Get the first element of the first sequence of length N of successively increasing numbers in R

Question

I am trying to find the most effective way to solve the following. Suppose we have some data that looks like this:

d1 <- seq(0, 3000, length.out = 1000) d2 <- cos(seq(0, 6*pi, length.out = 1000))*rev(seq(0, 1, length.out = 1000)) dd <- as.data.frame(cbind(d1, d2)) 

I need to determine from d2 first element of the first sequence of length 20 consecutively increasing numbers. In the figure above, it will be somewhere around d1 = 500 . My current approach is based on this function:

 getFirstBeforeSequence <- function(x, y, len){ a1 <- cbind(lapply(split(y, cumsum(c(1, diff(y) < 0))), length)) a2 <- which(a1 > len)[1]-1 a3 <- sum(unlist(a1)[1:a2])+1 a3 } 

This function gives me the desired result, the element is at position 164 and occurred when d1 = 489.4895 :

 getFirstBeforeSequence(dd$d1, dd$d2, 20) # 164 dd$d1[164] # 489.4895 

However, I had the impression that my decision was too complicated, and I am sure that others will have better solutions. Any help would be greatly appreciated.

Answer 1

Here is a hit:

 getFirstBefore<-function(x,len){ r<-rle(sign(diff(x))) n<-which(r$lengths>=len & r$values==1) if(length(n)==0) return(-1) 1+sum(r$lengths[seq_len(n[1]-1)]) } 

This is more efficient than the original, but there are probably still room for improvement:

 microbenchmark( getFirstBeforeSequence(dd$d1,dd$d2,20), getFirstBefore(dd$d2,20)) # Unit: microseconds # expr min lq median uq # getFirstBeforeSequence(dd$d1, dd$d2, 20) 2433.174 2464.457 2486.186 2502.2005 # getFirstBefore(dd$d2, 20) 181.354 187.081 192.808 196.6805 # max neval # 9932.534 100 # 239.700 100 

Answer 2

This is slower, but gives a completely different approach:

 firstOfSequence <- function(x, len){ v <- paste0(sign(diff(x))+1L, collapse="") regexpr(paste0("([2])\\1{", len-1L, "}"), v) } > microbenchmark( + firstOfSequence(dd$d2, 20), + getFirstBefore(dd$d2, 20)) Unit: microseconds expr min lq median uq max neval firstOfSequence(dd$d1, 20) 978.181 981.3875 982.9910 998.7060 1111.597 100 getFirstBefore(dd$d1, 20) 191.147 196.5990 200.4475 205.0975 333.865 100 

Answer 3

 y <- dd$d1 # indices of pits and peaks pit <- which(diff(sign(diff(y))) == 2) + 1 peak <- which(diff(sign(diff(y))) == -2) + 1 # distance between peak and pit -> length of increase len_incr <- peak - pit # index of first pit from which a consecutive increase in 20 'steps' starts idx <- pit[(len_incr > 20) == TRUE][1] # corresponding x-value dd$d2[idx] # [1] 489.4895 # similar approach but let 'turnpoint' find pits and peaks. library(pastecs) tp <- turnpoints(y) pit <- which(tp$pits == TRUE) peak <- which(tp$peaks == TRUE) len_incr <- peak - pit idx <- pit[(len_incr > 20) == TRUE][1] dd$d2[idx] # [1] 489.4895