For more information including compatibility, examples and test cases, see https://github.com/petercrlane/r7rs-libs
1. Statistics: (import (robin statistics))
A library of functions to compute statistical or other information about sets of data.
1.1. arithmetic-mean
Same as mean.
1.2. coefficient-of-variation
coefficient-of-variation describes the amount of spread in a dataset relative to its mean.
In the following example, both lists have the same mean (3), but the spread is greater in the second.
#|kawa:32|# (coefficient-of-variation '(1 2 3 4 5)) 52.70462766947299 #|kawa:33|# (coefficient-of-variation '(-2 2 3 4 8)) 120.18504251546631
1.3. combinations
combinations returns the number of ways to take k things from n without replacement,
when the order does not matter. The form is (combinations n k)
#|kawa:2|# (combinations 5 2) 10 #|kawa:3|# (combinations 1000 500) 270288240945436569515614693625975275496152008446548287007392875106625428705522193898612483924502370165362606085021546104802209750050679917549894219699518475423665484263751733356162464079737887344364574161119497604571044985756287880514600994219426752366915856603136862602484428109296905863799821216320
1.4. geometric-mean
The geometric mean takes the nth root of the
product of the numbers, where n is the size of the data. This yields the
central number within a geometric progression.
#|kawa:3|# (geometric-mean '(1 2 3 4 5)) 2.605171084697352 #|kawa:4|# (geometric-mean '(1 3 9 27 81)) 9.000000000000002 #|kawa:5|# (geometric-mean '(1 3 9 27)) 5.196152422706632
1.5. harmonic-mean
The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.
#|kawa:6|# (harmonic-mean '(1 2 3 4 5)) 300/137 #|kawa:7|# (inexact (harmonic-mean '(1 2 3 4 5))) 2.18978102189781
1.6. jaccard-distance
The Jaccard Distance is simply (1 - (jaccard-index)), and measures how dissimilar
the two sets are.
#|kawa:46|# (jaccard-distance '(1 2 3 4 5) '(3 4 5 6 7)) 4/7
1.7. jaccard-index
The Jaccard Index returns a number from 0 to 1 indicating how similar
two sets are. Sets here are represented as lists, and duplicates are ignored. An optional
third argument provides the set-equality function (which defaults to equal?).
#|kawa:40|# (jaccard-index '(1 2 3 4 5) '(3 4 5 6 7)) 3/7 #|kawa:42|# (jaccard-index '(1 2 3 4 5) '(3 4 5 1 2 2 1 1)) 1 #|kawa:43|# (jaccard-index '("a" "b" "c") '("A" "B" "F")) 0 #|kawa:45|# (jaccard-index '("a" "b" "c") '("A" "B" "D") string-ci=?) 1/2
1.8. mean
Computes the arithmetic mean of a list of numbers.
This is the familiar "add up all the numbers, divide by the total" average.
#|kawa:2|# (mean '(1 2 3 4 5)) 3
1.9. median
The median is the central number, when all the numbers are put in order
(or, when there are an even number of numbers, the average of the two middle numbers).
#|kawa:8|# (median '(5 3 1 2 4)) 3
1.10. mode
The mode is the number appearing most often. The mode function returns
two values: a list of the most frequent number or numbers, and their number of occurrences.
#|kawa:9|# (mode '(5 3 1 2 4)) (1 2 3 4 5) 1 #|kawa:11|# (let-values (((items count) (mode '(5 3 5 1 2 4)))) #|.....12|# (display items) (newline) (display count) (newline)) (5) 2
1.11. percentile
percentile takes two arguments, a list of data and a percent
value, and returns the item in the list at that percentile position along the
list, or an average of the nearest two values. percent values must be in the
range 1 to 99, inclusive. Note that a percent of 50 corresponds to the
median.
#|kawa:13|# (percentile '(1 2 3 4 5) 50) 3 #|kawa:14|# (percentile '(1 2 3 4 5) 75) 4 #|kawa:16|# (percentile '(1 2 3 4 5) 99) 5 #|kawa:19|# (percentile '(1 2 3 4 5) 85) 5 #|kawa:20|# (percentile '(1 2 3 4 5) 80) 9/2
1.12. perlin-noise
perlin-noise is a function returning a value computed using a gradient function.
Perlin Noise was invented by Ken Perlin and has been widely
applied in computer graphics. The implementation here is a conversion of the
Java reference implementation.
perlin-noise takes three numbers as input, and returns a single number (all numbers inexact).
sash> (perlin-noise 12.3 4.2 5.7) 0.4085747160714242
1.13. permutations
permutations returns the number of ways to take k things from n without replacement, when the order matters.
The form is (permutations n k)
#|kawa:4|# (permutations 5 2) 20 #|kawa:5|# (permutations 100 20) 1303995018204712451095685346159820800000
1.14. population-standard-deviation
population-standard-deviation of a list of data:
#|kawa:28|# (population-standard-deviation '(1 2 3 4 5)) 1.4142135623730951
Optionally, if you know the mean of your data, pass that as a second argument so the function does not have to recompute it:
#|kawa:39|# (population-standard-deviation '(1 2 3 4 5) 3) 1.4142135623730951
1.15. population-variance
population-variance of a list of data:
#|kawa:29|# (population-variance '(1 2 3 4 5)) 2
Optionally, if you know the mean of your data, pass that as a second argument so the function does not have to recompute it.
1.16. random-normal
random-normal is used to return a random number normally distributed with
a given mean and standard deviation.
#|kawa:2|# (random-normal 0 10) 3017/1250 #|kawa:3|# (inexact (random-normal 0 10)) 0.05948 #|kawa:4|# (inexact (random-normal 0 10)) 0.48029 #|kawa:5|# (inexact (random-normal 0 10)) -3.83553 #|kawa:7|# (inexact (random-normal 20 10)) 21.81053 #|kawa:8|# (inexact (random-normal 20 10)) 15.54491
1.17. random-pick
random-pick returns a random selection from a given list
#|kawa:20|# (random-pick '(1 2 3 4 5 6)) 6 #|kawa:21|# (random-pick '(1 2 3 4 5 6)) 3 #|kawa:22|# (random-pick '(1 2 3 4 5 6)) 2
1.18. random-sample
random-sample returns a random sample of n chosen from a list of items,
without replacement
#|kawa:25|# (random-sample 3 '(1 2 3 4 5 6)) (1 4 5) #|kawa:26|# (random-sample 3 '(1 2 3 4 5 6)) (6 5 1) #|kawa:27|# (random-sample 3 '(1 2 3 4 5 6)) (2 3 6)
1.19. random-weighted-sample
random-weighted-sample returns a random sample of n chosen from a list of items,
without replacement, but with the items weighted by the given list of weights.
The following gives a heavy bias to choosing 1 and 6:
#|kawa:28|# (random-weighted-sample 3 '(1 2 3 4 5 6) '(10 1 1 1 1 10)) (6 1 5) #|kawa:29|# (random-weighted-sample 3 '(1 2 3 4 5 6) '(10 1 1 1 1 10)) (1 6 4) #|kawa:30|# (random-weighted-sample 3 '(1 2 3 4 5 6) '(10 1 1 1 1 10)) (1 6 5)
The following is a lighter bias to choosing 1 and 4:
#|kawa:34|# (random-weighted-sample 3 '(1 2 3 4 5 6) '(2 1 1 2 1 1)) (4 6 2) #|kawa:35|# (random-weighted-sample 3 '(1 2 3 4 5 6) '(2 1 1 2 1 1)) (5 4 3) #|kawa:36|# (random-weighted-sample 3 '(1 2 3 4 5 6) '(2 1 1 2 1 1)) (1 3 2)
1.20. sign
sign returns 1 for positive numbers, 0 for zero, -1 for negative numbers
#|kawa:36|# (sign 10) 1 #|kawa:37|# (sign 0) 0 #|kawa:38|# (sign -0.7) -1
1.21. sorenson-dice-index
The Sorenson Dice Index is a
measure of the similarity of two sets. Sets here are represented as lists, and
duplicates are ignored. An optional third argument provides the set-equality
function (which defaults to equal?).
#|kawa:47|# (sorenson-dice-index '(1 2 3 4 5) '(3 4 5 6 7)) 3/5 #|kawa:48|# (sorenson-dice-index '("a" "b" "c") '("A" "B" "D")) 0 #|kawa:49|# (sorenson-dice-index '("a" "b" "c") '("A" "B" "D") string-ci=?) 2/3
1.22. standard-deviation
standard-deviation of a list of data:
#|kawa:30|# (standard-deviation '(1 2 3 4 5)) 1.5811388300841898
Optionally, if you know the mean of your data, pass that as a second argument so the function does not have to recompute it.
1.23. standard-error-of-the-mean
standard-error-of-the-mean describes the mean of the sampling distribution.
#|kawa:35|# (standard-error-of-the-mean '(1 2 3 4 5)) 0.7071067811865476
1.24. variance
variance of a list of data:
#|kawa:31|# (variance '(1 2 3 4 5)) 5/2
Optionally, if you know the mean of your data, pass that as a second argument so the function does not have to recompute it.