How to mutate multiple columns as function of multiple columns systematically?

You can do something like this with mutate(across..., however, for renaming columns there must be a shortcut.

df %>% 
  mutate(across(.cols = c(varA.t1, varA.t2),
                .fns = ~ .x / get(glue::glue(str_replace(cur_column(), "varA", "varB"))),
                .names = "V_{.col}")) %>%
  rename_with(~str_replace(., "V_varA", "varC"), starts_with("V_"))

# A tibble: 2 x 7
  id    varA.t1 varA.t2 varB.t1 varB.t2 varC.t1 varC.t2
  <chr>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
1 row_1       5      10       2       4     2.5    2.5 
2 row_2      20      50       4       6     5      8.33

If there is a long time series you can also create a vector for .cols beforehand.

I have a package on GitHub called {dplyover} which aims to solve this kind of problem in way similar to dplyr::across.

The function is called across2. It lets you define two sets of columns to which you can apply one or several functions. The .names argument supports two glue specifictions: {pre} and {suf}. They extract the shared pre- and suffix of the variable names. This makes it easy to put nice names on our output variables.

The function has one caveat. It is not performant when applied to highly grouped data (there is a vignette with benchmarks).

library(dplyr)
library(dplyover) # https://github.com/TimTeaFan/dplyover

df = tribble(
  ~id, ~varA.t1, ~varA.t2, ~varB.t1, ~varB.t2,
  'row_1', 5, 10, 2, 4,
  'row_2', 20, 50, 4, 6
)

df %>% 
  mutate(across2(starts_with("varA"),
                 starts_with("varB"),
                 ~ .x / .y,
                 .names = "{pre}C.{suf}"))

#> # A tibble: 2 x 7
#>   id    varA.t1 varA.t2 varB.t1 varB.t2 varC.t1 varC.t2
#>   <chr>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#> 1 row_1       5      10       2       4     2.5    2.5 
#> 2 row_2      20      50       4       6     5      8.33

^{Created on 2021-04-10 by the reprex package (v0.3.0)}

For such cases I find using base R easy and efficient.

varAcols <- sort(grep('varA', names(df), value = TRUE))
varBcols <- sort(grep('varB', names(df), value = TRUE))
df[sub('A', 'C', varAcols)] <- df[varAcols]/df[varBcols]

#    id    varA.t1 varA.t2 varB.t1 varB.t2 varC.t1 varC.t2
#  <chr>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#1 row_1       5      10       2       4     2.5    2.5 
#2 row_2      20      50       4       6     5      8.33

Another way to do this with some customization is

Initial setup

library(dplyr)
library(purrr)
library(stringr)

df = tribble(
  ~id, ~varA.t1, ~varA.t2, ~varB.t1, ~varB.t2,
  'row_1', 5, 10, 2, 4,
  'row_2', 20, 50, 4, 6
)

# A function take in a formula then parse it and correct the column name
operation_function <- function(df, formula) {
  # Extract the column name from the formula
  new_column_name <- str_extract(formula, "^.+=")
  new_column_name <- trimws(gsub("=", "", new_column_name))
  
  # Process the df
  df %>%
    # parse the formula - this reuslt in new column name  as value formula
    mutate(!!rlang::parse_expr(formula)) %>%
    # rename the new created column with the correct column name
    rename(!!new_column_name := last_col())
}

Note: I think there should be more efficient way to implement the formula that have proper name. Though I couldn't figure it out right now. Welcome ideas from others

Prepare the formula to be process by the data. In this case it simple

For more complicated formula you may want to do it a little bit differently

# Prepare the formula
base_formula <- c("varC.t# = varA.t# / varB.t#")
replacement_list <- c(1, 2)
list_formula <- map(replacement_list, .f = gsub,
  pattern = "#", x = base_formula)
list_formula
#> [[1]]
#> [1] "varC.t1 = varA.t1 / varB.t1"
#> 
#> [[2]]
#> [1] "varC.t2 = varA.t2 / varB.t2"

Finally process the data with the list of formulas

# process with the function and then reduce them with left_join
reduce(map(.x = list_formula, .f = operation_function, df = df),
  left_join)
#> Joining, by = c("id", "varA.t1", "varA.t2", "varB.t1", "varB.t2")
#> # A tibble: 2 x 7
#>   id    varA.t1 varA.t2 varB.t1 varB.t2 varC.t1 varC.t2
#>   <chr>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#> 1 row_1       5      10       2       4     2.5    2.5 
#> 2 row_2      20      50       4       6     5      8.33

^{Created on 2021-04-10 by the reprex package (v1.0.0)}