Most efficient/vectorization when using previous calculated value (rolling)

Question

Following those conversations:

1. Can I vectorize a calculation which depends on previous elements
2. sapply? tapply? ddply? dataframe variable based on rolling index of previous values of another variable

I wanted to test a more "real-life" case-study. I recently had to migrate SAS code to R and kdb code to R code. I tried to compiled a simple enough yet more sophisticated example to optimize.

let's build the training set

buildDF <- function(N){
    set.seed(123); dateTimes <- sort(as.POSIXct("2001-01-01 08:30:00") + floor(3600*runif(N)));
    set.seed(124); f <- floor(1+3*runif(N));
    set.seed(123); s <- floor(1+3*runif(N));
    return(data.frame(dateTime=dateTimes, f=f, s=s));
}

This is what need to be achieved

f1 <- function(DF){
    #init
    N <- nrow(DF);
    DF$num[1] = 1;

    for(i in 2:N){
        if(DF$f[i] == 2){
            DF$num[i] <- ifelse(DF$s[i-1] == DF$s[i],DF$num[i-1],1+DF$num[i-1]);        
        }else{ #meaning f in {1,3}
            if(DF$f[i-1] != 2){
                DF$num[i] = DF$num[i-1]; 
            }else{
                DF$num[i] = ifelse((DF$dateTime[i]-DF$dateTime[i-1])==0,DF$num[i-1],1+DF$num[i-1]);
            }
        }
    }
    return(DF)
}

This is off course hideous. Let's vectorize it a bit:

f2 <- function(DF){
    N <- nrow(DF);
    DF$add <- 1; DF$ds <- c(NA,diff(DF$s)); DF$lf <- c(NA,DF$f[1:(N-1)]);
    DF$dt <- c(NA,diff(DF$dateTime));
    DF$add[DF$f == 2 & DF$ds == 0] <- 0;
    DF$add[DF$f == 2 & DF$ds != 0] <- 1;
    DF$add[DF$f != 2 & DF$lf != 2] <- 0;
    DF$add[DF$f != 2 & DF$lf == 2 & DF$dt==0] <- 0;
    DF$num <- cumsum(DF$add);
    return(DF);
}

And using the most useful data.table:

f3 <- function(DT){
    N <- nrow(DT);
    DT[,add:=1]; DT[,ds:=c(NA,diff(s))]; DT[,lf:=c(NA,f[1:(N-1)])];
    DT[,dt:=c(NA,diff(dateTime))];
    DT[f == 2 & ds == 0, add:=0];
    DT[f == 2 & ds != 0, add:=1];
    DT[f != 2 & lf != 2, add:=0];
    DT[f != 2 & lf == 2 & dt == 0, add:=0];
    DT[,num:=cumsum(add)];
    return(DT);
}

On a 10K data-frame:

library(rbenchmark);
library(data.table);

N <- 1e4;
DF <- buildDF(N)
DT <- as.data.table(DF);#we can contruct the data.table as a data.frame so it's ok we don't count for this time.

#make sure everybody is equal
DF1 <- f1(DF) ; DF2 <- f2(DF); DT3 <- f3(DT);
identical(DF1$num,DF2$num,DT3$num) 
[1] TRUE

#let's benchmark
benchmark(f1(DF),f2(DF),f3(DT),columns=c("test", "replications", "elapsed",
+ "relative", "user.self", "sys.self"), order="relative",replications=1);
    test replications elapsed relative user.self sys.self
2 f2(DF)            1   0.010      1.0     0.012    0.000
3 f3(DT)            1   0.012      1.2     0.012    0.000
1 f1(DF)            1   9.085    908.5     8.980    0.072

Ok, now on a more decent 5M rows data.frame

N <- 5e6;
DF <- buildDF(N)
DT <- as.data.table(DF);
benchmark(f2(DF),f3(DT),columns=c("test", "replications", "elapsed",       
+ "relative", "user.self", "sys.self"), order="relative",replications=1);
    test replications elapsed relative user.self sys.self
2 f3(DT)            1   2.843    1.000     2.092    0.624
1 f2(DF)            1  10.920    3.841     4.016    5.137

We gain 5X with data.table.

I wonder if Rcpp or zoo:::rollapply can gain much on this. I would be happy with any suggestion

Answer 1

Simple inline Rcpp version:

library(Rcpp)
library(inline)

f4cxx <- cxxfunction(signature(input="data.frame"), plugin="Rcpp", body='
  Rcpp::DataFrame df(input);
  const int N = df.nrows();  

  Rcpp::NumericVector f = df["f"];
  Rcpp::NumericVector s = df["s"];
  Rcpp::NumericVector d = df["dateTime"]; // As far as we need only comparation
  Rcpp::NumericVector num(N);             // it is safe to convert Datetime to Numeric (faster) 

  num[0] = 1;
  for(int i=1; i<N; i++){
    bool cond1 = (f[i]==2) && (s[i]!=s[i-1]);
    bool cond2 = (f[i]!=2) && (f[i-1]==2) && (d[i]!=d[i-1]);
    num[i] = (cond1 || cond2)?1+num[i-1]:num[i-1];    
  }

  df["num"] = num;
  return df;                                // Returns list
  //return (Rcpp::as<Rcpp::DataFrame>(df)); // Returns data.frame (slower)
  ')

Checking out:

N<-1e4; df<-buildDF(N)
identical(f1(df)$num, f4cxx(df)$num)

[1] TRUE

Benchmarking:

N<-1e5; df<-buildDF(N); dt<-as.data.table(df)
benchmark(f2(df), f2j(df), f3(dt), f4cxx(df),
          columns=c("test", "replications", "elapsed", "relative", "user.self", "sys.self"),
          order="relative", replications=1);

       test replications elapsed relative user.self sys.self
4 f4cxx(df)            1   0.001        1     0.000        0
2   f2j(df)            1   0.037       37     0.040        0
3    f3(dt)            1   0.058       58     0.056        0
1    f2(df)            1   0.078       78     0.076        0

Answer 2

Converting your first function to C/C++ using Rcpp (or the "plain old C API" if you want to make Dirk scratch his head) would very likely be the fastest. A data.table solution would probably be a close second.

Here's a base R solution that's much faster than your f2 function because it avoids a lot of data.frame subsetting (which is very slow). This illustrates what to do/avoid in order to make base R code fast, but at some cost of code clarity/readability.

f2j <- function(DF){
  N <- nrow(DF)
  f2  <- DF$f == 2
  ds0 <- diff(DF$s) == 0
  lf2 <- f2[-N]
  f2  <- f2[-1]
  dt3 <- diff(DF$dateTime) == 0
  cond <- logical(N)
  cond[-1] <- (f2 & ds0) | (!f2 & !lf2) | (!f2 & lf2 & dt3)
  DF$num <- cumsum(!cond)
  DF
}