in norm
function, which computes the square root of the sum of the squares of the entries of A
in a way that avoids the possibility of spurious floating-point overflow (if the entries of A
are so large that they may overflow if squared): <lang julia>norm(A) / sqrt(length(A))</lang>
K
<lang K>
rms:{_sqrt (+/x^2)%#x} rms 1+!10
6.204837 </lang>
Kotlin
<lang scala>// version 1.0.5-2
fun quadraticMean(vector: Array<Double>) : Double {
val sum = vector.sumByDouble { it * it } return Math.sqrt(sum / vector.size)
}
fun main(args: Array<String>) {
val vector = Array(10, { (it + 1).toDouble() }) print("Quadratic mean of numbers 1 to 10 is ${quadraticMean(vector)}")
}</lang>
- Output:
Quadratic mean of numbers 1 to 10 is 6.2048368229954285
Lasso
<lang Lasso>define rms(a::staticarray)::decimal => { return math_sqrt((with n in #a sum #n*#n) / decimal(#a->size)) } rms(generateSeries(1,10)->asStaticArray)</lang>
- Output:
6.204837
Liberty BASIC
<lang lb>' [RC] Averages/Root mean square
SourceList$ ="1 2 3 4 5 6 7 8 9 10"
' If saved as an array we'd have to have a flag for last data. ' LB has the very useful word$() to read from delimited strings. ' The default delimiter is a space character, " ".
SumOfSquares =0 n =0 ' This holds index to number, and counts number of data. data$ ="666" ' temporary dummy to enter the loop.
while data$ <>"" ' we loop until no data left. data$ =word$( SourceList$, n +1) ' first data, as a string NewVal =val( data$) ' convert string to number SumOfSquares =SumOfSquares +NewVal^2 ' add to existing sum of squares n =n +1 ' increment number of data items found wend
n =n -1
print "Supplied data was "; SourceList$ print "This contained "; n; " numbers." print "R.M.S. value is "; ( SumOfSquares /n)^0.5
end</lang>
Logo
<lang logo>to rms :v
output sqrt quotient (apply "sum map [? * ?] :v) count :v
end
show rms iseq 1 10</lang>
Lua
<lang lua>function sumsq(a, ...) return a and a^2 + sumsq(...) or 0 end function rms(t) return (sumsq(unpack(t)) / #t)^.5 end
print(rms{1, 2, 3, 4, 5, 6, 7, 8, 9, 10})</lang>
Maple
<lang Maple>y := [ seq(1..10) ]: RMS := proc( x )
return sqrt( Statistics:-Mean( x ^~ 2 ) );
end proc: RMS( y ); </lang>
- Output:
6.20483682299543
Mathematica / Wolfram Language
<lang Mathematica>RootMeanSquare@Range[10]</lang>
The above will give the precise solution , to downgrade to 6.20484, use '10.
' to imply asking for numeric solution, or append '//N
' after the whole expression.
MATLAB
<lang MATLAB>function rms = quadraticMean(list)
rms = sqrt(mean(list.^2));
end</lang> Solution: <lang MATLAB>>> quadraticMean((1:10))
ans =
6.204836822995429</lang>
Maxima
<lang maxima>L: makelist(i, i, 10)$
rms(L) := sqrt(lsum(x^2, x, L)/length(L))$
rms(L), numer; /* 6.204836822995429 */</lang>
MAXScript
<lang MAXScript> fn RMS arr = ( local sumSquared = 0 for i in arr do sumSquared += i^2 return (sqrt (sumSquared/arr.count as float)) ) </lang> Output: <lang MAXScript> rms #{1..10} 6.20484 </lang>
МК-61/52
<lang>0 П0 П1 С/П x^2 ИП0 x^2 ИП1 * + ИП1 1 + П1 / КвКор П0 БП 03</lang>
Instruction: В/О С/П Number С/П Number ...
Each time you press the С/П on the indicator would mean already entered numbers.
Morfa
<lang morfa> import morfa.base; import morfa.functional.base;
template <TRange> func rms(d: TRange): float {
var count = 1; return sqrt(reduce( (a: float, b: float) { count += 1; return a + b * b; }, d) / count);
}
func main(): void {
println(rms(1 .. 11));
} </lang>
- Output:
6.204837
Nemerle
<lang Nemerle>using System; using System.Console; using System.Math;
module RMS {
RMS(x : list[int]) : double { def sum = x.Map(fun (x) {x*x}).FoldLeft(0, _+_); Sqrt((sum :> double) / x.Length) } Main() : void { WriteLine("RMS of [1 .. 10]: {0:g6}", RMS($[1 .. 10])); }
}</lang>
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols nobinary
parse arg maxV . if maxV = | maxV = '.' then maxV = 10
sum = 0 loop nr = 1 for maxV
sum = sum + nr ** 2 end nr
rmsD = Math.sqrt(sum / maxV)
say 'RMS of values from 1 to' maxV':' rmsD
return </lang>
- Output:
RMS of values from 1 to 10: 6.204836822995428
Nim
<lang nim>import math
proc qmean(num): float =
for n in num: result += n*n result = sqrt(result / float(num.len))
echo qmean([1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0])</lang>
- Output:
6.2048368229954285e+00
Oberon-2
Oxford Oberon-2 <lang oberon2> MODULE QM; IMPORT ML := MathL, Out; VAR nums: ARRAY 10 OF LONGREAL; i: INTEGER;
PROCEDURE Rms(a: ARRAY OF LONGREAL): LONGREAL; VAR i: INTEGER; s: LONGREAL; BEGIN s := 0.0; FOR i := 0 TO LEN(a) - 1 DO s := s + (a[i] * a[i]) END; RETURN ML.Sqrt(s / LEN(a)) END Rms;
BEGIN FOR i := 0 TO LEN(nums) - 1 DO nums[i] := i + 1 END; Out.String("Quadratic Mean: ");Out.LongReal(Rms(nums));Out.Ln END QM. </lang>
- Output:
Quadratic Mean: 6.20483682300
Objeck
<lang objeck>bundle Default {
class Hello { function : Main(args : String[]) ~ Nil { values := [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]; RootSquareMean(values)->PrintLine(); } function : native : RootSquareMean(values : Float[]) ~ Float { sum := 0.0; each(i : values) { x := values[i]->Power(2.0); sum += values[i]->Power(2.0); }; return (sum / values->Size())->SquareRoot(); } }
}</lang>
OCaml
<lang ocaml>let rms a =
sqrt (Array.fold_left (fun s x -> s +. x*.x) 0.0 a /. float_of_int (Array.length a))
rms (Array.init 10 (fun i -> float_of_int (i+1))) ;; (* 6.2048368229954285 *)</lang>
Oforth
<lang Oforth>10 seq map(#sq) sum 10.0 / sqrt .</lang>
- Output:
6.20483682299543
ooRexx
<lang ooRexx>call testAverage .array~of(10, 9, 8, 7, 6, 5, 4, 3, 2, 1) call testAverage .array~of(10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, .11) call testAverage .array~of(30, 10, 20, 30, 40, 50, -100, 4.7, -11e2)
- routine testAverage
use arg list say "list =" list~toString("l", ", ") say "root mean square =" rootmeansquare(list) say
- routine rootmeansquare
use arg numbers -- return zero for an empty list if numbers~isempty then return 0
sum = 0 do number over numbers sum += number * number end return rxcalcsqrt(sum/numbers~items)
- requires rxmath LIBRARY</lang>
- Output:
list = 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 root mean square = 6.20483682 list = 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, .11 root mean square = 5.06630766 list = 30, 10, 20, 30, 40, 50, -100, 4.7, -1100 root mean square = 369.146476
Oz
<lang oz>declare
fun {Square X} X*X end
fun {RMS Xs} {Sqrt {Int.toFloat {FoldL {Map Xs Square} Number.'+' 0}} / {Int.toFloat {Length Xs}}} end
in
{Show {RMS {List.number 1 10 1}}}</lang>
- Output:
6.2048
PARI/GP
General RMS calculation: <lang parigp>RMS(v)={
sqrt(sum(i=1,#v,v[i]^2)/#v)
};
RMS(vector(10,i,i))</lang>
Specific functions for the first n positive integers: <lang parigp>RMS_first(n)={
sqrt((n+1)*(2*n+1)/6)
};
RMS_first(10)</lang> Asymptotically this is n/sqrt(3).
Perl
<lang perl>use v5.10.0; sub rms {
my $r = 0; $r += $_**2 for @_; sqrt( $r/@_ );
}
say rms(1..10);</lang>
Perl 6
<lang perl6>sub rms(*@nums) { sqrt [+](@nums X** 2) / @nums }
say rms 1..10;</lang>
Here's a slightly more concise version, albeit arguably less readable: <lang perl6>sub rms { sqrt @_ R/ [+] @_ X** 2 }</lang>
Phix
<lang Phix>function rms(sequence s) atom sqsum = 0
for i=1 to length(s) do sqsum += power(s[i],2) end for return sqrt(sqsum/length(s))
end function
? rms({1,2,3,4,5,6,7,8,9,10})</lang>
- Output:
6.204836823
PHP
<lang PHP><?php // Created with PHP 7.0
function rms(array $numbers) {
$sum = 0;
foreach ($numbers as $number) { $sum += $number**2; }
return sqrt($sum / count($numbers));
}
echo rms(array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)); </lang>
- Output:
6.2048368229954
PicoLisp
<lang PicoLisp>(scl 5)
(let Lst (1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0)
(prinl (format (sqrt (*/ (sum '((N) (*/ N N 1.0)) Lst) 1.0 (length Lst) ) T ) *Scl ) ) )</lang>
- Output:
6.20484
PL/I
<lang PL/I> atest: Proc Options(main);
declare A(10) Dec Float(15) static initial (1,2,3,4,5,6,7,8,9,10); declare (n,RMS) Dec Float(15); n = hbound(A,1); RMS = sqrt(sum(A**2)/n); put Skip Data(rms); End;</lang>
- Output:
RMS= 6.20483682299543E+0000;
PostScript
<lang postscript>/findrms{ /x exch def /sum 0 def /i 0 def x length 0 eq{} { x length{ /sum x i get 2 exp sum add def /i i 1 add def }repeat /sum sum x length div sqrt def }ifelse sum == }def
[1 2 3 4 5 6 7 8 9 10] findrms</lang>
- Output:
6.20483685
<lang postscript>[1 10] 1 range dup 0 {dup * +} fold exch length div sqrt</lang>
Powerbuilder
<lang powerbuilder>long ll_x, ll_y, ll_product decimal ld_rms
ll_x = 1 ll_y = 10 DO WHILE ll_x <= ll_y ll_product += ll_x * ll_x ll_x ++ LOOP ld_rms = Sqrt(ll_product / ll_y)
//ld_rms value is 6.20483682299542849</lang>
PowerShell
<lang PowerShell>function get-rms([float[]]$nums){
$sqsum=$nums | foreach-object { $_*$_} | measure-object -sum | select-object -expand Sum return [math]::sqrt($sqsum/$nums.count)
}
get-rms @(1..10) </lang>
PureBasic
<lang PureBasic>NewList MyList() ; To hold a unknown amount of numbers to calculate
If OpenConsole()
Define.d result Define i, sum_of_squares ;Populate a random amounts of numbers to calculate For i=0 To (Random(45)+5) ; max elements is unknown to the program AddElement(MyList()) MyList()=Random(15) ; Put in a random number Next
Print("Averages/Root mean square"+#CRLF$+"of : ")
; Calculate square of each element, print each & add them together ForEach MyList() Print(Str(MyList())+" ") ; Present to our user sum_of_squares+MyList()*MyList() ; Sum the squares, e.g Next
;Present the result result=Sqr(sum_of_squares/ListSize(MyList())) PrintN(#CRLF$+"= "+StrD(result)) PrintN("Press ENTER to exit"): Input() CloseConsole()
EndIf</lang>
Python
<lang Python>>>> from math import sqrt >>> def qmean(num): return sqrt(sum(n*n for n in num)/len(num))
>>> qmean(range(1,11)) 6.2048368229954285</lang> Note that function range in Python includes the first limit of 1, excludes the second limit of 11, and has a default increment of 1.
The Python 2 version is nearly identical, except you must cast the sum to a float to get float division instead of integer division; or better, do a from __future__ import division
, which works on Python 2.2+ as well as Python 3, and makes division work consistently like it does in Python 3.
Qi
<lang qi>(define rms
R -> (sqrt (/ (APPLY + (MAPCAR * R R)) (length R))))</lang>
R
We may calculate the answer directly using R's built-in sqrt
and mean
functions:
<lang R>sqrt(mean((1:10)^2))</lang>
The following function works for any vector x:
<lang R>RMS = function(x){
sqrt(mean(x^2))
}</lang> Usage: <lang R>> RMS(1:10) [1] 6.204837 </lang>
Racket
<lang Racket>
- lang racket
(define (rms nums)
(sqrt (/ (for/sum ([n nums]) (* n n)) (length nums))))
</lang>
REXX
REXX has no built-in sqrt function, so a RYO version is included here.
This particular sqrt function was programmed for speed, as it has two critical components:
- the initial guess (for the square root)
- the number of (increasing) decimal digits used during the computations
The sqrt code was optimized to use the minimum amount of digits (precision) for each iteration of the
calculation as well as a reasonable attempt at providing a first-guess square root by essentially halving
the number using logarithmic (base ten) arithmetic.
<lang rexx>/*REXX program computes and displays the root mean square (RMS) of a number sequence. */
parse arg nums digs show . /*obtain the optional arguments from CL*/
if nums== | nums=="," then nums=10 /*Not specified? Then use the default.*/
if digs== | digs=="," then digs=50 /* " " " " " " */
if show== | show=="," then show=10 /* " " " " " " */
numeric digits digs /*uses DIGS decimal digits for calc. */
$=0; do j=1 for nums /*process each of the N integers. */
$=$ + j**2 /*sum the squares of the integers. */ end /*j*/ /* [↓] displays SHOW decimal digits.*/
rms=format( sqrt($/nums), , show ) / 1 /*divide by N, then calculate the SQRT.*/ say 'root mean square for 1──►'nums "is: " rms /*display the root mean square (RMS). */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; m.=9
numeric form; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_ % 2 h=d+6; do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/ do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/ return g</lang>
output when using the default inputs:
root mean square for 1──►10 is: 6.204836823
Ring
<lang ring> nums = [1,2,3,4,5,6,7,8,9,10] sum = 0 decimals(5) see "Average = " + average(nums) + nl
func average number
for i = 1 to len(number) sum = sum + pow(number[i],2) next x = sqrt(sum / len(number)) return x
</lang>
Ruby
<lang ruby>class Array
def quadratic_mean Math.sqrt( self.inject(0.0) {|s, y| s + y*y} / self.length ) end
end
class Range
def quadratic_mean self.to_a.quadratic_mean end
end
(1..10).quadratic_mean # => 6.2048368229954285</lang>
and a non object-oriented solution: <lang ruby>def rms(seq)
Math.sqrt(seq.inject(0.0) {|sum, x| sum + x*x} / seq.length)
end puts rms (1..10).to_a # => 6.2048368229954285</lang>
Run BASIC
<lang runbasic>valueList$ = "1 2 3 4 5 6 7 8 9 10" while word$(valueList$,i +1) <> "" ' grab values from list
thisValue = val(word$(valueList$,i +1)) ' turn values into numbers sumSquares = sumSquares + thisValue ^ 2 ' sum up the squares i = i +1 '
wend print "List of Values:";valueList$;" containing ";i;" values" print "Root Mean Square =";(sumSquares/i)^0.5</lang>
- Output:
List of Values:1 2 3 4 5 6 7 8 9 10 containing 10 values Root Mean Square =6.20483682
Rust
<lang rust>fn root_mean_square(vec: Vec<i32>) -> f32 {
let sum_squares = vec.iter().fold(0, |acc, &x| acc + x.pow(2)); return ((sum_squares as f32)/(vec.len() as f32)).sqrt();
}
fn main() {
let vec = (1..11).collect(); println!("The root mean square is: {}", root_mean_square(vec));
}</lang>
- Output:
The root mean square is: 6.204837
S-lang
Many of math operations in S-Lang are 'vectorized', that is, given an array, they apply themselves to each element. In this case, that means no array_map() function needed. Also, "range arrays" have a built-in syntax.
<lang S-lang>define rms(arr) {
return sqrt(sum(sqr(arr)) / length(arr));
}
print(rms([1:10]));</lang>
Sather
<lang sather>class MAIN is
-- irrms stands for Integer Ranged RMS irrms(i, f:INT):FLT pre i <= f is sum ::= 0; loop sum := sum + i.upto!(f).pow(2); end; return (sum.flt / (f-i+1).flt).sqrt; end;
main is #OUT + irrms(1, 10) + "\n"; end;
end;</lang>
Scala
<lang scala>def rms(nums: Seq[Int]) = math.sqrt(nums.map(math.pow(_, 2)).sum / nums.size) println(rms(1 to 10))</lang>
- Output:
6.2048368229954285
Scheme
<lang scheme>(define (rms nums)
(sqrt (/ (apply + (map * nums nums)) (length nums))))
(rms '(1 2 3 4 5 6 7 8 9 10))</lang>
- Output:
6.20483682299543
Seed7
<lang seed7>$ include "seed7_05.s7i";
include "float.s7i"; include "math.s7i";
const array float: numbers is [] (1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0);
const func float: rms (in array float: numbers) is func
result var float: rms is 0.0; local var float: number is 0.0; var float: sum is 0.0; begin for number range numbers do sum +:= number ** 2; end for; rms := sqrt(sum / flt(length(numbers))); end func;
const proc: main is func
begin writeln(rms(numbers) digits 7); end func;</lang>
Sidef
<lang ruby>func rms(a) {
Math.sqrt(a.map{.**2}.sum / a.len);
}
say rms(1..10);</lang>
- Output:
6.204836822995428298066620977724737849928
Smalltalk
<lang smalltalk>(((1 to: 10) inject: 0 into: [ :s :n | n*n + s ]) / 10) sqrt.</lang>
SNOBOL4
There is no built-in sqrt( ) function in Snobol4+. <lang SNOBOL4> define('rms(a)i,ssq') :(rms_end) rms i = i + 1; ssq = ssq + (a * a) :s(rms)
rms = sqrt(1.0 * ssq / prototype(a)) :(return)
rms_end
- # Fill array, test and display
str = '1 2 3 4 5 6 7 8 9 10'; a = array(10)
loop i = i + 1; str len(p) span('0123456789') . a @p :s(loop)
output = str ' -> ' rms(a)
end</lang>
- Output:
1 2 3 4 5 6 7 8 9 10 -> 6.20483682
Standard ML
<lang sml>fun rms(v: real vector) =
let val v' = Vector.map (fn x => x*x) v val sum = Vector.foldl op+ 0.0 v' in Math.sqrt( sum/real(Vector.length(v')) ) end;
rms(Vector.tabulate(10, fn n => real(n+1)));</lang>
- Output:
val it = 6.204836823 : real
Tcl
<lang tcl>proc qmean list {
set sum 0.0 foreach value $list { set sum [expr {$sum + $value**2}] } return [expr { sqrt($sum / [llength $list]) }]
}
puts "RMS(1..10) = [qmean {1 2 3 4 5 6 7 8 9 10}]"</lang>
- Output:
RMS(1..10) = 6.2048368229954285
Ursala
using the mean
function among others from the flo
library
<lang Ursala>#import nat
- import flo
- cast %e
rms = sqrt mean sqr* float* nrange(1,10)</lang>
- Output:
6.204837e+00
Vala
Valac probably needs to have the flag "-X -lm" added to include the C Math library. <lang vala>double rms(double[] list){ double sum_squares = 0; double mean;
foreach ( double number in list){ sum_squares += (number * number); }
mean = Math.sqrt(sum_squares / (double) list.length);
return mean; } // end rms
public static void main(){ double[] list = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; double mean = rms(list);
stdout.printf("%s\n", mean.to_string()); }</lang>
- Output:
6.2048368229954285
VBA
<lang vb> Function rms(iLow As Integer, iHigh As Integer)
Dim i As Integer If iLow > iHigh Then i = iLow iLow = iHigh iHigh = i End If For i = iLow To iHigh rms = rms + i ^ 2 Next i rms = Sqr(rms / (iHigh - iLow + 1))
End Function
Sub foo()
Debug.Print rms(1, 10)
End Sub </lang>
Output:
6.20483682299543
Wortel
<lang wortel>@let {
; using a composition and a fork (like you would do in J) rms1 ^(@sqrt @(@sum / #) *^@sq)
; using a function with a named argument rms2 &a @sqrt ~/ #a @sum !*^@sq a
[[ !rms1 @to 10 !rms2 @to 10 ]]
}</lang>
- Output:
[6.2048368229954285 6.2048368229954285]
XLISP
<lang lisp>(defun quadratic-mean (xs)
(sqrt (/ (apply + (mapcar (lambda (x) (expt x 2)) xs)) (length xs))))
- define a RANGE function, for testing purposes
(defun range (x y)
(if (< x y) (cons x (range (+ x 1) y))))
- test QUADRATIC-MEAN
(print (quadratic-mean (range 1 11)))</lang>
- Output:
6.20483682299543
XPL0
<lang XPL0>code CrLf=9; code real RlOut=48; int N; real S; [S:= 0.0; for N:= 1 to 10 do S:= S + sq(float(N)); RlOut(0, sqrt(S/10.0)); CrLf(0); ]</lang>
- Output:
6.20484
Yacas
<lang Yacas>Sqrt(Add((1 .. 10)^2)/10)</lang>
The above will give the precise solution , to downgrade to 6.20483682299, surround the expression with 'N()
'.
zkl
<lang zkl>fcn rms(z){(z.reduce(fcn(p,n){p+n*n},0.0)/z.len()).sqrt()}</lang> The order in the reduce function is important as it coerces n*n to float.
zkl: rms([1..10].walk()) //-->rms(T(1,2,3,4,5,6,7,8,9,10)) 6.20484