Loop for atan2 function by year in R

Question

I have an artificial data set that I created:

x<-rnorm(100,10,10)
y<-rnorm(100,20,10)
Location<-c((rep("AB", 40)),(rep("TA", 30)),(rep("OP", 30)))
Year<-c((rep("1999", 10)),(rep("2000", 9)),(rep("2001", 12)),(rep("2002", 9)),(rep("1999", 7)),(rep("2000", 6)),(rep("2001", 6)),(rep("2002", 11)),(rep("1999", 12)),(rep("2000", 8)),(rep("2001", 5)),(rep("2002", 5)))
Data<-cbind(x,y,Location,Year)

> head(Data)
       x                  y                  Location Year  
[1,] "1.8938661556415"  "19.851256070398"  "AB"     "1999"
[2,] "21.0735971323312" "17.4993965352294" "AB"     "1999"
[3,] "30.8347289164302" "7.63333686308105" "AB"     "1999"
[4,] "8.913993138201"   "14.7085296541221" "AB"     "1999"
[5,] "20.8309225677419" "12.0888505284667" "AB"     "1999"
[6,] "25.3978549194374" "20.47154776064"   "AB"     "1999"

I would like to take the arc2tan of each x and y such as:

 Theta<-atan2(y[i+1]-y[i],x[i+1]-x[i])

but I only want to do this for each year within year location, meaning I do not want to find theta between 1999 and 2000, or between 2001 and 2002 etc. Only between x and y points of the same year in the same location.

I had originally written a loop that did the above (what I don't want to do), and I was wondering if anyone knew how to alter it, so that the loop would stop and reset itself for each year. The original loop is provided below:

for (i in 1:length(x)-1){
  Theta[i]<-atan2(y[i+1]-y[i],x[i+1]-x[i])
}

Any helpers?

Answer 1

You may try this.

# a smaller test data set
x <- rnorm(24, 10, 10)
y <- rnorm(24, 20, 10)
loc <- rep(c("A", "B"), each = 4)
year <- rep(1999:2001, each = 8)
df <- data.frame(x, y, loc, year)

df

# apply function on subsets defined by location and year
# use tail and head to 'lag' y and x
by(df, df[ , c("loc", "year")], function(x){
with(x, atan2(y = tail(y, - 1) - head(y, -1), x = tail(x, -1) - head(x, - 1)))
})

# loc: A
# year: 1999
# [1]  2.306794 -2.363359  1.065151
# --------------------------------------------------------------------------- 
# loc: B
# year: 1999
# [1] -1.077345  1.161944 -2.101823
# --------------------------------------------------------------------------- 
# loc: A
# year: 2000
# [1] -1.76557207  1.79463661 -0.05251002
# --------------------------------------------------------------------------- 
# loc: B
# year: 2000
# [1]  2.753115 -1.468055 -1.624389
# ...snip...

A dplyr alternative. Because the length of the result of the function within each group does not equal the group size or 1 in this case, dplyr is not happy at all to chew on a data frame (see here and here). A work-around is to feed dplyr with a data.table. Of course a data.table only solution would then be cleanest here. I leave that to someone more familiar with data.table than me...

library(data.table)
library(dplyr)
dt <- data.table(df)
dt %.%
  group_by(loc, year) %.%
  mutate(
    atan = atan2(lead(y, default = NULL) - lag(y, default = NULL),
          lead(x, default = NULL) - lag(x, default = NULL)))

#            x         y loc year        atan
# 1  19.826573 18.354265   A 1999  2.30679446
# 2  11.856696 27.153197   A 1999 -2.36335869
# 3  -3.362242 12.150775   A 1999  1.06515149
# 4  11.126841 38.320662   A 1999  2.30679446
# 5  12.616396 31.782969   A 2000 -1.76557207
# 6   8.492305 10.877870   A 2000  1.79463661
# 7   4.921766 26.561845   A 2000 -0.05251002
# 8  14.398730 26.063752   A 2000 -1.76557207
# 9  11.800173 30.215422   A 2001 -2.74907150
# 10 -6.473259 22.650127   A 2001  0.11997030
# 11  6.528055 24.217425   A 2001 -1.71122202
# 12  4.951238 13.062497   A 2001 -2.74907150
# 13  1.640049 19.886848   B 1999 -1.07734532
# 14  4.123603 15.269110   B 1999  1.16194418
# 15 14.548780 39.330885   B 1999 -2.10182331
# 16  6.925468 26.350556   B 1999 -1.07734532
# ...snip...