Row-wise cumulative product on large data.table benchmarking - dataframe

Suppose I have a large data.table with about 1000 columns and 100,000 rows like this:
dt <- data.table(col1 = runif(10^4))
for (i in 2:10^3) set(dt, j = paste('col', as.character(i), sep = ''), value = dt[[i-1]] * 0.95^(i-1))
Think of these as representing 'daily mortality rates'. I want to calculate monthly survival rates, so I have the following chunk of code:
dt[, paste0('surv_rate_', 1:10^3) := Reduce('*', (1-dt[, paste0('col', 1:10^3)])^30, accumulate = T)]
I was not able to find any benchmarking on row-wise cumulative products like is shown above.
Can you think of any better/cleaner/faster methods for doing this in a data.table way?
(I thought of as.data.table(t(cumprod(t(dt))) as well but this appears to be taking forever with a table this size)

As mentionned in comments, another possible solution is to use apply along rows:
res1 <-
copy(dt)[, paste0('surv_rate_', 1:10^3) := transpose(apply((1-.SD)^30,1,cumprod,simplify=F))]
res2 <- copy(dt)[, paste0('surv_rate_', 1:10^3) := Reduce('*', (1-dt[, paste0('col', 1:10^3)])^30, accumulate = T)]
all.equal(res1,res2)
[1] TRUE
However, your solution remains 30% faster:
Unit: milliseconds
expr min
copy(dt)[, `:=`(paste0("surv_rate_", 1:10^3), transpose(apply((1-.SD)^30, 1, cumprod, simplify = F)))] 1011.7095
copy(dt)[, `:=`(paste0("surv_rate_", 1:10^3), Reduce("*", (1-dt[, paste0("col", 1:10^3)])^30, accumulate = T))] 793.5415
lq mean median uq max neval
1246.993 1743.854 1546.797 2119.166 2772.646 10
1046.194 1314.569 1249.636 1405.414 2496.858 10

Related

How can I optimize my for loop in order to be able to run it on a 320000 lines DataFrame table?

I think I have a problem with time calculation.
I want to run this code on a DataFrame of 320 000 lines, 6 columns:
index_data = data["clubid"].index.tolist()
for i in index_data:
for j in index_data:
if data["clubid"][i] == data["clubid"][j]:
if data["win_bool"][i] == 1:
if (data["startdate"][i] >= data["startdate"][j]) & (
data["win_bool"][j] == 1
):
NW_tot[i] += 1
else:
if (data["startdate"][i] >= data["startdate"][j]) & (
data["win_bool"][j] == 0
):
NL_tot[i] += 1
The objective is to determine the number of wins and the number of losses from a given match taking into account the previous match, this for every clubid.
The problem is, I don't get an error, but I never obtain any results either.
When I tried with a smaller DataFrame ( data[0:1000] ) I got a result in 13 seconds. This is why I think it's a time calculation problem.
I also tried to first use a groupby("clubid"), then do my for loop into every group but I drowned myself.
Something else that bothers me, I have at least 2 lines with the exact same date/hour, because I have at least two identical dates for 1 match. Because of this I can't put the date in index.
Could you help me with these issues, please?
As I pointed out in the comment above, I think you can simply sum the vector of win_bool by group. If the dates are sorted this should be equivalent to your loop, correct?
import pandas as pd
dat = pd.DataFrame({
"win_bool":[0,0,1,0,1,1,1,0,1,1,1,1,1,1,0],
"clubid": [1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],
"date" : [1,2,1,2,3,4,5,1,2,1,2,3,4,5,6],
"othercol":["a","b","b","b","b","b","b","b","b","b","b","b","b","b","b"]
})
temp = dat[["clubid", "win_bool"]].groupby("clubid")
NW_tot = temp.sum()
NL_tot = temp.count()
NL_tot = NL_tot["win_bool"] - NW_tot["win_bool"]
If you have duplicate dates that inflate the counts, you could first drop duplicates by dates (within groups):
# drop duplicate dates
temp = dat.drop_duplicates(["clubid", "date"])[["clubid", "win_bool"]].groupby("clubid")

How to vectorize to speed up Dataframe apply pandas

I have a tXn (5000 X 100) dataframe wts_df,
wts_df.tail().iloc[:, 0:6]
Out[71]:
B C H L R T
2020-09-25 0.038746 0.033689 -0.047835 -0.002641 0.009501 -0.030689
2020-09-28 0.038483 0.033189 -0.061742 0.001199 0.009490 -0.028370
2020-09-29 0.038620 0.034957 -0.031341 0.006179 0.007815 -0.027317
2020-09-30 0.038610 0.034902 -0.014271 0.004512 0.007836 -0.024672
2020-10-01 0.038790 0.029937 -0.044198 -0.008415 0.008347 -0.030980
and two similar txn dataframes, vol_df and rx_df (same index and columns). For now we can use,
rx_df = wts_df.applymap(lambda x: np.random.rand())
vol_df = wts_df.applymap(lambda x: np.random.rand())
I need to do this (simplified):
for date in wts_df.index:
wts = wts_df.loc[date] # is a vector now 1Xn
# mutliply all entries of rx_df and vol_df until this date by these wts, and sum across columns
rx = rx_df.truncate(after=date) # still a dataframe but truncated at a given date, kXn
vol = vol_df_df.truncate(after=date)
wtd_rx = (wts * rx).sum(1) # so a vector kX1
wtd_vol = (wts * vol).sum(1)
# take ratio
rx_vol = rx / vol
rate[date] = rx_vol.tail(20).std()
So rate looks like this
pd.Series(rate).tail()
Out[71]:
rate
2020-09-25 0.0546
2020-09-28 0.0383
2020-09-29 0.0920
2020-09-30 0.0510
2020-10-01 0.0890
The above loop is slow, so i tried this:
def rate_calc(wts, date, rx_df=rx_df, vol_df=vol_df):
wtd_rx = (rx_df * wts).sum(1)
wtd_vol = (vol_df * wts).sum(1)
rx_vol = wtd_rx / wtd_vol
rate = rx_vol.truncate(after=date).tail(20).std()
return rate
rates = wts_df.apply(lambda x: rate_calc(x, x.name), axis=1)
This is still very slow. Moreover I need to do this for multiple wts_df contained in a dict so the total operations takes a lot time.
rates = {key: val.apply(lambda x: rate_calc(x, x.name), axis=1) for key, val in wts_df_dict.iteritems()}
Any ideas how to speed such operations?
Your question falls under the category of 'optimization' so allow me to share with you few pointers to solve your problem.
First, when it comes to speed, always use %timeit to ensure you get better results with a new stratgegy.
Second, there are few ways to iterate a data:
with iterrows() -- use it only when the data sample is small (or better yet, try not to use it as it's too slow).
With apply --better alternative to iterrows and much more efficient but when the data set is large (like in your example) it may present a delay problem.
Vectorizing --simply put, you execute the operation on the entire column/array and its significantly fast. Winner!
So, in order to solve your speed problem your strategy should be in the form of vectorizing. So here's how it should work; (mind the .values):
df['new_column'] = my_function(df['column_1'].values, df['column_2'].values...) and you will note a super fast result.

Taking mean of N largest values of group by absolute value

I have some DataFrame:
d = {'fruit': ['apple', 'pear', 'peach'] * 6, 'values': np.random.uniform(-5,5,18), 'values2': np.random.uniform(-5,5,18)}
df = pd.DataFrame(data=d)
I can take the mean of each fruit group as such:
df.groupby('fruit').mean()
However, for each group of fruit, I'd like to take the mean of the N number of largest values as
ranked by absolute value.
So for example, if my values were as follows and N=3:
[ 0.7578507 , 3.81178045, -4.04810913, 3.08887538, 2.87999752, 4.65670954]
The desired outcome would be (4.65670954 + -4.04810913 + 3.81178045) / 3 = ~1.47
Edit - to clarify that sign is preserved in outcome:
(4.65670954 + -20.04810913 + 3.81178045) / 3 = -3.859
Updating with a new approach that I think is simpler. I was avoiding apply like the plague but maybe this is one of the more acceptable uses. Plus it fixes the fact that you want to mean the original values as ranked by their absolute values:
def foo(d):
return d[d.abs().nlargest(3).index].mean()
out = df.groupby('fruit')['values'].apply(foo)
So you index each group by the 3 largest absolute values, then mean.
And for the record my original, incorrect, and slower code was:
df['values'].abs().groupby(df['fruit']).nlargest(3).groupby("fruit").mean()

Creating similar samples based on three different categorical variables

I am trying to do an analysis where I am trying to create two similar samples based on three different attributes. I want to create these samples first and then do the analysis to see which out of those two samples is better. The categorical variables are sales_group, age_group, and country. So I want to make both samples such as the proportion of countries, age, and sales is similar in both samples.
For example: Sample A and B have following variables in it:
Id Country Age Sales
The proportion of Country in Sample A is:
USA- 58%
UK- 22%
India-8%
France- 6%
Germany- 6%
The proportion of country in Sample B is:
India- 42%
UK- 36%
USA-12%
France-3%
Germany- 5%
The same goes for other categorical variables: age_group, and sales_group
Thanks in advance for help
You do not need to establish special procedure for sampling as one-sample proportion is unbiased estimate of population proportion. In case you have, suppose, >1000 observations and you are sampling more than, let us say, 30 samples the estimate would be quite exact (Central Limit Theorem).
You can see it in the simulation below:
set.seed(123)
n <- 10000 # Amount of rows in the source data frame
df <- data.frame(sales_group = sample(LETTERS[1:4], n, replace = TRUE),
age_group = sample(c("old", "young"), n, replace = TRUE),
country = sample(c("USA", "UK", "India", "France", "Germany"), n, replace = TRUE),
amount = abs(100 * rnorm(n)))
s <- 100 # Amount of sampled rows
sampleA <- df[sample(nrow(df), s), ]
sampleB <- df[sample(nrow(df), s), ]
table(sampleA$sales_group)
# A B C D
# 23 22 32 23
table(sampleB$sales_group)
# A B C D
# 25 22 28 25
DISCLAIMER: However if you have some very small or very big proportion and have too little samples you will need to use some advanced procedures like Laplace smoothing

Create 20 unique bingo cards

I'm trying to create 20 unique cards with numbers, but I struggle a bit.. So basically I need to create 20 unique matrices 3x3 having numbers 1-10 in first column, numbers 11-20 in the second column and 21-30 in the third column.. Any ideas? I'd prefer to have it done in r, especially as I don't know Visual Basic. In excel I know how to generate the cards, but not sure how to ensure they are unique..
It seems to be quite precise and straightforward to me. Anyway, i needed to create 20 matrices that would look like :
[,1] [,2] [,3]
[1,] 5 17 23
[2,] 8 18 22
[3,] 3 16 24
Each of the matrices should be unique and each of the columns should consist of three unique numbers ( the 1st column - numbers 1-10, the 2nd column 11-20, the 3rd column - 21-30).
Generating random numbers is easy, though how to make sure that generated cards are unique?Please have a look at the post that i voted for as an answer - as it gives you thorough explanation how to achieve it.
(N.B. : I misread "rows" instead of "columns", so the following code and explanation will deal with matrices with random numbers 1-10 on 1st row, 11-20 on 2nd row etc., instead of columns, but it's exactly the same just transposed)
This code should guarantee uniqueness and good randomness :
library(gtools)
# helper function
getKthPermWithRep <- function(k,n,r){
k <- k - 1
if(n^r< k){
stop('k is greater than possibile permutations')
}
v <- rep.int(0,r)
index <- length(v)
while ( k != 0 )
{
remainder<- k %% n
k <- k %/% n
v[index] <- remainder
index <- index - 1
}
return(v+1)
}
# get all possible permutations of 10 elements taken 3 at a time
# (singlerowperms = 720)
allperms <- permutations(10,3)
singlerowperms <- nrow(allperms)
# get 20 random and unique bingo cards
cards <- lapply(sample.int(singlerowperms^3,20),FUN=function(k){
perm2use <- getKthPermWithRep(k,singlerowperms,3)
m <- allperms[perm2use,]
m[2,] <- m[2,] + 10
m[3,] <- m[3,] + 20
return(m)
# if you want transpose the result just do:
# return(t(m))
})
Explanation
(disclaimer tl;dr)
To guarantee both randomness and uniqueness, one safe approach is generating all the possibile bingo cards and then choose randomly among them without replacements.
To generate all the possible cards, we should :
generate all the possibilities for each row of 3 elements
get the cartesian product of them
Step (1) can be easily obtained using function permutations of package gtools (see the object allPerms in the code). Note that we just need the permutations for the first row (i.e. 3 elements taken from 1-10) since the permutations of the other rows can be easily obtained from the first by adding 10 and 20 respectively.
Step (2) is also easy to get in R, but let's first consider how many possibilities will be generated. Step (1) returned 720 cases for each row, so, in the end we will have 720*720*720 = 720^3 = 373248000 possible bingo cards!
Generate all of them is not practical since the occupied memory would be huge, thus we need to find a way to get 20 random elements in this big range of possibilities without actually keeping them in memory.
The solution comes from the function getKthPermWithRep, which, given an index k, it returns the k-th permutation with repetition of r elements taken from 1:n (note that in this case permutation with repetition corresponds to the cartesian product).
e.g.
# all permutations with repetition of 2 elements in 1:3 are
permutations(n = 3, r = 2,repeats.allowed = TRUE)
# [,1] [,2]
# [1,] 1 1
# [2,] 1 2
# [3,] 1 3
# [4,] 2 1
# [5,] 2 2
# [6,] 2 3
# [7,] 3 1
# [8,] 3 2
# [9,] 3 3
# using the getKthPermWithRep you can get directly the k-th permutation you want :
getKthPermWithRep(k=4,n=3,r=2)
# [1] 2 1
getKthPermWithRep(k=8,n=3,r=2)
# [1] 3 2
Hence now we just choose 20 random indexes in the range 1:720^3 (using sample.int function), then for each of them we get the corresponding permutation of 3 numbers taken from 1:720 using function getKthPermWithRep.
Finally these triplets of numbers, can be converted to actual card rows by using them as indexes to subset allPerms and get our final matrix (after, of course, adding +10 and +20 to the 2nd and 3rd row).
Bonus
Explanation of getKthPermWithRep
If you look at the example above (permutations with repetition of 2 elements in 1:3), and subtract 1 to all number of the results you get this :
> permutations(n = 3, r = 2,repeats.allowed = T) - 1
[,1] [,2]
[1,] 0 0
[2,] 0 1
[3,] 0 2
[4,] 1 0
[5,] 1 1
[6,] 1 2
[7,] 2 0
[8,] 2 1
[9,] 2 2
If you consider each number of each row as a number digit, you can notice that those rows (00, 01, 02...) are all the numbers from 0 to 8, represented in base 3 (yes, 3 as n). So, when you ask the k-th permutation with repetition of r elements in 1:n, you are also asking to translate k-1 into base n and return the digits increased by 1.
Therefore, given the algorithm to change any number from base 10 to base n :
changeBase <- function(num,base){
v <- NULL
while ( num != 0 )
{
remainder = num %% base # assume K > 1
num = num %/% base # integer division
v <- c(remainder,v)
}
if(is.null(v)){
return(0)
}
return(v)
}
you can easily obtain getKthPermWithRep function.
One 3x3 matrix with the desired value range can be generated with the following code:
mat <- matrix(c(sample(1:10,3), sample(11:20,3), sample(21:30, 3)), nrow=3)
Furthermore, you can use a for loop to generate a list of 20 unique matrices as follows:
for (i in 1:20) {
mat[[i]] <- list(matrix(c(sample(1:10,3), sample(11:20,3), sample(21:30,3)), nrow=3))
print(mat[[i]])
}
Well OK I may fall on my face here but I propose a checksum (using Excel).
This is a unique signature for each bingo card which will remain invariate if the order of numbers within any column is changed without changing the actual numbers. The formula is
=SUM(10^MOD(A2:A4,10)+2*10^MOD(B2:B4,10)+4*10^MOD(C2:C4,10))
where the bingo numbers for the first card are in A2:C4.
The idea is to generate a 10-digit number for each column, then multiply each by a constant and add them to get the signature.
So here I have generated two random bingo cards using a standard formula from here plus two which are deliberately made to be just permutations of each other.
Then I check if any of the signatures are duplicates using the formula
=MAX(COUNTIF(D5:D20,D5:D20))
which shouldn't given an answer more than 1.
In the unlikely event that there were duplicates, then you would just press F9 and generate some new cards.
All formulae are array formulae and must be entered with CtrlShiftEnter
Here is an inelegant way to do this. Generate all possible combinations and then sample without replacement. These are permutations, combinations: order does matter in bingo
library(dplyr)
library(tidyr)
library(magrittr)
generate_samples = function(n) {
first = data_frame(first = (n-9):n)
first %>%
merge(first %>% rename(second = first)) %>%
merge(first %>% rename(third = first)) %>%
sample_n(20)
}
suffix = function(df, suffix)
df %>%
setNames(names(.) %>%
paste0(suffix))
generate_samples(10) %>% suffix(10) %>%
bind_cols(generate_samples(20) %>% suffix(20)) %>%
bind_cols(generate_samples(30) %>% suffix(30)) %>%
rowwise %>%
do(matrix = t(.) %>% matrix(3)) %>%
use_series(matrix)