Rowwise matrix operations
Packages and setup
library(tidyverse)
set.seed(20)
The rowwise function
The rowwise function allows for the grouping
of data by rows in order to perform some operation across the values found in its columns.
Some basic data:
nums <- tibble(
x1 = sample(1:5, size=6, replace=TRUE),
x2 = sample(1:5, size=6, replace=TRUE),
x3 = sample(1:5, size=6, replace=TRUE),
x4 = sample(1:5, size=6, replace=TRUE)
)
nums
## # A tibble: 6 x 4
## x1 x2 x3 x4
## <int> <int> <int> <int>
## 1 3 1 4 5
## 2 2 3 1 1
## 3 1 5 5 5
## 4 2 1 1 2
## 5 5 5 1 1
## 6 5 2 4 5
I won't actually be using x4 in the demo below, but I'm including it to make the data a bit more
realistic. Oftentimes, you will have more variables in your data set than the ones you are trying
to operate on, i.e. you can't always just tidyselect::everything()!
Using c_across with rowwise
The c_across function is often used with
rowwise in order to combine values across columns. What happens if we use c_across without
rowwise?
nums %>%
mutate(test = mean(c_across(x1:x3)))
## # A tibble: 6 x 5
## x1 x2 x3 x4 test
## <int> <int> <int> <int> <dbl>
## 1 3 1 4 5 2.83
## 2 2 3 1 1 2.83
## 3 1 5 5 5 2.83
## 4 2 1 1 2 2.83
## 5 5 5 1 1 2.83
## 6 5 2 4 5 2.83
It can be seen that the test column has a single value that is repeated throughout. Without
grouping the data rowwise, the mean is computed using all the values across x1, x2, and
x3:
mean(c(nums$x1, nums$x2, nums$x3))
## [1] 2.833333
Now, if we group the data rowwise before computing the mean across x1, x2, and x3:
nums %>%
rowwise() %>%
mutate(test = mean(c_across(x1:x3)))
## # A tibble: 6 x 5
## # Rowwise:
## x1 x2 x3 x4 test
## <int> <int> <int> <int> <dbl>
## 1 3 1 4 5 2.67
## 2 2 3 1 1 2
## 3 1 5 5 5 3.67
## 4 2 1 1 2 1.33
## 5 5 5 1 1 3.67
## 6 5 2 4 5 3.67
We can check that the results are what we wanted:
mean(c(3, 1, 4))
## [1] 2.666667
mean(c(5, 2, 4))
## [1] 3.666667
They match — great!
Note: rowwise is a type of grouping. From the first two lines of the tibble output above, we
can see that after creating the test variable, the data is still grouped (rowwise)! Don't forget
to ungroup when you're done mutating.
Rowwise matrix operations
Output is a vector of length 1
Suppose you wanted to perform the following computation using the values found in each row:
$$ \mathbf{x}'\mathbf{A}\mathbf{x} $$We will first create a function that:
- Takes the combined values over a selection of columns (i.e. the result of
c_across) - Converts the values to a matrix (a $n \times 1$ column vector)
- Performs the matrix operation and reduces the resulting $1 \times 1$ matrix to a vector of length one
quadratic <- function(x, A) {
x <- as.matrix(x)
drop(t(x) %*% A %*% x)
}
For the $ \mathbf{A} $ matrix, let's use:
A <- matrix(
sample(0:5, size=9, replace=TRUE),
nrow=3, ncol=3
)
A
## [,1] [,2] [,3]
## [1,] 1 2 4
## [2,] 2 0 5
## [3,] 4 3 4
Putting it all together:
nums %>%
rowwise() %>%
mutate(test = quadratic(c_across(x1:x3), A)) %>%
ungroup()
## # A tibble: 6 x 5
## x1 x2 x3 x4 test
## <int> <int> <int> <int> <dbl>
## 1 3 1 4 5 213
## 2 2 3 1 1 72
## 3 1 5 5 5 361
## 4 2 1 1 2 40
## 5 5 5 1 1 209
## 6 5 2 4 5 353
Checking our work:
quadratic(c(3, 1, 4), A)
## [1] 213
quadratic(c(5, 2, 4), A)
## [1] 353
Output is a vector of length greater than 1
Suppose you wanted to perform the following computation using the values found in each row:
$$ \mathbf{A}\mathbf{x} $$and wanted each value to go into its own column. This can be accomplished by first creating a
function similar to the previous, but returning a list containing a named vector instead. Then we
can use unnest_wider to unnest the values
within the list into their own columns.
Creating the right-multiplying function:
right_mult <- function(x, A) {
x <- as.matrix(x)
drop(A %*% x) %>%
set_names(., paste0("new_x", 1:length(.))) %>%
list()
}
Creating the new list-column:
nums %>%
rowwise() %>%
mutate(test = right_mult(c_across(x1:x3), A)) %>%
ungroup()
## # A tibble: 6 x 5
## x1 x2 x3 x4 test
## <int> <int> <int> <int> <list>
## 1 3 1 4 5 <dbl [3]>
## 2 2 3 1 1 <dbl [3]>
## 3 1 5 5 5 <dbl [3]>
## 4 2 1 1 2 <dbl [3]>
## 5 5 5 1 1 <dbl [3]>
## 6 5 2 4 5 <dbl [3]>
Unnesting the list contents into their own columns:
nums %>%
rowwise() %>%
mutate(test = right_mult(c_across(x1:x3), A)) %>%
ungroup() %>%
unnest_wider(test)
## # A tibble: 6 x 7
## x1 x2 x3 x4 new_x1 new_x2 new_x3
## <int> <int> <int> <int> <dbl> <dbl> <dbl>
## 1 3 1 4 5 21 26 31
## 2 2 3 1 1 12 9 21
## 3 1 5 5 5 31 27 39
## 4 2 1 1 2 8 9 15
## 5 5 5 1 1 19 15 39
## 6 5 2 4 5 25 30 42
Checking our work:
right_mult(c(3, 1, 4), A)
## [[1]]
## new_x1 new_x2 new_x3
## 21 26 31
right_mult(c(5, 2, 4), A)
## [[1]]
## new_x1 new_x2 new_x3
## 25 30 42
