Generate a weighted sequence of numbers with an optional multiplier

weighted_sequences.coffee

# Generate a sequence of numbers:
#  - ordered with the highest values
#  - has a sum of 1
#  - has an optional multiplier to alter the decreasing rate

sequence = (n,m=0) ->

	f = (p,multiplier) -> p * p + multiplier

	s = ""
	max = n * n
	sum = 0
	sum += f(p,m) for p in [1..n]

	total = 0
	for p in [1..n]
		r = n - p + 1
		a = f(r,m) / sum
		total += a	
		
		s += ", " if s
		s += a.toFixed 4

	"#{s}\nfor n: #{n}, m: #{m}, total: #{total}\n"

print = (rest...) -> console.log rest...

print sequence 3		# 0.6429, 0.2857, 0.0714
print sequence 5, -0.5		# 0.4667, 0.2952, 0.1619, 0.0667, 0.0095
print sequence 5, 0		# 0.4545, 0.2909, 0.1636, 0.0727, 0.0182
print sequence 5, 1.5		# 0.4240, 0.2800, 0.1680, 0.0880, 0.0400
print sequence 5, 2		# 0.4154, 0.2769, 0.1692, 0.0923, 0.0462

weighted_sequences.fs

open System

let sequence n normalizer =

    let f p normalizer = p * p + normalizer

    let sum = 
        [1.0..n] 
        |> Seq.map (fun p -> f p normalizer) 
        |> Seq.sum

    let seq = 
        [1.0..n] 
        |> Seq.map (fun p -> f (n - p + 1.0) normalizer / sum)
        
    let sb = new System.Text.StringBuilder()
    seq 
        |> Seq.map (fun i -> Math.Round(i,2).ToString()) 
        |> Seq.iter (fun i -> sb.Append((if sb.Length > 0 then ", " else "") + i) |> ignore)

    let total = seq |> Seq.sum

    sprintf "%A\nfor n: %f, normalizer: %f, total %f" sb n normalizer total

printfn "%s" (sequence 3.0 0.0)
printfn "%s" (sequence 5.0 -0.5)
printfn "%s" (sequence 5.0 0.0)
printfn "%s" (sequence 5.0 1.5)
printfn "%s" (sequence 5.0 2.0)

weighted_sequences.js

#JavaScript output

var print, sequence;
var __slice = Array.prototype.slice;
sequence = function(n, m) {
  var a, f, max, p, r, s, sum, total;
  if (m == null) {
    m = 0;
  }
  f = function(p, multiplier) {
    return p * p + multiplier;
  };
  s = "";
  max = n * n;
  sum = 0;
  for (p = 1; 1 <= n ? p <= n : p >= n; 1 <= n ? p++ : p--) {
    sum += f(p, m);
  }
  total = 0;
  for (p = 1; 1 <= n ? p <= n : p >= n; 1 <= n ? p++ : p--) {
    r = n - p + 1;
    a = f(r, m) / sum;
    total += a;
    if (s) {
      s += ", ";
    }
    s += a.toFixed(4);
  }
  return "" + s + "\nfor n: " + n + ", m: " + m + ", total: " + total + "\n";
};
print = function() {
  var rest;
  rest = 1 <= arguments.length ? __slice.call(arguments, 0) : [];
  return console.log.apply(console, rest);
};
print(sequence(3));
print(sequence(5, -0.5));
print(sequence(5, 0));
print(sequence(5, 1.5));
print(sequence(5, 2));