Fivenum: Difference between revisions
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Given a large array, reduce a large array to five numbers that will have the same boxplot properties as the larger array. |
Given a large array, reduce a large array to five numbers that will have the same boxplot properties as the larger array. |
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=={{header|C}}== |
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{{trans|Kotlin}} |
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<lang c>#include <stdio.h> |
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#include <stdlib.h> |
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double median(double *x, int start, int end_inclusive) { |
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int size = end_inclusive - start + 1; |
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if (size <= 0) { |
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printf("Array slice cannot be empty\n"); |
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exit(1); |
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} |
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int m = start + size / 2; |
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if (size % 2) return x[m]; |
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return (x[m - 1] + x[m]) / 2.0; |
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} |
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int compare (const void *a, const void *b) { |
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double aa = *(double*)a; |
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double bb = *(double*)b; |
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if (aa > bb) return 1; |
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if (aa < bb) return -1; |
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return 0; |
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} |
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int fivenum(double *x, double *result, int x_len) { |
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int i, m, lower_end; |
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for (i = 0; i < x_len; i++) { |
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if (x[i] != x[i]) { |
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printf("Unable to deal with arrays containing NaN\n\n"); |
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return 1; |
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} |
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} |
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qsort(x, x_len, sizeof(double), compare); |
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result[0] = x[0]; |
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result[2] = median(x, 0, x_len - 1); |
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result[4] = x[x_len - 1]; |
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m = x_len / 2; |
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lower_end = (x_len % 2) ? m : m - 1; |
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result[1] = median(x, 0, lower_end); |
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result[3] = median(x, m, x_len - 1); |
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return 0; |
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} |
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int show(double *result, int places) { |
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int i; |
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char f[7]; |
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sprintf(f, "%%.%dlf", places); |
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printf("["); |
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for (i = 0; i < 5; i++) { |
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printf(f, result[i]); |
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if (i < 4) printf(", "); |
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} |
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printf("]\n\n"); |
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} |
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int main() { |
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double result[5]; |
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double x1[11] = {15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0}; |
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if (!fivenum(x1, result, 11)) show(result, 1); |
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double x2[6] = {36.0, 40.0, 7.0, 39.0, 41.0, 15.0}; |
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if (!fivenum(x2, result, 6)) show(result, 1); |
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double x3[20] = { |
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0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, |
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-0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, |
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-0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, |
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0.75775634, 0.32566578 |
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}; |
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if (!fivenum(x3, result, 20)) show(result, 9); |
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return 0; |
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}</lang> |
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{{out}} |
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<pre> |
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[6.0, 25.5, 40.0, 42.5, 49.0] |
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[7.0, 15.0, 37.5, 40.0, 41.0] |
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[-1.950595940, -0.676741205, 0.233247060, 0.746070945, 1.731315070] |
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</pre> |
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=={{header|Kotlin}}== |
=={{header|Kotlin}}== |
Revision as of 12:32, 22 February 2018
Many big data or scientific programs use boxplots to show distributions of data. However, sometimes saving large arrays for boxplots can be impractical and use extreme amounts of RAM. It can be useful to save large arrays as arrays with 5 numbers to save memory. The base statistics of the R programming language have this as the `fivenum` function.
Task Description
Given a large array, reduce a large array to five numbers that will have the same boxplot properties as the larger array.
C
<lang c>#include <stdio.h>
- include <stdlib.h>
double median(double *x, int start, int end_inclusive) {
int size = end_inclusive - start + 1; if (size <= 0) { printf("Array slice cannot be empty\n"); exit(1); } int m = start + size / 2; if (size % 2) return x[m]; return (x[m - 1] + x[m]) / 2.0;
}
int compare (const void *a, const void *b) {
double aa = *(double*)a; double bb = *(double*)b; if (aa > bb) return 1; if (aa < bb) return -1; return 0;
}
int fivenum(double *x, double *result, int x_len) {
int i, m, lower_end; for (i = 0; i < x_len; i++) { if (x[i] != x[i]) { printf("Unable to deal with arrays containing NaN\n\n"); return 1; } } qsort(x, x_len, sizeof(double), compare); result[0] = x[0]; result[2] = median(x, 0, x_len - 1); result[4] = x[x_len - 1]; m = x_len / 2; lower_end = (x_len % 2) ? m : m - 1; result[1] = median(x, 0, lower_end); result[3] = median(x, m, x_len - 1); return 0;
}
int show(double *result, int places) {
int i; char f[7]; sprintf(f, "%%.%dlf", places); printf("["); for (i = 0; i < 5; i++) { printf(f, result[i]); if (i < 4) printf(", "); } printf("]\n\n");
}
int main() {
double result[5];
double x1[11] = {15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0}; if (!fivenum(x1, result, 11)) show(result, 1);
double x2[6] = {36.0, 40.0, 7.0, 39.0, 41.0, 15.0}; if (!fivenum(x2, result, 6)) show(result, 1);
double x3[20] = { 0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578 }; if (!fivenum(x3, result, 20)) show(result, 9);
return 0;
}</lang>
- Output:
[6.0, 25.5, 40.0, 42.5, 49.0] [7.0, 15.0, 37.5, 40.0, 41.0] [-1.950595940, -0.676741205, 0.233247060, 0.746070945, 1.731315070]
Kotlin
The following uses Tukey's method for calculating the lower and upper quartiles (or 'hinges') which is what the R function, fivenum, appears to use.
As arrays containing NaNs and nulls cannot really be dealt with in a sensible fashion in Kotlin, they've been excluded altogether. <lang scala>// version 1.2.21
fun median(x: DoubleArray, start: Int, endInclusive: Int): Double {
val size = endInclusive - start + 1 require (size > 0) { "Array slice cannot be empty" } val m = start + size / 2 return if (size % 2 == 1) x[m] else (x[m - 1] + x[m]) / 2.0
}
fun fivenum(x: DoubleArray): DoubleArray {
require(x.none { it.isNaN() }) { "Unable to deal with arrays containing NaN" } val result = DoubleArray(5) x.sort() result[0] = x[0] result[2] = median(x, 0, x.size - 1) result[4] = x[x.lastIndex] val m = x.size / 2 var lowerEnd = if (x.size % 2 == 1) m else m - 1 result[1] = median(x, 0, lowerEnd) result[3] = median(x, m, x.size - 1) return result
}
fun main(args: Array<String>) {
var xl = listOf( doubleArrayOf(15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0), doubleArrayOf(36.0, 40.0, 7.0, 39.0, 41.0, 15.0), doubleArrayOf( 0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578 ) ) xl.forEach { println("${fivenum(it).asList()}\n") }
}</lang>
- Output:
[6.0, 25.5, 40.0, 42.5, 49.0] [7.0, 15.0, 37.5, 40.0, 41.0] [-1.95059594, -0.676741205, 0.23324706, 0.746070945, 1.73131507]
Perl
<lang Perl>
- !/usr/bin/env perl
use strict; use warnings; use Cwd 'getcwd'; use feature 'say'; my $TOP_DIRECTORY = getcwd(); local $SIG{__WARN__} = sub {#kill the program if there are any warnings my $message = shift; my $fail_filename = "$TOP_DIRECTORY/$0.FAIL"; open my $fh, '>', $fail_filename or die "Can't write $fail_filename: $!"; printf $fh ("$message @ %s\n", getcwd()); close $fh; die "$message\n"; };#http://perlmaven.com/how-to-capture-and-save-warnings-in-perl
use POSIX qw(ceil floor);
sub fivenum { my $array = shift; my @x = sort {$a <=> $b} @{ $array }; printf("There are %u elements.\n", scalar @{ $array }); my $n = scalar @{ $array }; if ($n == 0) { print "no values were entered into fivenum.\n"; die; } my $n4 = floor(($n+3)/2)/2; my @d = (1, $n4, ($n +1)/2, $n+1-$n4, $n);#d <- c(1, n4, (n + 1)/2, n + 1 - n4, n) my (@floor_d, @ceiling_d); foreach my $d (0..4) { $floor_d[$d] = floor($d[$d]); $ceiling_d[$d] = ceil($d[$d]); } my @sum_array; foreach my $e (0..4) { if (not defined $floor_d[$e]) { say "\$floor_d[$e] isn't defined."; die; } if (not defined $ceiling_d[$e]) { say "\$ceiling_d[$e] isn't defined."; die; } if (!defined $x[$floor_d[$e]-1]) { say "\$x[$floor_d[$e-1]-1] isn't defined."; die; } if (!defined $x[$ceiling_d[$e]-1]) { say "\$x[$ceiling_d[$e]-1] isn't defined."; die; } push @sum_array, (0.5 * ($x[$floor_d[$e]-1] + $x[$ceiling_d[$e]-1])); } return @sum_array; }
my @x = qw(0.14082834 0.09748790 1.73131507 0.87636009 -1.95059594 0.73438555 -0.03035726 1.46675970 -0.74621349 -0.72588772 0.63905160 0.61501527
-0.98983780 -1.00447874 -0.62759469 0.66206163 1.04312009 -0.10305385 0.75775634 0.32566578);
my @y = fivenum(\@x);
say join (',', @y); </lang>
- Output:
-1.95059594,-0.676741205,0.23324706,0.746070945,1.73131507
Perl 6
<lang perl6>sub fourths ( Int $end ) {
my $end_22 = $end div 2 / 2;
return 0, $end_22, $end/2, $end - $end_22, $end;
} sub fivenum ( @nums ) {
my @x = @nums.sort(+*) or die 'Input must have at least one element';
my @d = fourths(@x.end);
return ( @x[@d».floor] Z+ @x[@d».ceiling] ) »/» 2;
}
say .&fivenum for [15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43],
[36, 40, 7, 39, 41, 15], [ 0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578,
]; </lang>
- Output:
(6 25.5 40 42.5 49) (7 15 37.5 40 41) (-1.95059594 -0.676741205 0.23324706 0.746070945 1.73131507)
R
The commented lines are from R source code. This is extremely easy to execute in R. <lang R>
- > fivenum
- function (x, na.rm = TRUE)
- {
- xna <- is.na(x)
- if (any(xna)) {
- if (na.rm)
- x <- x[!xna]
- else return(rep.int(NA, 5))
- }
- x <- sort(x)
- n <- length(x)
- if (n == 0)
- rep.int(NA, 5)
- else {
- n4 <- floor((n + 3)/2)/2
- d <- c(1, n4, (n + 1)/2, n + 1 - n4, n)
- 0.5 * (x[floor(d)] + x[ceiling(d)])
- }
- }
- <bytecode: 0x7fd0db42a7b8>
- <environment: namespace:stats>
> fivenum(rnorm(4)) [1] -0.4366061 -0.2225105 0.3213424 0.7110099 0.7709201 </lang>
zkl
Uses GNU GSL library. <lang zkl>var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library) fcn fiveNum(v){ // V is a GSL Vector, --> min, 1st qu, median, 3rd qu, max
v.sort(); return(v.min(),v.quantile(0.25),v.median(),v.quantile(0.75),v.max())
} v:=GSL.VectorFromData(
0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578);
println(fiveNum(v));</lang>
- Output:
L(-1.9506,-0.652168,0.233247,0.740228,1.73132)