Comparing two columns of two dataframes (logical operators) - r

Question

I would like to compare two columns simultaneously. My data looks like this:
a <- data.frame("a1" = c(1,1,1,3,4), "a2" = c(2,1,2,1,2))
b <- data.frame("b1" = c(1,1,3,1,3), "b2" = c(2,2,1,2,1))
cbind(a, b)
# a1 a2 b1 b2
# 1 1 2 1 2
# 2 1 1 1 2
# 3 1 2 3 1
# 4 3 1 1 2
# 5 4 2 3 1
I would like to identify all rows of a where a1 is not in b1 or where a1 is in b1 but a2 for the special a1 is not in b2 for the special b2. So the second question is: When a1 is in b1 is then a2 for this row for a1 also in b2 for this row for b1.
Example for line 2: I am checking, if a1 = 1 is anywhere in b1 = c(1,1,3,1,3). It is, so I want to check if a2 = 1 in line 2 (where a1 = 1) is anywhere in b2 where b1 = a1 = 1, so here b2 = c(2, 2, 2). For line 2 a2 = 1 is not in b2 = c(2, 2, 2), so the result should show me this line.
The first question is easy to answer with the following code:
a[which(!(a$a1 %in% b$b1)), ]
# a1 a2
# 5 4 2
But I can't fix the second problem. Maybe I am working in a wrong way with the logical operators. My result should look like this:
a1 a2
2 1 1
4 4 2

Answer 1

Following the explanation in your edit, you want the rows where either the specific a1 from a is not in b1 from b or where the specific a1 from a is equal to b1 of the same row in b and a2 from a is not among the values of b2 from b of the rows for which b1 equals the value of the specific a1.
In R, you can write this like that:
cond <- sapply(seq(nrow(a)), # check each row, one by one
function (i){
!(a$a1[i] %in% b$b1) | # a1 of the specific row is not in b1 or
!(a$a2[i] %in% b$b2[b$b1==a$a1[i]]) # a2 of the specific row is not in the values of b2 for which b1 equals a1 of the sepcific row
})
a[cond, ]
# a1 a2
#2 1 1
#5 4 2

Answer 2

Obviously not a nice solution, but it works with my data (unequal dimension of rows of the two datasets, not the same position of the values in the variables) - here with new example data, because I chose the first really bad.
a <- data.frame("a1" = c(1,1,1,3,4), "a2" = c(2,1,2,1,2))
b <- data.frame("b1" = c(1,3,1,1), "b2" = c(2,1,2,2))
test <- function (data1, data2) {
for (i in unique(data1[data1$a1 %in% data2$b1, "a1"])) {
temp_data1 <- data1[data1$a1 == i, c("a1", "a2")]
temp_data2 <- data2[data2$b1 == i, c("b1", "b2")]
for (j in unique(temp_data1$a2)) {
test <- j %in% unique(temp_data2$b2)
if (test == FALSE) {
print(unique(temp_data1[temp_data1$a1 == i & temp_data1$a2 == j, ]))
}
}
}
for (k in unique(data1[which(!(data1$a1 %in% data2$b1)), "a1"])) {
print(unique(data1[data1$a1 == k, c("a1", "a2")]))
}
}
test(a, b)
a1 a2
2 1 1
a1 a2
5 4 2

Answer 3

Based on your answer I improved the function test(). This version returns a dataframe:
a <- data.frame(a1=c(1,1,1,3,4), a2=c(2,1,2,1,2))
b <- data.frame(b1=c(1,1,3,1,3), b2=c(2,2,1,2,1))
test <- function (a, b) {
R <- subset(a,!a1 %in% b$b1)
I <- unique(a$a1[a$a1 %in% b$b1])
for (i in I) {
ai <- subset(a, a1 == i)
bi <- subset(b, b1 == i)
J <- unique(bi$b2)
for (j in unique(ai$a2)) if (! j %in% J) R <- rbind(subset(ai, a2==j), R)
}
R
}
test(a, b)