R: Counting rows in a dataframe in which all values fall within individual ranges - r

Question

I have a dataframe (A rows x K columns). For each column, I get the 5th and 95th percentile value. I want to know how many rows in the df have all K of their values within these K sets of 5th and 95th percentile values.
Example code below works, removing rows that do not fall within the bounds (1 and 9 here, but in practice will be percentiles), and then counting what remains. But A will be 10K and K will be 40, and I am simulating this dataframe 10K times, so I am wondering if there is code that will run faster.
data <- rbind(c(1,2,3,4,5), c(3,5,7,8,5), c(2,8,9,5,9), c(9,1,1,8,9),
c(3,5,6,7,5))
Lower_Bound <- rbind(1,1,1,1,1)
Upper_Bound <- rbind(9,9,9,9,9)
for (i in c(1:5)) {
data <- data[data[,i] > Lower_Bound[i,],]
data <- data[data[,i] < Upper_Bound[i,],]
}
N <- nrow(data)

Answer 1

If I understand correctly, the OP is only interested in the number of rows which fulfill the condition. So, there is no need to actually remove rows fromdata that do not fall within the bounds. It is sufficient to count the number of rows which do fall within the bounds.
This answer contains solutions for
matrices
data.frames
and a benchmark which compares
OP's approach,
apply() with matrices and data.frames,
an approach using purrr's map() and reduce() functions.
apply() with matrices
Let's start with the provided sample data and fixed Lower_Bound and Upper_Bound. Please, note that all three objects are matrices created by rbind(). This is in contrast to the text of the question which refers to a dataframe (A rows x K columns). Anyhow, we will provide solutions for both cases.
apply(data, 1, function(x) all(x > Lower_Bound & x < Upper_Bound))
returns a vector of type logical
[1] FALSE TRUE FALSE FALSE TRUE
The number of rows which fulfill the condition can be derived by
N <- sum(apply(data, 1, function(x) all(x > Lower_Bound & x < Upper_Bound)))
N
[1] 2
because TRUE is coerced to 1L and FALSE to 0L.
The next step is to also compute the bounds for each column as 5th and 95th percentile. For this, we have to create a new sample dataset mat, again as matrix
# create sample data
n_col <- 5
n_row <- 10
set.seed(42) # required for reproducible results
mat <- sapply(1:n_col, function(x) rnorm(n_row, mean = x))
mat
[,1] [,2] [,3] [,4] [,5]
[1,] 2.3709584 3.3048697 2.693361 4.455450 5.205999
[2,] 0.4353018 4.2866454 1.218692 4.704837 4.638943
[3,] 1.3631284 0.6111393 2.828083 5.035104 5.758163
[4,] 1.6328626 1.7212112 4.214675 3.391074 4.273295
[5,] 1.4042683 1.8666787 4.895193 4.504955 3.631719
[6,] 0.8938755 2.6359504 2.569531 2.282991 5.432818
[7,] 2.5115220 1.7157471 2.742731 3.215541 4.188607
[8,] 0.9053410 -0.6564554 1.236837 3.149092 6.444101
[9,] 3.0184237 -0.4404669 3.460097 1.585792 4.568554
[10,] 0.9372859 3.3201133 2.360005 4.036123 5.655648
For demonstration, each column has a different mean.
# count number of rows
probs <- c(0.05, 0.95)
bounds <- apply(mat, 2, quantile, probs)
idx <- apply(mat, 1, function(x) all(x > bounds[1, ] & x < bounds[2, ]))
N <- sum(idx)
N
1 5
If required, the subset of mat which fulfills the condition can be derived by
mat[idx, ]
[,1] [,2] [,3] [,4] [,5]
[1,] 2.3709584 3.304870 2.693361 4.455450 5.205999
[2,] 1.6328626 1.721211 4.214675 3.391074 4.273295
[3,] 0.8938755 2.635950 2.569531 2.282991 5.432818
[4,] 2.5115220 1.715747 2.742731 3.215541 4.188607
[5,] 0.9372859 3.320113 2.360005 4.036123 5.655648
The bounds are
bounds
[,1] [,2] [,3] [,4] [,5]
5% 0.641660 -0.5592606 1.226857 1.899532 3.882318
95% 2.790318 3.8517060 4.588960 4.886484 6.135429
apply() with data.frames
In case the dataset is a data.frame we can use the same code, i.e.,
df <- as.data.frame(mat)
probs <- c(0.05, 0.95)
bounds <- apply(df, 2, quantile, probs)
idx <- apply(df, 1, function(x) all(x > bounds[1, ] & x < bounds[2, ]))
N <- sum(idx)
Benchmark
The OP is looking for code which is faster than OP's own approach because the OP wants to replicate the simulation 10000 times.
So, here is a benchmark which compares
OP1: OP's own approach using matrices
OP2: a slightly modified version of OP1
apply_mat: the apply() function with matrices
apply_df: the apply() function with data.frames
purrr: using map(), pmap(), and reduce() from the purrr package
(Note that the list of methods is not exhaustive)
The benchmark is repeated for varying problem sizes, i.e., 5, 10, and 40 columns as well as 100, 1000, and 10000 rows. The largest problem size corresponds to the size of OP's simulations. As some codes modify the input dataset, all runs start with a fresh copy of the input data.
library(bench)
library(purrr)
library(ggplot2)
bm <- press(
n_col = c(5L, 10L, 40L)
, n_row = 10L^(2:4)
, {
set.seed(42)
mat0 <- sapply(1:n_col, function(x) rnorm(n_row, mean = x))
df0 <- as.data.frame(mat0)
mark(
OP1 = {
data <- data.table::copy(mat0)
Lower_Bound <- as.matrix(apply(data, 2, quantile, probs = 0.05), ncol = 1L)
Upper_Bound <- as.matrix(apply(data, 2, quantile, probs = 0.95), ncol = 1L)
for (i in seq_len(ncol(data))) {
data <- data[data[, i] > Lower_Bound[i, ], ]
data <- data[data[, i] < Upper_Bound[i, ], ]
}
nrow(data)
},
OP2 = {
data <- data.table::copy(mat0)
Lower_Bound <- as.matrix(apply(data, 2, quantile, probs = 0.05), ncol = 1L)
Upper_Bound <- as.matrix(apply(data, 2, quantile, probs = 0.95), ncol = 1L)
for (i in seq_len(ncol(data))) {
data <- data[data[, i] > Lower_Bound[i, ] & data[, i] < Upper_Bound[i, ], ]
}
nrow(data)
},
apply_mat = {
mat <- data.table::copy(mat0)
probs <- c(0.05, 0.95)
bounds <- apply(mat, 2, quantile, probs)
idx <- apply(mat, 1, function(x) all(x > bounds[1, ] & x < bounds[2, ]))
sum(idx)
},
apply_df = {
df <- data.table::copy(df0)
probs <- c(0.05, 0.95)
bounds <- apply(df, 2, quantile, probs)
idx <- apply(df, 1, function(x) all(x > bounds[1, ] & x < bounds[2, ]))
sum(idx)
},
purrr = {
data.table::copy(df0) %>%
map2(map_dfc(., quantile, probs), ~ (.x > .y[1L] & .x < .y[2L])) %>%
pmap(all) %>%
reduce(`+`)
}
)
}
)
autoplot(bm)
Note the logarithmic time scale
print(bm[, 1:11], n = Inf)
# A tibble: 45 x 11
expression n_col n_row min median `itr/sec` mem_alloc `gc/sec` n_itr n_gc total_time
<bch:expr> <int> <dbl> <bch:tm> <bch:tm> <dbl> <bch:byt> <dbl> <int> <dbl> <bch:tm>
1 OP1 5 100 1.46ms 1.93ms 493. 88.44KB 0 248 0 503ms
2 OP2 5 100 1.34ms 1.78ms 534. 71.56KB 0 267 0 500ms
3 apply_mat 5 100 1.16ms 1.42ms 621. 26.66KB 2.17 286 1 461ms
4 apply_df 5 100 1.41ms 1.8ms 526. 34.75KB 0 263 0 500ms
5 purrr 5 100 2.34ms 2.6ms 374. 17.86KB 0 187 0 500ms
6 OP1 10 100 2.42ms 2.78ms 344. 205.03KB 0 172 0 500ms
7 OP2 10 100 2.37ms 2.71ms 354. 153.38KB 2.07 171 1 484ms
8 apply_mat 10 100 1.76ms 2.12ms 457. 51.64KB 0 229 0 501ms
9 apply_df 10 100 2.31ms 2.63ms 367. 67.78KB 0 184 0 501ms
10 purrr 10 100 3.44ms 4.1ms 222. 34.89KB 2.09 106 1 477ms
11 OP1 40 100 9.4ms 10.57ms 92.9 955.41KB 0 47 0 506ms
12 OP2 40 100 9.18ms 10.08ms 96.8 638.92KB 0 49 0 506ms
13 apply_mat 40 100 5.44ms 6.46ms 146. 429.95KB 2.12 69 1 472ms
14 apply_df 40 100 6.12ms 6.75ms 141. 608.66KB 0 71 0 503ms
15 purrr 40 100 10.43ms 11.8ms 84.9 149.53KB 0 43 0 507ms
16 OP1 5 1000 1.75ms 1.94ms 478. 837.55KB 2.10 228 1 477ms
17 OP2 5 1000 1.69ms 1.94ms 487. 674.36KB 0 244 0 501ms
18 apply_mat 5 1000 4.84ms 5.62ms 176. 255.17KB 0 89 0 506ms
19 apply_df 5 1000 6.37ms 7.66ms 122. 333.58KB 0 62 0 506ms
20 purrr 5 1000 9.86ms 11.22ms 87.7 165.52KB 2.14 41 1 467ms
21 OP1 10 1000 3.35ms 3.91ms 253. 1.89MB 0 127 0 503ms
22 OP2 10 1000 3.33ms 3.72ms 256. 1.41MB 2.06 124 1 484ms
23 apply_mat 10 1000 5.86ms 6.93ms 142. 491.09KB 0 72 0 508ms
24 apply_df 10 1000 7.74ms 10.08ms 99.2 647.86KB 0 50 0 504ms
25 purrr 10 1000 14.55ms 15.44ms 62.5 323.17KB 2.23 28 1 448ms
26 OP1 40 1000 13.8ms 16.28ms 58.8 8.68MB 2.18 27 1 459ms
27 OP2 40 1000 13.29ms 14.72ms 67.9 5.84MB 0 34 0 501ms
28 apply_mat 40 1000 12.17ms 13.85ms 68.5 4.1MB 2.14 32 1 467ms
29 apply_df 40 1000 14.61ms 15.86ms 62.9 5.78MB 0 32 0 509ms
30 purrr 40 1000 41.85ms 43.66ms 22.7 1.25MB 0 12 0 529ms
31 OP1 5 10000 5.57ms 6.55ms 147. 8.15MB 2.07 71 1 482ms
32 OP2 5 10000 5.38ms 6.27ms 157. 6.55MB 2.06 76 1 485ms
33 apply_mat 5 10000 43.98ms 46.9ms 20.7 2.48MB 0 11 0 532ms
34 apply_df 5 10000 53.59ms 56.53ms 17.8 3.24MB 3.57 5 1 280ms
35 purrr 5 10000 86.32ms 88.83ms 11.1 1.6MB 0 6 0 540ms
36 OP1 10 10000 12.03ms 13.63ms 72.3 18.97MB 2.07 35 1 484ms
37 OP2 10 10000 11.66ms 12.97ms 76.5 14.07MB 4.25 36 2 471ms
38 apply_mat 10 10000 50.31ms 51.77ms 18.5 4.77MB 0 10 0 541ms
39 apply_df 10 10000 62.09ms 65.17ms 15.1 6.3MB 0 8 0 528ms
40 purrr 10 10000 125.82ms 128.3ms 7.35 3.13MB 2.45 3 1 408ms
41 OP1 40 10000 53.38ms 56.34ms 16.2 87.79MB 5.41 6 2 369ms
42 OP2 40 10000 46.24ms 47.43ms 20.3 58.82MB 2.25 9 1 444ms
43 apply_mat 40 10000 78.25ms 83.79ms 11.4 40.94MB 2.85 4 1 351ms
44 apply_df 40 10000 95.66ms 97.02ms 10.3 57.58MB 2.06 5 1 486ms
45 purrr 40 10000 361.26ms 373.23ms 2.68 12.31MB 0 2 0 746ms
Conclusions
To my surprise, OPs approach does perform quite well despite the repeated copy operations. In fact, for OP's problem size of 10000 rows and 40 columns the modified version OP2 is nearly tow times faster than apply_mat.
A possible explanation (which needs to be verified, though) is that OPs approach is kind of recursive where the number of rows to be checked are reduced when iterating over the columns.
Interestingly, the purrr variant has the lowest memory requirements.
Taking the median run time of about 50 ms for the OP2 method from this benchmark, 10000 repetitions of the simulation may take less than 10 minutes.