Periodicity of variables in array in R - r

Question

Let's say that I have alpha
alpha = c(a,a,a,b,c,c,c,a,c,c)
How can I find the periodicity such that I can construct another array beta
beta = c(3,1,3,1,2)
without using the contents of alpha in the code? Is there a way to use lead or lag to answer this?

Answer 1

Here is an option using tabulate and rleid
library(data.table)
tabulate(rleid(alpha))
#[1] 3 1 3 1 2

Answer 2

Just for fun, here's a convoluted solution:
alpha <- c('a','a','a','b','c','c','c','a','c','c');
diff(c(0L,which(c(alpha[-1L]!=alpha[-length(alpha)],T))));
## [1] 3 1 3 1 2
Explanation
alpha[-1L]!=alpha[-length(alpha)];
## [1] FALSE FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE
First compute a logical vector representing which adjacent pairs of input elements constitute breaks in value equality, and which don't. The index of each element in the logical vector corresponds to the index of the first element of the pair in the input vector.
c(alpha[-1L]!=alpha[-length(alpha)],T);
## [1] FALSE FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE TRUE
Append a TRUE value to create a pseudo-break at the end of the vector. See next step for clarification.
which(c(alpha[-1L]!=alpha[-length(alpha)],T));
## [1] 3 4 7 8 10
Convert the logical vector to an index vector representing the endpoints of the run lengths in the input vector. Now it should be clear why we had to append TRUE in the previous step; the endpoint of the final run length would otherwise be omitted.
c(0L,which(c(alpha[-1L]!=alpha[-length(alpha)],T)));
## [1] 0 3 4 7 8 10
Prepend a zero. This can conceptually be thought of as transforming the index vector into a "boundaries vector", with each element representing either the internal or external boundaries of the input vector run lengths. See next step for clarification.
diff(c(0L,which(c(alpha[-1L]!=alpha[-length(alpha)],T))));
## [1] 3 1 3 1 2
Take the difference between consecutive boundaries. This provides the desired run lengths.
Benchmarking
library(data.table);
library(microbenchmark);
bgoldst <- function(alpha) diff(c(0L,which(c(alpha[-1L]!=alpha[-length(alpha)],T))));
akrun <- function(alpha) tabulate(rleid(alpha));
bethany <- function(alpha) { if (length(alpha)==0L) return(integer()); res <- integer(); last <- alpha[1L]; cnt <- 1L; i <- 2L; while (i<=length(alpha)) { if (alpha[i]==last) cnt <- cnt+1L else { res[length(res)+1L] <- cnt; last <- alpha[i]; cnt <- 1L; }; i <- i+1L; }; res[length(res)+1L] <- cnt; res; };
flick <- function(alpha) rle(alpha)$lengths;
alpha <- c('a','a','a','b','c','c','c','a','c','c');
expected <- c(3L,1L,3L,1L,2L);
identical(expected,bgoldst(alpha));
## [1] TRUE
identical(expected,akrun(alpha));
## [1] TRUE
identical(expected,bethany(alpha));
## [1] TRUE
identical(expected,flick(alpha));
## [1] TRUE
microbenchmark(bgoldst(alpha),akrun(alpha),bethany(alpha),flick(alpha));
## Unit: microseconds
## expr min lq mean median uq max neval
## bgoldst(alpha) 8.553 11.1200 14.85308 12.8300 15.3970 70.136 100
## akrun(alpha) 129.151 144.9745 163.64182 156.7350 171.4895 313.898 100
## bethany(alpha) 20.101 23.9500 30.43242 26.5155 37.8475 70.136 100
## flick(alpha) 20.100 23.9495 30.44956 28.0120 32.2890 62.866 100
set.seed(1L); N <- 1e5L; alpha <- sample(letters[1:3],N,T);
expected <- bgoldst(alpha);
identical(expected,akrun(alpha));
## [1] TRUE
identical(expected,bethany(alpha));
## [1] TRUE
identical(expected,flick(alpha));
## [1] TRUE
microbenchmark(bgoldst(alpha),akrun(alpha),bethany(alpha),flick(alpha),times=10L);
## Unit: milliseconds
## expr min lq mean median uq max neval
## bgoldst(alpha) 5.497899 6.469098 11.007558 6.521699 7.297460 49.891634 10
## akrun(alpha) 1.300492 1.370199 1.547461 1.401631 1.464282 2.816091 10
## bethany(alpha) 2865.335271 2891.594408 2941.352229 2924.165053 2997.881411 3024.234204 10
## flick(alpha) 8.060392 9.355323 13.646002 10.055176 10.841843 48.312741 10

Answer 3

If you want to keep the values in alpha blind, you can create a for loop and use logic to run up a counter to if this iteration of alpha equals the last. You will need to set a past alpha to accept the current value and compare the next one against.
Once the two values do not agree the counter number is concatenated to the vector you created outside of the loop and the counter goes back to one.
It is simple enough that you should do this yourself to learn how.
You can read a file into a variable, but not manually type in numbers or ever need to make them visible. IF the data is 'protected' in some way...