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Extract sorted rows from matrix

This matrix m:

      # [,1] [,2] [,3] [,4]
 # [1,]    2    1    3    4
 # [2,]    4    3    2    1
 # [3,]    2    3    1    4
 # [4,]    1    2    3    4
 # [5,]    4    2    3    1
 # [6,]    4    3    1    2
 # [7,]    2    4    3    1
 # [8,]    4    3    2    1
 # [9,]    3    2    1    4
# [10,]    1    2    3    4
# [11,]    3    2    4    1
# [12,]    4    3    2    1
# [13,]    2    1    3    4
# [14,]    2    1    3    4
# [15,]    1    2    3    4
# [16,]    4    3    2    1
# [17,]    2    1    3    4
# [18,]    1    4    3    2
# [19,]    3    2    1    4
# [20,]    1    2    3    4

m <- structure(c(2L, 4L, 2L, 1L, 4L, 4L, 2L, 4L, 3L, 1L, 3L, 4L, 2L, 
2L, 1L, 4L, 2L, 1L, 3L, 1L, 1L, 3L, 3L, 2L, 2L, 3L, 4L, 3L, 2L, 
2L, 2L, 3L, 1L, 1L, 2L, 3L, 1L, 4L, 2L, 2L, 3L, 2L, 1L, 3L, 3L, 
1L, 3L, 2L, 1L, 3L, 4L, 2L, 3L, 3L, 3L, 2L, 3L, 3L, 1L, 3L, 4L, 
1L, 4L, 4L, 1L, 2L, 1L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 
2L, 4L, 4L), .Dim = c(20L, 4L))

We can extract the sorted rows this way:

apply(m, 1, function(x) !is.unsorted(x) | !is.unsorted(rev(x)))

#[1] FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE 
#FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE

It’s good if the matrix is ​​small. But I'm talking about a matrix with millions of rows. Can we do better? Can we do this in vector form? The matrix mis given in exactly the same way as the given toys. I am looking for a general solution .

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6 answers

This is ugly, but you can get there by checking to see if all the differences in each column are negative or positive.

colSums(sign(diff(t(m)))) %in% c(-3,3)
# [1] FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE
#[13] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE

My quick testing shows that it is much faster to complete.

You can generalize it by simply checking the matrix size m:

colSums(sign(diff(t(m)))) %in% c(-(ncol(m)-1), ncol(m)-1)

, c(1,1,2,3), , :

sdm <- diff(t(m))
nc <- ncol(m) - 1
colSums(sdm <= 0)==nc | colSums(sdm >= 0)==nc
# [1] FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE
#[13] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE

( , ):

set.seed(1)
m2 <- m[sample(1:nrow(m),1e6,replace=T),]

## original apply code
system.time({
  apply(m2, 1, function(x) !is.unsorted(x) | !is.unsorted(rev(x)))
})
#   user  system elapsed 
# 14.888   0.272  15.153

:

system.time({
  n <- t(m2)
  forwards <- colSums(n == sort(m2[1,])) == ncol(m2)
  backwards  <- colSums(n == rev(sort(m2[1,]))) == ncol(m2)
  vec <- forwards | backwards
})
#   user  system elapsed 
#  0.104   0.020   0.123

system.time({
  sdm <- diff(t(m2))
  nc <- ncol(m) - 1
  colSums(sdm <= 0)==nc | colSums(sdm >= 0)==nc
})
#   user  system elapsed 
#  0.248   0.032   0.279

system.time({
  apply(m2[,-1] - m2[,-ncol(m2)], 1, function(x) all(x>=0) || all(x <= 0))
})
#   user  system elapsed 
#  3.724   0.004   3.731

library(matrixStats)
system.time(rowVarDiffs(m2) == 0)
#   user  system elapsed 
# 40.176   1.156  42.071
+5

:

n <- t(m)

forwards <- colSums(n == sort(m[1,])) == ncol(m)
backwards  <- colSums(n == rev(sort(m[1,]))) == ncol(m)

vec <- forwards | backwards
unvec <- apply(m, 1, function(x) !is.unsorted(x) | !is.unsorted(rev(x)))

identical(vec, unvec)
[1] TRUE
+3

, , diff 1, 0. rowVarDiffs matrixStats ,

library(matrixStats)

rowVarDiffs(m) == 0
#or 
rowVarDiffs(rowRanks(m)) == 0


#[1] FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE
+2

, , - , ( ) ( colSums , , !)

system.time({
    dm2 <- m2[,-1] - m2[,-ncol(m2)]
    vec <- rowSums(dm2>=0) == (ncol(m2)-1) |
           rowSums(dm2<=0) == (ncol(m2)-1) 
})

( ) .

:

   user  system elapsed 
   0.11    0.00    0.11

OP:

   user  system elapsed 
   8.98    0.00    8.98
+2

dim 1e+5 x 4, m . , m .

, , , :

  • f_m0h3n
  • f_thelatemail2
  • f_stephematician
  • f_Chirayu_Chamoli

, !

m <- structure(c(18, 1, 7, 1, 2, 12, 9, 6, 18, 20, 7, 2, 12, 13, 19, 
7, 20, 6, 5, 19, 17, 2, 2, 4, 5, 9, 18, 13, 9, 18, 1, 11, 13, 
7, 18, 10, 20, 2, 3, 3, 14, 8, 19, 8, 12, 7, 19, 16, 12, 16, 
17, 19, 7, 13, 15, 6, 18, 15, 2, 18, 9, 14, 8, 14, 15, 6, 13, 
18, 3, 10, 9, 5, 5, 9, 10, 6, 11, 17, 12, 15, 7, 15, 17, 15, 
16, 19, 3, 14, 2, 9, 4, 19, 14, 14, 7, 3, 10, 11, 18, 12, 3, 
18, 9, 18, 20, 12, 18, 10, 4, 7, 5, 2, 12, 11, 3, 4, 3, 7, 18, 
10), .Dim = c(20L, 6L))

set.seed(1)
library(matrixStats)
library(microbenchmark)
m1 <- structure(c(3, 1, 3, 3, 1, 5, 1, 5, 3, 5, 1, 3, 5, 3, 1, 3, 4, 
2, 5, 5, 5, 2, 2, 5, 5, 1, 2, 4, 2, 2, 2, 1, 4, 5, 2, 4, 1, 4, 
4, 3, 4, 3, 5, 2, 4, 2, 4, 3, 4, 4, 3, 5, 1, 1, 3, 5, 5, 1, 3, 
2, 2, 4, 1, 1, 2, 3, 3, 2, 1, 1, 4, 4, 3, 2, 4, 2, 3, 5, 2, 1, 
1, 5, 4, 4, 3, 4, 5, 1, 5, 3, 5, 2, 2, 4, 5, 1, 2, 3, 1, 4), .Dim = c(20L, 
5L))
m <- m1[sample(1:nrow(m1),1e5,replace=T),]
dim(m)
#[1] 100000  5
f_m0h3n <- function(m) apply(m, 1, function(x) !is.unsorted(x) || !is.unsorted(rev(x)))

f_thelatemail1 <- function(m) colSums(sign(diff(t(m)))) %in% c(-(ncol(m)-1), ncol(m)-1)
f_thelatemail2 <- function(m) {sdm <- diff(t(m));nc <- ncol(m) - 1;colSums(sdm <= 0)==nc | colSums(sdm >= 0)==nc}

f_sebastian_c <- function(m){n <- t(m);forwards <- colSums(n == sort(m[1,])) == ncol(m);
backwards  <- colSums(n == rev(sort(m[1,]))) == ncol(m);forwards | backwards}

f_Sotos1 <- function(m) rowVarDiffs(m) == 0
f_Sotos2 <- function(m) apply(m, 1, function(i) var(diff(i)) == 0)
f_Sotos3 <- function(m) rowVarDiffs(rowRanks(m)) == 0

f_stephematician <- function(m2)  {dm2 <- m2[,-1] - m2[,-ncol(m2)];
vec <- rowSums(dm2>=0) == (ncol(m2)-1) | rowSums(dm2<=0) == (ncol(m2)-1);vec}

f_Chirayu_Chamoli <- function(m) {i=apply(m, 1, is.unsorted);j=apply(m[,c(ncol(m):1),drop = FALSE], 1, is.unsorted);k=xor(i,j);k}

res <- f_m0h3n(m)
all(res==f_thelatemail1(m))
# [1] TRUE
all(res==f_thelatemail2(m))
# [1] TRUE
all(res==f_sebastian_c(m))
# [1] TRUE
all(res==f_Sotos1(m))
# [1] TRUE
all(res==f_Sotos2(m))
# [1] TRUE
all(res==f_Sotos3(m))
# [1] TRUE
all(res==f_stephematician(m))
# [1] TRUE
all(res==f_Chirayu_Chamoli(m))
# [1] TRUE

microbenchmark(f_m0h3n(m), f_thelatemail1(m), f_thelatemail2(m), f_sebastian_c(m), f_Sotos1(m), f_Sotos2(m), f_Sotos3(m), f_stephematician(m), f_Chirayu_Chamoli(m))

# Unit: milliseconds
                 # expr         min          lq        mean     median          uq        max neval
           # f_m0h3n(m)  504.901409  522.640977  542.398387  535.72417  561.723344  634.99808   100
    # f_thelatemail1(m)    9.426029   11.479137   23.454441   13.20548   17.308545   91.18738   100
    # f_thelatemail2(m)    8.841014   10.607174   25.820464   12.09675   17.740771  103.00244   100
     # f_sebastian_c(m)    5.358874    5.975436    9.709314    6.66186    8.725784   77.40695   100
          # f_Sotos1(m) 1526.461296 1604.177128 1639.571861 1644.11763 1669.721992 1752.77551   100
          # f_Sotos2(m) 1772.076169 1850.762817 1889.386328 1891.78832 1917.528489 2047.85548   100
          # f_Sotos3(m) 1538.428094 1600.285447 1637.314434 1644.03891 1671.703437 1738.84665   100
  # f_stephematician(m)    8.994555    9.986554   15.098616   10.97570   12.217240   83.86915   100
 # f_Chirayu_Chamoli(m)  273.571757  289.372545  321.199457  330.37146  346.979005  384.64962   100
+1

Here is another simple thing you could do. I think this is quite generalized, but the speed is wise, it is not close to a vectorized solution using latemail.

i=apply(m, 1, is.unsorted)
j=apply(m[,c(ncol(m):1),drop = FALSE], 1, is.unsorted)
k=xor(i,j)
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Source: https://habr.com/ru/post/1660675/

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