how catch values "approaching" to those within another vector R

Question

I have two vectors:

y
 [1] 54.36 70.43 36.49 39.59 15.06 34.60  0.24 24.00 20.22 24.73 29.86 49.30 37.36
[14] 29.68 37.64  7.99 22.42 28.99  3.09 63.92 17.72  9.51 13.06  3.83 51.91  1.79
[27] 16.86 50.74 28.41 20.03 24.24 33.70  7.70 24.83 53.98 -8.74 30.14 20.80 12.10
[40] 38.31 35.35 33.96 25.07 44.86 18.73 36.66 19.57 30.62 -0.65 21.66 54.59 35.28
[53] 27.83 48.27 17.99


z
  [1]  53.0  17.5  48.5  40.0  46.0  38.0  14.5  19.5  37.5   5.5  16.0  25.0  11.0
 [14]  17.5  14.0  21.0  22.5   0.0   3.0  18.5  37.0  53.0  33.0  47.0  18.5  22.0
 [27]  14.5  48.5  48.0  26.0  28.0  56.5  15.0  29.5   7.5  35.0   7.0  25.5  21.0
 [40]   8.5  53.0  51.5   9.0  15.0  20.5  13.0  23.0  15.0  18.0  38.5   7.0  17.5
 [53]  35.0  29.5  16.5  34.5  27.5  18.5  18.5  24.0  24.0  30.5  28.0  27.0  15.5
 [66]  12.5  23.0  22.0  45.0  12.0  19.0  10.0  85.5  16.0  34.5  43.0  27.0  13.0
 [79]  22.5  30.5  22.0  59.0  21.0   7.5  23.0  10.5  16.0  20.0  62.0  13.0  64.0
 [92]  52.0  18.5  33.0   0.0  25.0  11.0  16.5  17.0  48.0  30.5  21.5  18.0  19.5
[105]  11.0  95.0  38.0  17.5  42.5   7.0  48.0  38.0  23.5  16.5   7.5  51.0  14.5
[118]  20.5  23.5   8.0  46.0  45.0  64.0  75.0  35.0  10.0  10.0  10.5  12.0  12.0
[131]  13.0  15.5  39.0  29.5   3.0  13.0  25.0   5.0   0.0  29.0  28.0   7.5  14.0
[144]  26.5  19.5  62.0  23.0   8.5  31.5  23.5  26.0  11.0  18.5  28.0  31.0  42.0
[157]  57.0  54.0  10.0  12.5  13.5  11.0   8.0  35.5  60.0  18.0 101.5  15.0  21.5
[170]   9.5  17.5  18.0  16.0  28.5  35.0  47.0  26.0  50.5  13.0  18.5  14.0  18.5
[183]  27.0  33.0  28.5  24.5  34.5   9.0   9.0  53.5  15.0  14.0  18.0  16.5  27.0
[196]  11.5  14.0  27.0  10.0  46.0   0.0  18.0  27.5  67.5  22.5  12.5  26.0  24.5
[209]   0.0  22.0  12.0  30.5  23.5   2.5  15.5  34.5  50.0  62.0   5.0   9.5  11.0
[222]  10.5   6.5  23.0  12.5  18.0  17.5  31.5  42.5  15.0  54.5  48.5   9.5  16.5
[235]  18.0  42.0  49.0   4.0  42.0  47.0  13.5  28.0   8.0  43.0   8.5  10.0  26.5
[248]  13.5  28.0  37.0  23.5  10.5  45.0  15.0  10.0  35.0  36.0  20.5  17.0  22.5
[261]  64.5  21.0  25.0   8.0  12.5  21.5  24.0   8.5  27.0  70.0  34.0  31.5  12.0
[274]   5.5  36.0  28.0   6.5  14.5  18.5  21.5  20.0  23.5  20.0  27.0  19.0  17.0
[287]  10.0  50.0  36.0   8.0  22.0  58.5  30.0  19.5   0.0  22.0   0.0   7.5   0.0
[300]  59.0  13.0   4.5  19.0  14.0   0.0  17.5  19.5

I would select from the second subset z those approaching (meaning not being exactly the same) as much as possible within the y vector.

Which function is suggested in this case?

Answer 1

You could create a distance matrix using outer, then subset by a tolerance. To find the best value, we optimize the trade-off between low tolerance and length of result, in an interval between 0 and 1.

f <- \(a) {
  r <- z[rowSums(abs(abs(outer(z, y, `-`))) < abs(y*a)) > 0]
  a + length(r)/length(z)
}
(tol <- optimize(f, c(0, 1))$objective)
# [1] 0.00983826

(z1 <- z[rowSums(abs(abs(outer(z, y, `-`))) < abs(y*tol)) > 0])
#   [1] 17.5 38.0 19.5 37.5 25.0 22.5  3.0 18.5 37.0 18.5 22.0 48.0 28.0 15.0
#  [15] 29.5  7.5 35.0 21.0  8.5 13.0 15.0 18.0 17.5 35.0 29.5 34.5 18.5 24.0
#  [29] 24.0 30.5 15.5 22.0 45.0 12.0 34.5 13.0 22.5 30.5 22.0 21.0  7.5 20.0
#  [43] 64.0 52.0  0.0 25.0 17.0 30.5 21.5 18.0 19.5 38.0 38.0 20.5  8.0 45.0
#  [57] 35.0 10.0 12.0 13.0  3.0 13.0 25.0  0.0 29.0 28.0  7.5 19.5 28.0 54.0
#  [71] 12.5  8.0 35.5 18.0 15.0 21.5  9.5 17.5 18.0 28.5 35.0 50.5 13.0 18.5
#  [85] 24.5 34.5  9.0 15.0 18.0 18.0 27.5 22.5 24.5 12.0 30.5  2.5 34.5  9.5
#  [99] 18.0 17.5 15.0 54.5 48.5  9.5 18.0  8.0 28.0 37.0 23.5 45.0 15.0 35.0
# [113] 20.5 17.0 22.5 25.0  8.0 12.5 24.0 34.0 12.0 28.0 18.5 20.0 20.0 17.0
# [127]  8.0 22.0 30.0 19.5  7.5  0.0 13.0 19.0  0.0 17.5

Visualization:

stripchart(z, pch='|', col=8, axes=FALSE, panel.first=abline(h=.5, col=8))
axis(1, axTicks(1), lwd=0, lwd.ticks=1)
abline(v=y, col=2, lty=3)
stripchart(z1, pch='|', col=2, add=TRUE)
legend(80, 2.5, horiz=TRUE, bty='n', xpd=TRUE, lty=c(1, 3, 1), col=c(8, 2, 2), 
       legend=c('z', 'y', bquote(z[1])))

---

Data:

y <- c(54.36, 70.43, 36.49, 39.59, 15.06, 34.6, 0.24, 24, 20.22, 24.73, 
29.86, 49.3, 37.36, 29.68, 37.64, 7.99, 22.42, 28.99, 3.09, 63.92, 
17.72, 9.51, 13.06, 3.83, 51.91, 1.79, 16.86, 50.74, 28.41, 20.03, 
24.24, 33.7, 7.7, 24.83, 53.98, -8.74, 30.14, 20.8, 12.1, 38.31, 
35.35, 33.96, 25.07, 44.86, 18.73, 36.66, 19.57, 30.62, -0.65, 
21.66, 54.59, 35.28, 27.83, 48.27, 17.99)

z <- c(53, 17.5, 48.5, 40, 46, 38, 14.5, 19.5, 37.5, 5.5, 16, 25, 
11, 17.5, 14, 21, 22.5, 0, 3, 18.5, 37, 53, 33, 47, 18.5, 22, 
14.5, 48.5, 48, 26, 28, 56.5, 15, 29.5, 7.5, 35, 7, 25.5, 21, 
8.5, 53, 51.5, 9, 15, 20.5, 13, 23, 15, 18, 38.5, 7, 17.5, 35, 
29.5, 16.5, 34.5, 27.5, 18.5, 18.5, 24, 24, 30.5, 28, 27, 15.5, 
12.5, 23, 22, 45, 12, 19, 10, 85.5, 16, 34.5, 43, 27, 13, 22.5, 
30.5, 22, 59, 21, 7.5, 23, 10.5, 16, 20, 62, 13, 64, 52, 18.5, 
33, 0, 25, 11, 16.5, 17, 48, 30.5, 21.5, 18, 19.5, 11, 95, 38, 
17.5, 42.5, 7, 48, 38, 23.5, 16.5, 7.5, 51, 14.5, 20.5, 23.5, 
8, 46, 45, 64, 75, 35, 10, 10, 10.5, 12, 12, 13, 15.5, 39, 29.5, 
3, 13, 25, 5, 0, 29, 28, 7.5, 14, 26.5, 19.5, 62, 23, 8.5, 31.5, 
23.5, 26, 11, 18.5, 28, 31, 42, 57, 54, 10, 12.5, 13.5, 11, 8, 
35.5, 60, 18, 101.5, 15, 21.5, 9.5, 17.5, 18, 16, 28.5, 35, 47, 
26, 50.5, 13, 18.5, 14, 18.5, 27, 33, 28.5, 24.5, 34.5, 9, 9, 
53.5, 15, 14, 18, 16.5, 27, 11.5, 14, 27, 10, 46, 0, 18, 27.5, 
67.5, 22.5, 12.5, 26, 24.5, 0, 22, 12, 30.5, 23.5, 2.5, 15.5, 
34.5, 50, 62, 5, 9.5, 11, 10.5, 6.5, 23, 12.5, 18, 17.5, 31.5, 
42.5, 15, 54.5, 48.5, 9.5, 16.5, 18, 42, 49, 4, 42, 47, 13.5, 
28, 8, 43, 8.5, 10, 26.5, 13.5, 28, 37, 23.5, 10.5, 45, 15, 10, 
35, 36, 20.5, 17, 22.5, 64.5, 21, 25, 8, 12.5, 21.5, 24, 8.5, 
27, 70, 34, 31.5, 12, 5.5, 36, 28, 6.5, 14.5, 18.5, 21.5, 20, 
23.5, 20, 27, 19, 17, 10, 50, 36, 8, 22, 58.5, 30, 19.5, 0, 22, 
0, 7.5, 0, 59, 13, 4.5, 19, 14, 0, 17.5, 19.5)