John - 14 days ago 8

R Question

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

`x>1`

`y!=1`

`sin(x)<0`

`AND`

`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.

Answer

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
```