How to create matrix of distribution in R

The biggest challenge is that keys come in rows and columns.

I used 2 custom functions to count the occurrences:

• getcount(), which uses a condition argument (see here if you are not familiar with quosures), for your special conditional rows (TotalID, Blank_list, ...)
• getcount2(), which uses a simple character argument, for your cases rows (ABC, BCD, TR1...)

Both work mostly the same way. We calculate the count separately for all single cases and for the total, always grouping by ID and concatenate the results.

Here is the code:

library(tidyverse)
library(lubridate)

df <- structure(list(ID = c("P-10012", "P-10012", "P-10012", "P-10013", "P-10013", "P-10013", 
                            "P-10014", "P-10014", "P-10015", "P-10016", "P-10017"), 
                     Date = c("2020-04-15 12:13:15", "2020-04-15 12:13:15", "2020-04-15 12:13:15", 
                              "2020-04-12 17:10:05", "2020-04-12 17:10:05", "2020-04-12 17:10:05", 
                              "2020-04-10 04:30:19", "2020-04-10 04:30:19", "2020-04-10 14:13:15", 
                              "2020-04-10 13:13:15", "2020-03-18 10:13:15"), 
                     Type = c("TR1", "RES", "FTT", "TR1", "FTT", "ZXR", "TR1", "ZXR", NA, NA, "TR1"),
                     List = c("ABC,ABD,BCD", "ABC,ABD,BCD", "ABC,ABD,BCD", "", "", "", "ABD,BCD", 
                              "ABD,BCD", "ABC", "", "ABC,ABD,BCD")), 
                class = "data.frame", row.names = c(NA, -11L))

#extract all the individual values from Type and List
cases = c(df$Type, str_split(df$List, ", ?", simplify=TRUE)) %>% unique() %>% 
  sort() %>% .[.!=""] %>% rlang::set_names()

#util function
is_blank = function(x) is.na(x) | x==""

#get count for summary rows (TotalID, Blank_list, ...)
getcount = function(cond){
  x = map_dbl(cases, ~df %>% 
                filter(month(Date)==4) %>%
                group_by(ID) %>% 
                summarise(rtn=any({{cond}} & (str_detect(Type, .x) | str_detect(List, .x)))) %>% 
                pull() %>% sum(na.rm=TRUE)
  )
  x_tot = df %>% 
    filter(month(Date)==4) %>% 
    group_by(ID) %>% 
    summarise(rtn=any({{cond}})) %>% 
    pull() %>% sum(na.rm=TRUE)
  
  c(x_tot, x)
}

#get count for cases rows (ABC, BCD, TR1...)
getcount2 = function(key){
  x = map_dbl(cases, ~df %>% 
                filter(month(Date)==4) %>%
                group_by(ID) %>% 
                summarise(rtn=any(
                  (key %in% Type  | str_detect(List, key)) &
                    (str_detect(Type, .x ) | str_detect(List, .x ))
                )) %>% 
                pull() %>% sum(na.rm=TRUE)
  )
  x_tot = df %>% 
    filter(month(Date)==4) %>% 
    group_by(ID) %>% 
    summarise(rtn=any(List==key)) %>% 
    pull() %>% sum(na.rm=TRUE)
  
  c(tot=x_tot, x)
}


#here we go!
tibble(x=c("Distinct_Count", cases)) %>% 
  mutate(
    Total_ID=getcount(TRUE),
    Blank_List=getcount(is_blank(List)),
    Blank_Type=getcount(is_blank(Type)),
    Blank_Both=getcount(is_blank(List) & is_blank(Type)),
    Non_Blank_List=getcount(!is_blank(List)),
    Non_Blank_Type=getcount(!is_blank(Type)),
    Non_Blank_Both=getcount(!is_blank(List) & !is_blank(Type))
  ) %>% 
  bind_cols(map_dfc(cases, ~getcount2(.x))) %>% 
  column_to_rownames("x") %>% 
  t() %>% as.data.frame() %>% 
  mutate(Percentage = scales::percent(Distinct_Count/max(Distinct_Count)), .after="Distinct_Count")
#>                Distinct_Count Percentage ABC ABD BCD FTT RES TR1 ZXR
#> Total_ID                    5       100%   2   2   2   2   1   3   2
#> Blank_List                  2        40%   0   0   0   1   0   1   1
#> Blank_Type                  2        40%   1   0   0   0   0   0   0
#> Blank_Both                  1        20%   0   0   0   0   0   0   0
#> Non_Blank_List              3        60%   2   2   2   1   1   2   1
#> Non_Blank_Type              3        60%   1   2   2   2   1   3   2
#> Non_Blank_Both              2        40%   1   2   2   1   1   2   1
#> ABC                         1        20%   2   1   1   1   1   1   0
#> ABD                         0         0%   1   2   2   1   1   2   1
#> BCD                         0         0%   1   2   2   1   1   2   1
#> FTT                         0         0%   1   1   1   2   1   2   1
#> RES                         0         0%   1   1   1   1   1   1   0
#> TR1                         0         0%   1   2   2   2   1   3   2
#> ZXR                         0         0%   0   1   1   1   0   2   2

^{Created on 2021-05-12 by the reprex package (v2.0.0)}

Note that there are several minor differences with your expected output, but I assume they are little mistakes from your complex example. For instance, ABC has Distinct_Count==1 so out of 5 it should not make 33%. Also, ZXR can be seen with TR1 twice (ID 13 and 14).