You are really close.
df2 <-
df %>%
mutate(v1v3 = v1 * v3,
v2v4 = v2 * v4)
such a beautifully simple language, right?
For more great tricks please see here.
EDIT:
Thanks to @Facottons pointer to this answer: https://stackoverflow.com/a/34377242/5088194, here is a tidy approach to resolving this issue. It keeps one from having to write a line to hard code in each new column desired. While it is a bit more verbose than the Base R approach, the logic is at least more immediately transparent/readable. It is also worth noting that there must be at least half as many rows as there are columns for this approach to work.
# prep the product column names (also acting as row numbers)
df <-
df %>%
mutate(prod_grp = paste0("v", row_number(), "v", row_number() + 2))
# converting data to tidy format and pairing columns to be multiplied together.
tidy_df <-
df %>%
gather(column, value, -prod_grp) %>%
mutate(column = as.numeric(sub("v", "", column)),
pair = column - 2) %>%
mutate(pair = if_else(pair < 1, pair + 2, pair))
# summarize the products for each column
prod_df <-
tidy_df %>%
group_by(prod_grp, pair) %>%
summarize(val = prod(value)) %>%
spread(prod_grp, val) %>%
mutate(pair = paste0("v", pair, "v", pair + 2)) %>%
rename(prod_grp = pair)
# put the original frame and summary frames together
final_df <-
df %>%
left_join(prod_df) %>%
select(-prod_grp)
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