Bounded cumulative sum?

Question

How can I do a cumulative sum over a vector (like cumsum), but bounded so that the summation never goes below a lower bound or above an upper bound?

T

Answer 1

I suppose this might work.

library ("Rcpp")

cumsum.bounded <- cppFunction(
    'NumericVector cumsum_bounded (NumericVector x, const double lower, const double upper) {

        double acc = 0;
        NumericVector result(x.size());

        for(int i = 0; i < x.size(); i++) {
            acc += x[i];

            if (acc < lower) acc = lower;
            if (acc > upper) acc = upper;

            result[i] = acc;
        }

        return result;
    }')

Answer 2

Here are a couple of pure R versions. Not likely to be as fast as going to C/C++ but one of them might be fast enough for your needs and would be easier to maintain:

# 1 Reduce
cumsum.bounded <- function(x, lower.bound = 0, upper.bound = 500) {
    bsum <- function(x, y) min(upper.bound, max(lower.bound, x+y))
    if (length(x) > 1) Reduce(bsum, x, acc = TRUE) else x
}

# 2 for loop
cumsum.bounded2 <- function(x, lower.bound = 0, upper.bound = 500) {
   if (length(x) > 1) 
      for(i in  2:length(x)) x[i] <- min(upper.bound, max(lower.bound, x[i] + x[i-1]))
   x
}

These may be need to be enhanced slightly if x has length 0 or 1 depending on how strict the requirements are.

Answer 3

As mentioned in the comments, Rcpp is a good way to go.

cumsumBounded.cpp:

#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::export]]                                                             
NumericVector cumsumBounded(NumericVector x, double low, double high) {
  NumericVector res(x.size());
  double acc = 0;
  for (int i=0; i < x.size(); ++i) {
    acc += x[i];
    if (acc < low)  acc = low;
    else if (acc > high)  acc = high;
    res[i] = acc;
  }
  return res;
}

Compile and use new function:

library(Rcpp)
sourceCpp(file="cumsumBounded.cpp")
foo <- c(100, -200, 400, 200)
cumsumBounded(foo, 0, 500)
# [1] 100   0 400 500