R: fast sliding window with given coordinates

Question

I have a data table with nrow being around a million or two and ncol of about 200.

Each entry in a row has a coordinate associated with it.

Tiny portion of the data:

[1,] -2.80331471  -0.8874522 -2.34401863   -3.811584   -2.1292443
[2,]  0.03177716   0.2588624  0.82877467    1.955099    0.6321881
[3,] -1.32954665  -0.5433407 -2.19211837   -2.342554   -2.2142461
[4,] -0.60771429  -0.9758734  0.01558774    1.651459   -0.8137684

Coordinates for the first 4 rows:

9928202 9928251 9928288 9928319

What I would like is a function that given the data and window-size would return a data table of the same size with a mean sliding window applied on each column. Or in other words - for each row entry i it would find entries with coordinates between coords[i]-windsize and coords[i]+windsize and replace the initial value with the mean of the values inside that interval (separately for each column).

Speed is the main issue here.

Here is my first take of such function.

doSlidingWindow <- function(intensities, coords, windsize) {
windHalfSize <- ceiling(windsize/2)
### whole range inds
RANGE <- integer(max(coords)+windsize)
RANGE[coords] <- c(1:length(coords)[1])

### get indeces of rows falling in each window
COORDS <- as.list(coords)
WINDOWINDS <- sapply(COORDS, function(crds){ unique(RANGE[(crds-windHalfSize):
    (crds+windHalfSize)]) })

### do windowing

wind_ints <- intensities
wind_ints[] <- 0
for(i in 1:length(coords)) {
    wind_ints[i,] <- apply(as.matrix(intensities[WINDOWINDS[[i]],]), 2, mean)
}
return(wind_ints)
}

The code before the last for loop is quite fast and it gets me a list of the indexes I need to use for each entry. However then everything falls apart since I need to grind the for loop a million times, take subsets of my data table and also make sure that I have more than one row to be able to work with all the columns at once inside apply.

My second approach is to just stick the actual values in the RANGE list, fill the gaps with zeroes and do rollmean from zoo package, repeated for each column. But this is redundant since rollmean will go through all the gaps and I will only be using the values for original coordinates in the end.

Any help to make it faster without going to C would be very appreciated.

Answer 1

Data generation:

N <- 1e5 # rows
M <- 200 # columns
W <- 10  # window size

set.seed(1)
intensities <- matrix(rnorm(N*M), nrow=N, ncol=M)
coords <- 8000000 + sort(sample(1:(5*N), N))

Original function with minor modifications I used for benchmarks:

doSlidingWindow <- function(intensities, coords, windsize) {
  windHalfSize <- ceiling(windsize/2)
  ### whole range inds
  RANGE <- integer(max(coords)+windsize)
  RANGE[coords] <- c(1:length(coords)[1])

  ### get indices of rows falling in each window
  ### NOTE: Each elements of WINDOWINDS holds zero. Not a big problem though.
  WINDOWINDS <- sapply(coords, function(crds) ret <- unique(RANGE[(crds-windHalfSize):(crds+windHalfSize)]))

  ### do windowing
  wind_ints <- intensities
  wind_ints[] <- 0
  for(i in 1:length(coords)) {
    # CORRECTION: When it's only one row in window there was a trouble
    wind_ints[i,] <- apply(matrix(intensities[WINDOWINDS[[i]],], ncol=ncol(intensities)), 2, mean)
  }
  return(wind_ints)
}

---

POSSIBLE SOLUTIONS:

---

1) data.table

data.table is known to be fast with subsetting, but this page (and other related to sliding window) suggests, that this is not the case. Indeed, data.table code is elegant, but unfortunately very slow:

require(data.table)
require(plyr)
dt <- data.table(coords, intensities)
setkey(dt, coords)
aaply(1:N, 1, function(i) dt[WINDOWINDS[[i]], sapply(.SD,mean), .SDcols=2:(M+1)])

---

2) foreach+doSNOW

Basic routine is easy to run in parallel, so, we can benefit from it:

require(doSNOW)
doSlidingWindow2 <- function(intensities, coords, windsize) {
  NC <- 2 # number of nodes in cluster
  cl <- makeCluster(rep("localhost", NC), type="SOCK")
  registerDoSNOW(cl)

  N <- ncol(intensities) # total number of columns
  chunk <- ceiling(N/NC) # number of columns send to the single node

  result <- foreach(i=1:NC, .combine=cbind, .export=c("doSlidingWindow")) %dopar% {
    start <- (i-1)*chunk+1
    end   <- ifelse(i!=NC, i*chunk, N)
    doSlidingWindow(intensities[,start:end], coords, windsize)    
  }

  stopCluster(cl)
  return (result)
}

Benchmark shows notable speed-up on my Dual-Core processor:

system.time(res <- doSlidingWindow(intensities, coords, W))
#    user  system elapsed 
# 306.259   0.204 307.770
system.time(res2 <- doSlidingWindow2(intensities, coords, W))
#  user  system elapsed 
# 1.377   1.364 177.223
all.equal(res, res2, check.attributes=FALSE)
# [1] TRUE

---

3) Rcpp

Yes, I know you asked "without going to C". But, please, take a look. This code is inline and rather straightforward:

require(Rcpp)
require(inline)
doSlidingWindow3 <- cxxfunction(signature(intens="matrix", crds="numeric", wsize="numeric"), plugin="Rcpp", body='
  #include <vector>
  Rcpp::NumericMatrix intensities(intens);
  const int N = intensities.nrow();
  const int M = intensities.ncol();
  Rcpp::NumericMatrix wind_ints(N, M);

  std::vector<int> coords = as< std::vector<int> >(crds);
  int windsize = ceil(as<double>(wsize)/2);  

  for(int i=0; i<N; i++){
    // Simple search for window range (begin:end in coords)
    // Assumed that coords are non-decreasing
    int begin = (i-windsize)<0?0:(i-windsize);
    while(coords[begin]<(coords[i]-windsize)) ++begin;
    int end = (i+windsize)>(N-1)?(N-1):(i+windsize);
    while(coords[end]>(coords[i]+windsize)) --end;

    for(int j=0; j<M; j++){
      double result = 0.0;
      for(int k=begin; k<=end; k++){
        result += intensities(k,j);
      }
      wind_ints(i,j) = result/(end-begin+1);
    }
  }

  return wind_ints;
')

Benchmark:

system.time(res <- doSlidingWindow(intensities, coords, W))
#    user  system elapsed 
# 306.259   0.204 307.770
system.time(res3 <- doSlidingWindow3(intensities, coords, W))
#  user  system elapsed 
# 0.328   0.020   0.351
all.equal(res, res3, check.attributes=FALSE)
# [1] TRUE

I hope results are quite motivating. While data fits in memory Rcpp version is pretty fast. Say, with N <- 1e6 and M <-100 I got:

   user  system elapsed 
  2.873   0.076   2.951

Naturally, after R starts using swap everything slows down. With really large data that doesn't fit in memory you should consider sqldf, ff or bigmemory.

Answer 2

Rollapply works great with a small dataset. However, if you are working with several million rows (genomics) it is quite slow.

The following function is super fast:

data <- c(runif(100000, min=0, max=.1),runif(100000, min=.05, max=.1),runif(10000, min=.05, max=1), runif(100000, min=0, max=.2))
slideFunct <- function(data, window, step){
  total <- length(data)
  spots <- seq(from=1, to=(total-window), by=step)
  result <- vector(length = length(spots))
  for(i in 1:length(spots)){
    result[i] <- mean(data[spots[i]:(spots[i]+window)])
  }
  return(result)
}

Details here.