John - 1 year ago 73
R Question

# Logical "and" for multiple logical vectors

If I have a number of logical statements (logical vectors in general), like

`x>1`
,
`y!=1`
and
`sin(x)<0`
, is there a function
`AND`
in R:

``````AND(x>1, y!=1, sin(x)<0)
``````

giving the same results as

``````x>1 & y!=1 & sin(x)<0
``````

Note, the number of vectors are variable, and not restricted to 3.

As mentioned by @r2evans, if we only work with scalar rather than vector, we can use `all` safely:

``````all(1 < 4, 5 > 7, 6 == 6)
``````

My answer below addresses the case when you work with several logical vectors, and would like to take parallel / element-wise `all`. As a reproducible example, suppose we have logical vectors:

``````set.seed(0)

a1 <- sample(c(TRUE, FALSE), 5, replace = TRUE)
# [1] FALSE  TRUE  TRUE FALSE FALSE

a2 <- sample(c(TRUE, FALSE), 5, replace = TRUE)
# [1]  TRUE FALSE FALSE FALSE FALSE

a3 <- sample(c(TRUE, FALSE), 5, replace = TRUE)
# [1]  TRUE  TRUE  TRUE FALSE  TRUE
``````

We aim for a solution that are not subject to the number of logical vectors.

Option 1

We can use `Reduce` and `"&"`:

``````## define a function
AND1 <- function (...)  Reduce("&", list(...))

AND1(a1, a2, a3)
# [1] FALSE FALSE FALSE FALSE FALSE
``````

The binary operator `"&"` only works with two inputs, so we can do

``````"&"(a1, a2)
``````

but not

``````"&"(a1, a2, a3)
``````

`Reduce` is here to help, by iteratively applying `"&"`:

``````tmp <- "&"(a1, a2)
"&"(a2, a3)
``````

The following two options first collect all logical vectors into a matrix. Then option 2a uses row-wise `all`, while option 2b uses `rowSums`.

Option 2a

``````AND2a <- function (...) {
X <- do.call(cbind, list(...))
base::apply(X, 1L, all)
}

AND2a (a1, a2, a3)
# [1] FALSE FALSE FALSE FALSE FALSE
``````

Option 2b

``````AND2b <- function (...) {
X <- do.call(cbind, list(...))
## `TRUE` is 1 and `FALSE` is 0 when doing arithmetic sum
## all `TRUE` is as same as row sums equal to `ncol(X)` or `dim(X)[2]`
base::rowSums(X) == dim(X)[2L]
}

AND2b (a1, a2, a3)
# [1] FALSE FALSE FALSE FALSE FALSE
``````
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