Create new dataframe by dividing all possibles columns combination from another table

Question

I'm struggling to find an easy a fast solution to create a new data frame by multiplying all "group" of columns between them.

Data for example

a1 <- rnorm(n = 10)
b1 <- rnorm(n = 10)
c1 <- rnorm(n = 10)
a2 <- rnorm(n = 10)
b2 <- rnorm(n = 10)
c2 <- rnorm(n = 10)

For example in this in my initial datatable

Original <- data.frame(
  date = seq(today()-9, today(), by = 1),
  a1 = a1,
  b1 = b1,
  c1 = c1,
  a2 = a2,
  b2 = b2,
  c2 = c2)

and this datatable is what I would like to achieve (e.i., columns with all the possible combination between the columns that end with a 1 and columns with all the possible combination between the columns that end with a 2)

Objective <- data.frame(
  date = seq(today()-9, today(), by = 1),
  b1a1 = b1*a1,
  c1a1 = c1*a1,
  c1b1 = c1*b1,
  b2c2 = b2*c2,
  b2a2 = b2*a2,
  c2a2 = c2*a2)

I tried with loops but it's not a very elegant and efficient solution; or at least mine wasn't. A solution using the tidyverse would be very welcome

Thanks in advance

I.T

Answer 1

Here is base R option -

cbind(Original[1], do.call(cbind, 
      unname(lapply(split.default(Original[-1], 
      gsub('\\D', '', names(Original[-1]))), function(x) {
           do.call(cbind, combn(names(x), 2, function(y) {
               setNames(data.frame(do.call(`*`, Original[y])), 
               paste0(y, collapse = ''))
  }, simplify = FALSE))
}))))

#         date     a1b1      a1c1    b1c1    a2b2    a2c2    b2c2
#1  2021-05-28 -0.06708  1.393018 -0.1213  0.1795 -1.0878 -0.0947
#2  2021-05-29  0.33234  0.045563  0.0201  0.0607  0.0247  0.9219
#3  2021-05-30  0.05043  0.160582  0.0341  0.1748 -0.3893 -0.1184
#4  2021-05-31  0.93642  0.980333  0.8156  0.0746 -1.1128 -0.1571
#5  2021-06-01 -1.21365 -0.256619  0.3268 -1.0106 -0.3542  2.1991
#6  2021-06-02 -0.09550  1.311417 -0.0754 -0.8243 -0.5532  1.1986
#7  2021-06-03  0.32514  0.373324  2.3262 -1.1904 -3.0764  0.7171
#8  2021-06-04 -0.41219  1.034527 -0.8338 -1.8588 -1.0202  2.6916
#9  2021-06-05  0.12488 -0.155639 -0.2294  0.2380  0.4288  0.3711
#10 2021-06-06 -0.00665  0.000139 -0.0105 -2.0117 -0.6363  1.0802

---

Explanation of the answer -

1. split.default is used to split the data in groups.

split.default(Original[-1], gsub('\\D', '', names(Original[-1])))

#$`1`
#         a1      b1      c1
#1  -0.87773  0.0764 -1.5871
#2   0.86812  0.3828  0.0525
#3   0.48761  0.1034  0.3293
#4  -1.06095 -0.8826 -0.9240
#5   0.97625 -1.2432 -0.2629
#6  -1.28910  0.0741 -1.0173
#7  -0.22843 -1.4234 -1.6343
#8  -0.71512  0.5764 -1.4467
#9   0.29108  0.4290 -0.5347
#10 -0.00937  0.7098 -0.0149

#$`2`
#        a2     b2     c2
#1  -1.4360 -0.125  0.758
#2  -0.0403 -1.507 -0.612
#3  -0.7580 -0.231  0.514
#4   0.7270  0.103 -1.531
#5  -0.4035  2.505  0.878
#6   0.6168 -1.336 -0.897
#7   2.2599 -0.527 -1.361
#8  -0.8394  2.215  1.215
#9  -0.5244 -0.454 -0.818
#10  1.0886 -1.848 -0.585

where gsub is used to remove all non-numeric character from the column names which is used to create groups.

gsub('\\D', '', names(Original[-1]))
#[1] "1" "1" "1" "2" "2" "2"

2. For every group using lapply we create every combination of column names (combn(names(x), 2.....) taking 2 columns at a time.

3. Multiply each combination (do.call(*, Original[y])) create a one-column dataframe and give the name of the column using setNames that is name of the combination (paste0(y, collapse = ''))

4. All the combinations from step 3 are combined into one dataframe. (do.call(cbind, combn.....).

5. All such groups are again combined into one dataframe (do.call(cbind, lapply...).

6. First column with dates is kept as it is in the final output (cbind(Original[1], ....).

Answer 2

Very good question. A tidyverse approach. This approach will have combination of uneven number of columns per group. Explanation -

• Data is divided into a list with each sub-group as a separate item in the list. For this division
  • Firstly, the data is pivoted long using pivot_longer
  • then a dummy group (sub-group identification) column in created using gsub. You may use str_replace too.
• list created using dplyr::group_split
• data in all items reshaped back to its original form using tidyr::pivot_wider inside purrr::map now
• thereafter all individual items of list -
  • first combined using combn and Reduce. You may also use purrr::reduce here
  • secondly names of new columns generated using same combn and Reduce
  • these names bound above matrix into a named dataframe.
• lastly, using purrr::reduce in conjunction with dplyr::left_join list is converted back to intended shape

set.seed(123)
a1 <- rnorm(n = 10)
b1 <- rnorm(n = 10)
c1 <- rnorm(n = 10)
a2 <- rnorm(n = 10)
b2 <- rnorm(n = 10)
c2 <- rnorm(n = 10)

Original <- data.frame(
  date = seq(Sys.Date()-9, Sys.Date(), by = 1),
  a1 = a1,
  b1 = b1,
  c1 = c1,
  a2 = a2,
  b2 = b2,
  c2 = c2)

library(tidyverse)
Original %>% pivot_longer(!date) %>%
  mutate(grp = gsub('^\\D*(\\d)+$', '\\1', name)) %>%
  group_split(grp, .keep = F) %>%
  map(~ .x %>% pivot_wider(names_from = name, values_from = value)) %>%
  map(~ combn(.x[-1], 2, FUN = Reduce, f = `*`) %>% as.data.frame() %>%
        setNames(combn(names(.x[-1]), 2, FUN = Reduce, f = paste0)) %>% cbind(.x[1], .)) %>%
  reduce(~left_join(.x, .y, by = 'date'))

         date        a1b1        a1c1        b1c1        a2b2         a2c2         b2c2
1  2021-05-28 -0.68606804  0.59848918 -1.30710356 -0.29626767  0.108031283 -0.175982140
2  2021-05-29 -0.08282104  0.05017292 -0.07843039  0.06135046  0.008423333  0.005935364
3  2021-05-30  0.62468579 -1.59924166 -0.41119329 -1.13268875 -0.038374446  0.054248120
4  2021-05-31  0.00780406 -0.05139295 -0.08067566  1.90463287  1.201815497  2.968438088
5  2021-06-01 -0.07186344 -0.08080991  0.34742254  0.99243873 -0.185489171 -0.272722771
6  2021-06-02  3.06467216 -2.89278864 -3.01397443 -0.77341778  1.044302702 -1.703161152
7  2021-06-03  0.22946735  0.38614963  0.41709268 -0.22316502 -0.857881519  0.623969018
8  2021-06-04  2.48789113 -0.19402639 -0.30162620  0.02889143 -0.036194437 -0.272813136
9  2021-06-05 -0.48172830  0.78173260 -0.79823906 -0.23864021 -0.037894774  0.096601990
10 2021-06-06  0.21070515 -0.55877763 -0.59279292  0.03171951 -0.082159505 -0.018002847

Check it for this extended dataset

set.seed(123)
a1 <- rnorm(n = 10)
b1 <- rnorm(n = 10)
c1 <- rnorm(n = 10)
a2 <- rnorm(n = 10)
b2 <- rnorm(n = 10)
c2 <- rnorm(n = 10)
d2 <- rnorm(n = 10)

Original <- data.frame(
  date = seq(Sys.Date()-9, Sys.Date(), by = 1),
  a1 = a1,
  b1 = b1,
  c1 = c1,
  a2 = a2,
  b2 = b2,
  c2 = c2,
  d2 = d2)

library(tidyverse)
Original %>% pivot_longer(!date) %>%
  mutate(grp = gsub('^\\D*(\\d)+$', '\\1', name)) %>%
  group_split(grp, .keep = F) %>%
  map(~ .x %>% pivot_wider(names_from = name, values_from = value)) %>%
  map(~ combn(.x[-1], 2, FUN = Reduce, f = `*`) %>% as.data.frame() %>%
        setNames(combn(names(.x[-1]), 2, FUN = Reduce, f = paste0)) %>% cbind(.x[1], .)) %>%
  reduce(~left_join(.x, .y, by = 'date'))

         date        a1b1        a1c1        b1c1        a2b2         a2c2         a2d2         b2c2        b2d2        c2d2
1  2021-05-28 -0.68606804  0.59848918 -1.30710356 -0.29626767  0.108031283  0.161902656 -0.175982140 -0.26373820  0.09616971
2  2021-05-29 -0.08282104  0.05017292 -0.07843039  0.06135046  0.008423333  0.148221326  0.005935364  0.10444173  0.01433970
3  2021-05-30  0.62468579 -1.59924166 -0.41119329 -1.13268875 -0.038374446 -0.298262480  0.054248120  0.42163941  0.01428475
4  2021-05-31  0.00780406 -0.05139295 -0.08067566  1.90463287  1.201815497 -0.894445153  2.968438088 -2.20924515 -1.39402460
5  2021-06-01 -0.07186344 -0.08080991  0.34742254  0.99243873 -0.185489171 -0.880563395 -0.272722771 -1.29468307  0.24197936
6  2021-06-02  3.06467216 -2.89278864 -3.01397443 -0.77341778  1.044302702  0.209022041 -1.703161152 -0.34089562  0.46029226
7  2021-06-03  0.22946735  0.38614963  0.41709268 -0.22316502 -0.857881519  0.248271309  0.623969018 -0.18057692 -0.69416615
8  2021-06-04  2.48789113 -0.19402639 -0.30162620  0.02889143 -0.036194437 -0.003281582 -0.272813136 -0.02473471  0.03098700
9  2021-06-05 -0.48172830  0.78173260 -0.79823906 -0.23864021 -0.037894774 -0.282179411  0.096601990  0.71933645  0.11422674
10 2021-06-06  0.21070515 -0.55877763 -0.59279292  0.03171951 -0.082159505 -0.779997773 -0.018002847 -0.17091365  0.44269850

^{Created on 2021-06-06 by the reprex package (v2.0.0)}

Answer 3

You can also use the following solution, not as concise as other answers but here is a different approach that might have some points worthy of consideration. Much of the first chunk of codes I tried to emulate combn function with tidyverse equivalences. So first chuck which leads to df2 data set creates all the combinations whose products you would like to calculate and the second chunk just evaluates them in the context of Original data set. Anyway thank you for this fantastic question that pushed me to the limits.

library(dplyr)
library(tidyr)
library(purrr)
library(stringr)
library(rlang)

cols <- c("(\\w1)", "(\\w2)") 

cols %>% 
  map_dfc(~ names(Original)[str_detect(names(Original), .x)] %>%
            as_tibble() %>%
            mutate(value2 = rev(value)) %>%
            expand(value, value2) %>%
            filter(value != value2) %>%
            rowwise() %>%
            mutate(comb = paste0(sort(c(value, value2)), collapse = "*")) %>%
            select(comb) %>%
            distinct(comb)) %>%
  rename_with(~ str_remove(., "\\.\\.\\."), everything()) %>%
  pivot_longer(everything(), names_to = c(".value", "id"), 
               names_pattern = "(\\w+)(\\d)") -> df2


df2 %>%
  select(comb) %>%
  rowwise() %>%
  mutate(data = map(comb, ~ eval_tidy(parse_expr(.x), data = Original))) %>%
  unnest(cols = c(data)) %>%
  group_by(comb) %>%
  mutate(id = row_number()) %>%
  pivot_wider(names_from = comb, values_from = data) %>%
  relocate(ends_with("1")) %>%
  bind_cols(Original$date) %>%
  rename_with(~ str_remove(., "\\*"), everything()) %>%
  rename(Date = ...8) %>%
  relocate(Date) %>%
  select(-id)

# A tibble: 10 x 7
   Date           a1b1    a1c1      b1c1      a2b2     a2c2    b2c2
   <date>        <dbl>   <dbl>     <dbl>     <dbl>    <dbl>   <dbl>
 1 2021-05-28 -0.129    0.0912 -0.0838   -1.55     -1.52     2.11  
 2 2021-05-29 -0.477   -1.58    0.352    -3.55     -0.144    0.101 
 3 2021-05-30  0.195    0.708   0.105     0.910    -0.356   -0.177 
 4 2021-05-31 -0.194    0.0219 -0.0111   -1.35      0.261   -0.200 
 5 2021-06-01  0.0140   0.107   0.000601 -0.0279   -0.126    0.104 
 6 2021-06-02  0.242    0.141   0.174    -0.0174    0.695   -0.0570
 7 2021-06-03 -0.439   -0.360   0.589     0.804    -2.76    -1.79  
 8 2021-06-04 -1.02    -0.0349  0.0137    2.07      0.357    0.495 
 9 2021-06-05 -0.00670  0.550  -0.00161  -0.000907  0.00503 -0.925 
10 2021-06-06 -0.287   -0.505   0.718    -0.0290   -0.00351  0.0256