using LINQ to find the cumulative sum of an array of numbers in C#

Question

I have a csv string containing doubles (e.g "0.3,0.4,0.3"), and I want to be able to output a double array containing the cumulative sum of these numbers (e.g [0.3,0.7,1.0]).

So far, I have

double[] probabilities = textBox_f.Text.Split(new char[]{','}).Select(s => double.Parse(s)).ToArray();

which gives the numbers as an array, but not the cumulative sum of the numbers.

Is there any way to continue this expression to get what I want, or do I need to use iteration to create a new array from the array I already have?

Answer 1

There's a time for generality, and there's a time for solving the problem actually posed. This is one of the latter times. If you want to make a method that turns a sequence of doubles into a sequence of partial sums, then just do that:

public static IEnumerable<double> CumulativeSum(this IEnumerable<double> sequence)
{
    double sum = 0;
    foreach(var item in sequence)
    {
        sum += item;
        yield return sum;
    }        
}

Easy. No messing around with aggregates and complicated queries and whatnot. Easy to understand, easy to debug, easy to use:

textBox_f.Text
    .Split(new char[]{','})
    .Select(s => double.Parse(s))
    .CumulativeSum()
    .ToArray();

Now, I note that if that is user input then double.Parse can throw an exception; it might be a better idea to do something like:

public static double? MyParseDouble(this string s)
{
    double d;
    if (double.TryParse(s, out d))
        return d;
    return null;
}

public static IEnumerable<double?> CumulativeSum(this IEnumerable<double?> sequence)
{
    double? sum = 0;
    foreach(var item in sequence)
    {
        sum += item;
        yield return sum;
    }        
}
...
textBox_f.Text
    .Split(new char[]{','})
    .Select(s => s.MyParseDouble())
    .CumulativeSum()
    .ToArray();

and now you don't get an exception if the user makes a typing mistake; you get nulls.

Answer 2

I had a similar requirement some time ago. Basically, I needed to do an aggregation, but I also needed to select each intermediate value. So I wrote an extension method named SelectAggregate (probably not the most appropriate name, but I couldn't find anything better then) that can be used like that:

double[] numbers = new [] { 0.3, 0.4, 0.3 };
double[] cumulativeSums = numbers.SelectAggregate(0.0, (acc, x) => acc + x).ToArray();

Here's the code :

    public static IEnumerable<TAccumulate> SelectAggregate<TSource, TAccumulate>(
        this IEnumerable<TSource> source,
        TAccumulate seed,
        Func<TAccumulate, TSource, TAccumulate> func)
    {
        source.CheckArgumentNull("source");
        func.CheckArgumentNull("func");
        return source.SelectAggregateIterator(seed, func);
    }

    private static IEnumerable<TAccumulate> SelectAggregateIterator<TSource, TAccumulate>(
        this IEnumerable<TSource> source,
        TAccumulate seed,
        Func<TAccumulate, TSource, TAccumulate> func)
    {
        TAccumulate previous = seed;
        foreach (var item in source)
        {
            TAccumulate result = func(previous, item);
            previous = result;
            yield return result;
        }
    }

Answer 3

You want to use the Aggregate operator, with a List<double> as the aggregation accumulator. That way you can produce a projection which is itself a sequence of sums.

Here's an example to get you started:

double[] runningTotal = textBox_f.Text
            .Split(new char[]{','})
            .Select(s => double.Parse(s))
            .Aggregate((IEnumerable<double>)new List<double>(), 
                       (a,i) => a.Concat(new[]{a.LastOrDefault() + i}))
            .ToArray();

Answer 4

var input=new double[]{ ... }
double sum=0;

var output=input
    .Select(w=>sum+=w);

Answer 5

Why does it need to be LINQ?

var cumulative = new double[probabilities.Length];
for (int i = 0; i < probabilities.Length; i++)
    cumulative[i] = probabilities[i] + (i == 0 ? 0 : cumulative[i-1]);

Answer 6

First of all i don't think that it is good task for Linq. Plain old foreach will do it better. But as a puzzle it is fine.

First idea was to use subqueries, but i don't like it, because it is O(n^2). Here is my linear solution:

        double[] probabilities = new double[] { 0.3, 0.4, 0.3};
        probabilities
            .Aggregate(
                new {sum=Enumerable.Empty<double>(), last = 0.0d},
                (a, c) => new {
                    sum = a.sum.Concat(Enumerable.Repeat(a.last+c,1)),
                    last = a.last + c
                },
                a => a.sum
            );

Answer 7

use RX :

var input=new double[]{ ... }
var output = new List<double>();
input.ToObservable().Scan((e, f) => f + e).Subscribe(output.Add);

Answer 8

This is actually pretty straightforward to generalize using generator. Here is a new extension method called Accumulate that works like a combination of Select and Aggregate. It returns a new sequence by applying a binary function to each element in the sequence and accumulated value so far.

 public static class EnumerableHelpers 
 {
    public static IEnumerable<U> Accumulate<T, U>(this IEnumerable<T> self, U init, Func<U, T, U> f) 
    {
        foreach (var x in self)
            yield return init = f(init, x);
    }

    public static IEnumerable<T> Accumulate<T>(this IEnumerable<T> self, Func<T, T, T> f)
    {
        return self.Accumulate(default(T), f);
    }

    public static IEnumerable<double> PartialSums(this IEnumerable<double> self)
    {
        return self.Accumulate((x, y) => x + y);
    }

    public static IEnumerable<int> PartialSums(this IEnumerable<int> self)
    {
        return self.Accumulate((x, y) => x + y);
    }
 }

Answer 9

Here's my solution:

• Linq
• linear time
• linear memory
• no side effects

Only caveat is that it doesn't work for empty lists (trivial to handle).

    var doublesSummed  = doubles.Skip(1).Aggregate(
        new {
            sum = doubles.First(),
            doubles = new [] {doubles.First()}.AsEnumerable()
        },  
        (acc, nextDouble) => new {
            sum = acc.sum + nextDouble,
            doubles = acc.doubles.Append(acc.sum + nextDouble)
        }
    );

Demo

Answer 10

Here's a way of doing it using LINQ:

double[] doubles = { 1.7, 2.3, 1.9, 4.1, 2.9 };
var doublesSummed = new List<double>();

Enumerable.Aggregate(doubles, (runningSum, nextFactor) => {
    double currentSum = runningSum + nextFactor;
    doublesSummed.Add(currentSum);
    return currentSum;
});

doublesSummed.Dump();

In LINQPad:

• 4
• 5.9
• 10
• 12.9

Answer 11

Cumulative sum for List<double>:

var nums = new List<double>() { 0.3, 0.0, 0.4, 1.1 };
var cumsum = nums.Aggregate(new List<double> (), 
              (list, next) => { list.Add(list.LastOrDefault() + next); return list; });