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NicklasXYZ 2024-12-07 23:46:49 +01:00
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30
README.md
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@ -11,46 +11,44 @@ The library supports both targets: Erlang and JavaScript.
```gleam ```gleam
import gleam/float import gleam/float
import gleam/iterator import gleam/yielder
import gleam/option.{Some} import gleam_community/maths
import gleam_community/maths/arithmetics
import gleam_community/maths/combinatorics.{WithoutRepetitions}
import gleam_community/maths/elementary
import gleam_community/maths/piecewise
import gleam_community/maths/predicates
import gleeunit/should import gleeunit/should
pub fn example() { pub fn example() {
// Evaluate the sine function // Evaluate the sine function
let result = elementary.sin(elementary.pi()) let result = maths.sin(maths.pi())
// Set the relative and absolute tolerance // Set the relative and absolute tolerance
let assert Ok(absolute_tol) = elementary.power(10.0, -6.0) let assert Ok(absolute_tol) = float.power(10.0, -6.0)
let relative_tol = 0.0 let relative_tol = 0.0
// Check that the value is very close to 0.0 // Check that the value is very close to 0.0
// That is, if 'result' is within +/- 10^(-6) // That is, if 'result' is within +/- 10^(-6)
predicates.is_close(result, 0.0, relative_tol, absolute_tol) maths.is_close(result, 0.0, relative_tol, absolute_tol)
|> should.be_true() |> should.be_true()
// Find the greatest common divisor // Find the greatest common divisor
arithmetics.gcd(54, 24) maths.gcd(54, 24)
|> should.equal(6) |> should.equal(6)
// Find the minimum and maximum of a list // Find the minimum and maximum of a list
piecewise.extrema([10.0, 3.0, 50.0, 20.0, 3.0], float.compare) maths.extrema([10.0, 3.0, 50.0, 20.0, 3.0], float.compare)
|> should.equal(Ok(#(3.0, 50.0))) |> should.equal(Ok(#(3.0, 50.0)))
// Determine if a number is fractional // Determine if a number is fractional
predicates.is_fractional(0.3333) maths.is_fractional(0.3333)
|> should.equal(True) |> should.equal(True)
// Generate all k = 2 combinations of [1, 2, 3] // Generate all k = 2 combinations of [1, 2, 3]
let assert Ok(combinations) = let assert Ok(combinations) = maths.list_combination([1, 2, 3], 2)
combinatorics.list_combination([1, 2, 3], 2, Some(WithoutRepetitions))
combinations combinations
|> iterator.to_list() |> yielder.to_list()
|> should.equal([[1, 2], [1, 3], [2, 3]]) |> should.equal([[1, 2], [1, 3], [2, 3]])
// Compute the Cosine Similarity between two (orthogonal) vectors
maths.cosine_similarity([#(-1.0, 1.0), #(1.0, 1.0), #(0.0, -1.0)])
|> should.equal(Ok(0.0))
} }
``` ```

1
gleam.toml
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@ -8,6 +8,7 @@ gleam = ">= 0.32.0"
[dependencies] [dependencies]
gleam_stdlib = "~> 0.38" gleam_stdlib = "~> 0.38"
gleam_yielder = ">= 1.1.0 and < 2.0.0"
[dev-dependencies] [dev-dependencies]
gleeunit = "~> 1.0" gleeunit = "~> 1.0"

4
manifest.toml
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@ -2,10 +2,12 @@
# You typically do not need to edit this file # You typically do not need to edit this file
packages = [ packages = [
{ name = "gleam_stdlib", version = "0.39.0", build_tools = ["gleam"], requirements = [], otp_app = "gleam_stdlib", source = "hex", outer_checksum = "2D7DE885A6EA7F1D5015D1698920C9BAF7241102836CE0C3837A4F160128A9C4" }, { name = "gleam_stdlib", version = "0.45.0", build_tools = ["gleam"], requirements = [], otp_app = "gleam_stdlib", source = "hex", outer_checksum = "206FCE1A76974AECFC55AEBCD0217D59EDE4E408C016E2CFCCC8FF51278F186E" },
{ name = "gleam_yielder", version = "1.1.0", build_tools = ["gleam"], requirements = ["gleam_stdlib"], otp_app = "gleam_yielder", source = "hex", outer_checksum = "8E4E4ECFA7982859F430C57F549200C7749823C106759F4A19A78AEA6687717A" },
{ name = "gleeunit", version = "1.2.0", build_tools = ["gleam"], requirements = ["gleam_stdlib"], otp_app = "gleeunit", source = "hex", outer_checksum = "F7A7228925D3EE7D0813C922E062BFD6D7E9310F0BEE585D3A42F3307E3CFD13" }, { name = "gleeunit", version = "1.2.0", build_tools = ["gleam"], requirements = ["gleam_stdlib"], otp_app = "gleeunit", source = "hex", outer_checksum = "F7A7228925D3EE7D0813C922E062BFD6D7E9310F0BEE585D3A42F3307E3CFD13" },
] ]
[requirements] [requirements]
gleam_stdlib = { version = "~> 0.38" } gleam_stdlib = { version = "~> 0.38" }
gleam_yielder = { version = ">= 1.1.0 and < 2.0.0" }
gleeunit = { version = "~> 1.0" } gleeunit = { version = "~> 1.0" }

5675
src/gleam_community/maths.gleam Normal file
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720
src/gleam_community/maths/arithmetics.gleam
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@ -1,720 +0,0 @@
////<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css" integrity="sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+" crossorigin="anonymous">
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js" integrity="sha384-7zkQWkzuo3B5mTepMUcHkMB5jZaolc2xDwL6VFqjFALcbeS9Ggm/Yr2r3Dy4lfFg" crossorigin="anonymous"></script>
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
////<script>
//// document.addEventListener("DOMContentLoaded", function() {
//// renderMathInElement(document.body, {
//// // customised options
//// // • auto-render specific keys, e.g.:
//// delimiters: [
//// {left: '$$', right: '$$', display: false},
//// {left: '$', right: '$', display: false},
//// {left: '\\(', right: '\\)', display: false},
//// {left: '\\[', right: '\\]', display: true}
//// ],
//// // • rendering keys, e.g.:
//// throwOnError : true
//// });
//// });
////</script>
////<style>
//// .katex { font-size: 1.1em; }
////</style>
////
//// ---
////
//// Arithmetics: A module containing a collection of fundamental mathematical functions relating to simple arithmetics (addition, subtraction, multiplication, etc.), but also number theory.
////
//// * **Division functions**
//// * [`gcd`](#gcd)
//// * [`lcm`](#lcm)
//// * [`divisors`](#divisors)
//// * [`proper_divisors`](#proper_divisors)
//// * [`int_euclidean_modulo`](#int_euclidean_modulo)
//// * **Sums and products**
//// * [`float_sum`](#float_sum)
//// * [`int_sum`](#int_sum)
//// * [`float_product`](#float_product)
//// * [`int_product`](#int_product)
//// * [`float_cumulative_sum`](#float_cumulative_sum)
//// * [`int_cumulative_sum`](#int_cumulative_sum)
//// * [`float_cumulative_product`](#float_cumulative_product)
//// * [`int_cumulative_product`](#int_cumulative_product)
////
import gleam/int
import gleam/list
import gleam/option
import gleam/pair
import gleam/result
import gleam_community/maths/conversion
import gleam_community/maths/elementary
import gleam_community/maths/piecewise
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function calculates the greatest common divisor of two integers
/// \\(x, y \in \mathbb{Z}\\). The greatest common divisor is the largest positive
/// integer that is divisible by both \\(x\\) and \\(y\\).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example() {
/// arithmetics.gcd(1, 1)
/// |> should.equal(1)
///
/// arithmetics.gcd(100, 10)
/// |> should.equal(10)
///
/// arithmetics.gcd(-36, -17)
/// |> should.equal(1)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn gcd(x: Int, y: Int) -> Int {
let absx = piecewise.int_absolute_value(x)
let absy = piecewise.int_absolute_value(y)
do_gcd(absx, absy)
}
fn do_gcd(x: Int, y: Int) -> Int {
case x == 0 {
True -> y
False -> {
let assert Ok(z) = int.modulo(y, x)
do_gcd(z, x)
}
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
///
/// Given two integers, \\(x\\) (dividend) and \\(y\\) (divisor), the Euclidean modulo
/// of \\(x\\) by \\(y\\), denoted as \\(x \mod y\\), is the remainder \\(r\\) of the
/// division of \\(x\\) by \\(y\\), such that:
///
/// \\[
/// x = q \cdot y + r \quad \text{and} \quad 0 \leq r < |y|,
/// \\]
///
/// where \\(q\\) is an integer that represents the quotient of the division.
///
/// The Euclidean modulo function of two numbers, is the remainder operation most
/// commonly utilized in mathematics. This differs from the standard truncating
/// modulo operation frequently employed in programming via the `%` operator.
/// Unlike the `%` operator, which may return negative results depending on the
/// divisor's sign, the Euclidean modulo function is designed to always yield a
/// positive outcome, ensuring consistency with mathematical conventions.
///
/// Note that like the Gleam division operator `/` this will return `0` if one of
/// the arguments is `0`.
///
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example() {
/// arithmetics.euclidean_modulo(15, 4)
/// |> should.equal(3)
///
/// arithmetics.euclidean_modulo(-3, -2)
/// |> should.equal(1)
///
/// arithmetics.euclidean_modulo(5, 0)
/// |> should.equal(0)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn int_euclidean_modulo(x: Int, y: Int) -> Int {
case x % y, x, y {
_, 0, _ -> 0
_, _, 0 -> 0
md, _, _ if md < 0 -> md + int.absolute_value(y)
md, _, _ -> md
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function calculates the least common multiple of two integers
/// \\(x, y \in \mathbb{Z}\\). The least common multiple is the smallest positive
/// integer that has both \\(x\\) and \\(y\\) as factors.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example() {
/// arithmetics.lcm(1, 1)
/// |> should.equal(1)
///
/// arithmetics.lcm(100, 10)
/// |> should.equal(100)
///
/// arithmetics.lcm(-36, -17)
/// |> should.equal(612)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn lcm(x: Int, y: Int) -> Int {
let absx = piecewise.int_absolute_value(x)
let absy = piecewise.int_absolute_value(y)
absx * absy / do_gcd(absx, absy)
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function returns all the positive divisors of an integer, including the
/// number itself.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example() {
/// arithmetics.divisors(4)
/// |> should.equal([1, 2, 4])
///
/// arithmetics.divisors(6)
/// |> should.equal([1, 2, 3, 6])
///
/// arithmetics.proper_divisors(13)
/// |> should.equal([1, 13])
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn divisors(n: Int) -> List(Int) {
find_divisors(n)
}
fn find_divisors(n: Int) -> List(Int) {
let nabs = piecewise.float_absolute_value(conversion.int_to_float(n))
let assert Ok(sqrt_result) = elementary.square_root(nabs)
let max = conversion.float_to_int(sqrt_result) + 1
list.range(2, max)
|> list.fold([1, n], fn(acc, i) {
case n % i == 0 {
True -> [i, n / i, ..acc]
False -> acc
}
})
|> list.unique()
|> list.sort(int.compare)
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function returns all the positive divisors of an integer, excluding the
/// number iteself.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example() {
/// arithmetics.proper_divisors(4)
/// |> should.equal([1, 2])
///
/// arithmetics.proper_divisors(6)
/// |> should.equal([1, 2, 3])
///
/// arithmetics.proper_divisors(13)
/// |> should.equal([1])
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn proper_divisors(n: Int) -> List(Int) {
let divisors = find_divisors(n)
divisors
|> list.take(list.length(divisors) - 1)
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the (weighted) sum of the elements in a list:
///
/// \\[
/// \sum_{i=1}^n w_i x_i
/// \\]
///
/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{R}\\) is
/// the value in the input list indexed by \\(i\\), while the \\(w_i \in \mathbb{R}\\)
/// are corresponding weights (\\(w_i = 1.0\\;\forall i=1...n\\) by default).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam/option
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// // An empty list returns an error
/// []
/// |> arithmetics.float_sum(option.None)
/// |> should.equal(0.0)
///
/// // Valid input returns a result
/// [1.0, 2.0, 3.0]
/// |> arithmetics.float_sum(option.None)
/// |> should.equal(6.0)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn float_sum(arr: List(Float), weights: option.Option(List(Float))) -> Float {
case arr, weights {
[], _ -> 0.0
_, option.None ->
arr
|> list.fold(0.0, fn(acc, a) { a +. acc })
_, option.Some(warr) -> {
list.zip(arr, warr)
|> list.fold(0.0, fn(acc, a) { pair.first(a) *. pair.second(a) +. acc })
}
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the sum of the elements in a list:
///
/// \\[
/// \sum_{i=1}^n x_i
/// \\]
///
/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{Z}\\) is
/// the value in the input list indexed by \\(i\\).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// // An empty list returns 0
/// []
/// |> arithmetics.int_sum()
/// |> should.equal(0)
///
/// // Valid input returns a result
/// [1, 2, 3]
/// |> arithmetics.int_sum()
/// |> should.equal(6)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn int_sum(arr: List(Int)) -> Int {
case arr {
[] -> 0
_ ->
arr
|> list.fold(0, fn(acc, a) { a + acc })
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the (weighted) product of the elements in a list:
///
/// \\[
/// \prod_{i=1}^n x_i^{w_i}
/// \\]
///
/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{R}\\) is
/// the value in the input list indexed by \\(i\\), while the \\(w_i \in \mathbb{R}\\)
/// are corresponding weights (\\(w_i = 1.0\\;\forall i=1...n\\) by default).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam/option
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// // An empty list returns 1.0
/// []
/// |> arithmetics.float_product(option.None)
/// |> should.equal(1.0)
///
/// // Valid input returns a result
/// [1.0, 2.0, 3.0]
/// |> arithmetics.float_product(option.None)
/// |> should.equal(6.0)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn float_product(
arr: List(Float),
weights: option.Option(List(Float)),
) -> Result(Float, Nil) {
case arr, weights {
[], _ ->
1.0
|> Ok
_, option.None ->
arr
|> list.fold(1.0, fn(acc, a) { a *. acc })
|> Ok
_, option.Some(warr) -> {
list.zip(arr, warr)
|> list.map(fn(a: #(Float, Float)) -> Result(Float, Nil) {
pair.first(a)
|> elementary.power(pair.second(a))
})
|> result.all
|> result.map(fn(prods) {
prods
|> list.fold(1.0, fn(acc: Float, a: Float) -> Float { a *. acc })
})
}
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the product of the elements in a list:
///
/// \\[
/// \prod_{i=1}^n x_i
/// \\]
///
/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{Z}\\) is
/// the value in the input list indexed by \\(i\\).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// // An empty list returns 1
/// []
/// |> arithmetics.int_product()
/// |> should.equal(1)
///
/// // Valid input returns a result
/// [1, 2, 3]
/// |> arithmetics.int_product()
/// |> should.equal(6)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn int_product(arr: List(Int)) -> Int {
case arr {
[] -> 1
_ ->
arr
|> list.fold(1, fn(acc, a) { a * acc })
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the cumulative sum of the elements in a list:
///
/// \\[
/// v_j = \sum_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
/// \\]
///
/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative sum of \\(n\\)
/// elements. That is, \\(n\\) is the length of the list and \\(x_i \in \mathbb{R}\\)
/// is the value in the input list indexed by \\(i\\). The value \\(v_j\\) is thus the
/// sum of the \\(1\\) to \\(j\\) first elements in the given list.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// []
/// |> arithmetics.float_cumulative_sum()
/// |> should.equal([])
///
/// // Valid input returns a result
/// [1.0, 2.0, 3.0]
/// |> arithmetics.float_cumulative_sum()
/// |> should.equal([1.0, 3.0, 6.0])
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn float_cumulative_sum(arr: List(Float)) -> List(Float) {
case arr {
[] -> []
_ ->
arr
|> list.scan(0.0, fn(acc, a) { a +. acc })
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the cumulative sum of the elements in a list:
///
/// \\[
/// v_j = \sum_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
/// \\]
///
/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative sum of \\(n\\)
/// elements. That is, \\(n\\) is the length of the list and \\(x_i \in \mathbb{Z}\\)
/// is the value in the input list indexed by \\(i\\). The value \\(v_j\\) is thus the
/// sum of the \\(1\\) to \\(j\\) first elements in the given list.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// []
/// |> arithmetics.int_cumulative_sum()
/// |> should.equal([])
///
/// // Valid input returns a result
/// [1, 2, 3]
/// |> arithmetics.int_cumulative_sum()
/// |> should.equal([1, 3, 6])
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn int_cumulative_sum(arr: List(Int)) -> List(Int) {
case arr {
[] -> []
_ ->
arr
|> list.scan(0, fn(acc, a) { a + acc })
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the cumulative product of the elements in a list:
///
/// \\[
/// v_j = \prod_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
/// \\]
///
/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative product of
/// \\(n\\) elements. That is, \\(n\\) is the length of the list and
/// \\(x_i \in \mathbb{R}\\) is the value in the input list indexed by \\(i\\). The
/// value \\(v_j\\) is thus the sum of the \\(1\\) to \\(j\\) first elements in the
/// given list.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// // An empty list returns an error
/// []
/// |> arithmetics.float_cumulative_product()
/// |> should.equal([])
///
/// // Valid input returns a result
/// [1.0, 2.0, 3.0]
/// |> arithmetics.float_cumulative_product()
/// |> should.equal([1.0, 2.0, 6.0])
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn float_cumulative_product(arr: List(Float)) -> List(Float) {
case arr {
[] -> []
_ ->
arr
|> list.scan(1.0, fn(acc, a) { a *. acc })
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Calculate the cumulative product of the elements in a list:
///
/// \\[
/// v_j = \prod_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
/// \\]
///
/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative product of
/// \\(n\\) elements. That is, \\(n\\) is the length of the list and
/// \\(x_i \in \mathbb{Z}\\) is the value in the input list indexed by \\(i\\). The
/// value \\(v_j\\) is thus the product of the \\(1\\) to \\(j\\) first elements in the
/// given list.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/arithmetics
///
/// pub fn example () {
/// // An empty list returns an error
/// []
/// |> arithmetics.int_cumulative_product()
/// |> should.equal([])
///
/// // Valid input returns a result
/// [1, 2, 3]
/// |> arithmetics.int_cumulative_product()
/// |> should.equal([1, 2, 6])
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn int_cumulative_product(arr: List(Int)) -> List(Int) {
case arr {
[] -> []
_ ->
arr
|> list.scan(1, fn(acc, a) { a * acc })
}
}

630
src/gleam_community/maths/combinatorics.gleam
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@ -1,630 +0,0 @@
////<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css" integrity="sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+" crossorigin="anonymous">
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js" integrity="sha384-7zkQWkzuo3B5mTepMUcHkMB5jZaolc2xDwL6VFqjFALcbeS9Ggm/Yr2r3Dy4lfFg" crossorigin="anonymous"></script>
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
////<script>
//// document.addEventListener("DOMContentLoaded", function() {
//// renderMathInElement(document.body, {
//// // customised options
//// // • auto-render specific keys, e.g.:
//// delimiters: [
//// {left: '$$', right: '$$', display: false},
//// {left: '$', right: '$', display: false},
//// {left: '\\(', right: '\\)', display: false},
//// {left: '\\[', right: '\\]', display: true}
//// ],
//// // • rendering keys, e.g.:
//// throwOnError : true
//// });
//// });
////</script>
////<style>
//// .katex { font-size: 1.1em; }
////</style>
////
//// ---
////
//// Combinatorics: A module that offers mathematical functions related to counting, arrangements,
//// and permutations/combinations.
////
//// * **Combinatorial functions**
//// * [`combination`](#combination)
//// * [`factorial`](#factorial)
//// * [`permutation`](#permutation)
//// * [`list_combination`](#list_combination)
//// * [`list_permutation`](#list_permutation)
//// * [`cartesian_product`](#cartesian_product)
////
import gleam/iterator
import gleam/list
import gleam/option
import gleam/set
import gleam_community/maths/conversion
import gleam_community/maths/elementary
pub type CombinatoricsMode {
WithRepetitions
WithoutRepetitions
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A combinatorial function for computing the number of \\(k\\)-combinations of \\(n\\) elements.
///
/// **Without Repetitions:**
///
/// \\[
/// C(n, k) = \binom{n}{k} = \frac{n!}{k! (n-k)!}
/// \\]
/// Also known as "\\(n\\) choose \\(k\\)" or the binomial coefficient.
///
/// **With Repetitions:**
///
/// \\[
/// C^*(n, k) = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{k! (n - 1)!}
/// \\]
/// Also known as the "stars and bars" problem in combinatorics.
///
/// The implementation uses an efficient iterative multiplicative formula for computing the result.
///
/// <details>
/// <summary>Details</summary>
///
/// A \\(k\\)-combination is a sequence of \\(k\\) elements selected from \\(n\\) elements where
/// the order of selection does not matter. For example, consider selecting 2 elements from a list
/// of 3 elements: `["A", "B", "C"]`:
///
/// - For \\(k\\)-combinations (without repetitions), where order does not matter, the possible
/// selections are:
/// - `["A", "B"]`
/// - `["A", "C"]`
/// - `["B", "C"]`
///
/// - For \\(k\\)-combinations (with repetitions), where order does not matter but elements can
/// repeat, the possible selections are:
/// - `["A", "A"], ["A", "B"], ["A", "C"]`
/// - `["B", "B"], ["B", "C"], ["C", "C"]`
///
/// - On the contrary, for \\(k\\)-permutations (without repetitions), the order matters, so the
/// possible selections are:
/// - `["A", "B"], ["B", "A"]`
/// - `["A", "C"], ["C", "A"]`
/// - `["B", "C"], ["C", "B"]`
/// </details>
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/option
/// import gleeunit/should
/// import gleam_community/maths/combinatorics
///
/// pub fn example() {
/// // Invalid input gives an error
/// combinatorics.combination(-1, 1, option.None)
/// |> should.be_error()
///
/// // Valid input: n = 4 and k = 0
/// combinatorics.combination(4, 0, option.Some(combinatorics.WithoutRepetitions))
/// |> should.equal(Ok(1))
///
/// // Valid input: k = n (n = 4, k = 4)
/// combinatorics.combination(4, 4, option.Some(combinatorics.WithoutRepetitions))
/// |> should.equal(Ok(1))
///
/// // Valid input: combinations with repetition (n = 2, k = 3)
/// combinatorics.combination(2, 3, option.Some(combinatorics.WithRepetitions))
/// |> should.equal(Ok(4))
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn combination(
n: Int,
k: Int,
mode: option.Option(CombinatoricsMode),
) -> Result(Int, Nil) {
case n, k {
_, _ if n < 0 -> Error(Nil)
_, _ if k < 0 -> Error(Nil)
_, _ -> {
case mode {
option.Some(WithRepetitions) -> combination_with_repetitions(n, k)
_ -> combination_without_repetitions(n, k)
}
}
}
}
fn combination_with_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
combination_without_repetitions(n + k - 1, k)
}
fn combination_without_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
case n, k {
_, _ if k == 0 || k == n -> {
1 |> Ok
}
_, _ -> {
let min = case k < n - k {
True -> k
False -> n - k
}
list.range(1, min)
|> list.fold(1, fn(acc, x) { acc * { n + 1 - x } / x })
|> Ok
}
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A combinatorial function for computing the total number of combinations of \\(n\\)
/// elements, that is \\(n!\\).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/combinatorics
///
/// pub fn example() {
/// // Invalid input gives an error
/// combinatorics.factorial(-1)
/// |> should.be_error()
///
/// // Valid input returns a result (n = 0)
/// combinatorics.factorial(0)
/// |> should.equal(Ok(1))
///
/// combinatorics.factorial(3)
/// |> should.equal(Ok(6))
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn factorial(n) -> Result(Int, Nil) {
case n {
_ if n < 0 -> Error(Nil)
0 -> Ok(1)
1 -> Ok(1)
_ ->
list.range(1, n)
|> list.fold(1, fn(acc, x) { acc * x })
|> Ok
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A combinatorial function for computing the number of \\(k\\)-permutations.
///
/// **Without** repetitions:
///
/// \\[
/// P(n, k) = \binom{n}{k} \cdot k! = \frac{n!}{(n - k)!}
/// \\]
///
/// **With** repetitions:
///
/// \\[
/// P^*(n, k) = n^k
/// \\]
///
/// The implementation uses an efficient iterative multiplicative formula for computing the result.
///
/// <details>
/// <summary>Details</summary>
///
/// A \\(k\\)-permutation (without repetitions) is a sequence of \\(k\\) elements selected from \
/// \\(n\\) elements where the order of selection matters. For example, consider selecting 2
/// elements from a list of 3 elements: `["A", "B", "C"]`:
///
/// - For \\(k\\)-permutations (without repetitions), the order matters, so the possible selections
/// are:
/// - `["A", "B"], ["B", "A"]`
/// - `["A", "C"], ["C", "A"]`
/// - `["B", "C"], ["C", "B"]`
///
/// - For \\(k\\)-permutations (with repetitions), the order also matters, but we have repeated
/// selections:
/// - `["A", "A"], ["A", "B"], ["A", "C"]`
/// - `["B", "A"], ["B", "B"], ["B", "C"]`
/// - `["C", "A"], ["C", "B"], ["C", "C"]`
///
/// - On the contrary, for \\(k\\)-combinations (without repetitions), where order does not matter,
/// the possible selections are:
/// - `["A", "B"]`
/// - `["A", "C"]`
/// - `["B", "C"]`
/// </details>
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/option
/// import gleeunit/should
/// import gleam_community/maths/combinatorics
///
/// pub fn example() {
/// // Invalid input gives an error
/// combinatorics.permutation(-1, 1, option.None)
/// |> should.be_error()
///
/// // Valid input returns a result (n = 4, k = 0)
/// combinatorics.permutation(4, 0, option.Some(combinatorics.WithoutRepetitions))
/// |> should.equal(Ok(1))
///
/// // Valid input returns the correct number of permutations (n = 4, k = 2)
/// combinatorics.permutation(4, 2, option.Some(combinatorics.WithoutRepetitions))
/// |> should.equal(Ok(12))
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn permutation(
n: Int,
k: Int,
mode: option.Option(CombinatoricsMode),
) -> Result(Int, Nil) {
case n, k, mode {
_, _, _ if n < 0 -> Error(Nil)
_, _, _ if k < 0 -> Error(Nil)
_, _, option.Some(WithRepetitions) -> permutation_with_repetitions(n, k)
_, _, _ -> permutation_without_repetitions(n, k)
}
}
fn permutation_without_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
case n, k {
_, _ if k < 0 || k > n -> {
0 |> Ok
}
_, _ if k == 0 -> {
1 |> Ok
}
_, _ ->
list.range(0, k - 1)
|> list.fold(1, fn(acc, x) { acc * { n - x } })
|> Ok
}
}
fn permutation_with_repetitions(n: Int, k: Int) -> Result(Int, Nil) {
let n_float = conversion.int_to_float(n)
let k_float = conversion.int_to_float(k)
// 'n' ank 'k' are positive integers, so no errors here...
let assert Ok(result) = elementary.power(n_float, k_float)
result
|> conversion.float_to_int()
|> Ok
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Generates all possible combinations of \\(k\\) elements selected from a given list of size
/// \\(n\\).
///
/// The function can handle cases with and without repetitions
/// (see more details [here](#combination)). Also, note that repeated elements are treated as
/// distinct.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/set
/// import gleam/option
/// import gleam/iterator
/// import gleeunit/should
/// import gleam_community/maths/combinatorics
///
/// pub fn example () {
/// // Generate all 3-combinations without repetition
/// let assert Ok(result) =
/// combinatorics.list_combination(
/// [1, 2, 3, 4],
/// 3,
/// option.Some(combinatorics.WithoutRepetitions),
/// )
///
/// result
/// |> iterator.to_list()
/// |> set.from_list()
/// |> should.equal(set.from_list([[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]))
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn list_combination(
arr: List(a),
k: Int,
mode: option.Option(CombinatoricsMode),
) -> Result(iterator.Iterator(List(a)), Nil) {
case k, mode {
_, _ if k < 0 -> Error(Nil)
_, option.Some(WithRepetitions) -> list_combination_with_repetitions(arr, k)
_, _ -> list_combination_without_repetitions(arr, k)
}
}
fn list_combination_without_repetitions(
arr: List(a),
k: Int,
) -> Result(iterator.Iterator(List(a)), Nil) {
case k, list.length(arr) {
_, arr_length if k > arr_length -> Error(Nil)
// Special case: When k = n, then the entire list is the only valid combination
_, arr_length if k == arr_length -> {
iterator.single(arr) |> Ok
}
_, _ -> {
Ok(
do_list_combination_without_repetitions(iterator.from_list(arr), k, []),
)
}
}
}
fn do_list_combination_without_repetitions(
arr: iterator.Iterator(a),
k: Int,
prefix: List(a),
) -> iterator.Iterator(List(a)) {
case k {
0 -> iterator.single(list.reverse(prefix))
_ ->
case arr |> iterator.step {
iterator.Done -> iterator.empty()
iterator.Next(x, xs) -> {
let with_x =
do_list_combination_without_repetitions(xs, k - 1, [x, ..prefix])
let without_x = do_list_combination_without_repetitions(xs, k, prefix)
iterator.concat([with_x, without_x])
}
}
}
}
fn list_combination_with_repetitions(
arr: List(a),
k: Int,
) -> Result(iterator.Iterator(List(a)), Nil) {
Ok(do_list_combination_with_repetitions(iterator.from_list(arr), k, []))
}
fn do_list_combination_with_repetitions(
arr: iterator.Iterator(a),
k: Int,
prefix: List(a),
) -> iterator.Iterator(List(a)) {
case k {
0 -> iterator.single(list.reverse(prefix))
_ ->
case arr |> iterator.step {
iterator.Done -> iterator.empty()
iterator.Next(x, xs) -> {
let with_x =
do_list_combination_with_repetitions(arr, k - 1, [x, ..prefix])
let without_x = do_list_combination_with_repetitions(xs, k, prefix)
iterator.concat([with_x, without_x])
}
}
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Generates all possible permutations of \\(k\\) elements selected from a given list of size
/// \\(n\\).
///
/// The function can handle cases with and without repetitions
/// (see more details [here](#permutation)). Also, note that repeated elements are treated as
/// distinct.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/set
/// import gleam/option
/// import gleam/iterator
/// import gleeunit/should
/// import gleam_community/maths/combinatorics
///
/// pub fn example () {
/// // Generate all 3-permutations without repetition
/// let assert Ok(result) =
/// combinatorics.list_permutation(
/// [1, 2, 3],
/// 3,
/// option.Some(combinatorics.WithoutRepetitions),
/// )
///
/// result
/// |> iterator.to_list()
/// |> set.from_list()
/// |> should.equal(
/// set.from_list([
/// [1, 2, 3],
/// [2, 1, 3],
/// [3, 1, 2],
/// [1, 3, 2],
/// [2, 3, 1],
/// [3, 2, 1],
/// ]),
/// )
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
///
pub fn list_permutation(
arr: List(a),
k: Int,
mode: option.Option(CombinatoricsMode),
) -> Result(iterator.Iterator(List(a)), Nil) {
case k, mode {
_, _ if k < 0 -> Error(Nil)
_, option.Some(WithRepetitions) ->
Ok(list_permutation_with_repetitions(arr, k))
_, _ -> list_permutation_without_repetitions(arr, k)
}
}
fn remove_first_by_index(
arr: iterator.Iterator(#(Int, a)),
index_to_remove: Int,
) -> iterator.Iterator(#(Int, a)) {
iterator.flat_map(arr, fn(arg) {
let #(index, element) = arg
case index == index_to_remove {
True -> iterator.empty()
False -> iterator.single(#(index, element))
}
})
}
fn list_permutation_without_repetitions(
arr: List(a),
k: Int,
) -> Result(iterator.Iterator(List(a)), Nil) {
case k, list.length(arr) {
_, arr_length if k > arr_length -> Error(Nil)
_, _ -> {
let indexed_arr = list.index_map(arr, fn(x, i) { #(i, x) })
Ok(do_list_permutation_without_repetitions(
iterator.from_list(indexed_arr),
k,
))
}
}
}
fn do_list_permutation_without_repetitions(
arr: iterator.Iterator(#(Int, a)),
k: Int,
) -> iterator.Iterator(List(a)) {
case k {
0 -> iterator.single([])
_ ->
iterator.flat_map(arr, fn(arg) {
let #(index, element) = arg
let remaining = remove_first_by_index(arr, index)
let permutations =
do_list_permutation_without_repetitions(remaining, k - 1)
iterator.map(permutations, fn(permutation) { [element, ..permutation] })
})
}
}
fn list_permutation_with_repetitions(
arr: List(a),
k: Int,
) -> iterator.Iterator(List(a)) {
let indexed_arr = list.index_map(arr, fn(x, i) { #(i, x) })
do_list_permutation_with_repetitions(indexed_arr, k)
}
fn do_list_permutation_with_repetitions(
arr: List(#(Int, a)),
k: Int,
) -> iterator.Iterator(List(a)) {
case k {
0 -> iterator.single([])
_ ->
iterator.flat_map(arr |> iterator.from_list, fn(arg) {
let #(_, element) = arg
// Allow the same element (by index) to be reused in future recursive calls
let permutations = do_list_permutation_with_repetitions(arr, k - 1)
// Prepend the current element to each generated permutation
iterator.map(permutations, fn(permutation) { [element, ..permutation] })
})
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Generate a list containing all combinations of pairs of elements coming from two given lists.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/set
/// import gleeunit/should
/// import gleam_community/maths/combinatorics
///
/// pub fn example () {
/// // Cartesian product of two empty sets
/// set.from_list([])
/// |> combinatorics.cartesian_product(set.from_list([]))
/// |> should.equal(set.from_list([]))
///
/// // Cartesian product of two sets with numeric values
/// set.from_list([1.0, 10.0])
/// |> combinatorics.cartesian_product(set.from_list([1.0, 2.0]))
/// |> should.equal(
/// set.from_list([#(1.0, 1.0), #(1.0, 2.0), #(10.0, 1.0), #(10.0, 2.0)]),
/// )
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn cartesian_product(xset: set.Set(a), yset: set.Set(b)) -> set.Set(#(a, b)) {
xset
|> set.fold(set.new(), fn(accumulator0: set.Set(#(a, b)), member0: a) {
set.fold(yset, accumulator0, fn(accumulator1: set.Set(#(a, b)), member1: b) {
set.insert(accumulator1, #(member0, member1))
})
})
}

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@ -1,185 +0,0 @@
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////<script>
//// document.addEventListener("DOMContentLoaded", function() {
//// renderMathInElement(document.body, {
//// // customised options
//// // • auto-render specific keys, e.g.:
//// delimiters: [
//// {left: '$$', right: '$$', display: false},
//// {left: '$', right: '$', display: false},
//// {left: '\\(', right: '\\)', display: false},
//// {left: '\\[', right: '\\]', display: true}
//// ],
//// // • rendering keys, e.g.:
//// throwOnError : true
//// });
//// });
////</script>
////<style>
//// .katex { font-size: 1.1em; }
////</style>
////
//// ---
////
//// Conversion: A module containing various functions for converting between types and quantities.
////
//// * **Misc. functions**
//// * [`float_to_int`](#float_to_int)
//// * [`int_to_float`](#int_to_float)
//// * [`degrees_to_radians`](#degrees_to_radians)
//// * [`radians_to_degrees`](#radians_to_degrees)
////
import gleam/int
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that produces a number of type `Float` from an `Int`.
///
/// Note: The function is equivalent to the `int.to_float` function in the Gleam stdlib.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/conversion
///
/// pub fn example() {
/// conversion.int_to_float(-1)
/// |> should.equal(-1.0)
///
/// conversion.int_to_float(1)
/// |> should.equal(1.0)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn int_to_float(x: Int) -> Float {
int.to_float(x)
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function returns the integral part of a given floating point value.
/// That is, everything after the decimal point of a given floating point value is discarded
/// and only the integer value before the decimal point is returned.
///
/// <details>
/// <summary>Example</summary>
///
/// import gleeunit/should
/// import gleam/option
/// import gleam_community/maths/conversion
/// import gleam_community/maths/piecewise
///
/// pub fn example() {
/// conversion.float_to_int(12.0654)
/// |> should.equal(12)
///
/// // Note: Making the following function call is equivalent
/// // but instead of returning a value of type 'Int' a value
/// // of type 'Float' is returned.
/// piecewise.round(12.0654, option.Some(0), option.Some(piecewise.RoundToZero))
/// |> should.equal(Ok(12.0))
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn float_to_int(x: Float) -> Int {
do_to_int(x)
}
@external(erlang, "erlang", "trunc")
@external(javascript, "../../maths.mjs", "truncate")
fn do_to_int(a: Float) -> Int
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Convert a value in degrees to a value measured in radians.
/// That is, \\(1 \text{ degrees } = \frac{\pi}{180} \text{ radians }\\).
///
/// <details>
/// <summary>Example</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/conversion
/// import gleam_community/maths/elementary
///
/// pub fn example() {
/// conversion.degrees_to_radians(360.)
/// |> should.equal(2. *. elementary.pi())
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn degrees_to_radians(x: Float) -> Float {
x *. do_pi() /. 180.0
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Convert a value in degrees to a value measured in radians.
/// That is, \\(1 \text{ radians } = \frac{180}{\pi} \text{ degrees }\\).
///
/// <details>
/// <summary>Example</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/conversion
/// import gleam_community/maths/elementary
///
/// pub fn example() {
/// conversion.radians_to_degrees(0.0)
/// |> should.equal(0.0)
///
/// conversion.radians_to_degrees(2. *. elementary.pi())
/// |> should.equal(360.)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn radians_to_degrees(x: Float) -> Float {
x *. 180.0 /. do_pi()
}
@external(erlang, "math", "pi")
@external(javascript, "../../maths.mjs", "pi")
fn do_pi() -> Float

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////<script>
//// document.addEventListener("DOMContentLoaded", function() {
//// renderMathInElement(document.body, {
//// // customised options
//// // • auto-render specific keys, e.g.:
//// delimiters: [
//// {left: '$$', right: '$$', display: false},
//// {left: '$', right: '$', display: false},
//// {left: '\\(', right: '\\)', display: false},
//// {left: '\\[', right: '\\]', display: true}
//// ],
//// // • rendering keys, e.g.:
//// throwOnError : true
//// });
//// });
////</script>
////<style>
//// .katex { font-size: 1.1em; }
////</style>
////
//// ---
////
//// Predicates: A module containing functions for testing various mathematical
//// properties of numbers.
////
//// * **Tests**
//// * [`is_close`](#is_close)
//// * [`list_all_close`](#all_close)
//// * [`is_fractional`](#is_fractional)
//// * [`is_between`](#is_between)
//// * [`is_power`](#is_power)
//// * [`is_perfect`](#is_perfect)
//// * [`is_even`](#is_even)
//// * [`is_odd`](#is_odd)
//// * [`is_divisible`](#is_divisible)
//// * [`is_multiple`](#is_multiple)
//// * [`is_prime`](#is_prime)
////
import gleam/int
import gleam/list
import gleam/option
import gleam/pair
import gleam_community/maths/arithmetics
import gleam_community/maths/elementary
import gleam_community/maths/piecewise
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Determine if a given value \\(a\\) is close to or equivalent to a reference value
/// \\(b\\) based on supplied relative \\(r_{tol}\\) and absolute \\(a_{tol}\\) tolerance
/// values. The equivalance of the two given values are then determined based on
/// the equation:
///
/// \\[
/// \|a - b\| \leq (a_{tol} + r_{tol} \cdot \|b\|)
/// \\]
///
/// `True` is returned if statement holds, otherwise `False` is returned.
/// <details>
/// <summary>Example</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example () {
/// let val = 99.
/// let ref_val = 100.
/// // We set 'atol' and 'rtol' such that the values are equivalent
/// // if 'val' is within 1 percent of 'ref_val' +/- 0.1
/// let rtol = 0.01
/// let atol = 0.10
/// floatx.is_close(val, ref_val, rtol, atol)
/// |> should.be_true()
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_close(a: Float, b: Float, rtol: Float, atol: Float) -> Bool {
let x = float_absolute_difference(a, b)
let y = atol +. rtol *. float_absolute_value(b)
case x <=. y {
True -> True
False -> False
}
}
fn float_absolute_value(x: Float) -> Float {
case x >. 0.0 {
True -> x
False -> -1.0 *. x
}
}
fn float_absolute_difference(a: Float, b: Float) -> Float {
a -. b
|> float_absolute_value()
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Determine if a list of values are close to or equivalent to a another list of
/// reference values.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam/list
/// import gleam_community/maths/predicates
///
/// pub fn example () {
/// let val = 99.
/// let ref_val = 100.
/// let xarr = list.repeat(val, 42)
/// let yarr = list.repeat(ref_val, 42)
/// // We set 'atol' and 'rtol' such that the values are equivalent
/// // if 'val' is within 1 percent of 'ref_val' +/- 0.1
/// let rtol = 0.01
/// let atol = 0.10
/// predicates.all_close(xarr, yarr, rtol, atol)
/// |> fn(zarr: Result(List(Bool), Nil)) -> Result(Bool, Nil) {
/// case zarr {
/// Ok(arr) ->
/// arr
/// |> list.all(fn(a) { a })
/// |> Ok
/// _ -> Nil |> Error
/// }
/// }
/// |> should.equal(Ok(True))
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn all_close(
xarr: List(Float),
yarr: List(Float),
rtol: Float,
atol: Float,
) -> Result(List(Bool), Nil) {
let xlen = list.length(xarr)
let ylen = list.length(yarr)
case xlen == ylen {
False -> Error(Nil)
True ->
list.zip(xarr, yarr)
|> list.map(fn(z) { is_close(pair.first(z), pair.second(z), rtol, atol) })
|> Ok
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// Determine if a given value is fractional.
///
/// `True` is returned if the given value is fractional, otherwise `False` is
/// returned.
///
/// <details>
/// <summary>Example</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example () {
/// predicates.is_fractional(0.3333)
/// |> should.equal(True)
///
/// predicates.is_fractional(1.0)
/// |> should.equal(False)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_fractional(x: Float) -> Bool {
do_ceiling(x) -. x >. 0.0
}
@external(erlang, "math", "ceil")
@external(javascript, "../../maths.mjs", "ceiling")
fn do_ceiling(a: Float) -> Float
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given integer value \\(x \in \mathbb{Z}\\) is a
/// power of another integer value \\(y \in \mathbb{Z}\\).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// // Check if 4 is a power of 2 (it is)
/// predicates.is_power(4, 2)
/// |> should.equal(True)
///
/// // Check if 5 is a power of 2 (it is not)
/// predicates.is_power(5, 2)
/// |> should.equal(False)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_power(x: Int, y: Int) -> Bool {
let assert Ok(value) =
elementary.logarithm(int.to_float(x), option.Some(int.to_float(y)))
let truncated = piecewise.truncate(value, option.Some(0))
let remainder = value -. truncated
remainder == 0.0
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given integer value \\(n \in \mathbb{Z}\\) is a
/// perfect number. A number is perfect if it is equal to the sum of its proper
/// positive divisors.
///
/// <details>
/// <summary>Details</summary>
///
/// For example:
/// - \\(6\\) is a perfect number since the divisors of 6 are \\(1 + 2 + 3 = 6\\).
/// - \\(28\\) is a perfect number since the divisors of 28 are \\(1 + 2 + 4 + 7 + 14 = 28\\).
///
/// </details>
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// predicates.is_perfect(6)
/// |> should.equal(True)
///
/// predicates.is_perfect(28)
/// |> should.equal(True)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_perfect(n: Int) -> Bool {
do_sum(arithmetics.proper_divisors(n)) == n
}
fn do_sum(arr: List(Int)) -> Int {
case arr {
[] -> 0
_ ->
arr
|> list.fold(0, fn(acc, a) { a + acc })
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given integer value \\(x \in \mathbb{Z}\\) is even.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// predicates.is_even(-3)
/// |> should.equal(False)
///
/// predicates.is_even(-4)
/// |> should.equal(True)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_even(x: Int) -> Bool {
x % 2 == 0
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given integer value \\(x \in \mathbb{Z}\\) is odd.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// predicates.is_odd(-3)
/// |> should.equal(True)
///
/// predicates.is_odd(-4)
/// |> should.equal(False)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_odd(x: Int) -> Bool {
x % 2 != 0
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given integer value \\(x \in \mathbb{Z}\\) is a
/// prime number. A prime number is a natural number greater than 1 that has no
/// positive divisors other than 1 and itself.
///
/// The function uses the Miller-Rabin primality test to assess if \\(x\\) is prime.
/// It is a probabilistic test, so it can mistakenly identify a composite number
/// as prime. However, the probability of such errors decreases with more testing
/// iterations (the function uses 64 iterations internally, which is typically
/// more than sufficient). The Miller-Rabin test is particularly useful for large
/// numbers.
///
/// <details>
/// <summary>Details</summary>
///
/// Examples of prime numbers:
/// - \\(2\\) is a prime number since it has only two divisors: \\(1\\) and \\(2\\).
/// - \\(7\\) is a prime number since it has only two divisors: \\(1\\) and \\(7\\).
/// - \\(4\\) is not a prime number since it has divisors other than \\(1\\) and itself, such
/// as \\(2\\).
///
/// </details>
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// predicates.is_prime(2)
/// |> should.equal(True)
///
/// predicates.is_prime(4)
/// |> should.equal(False)
///
/// // Test the 2nd Carmichael number
/// predicates.is_prime(1105)
/// |> should.equal(False)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_prime(x: Int) -> Bool {
case x {
x if x < 2 -> {
False
}
x if x == 2 -> {
True
}
_ -> {
miller_rabin_test(x, 64)
}
}
}
fn miller_rabin_test(n: Int, k: Int) -> Bool {
case n, k {
_, 0 -> True
_, _ -> {
// Generate a random int in the range [2, n]
let random_candidate = 2 + int.random(n - 2)
case powmod_with_check(random_candidate, n - 1, n) == 1 {
True -> miller_rabin_test(n, k - 1)
False -> False
}
}
}
}
fn powmod_with_check(base: Int, exponent: Int, modulus: Int) -> Int {
case exponent, { exponent % 2 } == 0 {
0, _ -> 1
_, True -> {
let x = powmod_with_check(base, exponent / 2, modulus)
case { x * x } % modulus, x != 1 && x != { modulus - 1 } {
1, True -> 0
_, _ -> { x * x } % modulus
}
}
_, _ -> { base * powmod_with_check(base, exponent - 1, modulus) } % modulus
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given real number \\(x \in \mathbb{R}\\) is strictly
/// between two other real numbers, \\(a,b \in \mathbb{R}\\), such that \\(a < x < b\\).
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// predicates.is_between(5.5, 5.0, 6.0)
/// |> should.equal(True)
///
/// predicates.is_between(5.0, 5.0, 6.0)
/// |> should.equal(False)
///
/// predicates.is_between(6.0, 5.0, 6.0)
/// |> should.equal(False)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_between(x: Float, lower: Float, upper: Float) -> Bool {
lower <. x && x <. upper
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given integer \\(n \in \mathbb{Z}\\) is divisible by another
/// integer \\(d \in \mathbb{Z}\\), such that \\(n \mod d = 0\\).
///
/// <details>
/// <summary>Details</summary>
///
/// For example:
/// - \\(n = 10\\) is divisible by \\(d = 2\\) because \\(10 \mod 2 = 0\\).
/// - \\(n = 7\\) is not divisible by \\(d = 3\\) because \\(7 \mod 3 \neq 0\\).
///
/// </details>
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// predicates.is_divisible(10, 2)
/// |> should.equal(True)
///
/// predicates.is_divisible(7, 3)
/// |> should.equal(False)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_divisible(n: Int, d: Int) -> Bool {
n % d == 0
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// A function that tests whether a given integer \\(m \in \mathbb{Z}\\) is a multiple of another
/// integer \\(k \in \mathbb{Z}\\), such that \\(m = k \times q\\), with \\(q \in \mathbb{Z}\\).
///
/// <details>
/// <summary>Details</summary>
///
/// For example:
/// - \\(m = 15\\) is a multiple of \\(k = 5\\) because \\(15 = 5 \times 3\\).
/// - \\(m = 14\\) is not a multiple of \\(k = 5\\) because \\(14 \div 5\\) does not yield an
/// integer quotient.
///
/// </details>
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleeunit/should
/// import gleam_community/maths/predicates
///
/// pub fn example() {
/// predicates.is_multiple(15, 5)
/// |> should.equal(True)
///
/// predicates.is_multiple(14, 5)
/// |> should.equal(False)
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn is_multiple(m: Int, k: Int) -> Bool {
m % k == 0
}

328
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@ -1,328 +0,0 @@
////<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css" integrity="sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+" crossorigin="anonymous">
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js" integrity="sha384-7zkQWkzuo3B5mTepMUcHkMB5jZaolc2xDwL6VFqjFALcbeS9Ggm/Yr2r3Dy4lfFg" crossorigin="anonymous"></script>
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
////<script>
//// document.addEventListener("DOMContentLoaded", function() {
//// renderMathInElement(document.body, {
//// // customised options
//// // • auto-render specific keys, e.g.:
//// delimiters: [
//// {left: '$$', right: '$$', display: false},
//// {left: '$', right: '$', display: false},
//// {left: '\\(', right: '\\)', display: false},
//// {left: '\\[', right: '\\]', display: true}
//// ],
//// // • rendering keys, e.g.:
//// throwOnError : true
//// });
//// });
////</script>
////<style>
//// .katex { font-size: 1.1em; }
////</style>
////
//// ---
////
//// Sequences: A module containing functions for generating various types of
//// sequences, ranges and intervals.
////
//// * **Ranges and intervals**
//// * [`arange`](#arange)
//// * [`linear_space`](#linear_space)
//// * [`logarithmic_space`](#logarithmic_space)
//// * [`geometric_space`](#geometric_space)
////
import gleam/iterator
import gleam_community/maths/conversion
import gleam_community/maths/elementary
import gleam_community/maths/piecewise
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function returns an iterator generating evenly spaced values within a given interval.
/// based on a start value but excludes the stop value. The spacing between values is determined
/// by the step size provided. The function supports both positive and negative step values.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/iterator
/// import gleeunit/should
/// import gleam_community/maths/sequences
///
/// pub fn example () {
/// sequences.arange(1.0, 5.0, 1.0)
/// |> iterator.to_list()
/// |> should.equal([1.0, 2.0, 3.0, 4.0])
///
/// // No points returned since
/// // start is smaller than stop and the step is positive
/// sequences.arange(5.0, 1.0, 1.0)
/// |> iterator.to_list()
/// |> should.equal([])
///
/// // Points returned since
/// // start smaller than stop but negative step
/// sequences.arange(5.0, 1.0, -1.0)
/// |> iterator.to_list()
/// |> should.equal([5.0, 4.0, 3.0, 2.0])
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn arange(
start: Float,
stop: Float,
step: Float,
) -> iterator.Iterator(Float) {
case start >=. stop && step >. 0.0 || start <=. stop && step <. 0.0 {
True -> iterator.empty()
False -> {
let direction = case start <=. stop {
True -> {
1.0
}
False -> {
-1.0
}
}
let step_abs = piecewise.float_absolute_value(step)
let num =
piecewise.float_absolute_value(start -. stop) /. step_abs
|> conversion.float_to_int()
iterator.range(0, num - 1)
|> iterator.map(fn(i) {
start +. conversion.int_to_float(i) *. step_abs *. direction
})
}
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function returns an iterator for generating linearly spaced points over a specified
/// interval. The endpoint of the interval can optionally be included/excluded. The number of
/// points and whether the endpoint is included determine the spacing between values.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/iterator
/// import gleeunit/should
/// import gleam_community/maths/elementary
/// import gleam_community/maths/sequences
/// import gleam_community/maths/predicates
///
/// pub fn example () {
/// let assert Ok(tol) = elementary.power(10.0, -6.0)
/// let assert Ok(linspace) = sequences.linear_space(10.0, 20.0, 5, True)
/// let assert Ok(result) =
/// predicates.all_close(
/// linspace |> iterator.to_list(),
/// [10.0, 12.5, 15.0, 17.5, 20.0],
/// 0.0,
/// tol,
/// )
///
/// result
/// |> list.all(fn(x) { x == True })
/// |> should.be_true()
///
/// // A negative number of points (-5) does not work
/// sequences.linear_space(10.0, 50.0, -5, True)
/// |> should.be_error()
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn linear_space(
start: Float,
stop: Float,
num: Int,
endpoint: Bool,
) -> Result(iterator.Iterator(Float), Nil) {
let direction = case start <=. stop {
True -> 1.0
False -> -1.0
}
let increment = case endpoint {
True -> {
piecewise.float_absolute_value(start -. stop)
/. conversion.int_to_float(num - 1)
}
False -> {
piecewise.float_absolute_value(start -. stop)
/. conversion.int_to_float(num)
}
}
case num > 0 {
True -> {
iterator.range(0, num - 1)
|> iterator.map(fn(i) {
start +. conversion.int_to_float(i) *. increment *. direction
})
|> Ok
}
False -> Error(Nil)
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function returns an iterator of logarithmically spaced points over a specified interval.
/// The endpoint of the interval can optionally be included/excluded. The number of points, base,
/// and whether the endpoint is included determine the spacing between values.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/iterator
/// import gleeunit/should
/// import gleam_community/maths/elementary
/// import gleam_community/maths/sequences
/// import gleam_community/maths/predicates
///
/// pub fn example () {
/// let assert Ok(tol) = elementary.power(10.0, -6.0)
/// let assert Ok(logspace) = sequences.logarithmic_space(1.0, 3.0, 3, True, 10.0)
/// let assert Ok(result) =
/// predicates.all_close(
/// logspace |> iterator.to_list(),
/// [10.0, 100.0, 1000.0],
/// 0.0,
/// tol,
/// )
/// result
/// |> list.all(fn(x) { x == True })
/// |> should.be_true()
///
/// // A negative number of points (-3) does not work
/// sequences.logarithmic_space(1.0, 3.0, -3, False, 10.0)
/// |> should.be_error()
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn logarithmic_space(
start: Float,
stop: Float,
num: Int,
endpoint: Bool,
base: Float,
) -> Result(iterator.Iterator(Float), Nil) {
case num > 0 {
True -> {
let assert Ok(linspace) = linear_space(start, stop, num, endpoint)
linspace
|> iterator.map(fn(i) {
let assert Ok(result) = elementary.power(base, i)
result
})
|> Ok
}
False -> Error(Nil)
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The function returns an iterator of numbers spaced evenly on a log scale (a geometric
/// progression). Each point in the list is a constant multiple of the previous. The function is
/// similar to the [`logarithmic_space`](#logarithmic_space) function, but with endpoints
/// specified directly.
///
/// <details>
/// <summary>Example:</summary>
///
/// import gleam/iterator
/// import gleeunit/should
/// import gleam_community/maths/elementary
/// import gleam_community/maths/sequences
/// import gleam_community/maths/predicates
///
/// pub fn example () {
/// let assert Ok(tol) = elementary.power(10.0, -6.0)
/// let assert Ok(logspace) = sequences.geometric_space(10.0, 1000.0, 3, True)
/// let assert Ok(result) =
/// predicates.all_close(
/// logspace |> iterator.to_list(),
/// [10.0, 100.0, 1000.0],
/// 0.0,
/// tol,
/// )
/// result
/// |> list.all(fn(x) { x == True })
/// |> should.be_true()
///
/// // Input (start and stop can't be equal to 0.0)
/// sequences.geometric_space(0.0, 1000.0, 3, False)
/// |> should.be_error()
///
/// sequences.geometric_space(-1000.0, 0.0, 3, False)
/// |> should.be_error()
///
/// // A negative number of points (-3) does not work
/// sequences.geometric_space(10.0, 1000.0, -3, False)
/// |> should.be_error()
/// }
/// </details>
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn geometric_space(
start: Float,
stop: Float,
num: Int,
endpoint: Bool,
) -> Result(iterator.Iterator(Float), Nil) {
case start == 0.0 || stop == 0.0 {
True -> Error(Nil)
False ->
case num > 0 {
True -> {
let assert Ok(log_start) = elementary.logarithm_10(start)
let assert Ok(log_stop) = elementary.logarithm_10(stop)
logarithmic_space(log_start, log_stop, num, endpoint, 10.0)
}
False -> Error(Nil)
}
}
}

195
src/gleam_community/maths/special.gleam
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@ -1,195 +0,0 @@
////<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css" integrity="sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+" crossorigin="anonymous">
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js" integrity="sha384-7zkQWkzuo3B5mTepMUcHkMB5jZaolc2xDwL6VFqjFALcbeS9Ggm/Yr2r3Dy4lfFg" crossorigin="anonymous"></script>
////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
////<script>
//// document.addEventListener("DOMContentLoaded", function() {
//// renderMathInElement(document.body, {
//// // customised options
//// // • auto-render specific keys, e.g.:
//// delimiters: [
//// {left: '$$', right: '$$', display: false},
//// {left: '$', right: '$', display: false},
//// {left: '\\(', right: '\\)', display: false},
//// {left: '\\[', right: '\\]', display: true}
//// ],
//// // • rendering keys, e.g.:
//// throwOnError : true
//// });
//// });
////</script>
////<style>
//// .katex { font-size: 1.1em; }
////</style>
////
//// ---
////
//// Special: A module containing special mathematical functions.
////
//// * **Special mathematical functions**
//// * [`beta`](#beta)
//// * [`erf`](#erf)
//// * [`gamma`](#gamma)
//// * [`incomplete_gamma`](#incomplete_gamma)
////
import gleam/list
import gleam_community/maths/conversion
import gleam_community/maths/elementary
import gleam_community/maths/piecewise
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The beta function over the real numbers:
///
/// \\[
/// \text{B}(x, y) = \frac{\Gamma(x) \cdot \Gamma(y)}{\Gamma(x + y)}
/// \\]
///
/// The beta function is evaluated through the use of the gamma function.
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn beta(x: Float, y: Float) -> Float {
gamma(x) *. gamma(y) /. gamma(x +. y)
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The error function.
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn erf(x: Float) -> Float {
let assert [a1, a2, a3, a4, a5] = [
0.254829592, -0.284496736, 1.421413741, -1.453152027, 1.061405429,
]
let p = 0.3275911
let sign = piecewise.float_sign(x)
let x = piecewise.float_absolute_value(x)
// Formula 7.1.26 given in Abramowitz and Stegun.
let t = 1.0 /. { 1.0 +. p *. x }
let y =
1.0
-. { { { { a5 *. t +. a4 } *. t +. a3 } *. t +. a2 } *. t +. a1 }
*. t
*. elementary.exponential(-1.0 *. x *. x)
sign *. y
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The gamma function over the real numbers. The function is essentially equal to
/// the factorial for any positive integer argument: \\(\Gamma(n) = (n - 1)!\\)
///
/// The implemented gamma function is approximated through Lanczos approximation
/// using the same coefficients used by the GNU Scientific Library.
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn gamma(x: Float) -> Float {
gamma_lanczos(x)
}
const lanczos_g: Float = 7.0
const lanczos_p: List(Float) = [
0.99999999999980993, 676.5203681218851, -1259.1392167224028,
771.32342877765313, -176.61502916214059, 12.507343278686905,
-0.13857109526572012, 0.0000099843695780195716, 0.00000015056327351493116,
]
fn gamma_lanczos(x: Float) -> Float {
case x <. 0.5 {
True ->
elementary.pi()
/. { elementary.sin(elementary.pi() *. x) *. gamma_lanczos(1.0 -. x) }
False -> {
let z = x -. 1.0
let x =
list.index_fold(lanczos_p, 0.0, fn(acc, v, index) {
case index > 0 {
True -> acc +. v /. { z +. conversion.int_to_float(index) }
False -> v
}
})
let t = z +. lanczos_g +. 0.5
let assert Ok(v1) = elementary.power(2.0 *. elementary.pi(), 0.5)
let assert Ok(v2) = elementary.power(t, z +. 0.5)
v1 *. v2 *. elementary.exponential(-1.0 *. t) *. x
}
}
}
/// <div style="text-align: right;">
/// <a href="https://github.com/gleam-community/maths/issues">
/// <small>Spot a typo? Open an issue!</small>
/// </a>
/// </div>
///
/// The lower incomplete gamma function over the real numbers.
///
/// The implemented incomplete gamma function is evaluated through a power series
/// expansion.
///
/// <div style="text-align: right;">
/// <a href="#">
/// <small>Back to top ↑</small>
/// </a>
/// </div>
///
pub fn incomplete_gamma(a: Float, x: Float) -> Result(Float, Nil) {
case a >. 0.0 && x >=. 0.0 {
True -> {
let assert Ok(v) = elementary.power(x, a)
v
*. elementary.exponential(-1.0 *. x)
*. incomplete_gamma_sum(a, x, 1.0 /. a, 0.0, 1.0)
|> Ok
}
False -> Error(Nil)
}
}
fn incomplete_gamma_sum(
a: Float,
x: Float,
t: Float,
s: Float,
n: Float,
) -> Float {
case t {
0.0 -> s
_ -> {
let ns = s +. t
let nt = t *. { x /. { a +. n } }
incomplete_gamma_sum(a, x, nt, ns, n +. 1.0)
}
}
}

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test/gleam_community/arithmetics_test.gleam Normal file
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import gleam/float
import gleam_community/maths
import gleeunit/should
pub fn int_gcd_test() {
maths.gcd(1, 1)
|> should.equal(1)
maths.gcd(100, 10)
|> should.equal(10)
maths.gcd(10, 100)
|> should.equal(10)
maths.gcd(100, -10)
|> should.equal(10)
maths.gcd(-36, -17)
|> should.equal(1)
maths.gcd(-30, -42)
|> should.equal(6)
}
pub fn int_euclidean_modulo_test() {
// Base Case: Positive x, Positive y
// Note that the truncated, floored, and euclidean
// definitions should agree for this base case
maths.int_euclidean_modulo(15, 4)
|> should.equal(3)
// Case: Positive x, Negative y
maths.int_euclidean_modulo(15, -4)
|> should.equal(3)
// Case: Negative x, Positive y
maths.int_euclidean_modulo(-15, 4)
|> should.equal(1)
// Case: Negative x, Negative y
maths.int_euclidean_modulo(-15, -4)
|> should.equal(1)
// Case: Positive x, Zero y
maths.int_euclidean_modulo(5, 0)
|> should.equal(0)
// Case: Zero x, Negative y
maths.int_euclidean_modulo(0, 5)
|> should.equal(0)
}
pub fn int_lcm_test() {
maths.lcm(1, 1)
|> should.equal(1)
maths.lcm(100, 10)
|> should.equal(100)
maths.lcm(10, 100)
|> should.equal(100)
maths.lcm(100, -10)
|> should.equal(100)
maths.lcm(-36, -17)
|> should.equal(612)
maths.lcm(-30, -42)
|> should.equal(210)
}
pub fn int_proper_divisors_test() {
maths.proper_divisors(2)
|> should.equal([1])
maths.proper_divisors(6)
|> should.equal([1, 2, 3])
maths.proper_divisors(13)
|> should.equal([1])
maths.proper_divisors(18)
|> should.equal([1, 2, 3, 6, 9])
}
pub fn int_divisors_test() {
maths.divisors(2)
|> should.equal([1, 2])
maths.divisors(6)
|> should.equal([1, 2, 3, 6])
maths.divisors(13)
|> should.equal([1, 13])
maths.divisors(18)
|> should.equal([1, 2, 3, 6, 9, 18])
}
pub fn float_list_cumulative_sum_test() {
// An empty lists returns an empty list
[]
|> maths.float_cumulative_sum()
|> should.equal([])
// Valid input returns a result
[1.0, 2.0, 3.0]
|> maths.float_cumulative_sum()
|> should.equal([1.0, 3.0, 6.0])
[-2.0, 4.0, 6.0]
|> maths.float_cumulative_sum()
|> should.equal([-2.0, 2.0, 8.0])
}
pub fn int_list_cumulative_sum_test() {
// An empty lists returns an empty list
[]
|> maths.int_cumulative_sum()
|> should.equal([])
// Valid input returns a result
[1, 2, 3]
|> maths.int_cumulative_sum()
|> should.equal([1, 3, 6])
[-2, 4, 6]
|> maths.int_cumulative_sum()
|> should.equal([-2, 2, 8])
}
pub fn float_list_cumulative_product_test() {
// An empty lists returns an empty list
[]
|> maths.float_cumulative_product()
|> should.equal([])
// Valid input returns a result
[1.0, 2.0, 3.0]
|> maths.float_cumulative_product()
|> should.equal([1.0, 2.0, 6.0])
[-2.0, 4.0, 6.0]
|> maths.float_cumulative_product()
|> should.equal([-2.0, -8.0, -48.0])
}
pub fn int_list_cumulative_product_test() {
// An empty lists returns an empty list
[]
|> maths.int_cumulative_product()
|> should.equal([])
// Valid input returns a result
[1, 2, 3]
|> maths.int_cumulative_product()
|> should.equal([1, 2, 6])
[-2, 4, 6]
|> maths.int_cumulative_product()
|> should.equal([-2, -8, -48])
}
pub fn float_weighted_product_test() {
[]
|> maths.float_weighted_product()
|> should.equal(Ok(1.0))
[#(1.0, 0.0), #(2.0, 0.0), #(3.0, 0.0)]
|> maths.float_weighted_product()
|> should.equal(Ok(1.0))
[#(1.0, 1.0), #(2.0, 1.0), #(3.0, 1.0)]
|> maths.float_weighted_product()
|> should.equal(Ok(6.0))
let assert Ok(tolerance) = float.power(10.0, -6.0)
let assert Ok(result) =
[#(9.0, 0.5), #(10.0, 0.5), #(10.0, 0.5)]
|> maths.float_weighted_product()
result
|> maths.is_close(30.0, 0.0, tolerance)
|> should.be_true()
}
pub fn float_weighted_sum_test() {
[]
|> maths.float_weighted_sum()
|> should.equal(Ok(0.0))
[#(1.0, 0.0), #(2.0, 0.0), #(3.0, 0.0)]
|> maths.float_weighted_sum()
|> should.equal(Ok(0.0))
[#(1.0, 1.0), #(2.0, 1.0), #(3.0, 1.0)]
|> maths.float_weighted_sum()
|> should.equal(Ok(6.0))
[#(9.0, 0.5), #(10.0, 0.5), #(10.0, 0.5)]
|> maths.float_weighted_sum()
|> should.equal(Ok(14.5))
}

812
test/gleam_community/maths/combinatorics_test.gleam → test/gleam_community/combinatorics_test.gleam
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113
test/gleam_community/conversion_test.gleam Normal file
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import gleam/float
import gleam_community/maths
import gleeunit/should
pub fn float_to_degree_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
maths.radians_to_degrees(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.radians_to_degrees(2.0 *. maths.pi())
|> maths.is_close(360.0, 0.0, tol)
|> should.be_true()
}
pub fn float_to_radian_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
maths.degrees_to_radians(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.degrees_to_radians(360.0)
|> maths.is_close(2.0 *. maths.pi(), 0.0, tol)
|> should.be_true()
}
pub fn float_cartesian_to_polar_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Test: Cartesian (1, 0) -> Polar (1, 0)
let #(r, theta) = maths.cartesian_to_polar(1.0, 0.0)
r
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
theta
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
// Test: Cartesian (0, 1) -> Polar (1, pi/2)
let #(r, theta) = maths.cartesian_to_polar(0.0, 1.0)
r
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
theta
|> maths.is_close(maths.pi() /. 2.0, 0.0, tol)
|> should.be_true()
// Test: Cartesian (-1, 0) -> Polar (1, pi)
let #(r, theta) = maths.cartesian_to_polar(-1.0, 0.0)
r
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
theta
|> maths.is_close(maths.pi(), 0.0, tol)
|> should.be_true()
// Test: Cartesian (0, -1) -> Polar (1, -pi/2)
let #(r, theta) = maths.cartesian_to_polar(0.0, -1.0)
r
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
theta
|> maths.is_close(-1.0 *. maths.pi() /. 2.0, 0.0, tol)
|> should.be_true()
}
pub fn float_polar_to_cartesian_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Test: Polar (1, 0) -> Cartesian (1, 0)
let #(x, y) = maths.polar_to_cartesian(1.0, 0.0)
x
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
y
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
// Test: Polar (1, pi/2) -> Cartesian (0, 1)
let #(x, y) = maths.polar_to_cartesian(1.0, maths.pi() /. 2.0)
x
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
y
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
// Test: Polar (1, pi) -> Cartesian (-1, 0)
let #(x, y) = maths.polar_to_cartesian(1.0, maths.pi())
x
|> maths.is_close(-1.0, 0.0, tol)
|> should.be_true()
y
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
// Test: Polar (1, -pi/2) -> Cartesian (0, -1)
let #(x, y) = maths.polar_to_cartesian(1.0, -1.0 *. maths.pi() /. 2.0)
x
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
y
|> maths.is_close(-1.0, 0.0, tol)
|> should.be_true()
}

419
test/gleam_community/elementary_test.gleam Normal file
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import gleam/float
import gleam_community/maths
import gleeunit/should
pub fn float_acos_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = maths.acos(1.0)
result
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = maths.acos(0.5)
result
|> maths.is_close(1.047197, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
maths.acos(1.1)
|> should.be_error()
maths.acos(-1.1)
|> should.be_error()
}
pub fn float_acosh_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = maths.acosh(1.0)
result
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
maths.acosh(0.0)
|> should.be_error()
}
pub fn float_asin_test() {
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.asin(0.0)
|> should.equal(Ok(0.0))
let assert Ok(tol) = float.power(10.0, -6.0)
let assert Ok(result) = maths.asin(0.5)
result
|> maths.is_close(0.523598, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
maths.asin(1.1)
|> should.be_error()
maths.asin(-1.1)
|> should.be_error()
}
pub fn float_asinh_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.asinh(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.asinh(0.5)
|> maths.is_close(0.481211, 0.0, tol)
|> should.be_true()
}
pub fn float_atan_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.atan(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.atan(0.5)
|> maths.is_close(0.463647, 0.0, tol)
|> should.be_true()
}
pub fn math_atan2_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.atan2(0.0, 0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.atan2(0.0, 1.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
// Check atan2(y=1.0, x=0.5)
// Should be equal to atan(y / x) for any x > 0 and any y
let result = maths.atan(1.0 /. 0.5)
maths.atan2(1.0, 0.5)
|> maths.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=2.0, x=-1.5)
// Should be equal to pi + atan(y / x) for any x < 0 and y >= 0
let result = maths.pi() +. maths.atan(2.0 /. -1.5)
maths.atan2(2.0, -1.5)
|> maths.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=-2.0, x=-1.5)
// Should be equal to atan(y / x) - pi for any x < 0 and y < 0
let result = maths.atan(-2.0 /. -1.5) -. maths.pi()
maths.atan2(-2.0, -1.5)
|> maths.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=1.5, x=0.0)
// Should be equal to pi/2 for x = 0 and any y > 0
let result = maths.pi() /. 2.0
maths.atan2(1.5, 0.0)
|> maths.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=-1.5, x=0.0)
// Should be equal to -pi/2 for x = 0 and any y < 0
let result = -1.0 *. maths.pi() /. 2.0
maths.atan2(-1.5, 0.0)
|> maths.is_close(result, 0.0, tol)
|> should.be_true()
}
pub fn float_atanh_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = maths.atanh(0.0)
result
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = maths.atanh(0.5)
result
|> maths.is_close(0.549306, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
maths.atanh(1.0)
|> should.be_error()
maths.atanh(2.0)
|> should.be_error()
maths.atanh(1.0)
|> should.be_error()
maths.atanh(-2.0)
|> should.be_error()
}
pub fn float_cos_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.cos(0.0)
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
maths.cos(maths.pi())
|> maths.is_close(-1.0, 0.0, tol)
|> should.be_true()
maths.cos(0.5)
|> maths.is_close(0.877582, 0.0, tol)
|> should.be_true()
}
pub fn float_cosh_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.cosh(0.0)
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
maths.cosh(0.5)
|> maths.is_close(1.127625, 0.0, tol)
|> should.be_true()
// An (overflow) error might occur when given an input
// value that will result in a too large output value
// e.g. maths.cosh(1000.0) but this is a property of the
// runtime.
}
pub fn float_sin_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.sin(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.sin(0.5 *. maths.pi())
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
maths.sin(0.5)
|> maths.is_close(0.479425, 0.0, tol)
|> should.be_true()
}
pub fn float_sinh_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.sinh(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.sinh(0.5)
|> maths.is_close(0.521095, 0.0, tol)
|> should.be_true()
// An (overflow) error might occur when given an input
// value that will result in a too large output value
// e.g. maths.sinh(1000.0) but this is a property of the
// runtime.
}
pub fn math_tan_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.tan(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.tan(0.5)
|> maths.is_close(0.546302, 0.0, tol)
|> should.be_true()
}
pub fn math_tanh_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.tanh(0.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.tanh(25.0)
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
maths.tanh(-25.0)
|> maths.is_close(-1.0, 0.0, tol)
|> should.be_true()
maths.tanh(0.5)
|> maths.is_close(0.462117, 0.0, tol)
|> should.be_true()
}
pub fn float_exponential_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.exponential(0.0)
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
maths.exponential(0.5)
|> maths.is_close(1.648721, 0.0, tol)
|> should.be_true()
// An (overflow) error might occur when given an input
// value that will result in a too large output value
// e.g. maths.exponential(1000.0) but this is a property of the
// runtime.
}
pub fn float_natural_logarithm_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.natural_logarithm(1.0)
|> should.equal(Ok(0.0))
let assert Ok(result) = maths.natural_logarithm(0.5)
result
|> maths.is_close(-0.693147, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
maths.natural_logarithm(-1.0)
|> should.be_error()
}
pub fn float_logarithm_test() {
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.logarithm(10.0, 10.0)
|> should.equal(Ok(1.0))
maths.logarithm(10.0, 100.0)
|> should.equal(Ok(0.5))
maths.logarithm(1.0, 0.25)
|> should.equal(Ok(0.0))
// Check that we get an error when the function is evaluated
// outside its domain
maths.logarithm(1.0, 1.0)
|> should.be_error()
maths.logarithm(10.0, 1.0)
|> should.be_error()
maths.logarithm(-1.0, 1.0)
|> should.be_error()
maths.logarithm(1.0, 10.0)
|> should.equal(Ok(0.0))
maths.logarithm(maths.e(), maths.e())
|> should.equal(Ok(1.0))
maths.logarithm(-1.0, 2.0)
|> should.be_error()
}
pub fn float_logarithm_2_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
maths.logarithm_2(1.0)
|> should.equal(Ok(0.0))
maths.logarithm_2(2.0)
|> should.equal(Ok(1.0))
let assert Ok(result) = maths.logarithm_2(5.0)
result
|> maths.is_close(2.321928, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
maths.logarithm_2(-1.0)
|> should.be_error()
}
pub fn float_logarithm_10_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = maths.logarithm_10(1.0)
result
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = maths.logarithm_10(10.0)
result
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = maths.logarithm_10(50.0)
result
|> maths.is_close(1.69897, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
maths.logarithm_10(-1.0)
|> should.be_error()
}
pub fn float_nth_root_test() {
maths.nth_root(9.0, 2)
|> should.equal(Ok(3.0))
maths.nth_root(27.0, 3)
|> should.equal(Ok(3.0))
maths.nth_root(1.0, 4)
|> should.equal(Ok(1.0))
maths.nth_root(256.0, 4)
|> should.equal(Ok(4.0))
// An error should be returned as an imaginary number would otherwise
// have to be returned
maths.nth_root(-1.0, 4)
|> should.be_error()
}
pub fn float_constants_test() {
let assert Ok(tolerance) = float.power(10.0, -12.0)
// Test that the constant is approximately equal to 2.7128...
maths.e()
|> maths.is_close(2.7182818284590452353602, 0.0, tolerance)
|> should.be_true()
// Test that the constant is approximately equal to 2.7128...
maths.pi()
|> maths.is_close(3.14159265359, 0.0, tolerance)
|> should.be_true()
// Test that the constant is approximately equal to 1.6180...
maths.golden_ratio()
|> maths.is_close(1.618033988749895, 0.0, tolerance)
|> should.be_true()
}

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test/gleam_community/maths/arithmetics_test.gleam
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import gleam/option
import gleam_community/maths/arithmetics
import gleeunit/should
pub fn int_gcd_test() {
arithmetics.gcd(1, 1)
|> should.equal(1)
arithmetics.gcd(100, 10)
|> should.equal(10)
arithmetics.gcd(10, 100)
|> should.equal(10)
arithmetics.gcd(100, -10)
|> should.equal(10)
arithmetics.gcd(-36, -17)
|> should.equal(1)
arithmetics.gcd(-30, -42)
|> should.equal(6)
}
pub fn int_euclidean_modulo_test() {
// Base Case: Positive x, Positive y
// Note that the truncated, floored, and euclidean
// definitions should agree for this base case
arithmetics.int_euclidean_modulo(15, 4)
|> should.equal(3)
// Case: Positive x, Negative y
arithmetics.int_euclidean_modulo(15, -4)
|> should.equal(3)
// Case: Negative x, Positive y
arithmetics.int_euclidean_modulo(-15, 4)
|> should.equal(1)
// Case: Negative x, Negative y
arithmetics.int_euclidean_modulo(-15, -4)
|> should.equal(1)
// Case: Positive x, Zero y
arithmetics.int_euclidean_modulo(5, 0)
|> should.equal(0)
// Case: Zero x, Negative y
arithmetics.int_euclidean_modulo(0, 5)
|> should.equal(0)
}
pub fn int_lcm_test() {
arithmetics.lcm(1, 1)
|> should.equal(1)
arithmetics.lcm(100, 10)
|> should.equal(100)
arithmetics.lcm(10, 100)
|> should.equal(100)
arithmetics.lcm(100, -10)
|> should.equal(100)
arithmetics.lcm(-36, -17)
|> should.equal(612)
arithmetics.lcm(-30, -42)
|> should.equal(210)
}
pub fn int_proper_divisors_test() {
arithmetics.proper_divisors(2)
|> should.equal([1])
arithmetics.proper_divisors(6)
|> should.equal([1, 2, 3])
arithmetics.proper_divisors(13)
|> should.equal([1])
arithmetics.proper_divisors(18)
|> should.equal([1, 2, 3, 6, 9])
}
pub fn int_divisors_test() {
arithmetics.divisors(2)
|> should.equal([1, 2])
arithmetics.divisors(6)
|> should.equal([1, 2, 3, 6])
arithmetics.divisors(13)
|> should.equal([1, 13])
arithmetics.divisors(18)
|> should.equal([1, 2, 3, 6, 9, 18])
}
pub fn float_list_sum_test() {
// An empty list returns 0
[]
|> arithmetics.float_sum(option.None)
|> should.equal(0.0)
// Valid input returns a result
[1.0, 2.0, 3.0]
|> arithmetics.float_sum(option.None)
|> should.equal(6.0)
[-2.0, 4.0, 6.0]
|> arithmetics.float_sum(option.None)
|> should.equal(8.0)
}
pub fn int_list_sum_test() {
// An empty list returns 0
[]
|> arithmetics.int_sum()
|> should.equal(0)
// Valid input returns a result
[1, 2, 3]
|> arithmetics.int_sum()
|> should.equal(6)
[-2, 4, 6]
|> arithmetics.int_sum()
|> should.equal(8)
}
pub fn float_list_product_test() {
// An empty list returns 0
[]
|> arithmetics.float_product(option.None)
|> should.equal(Ok(1.0))
// Valid input returns a result
[1.0, 2.0, 3.0]
|> arithmetics.float_product(option.None)
|> should.equal(Ok(6.0))
[-2.0, 4.0, 6.0]
|> arithmetics.float_product(option.None)
|> should.equal(Ok(-48.0))
}
pub fn int_list_product_test() {
// An empty list returns 0
[]
|> arithmetics.int_product()
|> should.equal(1)
// Valid input returns a result
[1, 2, 3]
|> arithmetics.int_product()
|> should.equal(6)
[-2, 4, 6]
|> arithmetics.int_product()
|> should.equal(-48)
}
pub fn float_list_cumulative_sum_test() {
// An empty lists returns an empty list
[]
|> arithmetics.float_cumulative_sum()
|> should.equal([])
// Valid input returns a result
[1.0, 2.0, 3.0]
|> arithmetics.float_cumulative_sum()
|> should.equal([1.0, 3.0, 6.0])
[-2.0, 4.0, 6.0]
|> arithmetics.float_cumulative_sum()
|> should.equal([-2.0, 2.0, 8.0])
}
pub fn int_list_cumulative_sum_test() {
// An empty lists returns an empty list
[]
|> arithmetics.int_cumulative_sum()
|> should.equal([])
// Valid input returns a result
[1, 2, 3]
|> arithmetics.int_cumulative_sum()
|> should.equal([1, 3, 6])
[-2, 4, 6]
|> arithmetics.int_cumulative_sum()
|> should.equal([-2, 2, 8])
}
pub fn float_list_cumulative_product_test() {
// An empty lists returns an empty list
[]
|> arithmetics.float_cumulative_product()
|> should.equal([])
// Valid input returns a result
[1.0, 2.0, 3.0]
|> arithmetics.float_cumulative_product()
|> should.equal([1.0, 2.0, 6.0])
[-2.0, 4.0, 6.0]
|> arithmetics.float_cumulative_product()
|> should.equal([-2.0, -8.0, -48.0])
}
pub fn int_list_cumulative_product_test() {
// An empty lists returns an empty list
[]
|> arithmetics.int_cumulative_product()
|> should.equal([])
// Valid input returns a result
[1, 2, 3]
|> arithmetics.int_cumulative_product()
|> should.equal([1, 2, 6])
[-2, 4, 6]
|> arithmetics.int_cumulative_product()
|> should.equal([-2, -8, -48])
}

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test/gleam_community/maths/conversion_test.gleam
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import gleam_community/maths/conversion
import gleam_community/maths/elementary
import gleam_community/maths/predicates
import gleeunit/should
pub fn float_to_degree_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
conversion.radians_to_degrees(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
conversion.radians_to_degrees(2.0 *. elementary.pi())
|> predicates.is_close(360.0, 0.0, tol)
|> should.be_true()
}
pub fn float_to_radian_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
conversion.degrees_to_radians(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
conversion.degrees_to_radians(360.0)
|> predicates.is_close(2.0 *. elementary.pi(), 0.0, tol)
|> should.be_true()
}
pub fn float_to_int_test() {
conversion.float_to_int(12.0654)
|> should.equal(12)
}
pub fn int_to_float_test() {
conversion.int_to_float(-1)
|> should.equal(-1.0)
conversion.int_to_float(1)
|> should.equal(1.0)
}

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test/gleam_community/maths/elementary_test.gleam
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import gleam/option
import gleam_community/maths/elementary
import gleam_community/maths/predicates
import gleeunit/should
pub fn float_acos_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = elementary.acos(1.0)
result
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = elementary.acos(0.5)
result
|> predicates.is_close(1.047197, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
elementary.acos(1.1)
|> should.be_error()
elementary.acos(-1.1)
|> should.be_error()
}
pub fn float_acosh_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = elementary.acosh(1.0)
result
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
elementary.acosh(0.0)
|> should.be_error()
}
pub fn float_asin_test() {
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.asin(0.0)
|> should.equal(Ok(0.0))
let assert Ok(tol) = elementary.power(10.0, -6.0)
let assert Ok(result) = elementary.asin(0.5)
result
|> predicates.is_close(0.523598, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
elementary.asin(1.1)
|> should.be_error()
elementary.asin(-1.1)
|> should.be_error()
}
pub fn float_asinh_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.asinh(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
elementary.asinh(0.5)
|> predicates.is_close(0.481211, 0.0, tol)
|> should.be_true()
}
pub fn float_atan_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.atan(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
elementary.atan(0.5)
|> predicates.is_close(0.463647, 0.0, tol)
|> should.be_true()
}
pub fn math_atan2_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.atan2(0.0, 0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
elementary.atan2(0.0, 1.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
// Check atan2(y=1.0, x=0.5)
// Should be equal to atan(y / x) for any x > 0 and any y
let result = elementary.atan(1.0 /. 0.5)
elementary.atan2(1.0, 0.5)
|> predicates.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=2.0, x=-1.5)
// Should be equal to pi + atan(y / x) for any x < 0 and y >= 0
let result = elementary.pi() +. elementary.atan(2.0 /. -1.5)
elementary.atan2(2.0, -1.5)
|> predicates.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=-2.0, x=-1.5)
// Should be equal to atan(y / x) - pi for any x < 0 and y < 0
let result = elementary.atan(-2.0 /. -1.5) -. elementary.pi()
elementary.atan2(-2.0, -1.5)
|> predicates.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=1.5, x=0.0)
// Should be equal to pi/2 for x = 0 and any y > 0
let result = elementary.pi() /. 2.0
elementary.atan2(1.5, 0.0)
|> predicates.is_close(result, 0.0, tol)
|> should.be_true()
// Check atan2(y=-1.5, x=0.0)
// Should be equal to -pi/2 for x = 0 and any y < 0
let result = -1.0 *. elementary.pi() /. 2.0
elementary.atan2(-1.5, 0.0)
|> predicates.is_close(result, 0.0, tol)
|> should.be_true()
}
pub fn float_atanh_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = elementary.atanh(0.0)
result
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = elementary.atanh(0.5)
result
|> predicates.is_close(0.549306, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
elementary.atanh(1.0)
|> should.be_error()
elementary.atanh(2.0)
|> should.be_error()
elementary.atanh(1.0)
|> should.be_error()
elementary.atanh(-2.0)
|> should.be_error()
}
pub fn float_cos_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.cos(0.0)
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
elementary.cos(elementary.pi())
|> predicates.is_close(-1.0, 0.0, tol)
|> should.be_true()
elementary.cos(0.5)
|> predicates.is_close(0.877582, 0.0, tol)
|> should.be_true()
}
pub fn float_cosh_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.cosh(0.0)
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
elementary.cosh(0.5)
|> predicates.is_close(1.127625, 0.0, tol)
|> should.be_true()
// An (overflow) error might occur when given an input
// value that will result in a too large output value
// e.g. elementary.cosh(1000.0) but this is a property of the
// runtime.
}
pub fn float_sin_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.sin(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
elementary.sin(0.5 *. elementary.pi())
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
elementary.sin(0.5)
|> predicates.is_close(0.479425, 0.0, tol)
|> should.be_true()
}
pub fn float_sinh_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.sinh(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
elementary.sinh(0.5)
|> predicates.is_close(0.521095, 0.0, tol)
|> should.be_true()
// An (overflow) error might occur when given an input
// value that will result in a too large output value
// e.g. elementary.sinh(1000.0) but this is a property of the
// runtime.
}
pub fn math_tan_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.tan(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
elementary.tan(0.5)
|> predicates.is_close(0.546302, 0.0, tol)
|> should.be_true()
}
pub fn math_tanh_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.tanh(0.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
elementary.tanh(25.0)
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
elementary.tanh(-25.0)
|> predicates.is_close(-1.0, 0.0, tol)
|> should.be_true()
elementary.tanh(0.5)
|> predicates.is_close(0.462117, 0.0, tol)
|> should.be_true()
}
pub fn float_exponential_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.exponential(0.0)
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
elementary.exponential(0.5)
|> predicates.is_close(1.648721, 0.0, tol)
|> should.be_true()
// An (overflow) error might occur when given an input
// value that will result in a too large output value
// e.g. elementary.exponential(1000.0) but this is a property of the
// runtime.
}
pub fn float_natural_logarithm_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.natural_logarithm(1.0)
|> should.equal(Ok(0.0))
let assert Ok(result) = elementary.natural_logarithm(0.5)
result
|> predicates.is_close(-0.693147, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
elementary.natural_logarithm(-1.0)
|> should.be_error()
}
pub fn float_logarithm_test() {
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.logarithm(10.0, option.Some(10.0))
|> should.equal(Ok(1.0))
elementary.logarithm(10.0, option.Some(100.0))
|> should.equal(Ok(0.5))
elementary.logarithm(1.0, option.Some(0.25))
|> should.equal(Ok(0.0))
// Check that we get an error when the function is evaluated
// outside its domain
elementary.logarithm(1.0, option.Some(1.0))
|> should.be_error()
elementary.logarithm(10.0, option.Some(1.0))
|> should.be_error()
elementary.logarithm(-1.0, option.Some(1.0))
|> should.be_error()
elementary.logarithm(1.0, option.Some(10.0))
|> should.equal(Ok(0.0))
elementary.logarithm(elementary.e(), option.Some(elementary.e()))
|> should.equal(Ok(1.0))
elementary.logarithm(-1.0, option.Some(2.0))
|> should.be_error()
}
pub fn float_logarithm_2_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
elementary.logarithm_2(1.0)
|> should.equal(Ok(0.0))
elementary.logarithm_2(2.0)
|> should.equal(Ok(1.0))
let assert Ok(result) = elementary.logarithm_2(5.0)
result
|> predicates.is_close(2.321928, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
elementary.logarithm_2(-1.0)
|> should.be_error()
}
pub fn float_logarithm_10_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) = elementary.logarithm_10(1.0)
result
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = elementary.logarithm_10(10.0)
result
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) = elementary.logarithm_10(50.0)
result
|> predicates.is_close(1.69897, 0.0, tol)
|> should.be_true()
// Check that we get an error when the function is evaluated
// outside its domain
elementary.logarithm_10(-1.0)
|> should.be_error()
}
pub fn float_power_test() {
elementary.power(2.0, 2.0)
|> should.equal(Ok(4.0))
elementary.power(-5.0, 3.0)
|> should.equal(Ok(-125.0))
elementary.power(10.5, 0.0)
|> should.equal(Ok(1.0))
elementary.power(16.0, 0.5)
|> should.equal(Ok(4.0))
elementary.power(2.0, -1.0)
|> should.equal(Ok(0.5))
elementary.power(2.0, -1.0)
|> should.equal(Ok(0.5))
// When y = 0, the result should universally be 1, regardless of the value of x
elementary.power(10.0, 0.0)
|> should.equal(Ok(1.0))
elementary.power(-10.0, 0.0)
|> should.equal(Ok(1.0))
elementary.power(2.0, -1.0)
|> should.equal(Ok(0.5))
// elementary.power(-1.0, 0.5) is equivalent to float.square_root(-1.0)
// and should return an error as an imaginary number would otherwise
// have to be returned
elementary.power(-1.0, 0.5)
|> should.be_error()
// Check another case with a negative base and fractional exponent
elementary.power(-1.5, 1.5)
|> should.be_error()
// elementary.power(0.0, -1.0) is equivalent to 1. /. 0 and is expected
// to be an error
elementary.power(0.0, -1.0)
|> should.be_error()
// Check that a negative base and exponent is fine as long as the
// exponent is not fractional
elementary.power(-2.0, -1.0)
|> should.equal(Ok(-0.5))
}
pub fn float_square_root_test() {
elementary.square_root(1.0)
|> should.equal(Ok(1.0))
elementary.square_root(9.0)
|> should.equal(Ok(3.0))
// An error should be returned as an imaginary number would otherwise
// have to be returned
elementary.square_root(-1.0)
|> should.be_error()
}
pub fn float_cube_root_test() {
elementary.cube_root(1.0)
|> should.equal(Ok(1.0))
elementary.cube_root(27.0)
|> should.equal(Ok(3.0))
// An error should be returned as an imaginary number would otherwise
// have to be returned
elementary.cube_root(-1.0)
|> should.be_error()
}
pub fn float_nth_root_test() {
elementary.nth_root(9.0, 2)
|> should.equal(Ok(3.0))
elementary.nth_root(27.0, 3)
|> should.equal(Ok(3.0))
elementary.nth_root(1.0, 4)
|> should.equal(Ok(1.0))
elementary.nth_root(256.0, 4)
|> should.equal(Ok(4.0))
// An error should be returned as an imaginary number would otherwise
// have to be returned
elementary.nth_root(-1.0, 4)
|> should.be_error()
}
pub fn float_constants_test() {
elementary.e()
|> predicates.is_close(2.71828, 0.0, 0.00001)
|> should.be_true()
elementary.pi()
|> predicates.is_close(3.14159, 0.0, 0.00001)
|> should.be_true()
}

629
test/gleam_community/maths/metrics_test.gleam
View file

@ -1,629 +0,0 @@
import gleam/option
import gleam/set
import gleam_community/maths/elementary
import gleam_community/maths/metrics
import gleam_community/maths/predicates
import gleeunit/should
pub fn float_list_norm_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// An empty lists returns 0.0
[]
|> metrics.norm(1.0, option.None)
|> should.equal(Ok(0.0))
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) =
[1.0, 1.0, 1.0]
|> metrics.norm(1.0, option.None)
result
|> predicates.is_close(3.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[1.0, 1.0, 1.0]
|> metrics.norm(-1.0, option.None)
result
|> predicates.is_close(0.3333333333333333, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -1.0, -1.0]
|> metrics.norm(-1.0, option.None)
result
|> predicates.is_close(0.3333333333333333, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -1.0, -1.0]
|> metrics.norm(1.0, option.None)
result
|> predicates.is_close(3.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -2.0, -3.0]
|> metrics.norm(-10.0, option.None)
result
|> predicates.is_close(0.9999007044905545, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -2.0, -3.0]
|> metrics.norm(-100.0, option.None)
result
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -2.0, -3.0]
|> metrics.norm(2.0, option.None)
result
|> predicates.is_close(3.7416573867739413, 0.0, tol)
|> should.be_true()
}
pub fn float_list_manhattan_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Empty lists returns an error
metrics.manhattan_distance([], [], option.None)
|> should.be_error()
// Differing lengths returns error
metrics.manhattan_distance([], [1.0], option.None)
|> should.be_error()
// Try with valid input (same as Minkowski distance with p = 1)
let assert Ok(result) =
metrics.manhattan_distance([0.0, 0.0], [1.0, 2.0], option.None)
result
|> predicates.is_close(3.0, 0.0, tol)
|> should.be_true()
metrics.manhattan_distance([1.0, 2.0, 3.0], [4.0, 5.0, 6.0], option.None)
|> should.equal(Ok(9.0))
metrics.manhattan_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([1.0, 1.0, 1.0]),
)
|> should.equal(Ok(9.0))
metrics.manhattan_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([1.0, 2.0, 3.0]),
)
|> should.equal(Ok(18.0))
// Try invalid input with weights (different sized lists returns an error)
metrics.manhattan_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([7.0, 8.0]),
)
|> should.be_error()
// Try invalid input with weights that are negative
metrics.manhattan_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([-7.0, -8.0, -9.0]),
)
|> should.be_error()
}
pub fn float_list_minkowski_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Empty lists returns an error
metrics.minkowski_distance([], [], 1.0, option.None)
|> should.be_error()
// Differing lengths returns error
metrics.minkowski_distance([], [1.0], 1.0, option.None)
|> should.be_error()
// Test order < 1
metrics.minkowski_distance([0.0, 0.0], [0.0, 0.0], -1.0, option.None)
|> should.be_error()
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) =
metrics.minkowski_distance([1.0, 1.0], [1.0, 1.0], 1.0, option.None)
result
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 10.0, option.None)
result
|> predicates.is_close(1.0717734625362931, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 100.0, option.None)
result
|> predicates.is_close(1.0069555500567189, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
metrics.minkowski_distance([0.0, 0.0], [1.0, 1.0], 10.0, option.None)
result
|> predicates.is_close(1.0717734625362931, 0.0, tol)
|> should.be_true()
// Euclidean distance (p = 2)
let assert Ok(result) =
metrics.minkowski_distance([0.0, 0.0], [1.0, 2.0], 2.0, option.None)
result
|> predicates.is_close(2.23606797749979, 0.0, tol)
|> should.be_true()
// Manhattan distance (p = 1)
let assert Ok(result) =
metrics.minkowski_distance([0.0, 0.0], [1.0, 2.0], 1.0, option.None)
result
|> predicates.is_close(3.0, 0.0, tol)
|> should.be_true()
// Try different valid input
let assert Ok(result) =
metrics.minkowski_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
4.0,
option.None,
)
result
|> predicates.is_close(3.9482220388574776, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
metrics.minkowski_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
4.0,
option.Some([1.0, 1.0, 1.0]),
)
result
|> predicates.is_close(3.9482220388574776, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
metrics.minkowski_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
4.0,
option.Some([1.0, 2.0, 3.0]),
)
result
|> predicates.is_close(4.6952537402198615, 0.0, tol)
|> should.be_true()
// Try invalid input with weights (different sized lists returns an error)
metrics.minkowski_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
2.0,
option.Some([7.0, 8.0]),
)
|> should.be_error()
// Try invalid input with weights that are negative
metrics.minkowski_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
2.0,
option.Some([-7.0, -8.0, -9.0]),
)
|> should.be_error()
}
pub fn float_list_euclidean_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Empty lists returns an error
metrics.euclidean_distance([], [], option.None)
|> should.be_error()
// Differing lengths returns error
metrics.euclidean_distance([], [1.0], option.None)
|> should.be_error()
// Try with valid input (same as Minkowski distance with p = 2)
let assert Ok(result) =
metrics.euclidean_distance([0.0, 0.0], [1.0, 2.0], option.None)
result
|> predicates.is_close(2.23606797749979, 0.0, tol)
|> should.be_true()
// Try different valid input
let assert Ok(result) =
metrics.euclidean_distance([1.0, 2.0, 3.0], [4.0, 5.0, 6.0], option.None)
result
|> predicates.is_close(5.196152422706632, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
metrics.euclidean_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([1.0, 1.0, 1.0]),
)
result
|> predicates.is_close(5.196152422706632, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
metrics.euclidean_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([1.0, 2.0, 3.0]),
)
result
|> predicates.is_close(7.3484692283495345, 0.0, tol)
|> should.be_true()
// Try invalid input with weights (different sized lists returns an error)
metrics.euclidean_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([7.0, 8.0]),
)
|> should.be_error()
// Try invalid input with weights that are negative
metrics.euclidean_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([-7.0, -8.0, -9.0]),
)
|> should.be_error()
}
pub fn mean_test() {
// An empty list returns an error
[]
|> metrics.mean()
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> metrics.mean()
|> should.equal(Ok(2.0))
}
pub fn median_test() {
// An empty list returns an error
[]
|> metrics.median()
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> metrics.median()
|> should.equal(Ok(2.0))
[1.0, 2.0, 3.0, 4.0]
|> metrics.median()
|> should.equal(Ok(2.5))
}
pub fn variance_test() {
// Degrees of freedom
let ddof = 1
// An empty list returns an error
[]
|> metrics.variance(ddof)
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> metrics.variance(ddof)
|> should.equal(Ok(1.0))
}
pub fn standard_deviation_test() {
// Degrees of freedom
let ddof = 1
// An empty list returns an error
[]
|> metrics.standard_deviation(ddof)
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> metrics.standard_deviation(ddof)
|> should.equal(Ok(1.0))
}
pub fn jaccard_index_test() {
metrics.jaccard_index(set.from_list([]), set.from_list([]))
|> should.equal(0.0)
let set_a = set.from_list([0, 1, 2, 5, 6, 8, 9])
let set_b = set.from_list([0, 2, 3, 4, 5, 7, 9])
metrics.jaccard_index(set_a, set_b)
|> should.equal(4.0 /. 10.0)
let set_c = set.from_list([0, 1, 2, 3, 4, 5])
let set_d = set.from_list([6, 7, 8, 9, 10])
metrics.jaccard_index(set_c, set_d)
|> should.equal(0.0 /. 11.0)
let set_e = set.from_list(["cat", "dog", "hippo", "monkey"])
let set_f = set.from_list(["monkey", "rhino", "ostrich", "salmon"])
metrics.jaccard_index(set_e, set_f)
|> should.equal(1.0 /. 7.0)
}
pub fn sorensen_dice_coefficient_test() {
metrics.sorensen_dice_coefficient(set.from_list([]), set.from_list([]))
|> should.equal(0.0)
let set_a = set.from_list([0, 1, 2, 5, 6, 8, 9])
let set_b = set.from_list([0, 2, 3, 4, 5, 7, 9])
metrics.sorensen_dice_coefficient(set_a, set_b)
|> should.equal(2.0 *. 4.0 /. { 7.0 +. 7.0 })
let set_c = set.from_list([0, 1, 2, 3, 4, 5])
let set_d = set.from_list([6, 7, 8, 9, 10])
metrics.sorensen_dice_coefficient(set_c, set_d)
|> should.equal(2.0 *. 0.0 /. { 6.0 +. 5.0 })
let set_e = set.from_list(["cat", "dog", "hippo", "monkey"])
let set_f = set.from_list(["monkey", "rhino", "ostrich", "salmon", "spider"])
metrics.sorensen_dice_coefficient(set_e, set_f)
|> should.equal(2.0 *. 1.0 /. { 4.0 +. 5.0 })
}
pub fn overlap_coefficient_test() {
metrics.overlap_coefficient(set.from_list([]), set.from_list([]))
|> should.equal(0.0)
let set_a = set.from_list([0, 1, 2, 5, 6, 8, 9])
let set_b = set.from_list([0, 2, 3, 4, 5, 7, 9])
metrics.overlap_coefficient(set_a, set_b)
|> should.equal(4.0 /. 7.0)
let set_c = set.from_list([0, 1, 2, 3, 4, 5])
let set_d = set.from_list([6, 7, 8, 9, 10])
metrics.overlap_coefficient(set_c, set_d)
|> should.equal(0.0 /. 5.0)
let set_e = set.from_list(["horse", "dog", "hippo", "monkey", "bird"])
let set_f = set.from_list(["monkey", "bird", "ostrich", "salmon"])
metrics.overlap_coefficient(set_e, set_f)
|> should.equal(2.0 /. 4.0)
}
pub fn cosine_similarity_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Empty lists returns an error
metrics.cosine_similarity([], [], option.None)
|> should.be_error()
// One empty list returns an error
metrics.cosine_similarity([1.0, 2.0, 3.0], [], option.None)
|> should.be_error()
// One empty list returns an error
metrics.cosine_similarity([], [1.0, 2.0, 3.0], option.None)
|> should.be_error()
// Different sized lists returns an error
metrics.cosine_similarity([1.0, 2.0], [1.0, 2.0, 3.0, 4.0], option.None)
|> should.be_error()
// Two orthogonal vectors (represented by lists)
metrics.cosine_similarity([-1.0, 1.0, 0.0], [1.0, 1.0, -1.0], option.None)
|> should.equal(Ok(0.0))
// Two identical (parallel) vectors (represented by lists)
metrics.cosine_similarity([1.0, 2.0, 3.0], [1.0, 2.0, 3.0], option.None)
|> should.equal(Ok(1.0))
// Two parallel, but oppositely oriented vectors (represented by lists)
metrics.cosine_similarity([-1.0, -2.0, -3.0], [1.0, 2.0, 3.0], option.None)
|> should.equal(Ok(-1.0))
// Try with arbitrary valid input
let assert Ok(result) =
metrics.cosine_similarity([1.0, 2.0, 3.0], [4.0, 5.0, 6.0], option.None)
result
|> predicates.is_close(0.9746318461970762, 0.0, tol)
|> should.be_true()
// Try valid input with weights
let assert Ok(result) =
metrics.cosine_similarity(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([1.0, 1.0, 1.0]),
)
result
|> predicates.is_close(0.9746318461970762, 0.0, tol)
|> should.be_true()
// Try with different weights
let assert Ok(result) =
metrics.cosine_similarity(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([1.0, 2.0, 3.0]),
)
result
|> predicates.is_close(0.9855274566525745, 0.0, tol)
|> should.be_true()
// Try invalid input with weights (different sized lists returns an error)
metrics.cosine_similarity(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([7.0, 8.0]),
)
|> should.be_error()
// Try invalid input with weights that are negative
metrics.cosine_similarity(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([-7.0, -8.0, -9.0]),
)
|> should.be_error()
}
pub fn chebyshev_distance_test() {
// Empty lists returns an error
metrics.chebyshev_distance([], [])
|> should.be_error()
// One empty list returns an error
metrics.chebyshev_distance([1.0, 2.0, 3.0], [])
|> should.be_error()
// One empty list returns an error
metrics.chebyshev_distance([], [1.0, 2.0, 3.0])
|> should.be_error()
// Different sized lists returns an error
metrics.chebyshev_distance([1.0, 2.0], [1.0, 2.0, 3.0, 4.0])
|> should.be_error()
// Try different types of valid input
metrics.chebyshev_distance([1.0, 0.0], [0.0, 2.0])
|> should.equal(Ok(2.0))
metrics.chebyshev_distance([1.0, 0.0], [2.0, 0.0])
|> should.equal(Ok(1.0))
metrics.chebyshev_distance([1.0, 0.0], [-2.0, 0.0])
|> should.equal(Ok(3.0))
metrics.chebyshev_distance([-5.0, -10.0, -3.0], [-1.0, -12.0, -3.0])
|> should.equal(Ok(4.0))
metrics.chebyshev_distance([1.0, 2.0, 3.0], [1.0, 2.0, 3.0])
|> should.equal(Ok(0.0))
}
pub fn canberra_distance_test() {
// Empty lists returns an error
metrics.canberra_distance([], [], option.None)
|> should.be_error()
// One empty list returns an error
metrics.canberra_distance([1.0, 2.0, 3.0], [], option.None)
|> should.be_error()
// One empty list returns an error
metrics.canberra_distance([], [1.0, 2.0, 3.0], option.None)
|> should.be_error()
// Different sized lists returns an error
metrics.canberra_distance([1.0, 2.0], [1.0, 2.0, 3.0, 4.0], option.None)
|> should.be_error()
// Try different types of valid input
metrics.canberra_distance([0.0, 0.0], [0.0, 0.0], option.None)
|> should.equal(Ok(0.0))
metrics.canberra_distance([1.0, 2.0], [-2.0, -1.0], option.None)
|> should.equal(Ok(2.0))
metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.None)
|> should.equal(Ok(2.0))
metrics.canberra_distance([1.0, 0.0], [2.0, 0.0], option.None)
|> should.equal(Ok(1.0 /. 3.0))
metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.Some([1.0, 1.0]))
|> should.equal(Ok(2.0))
metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.Some([1.0, 0.5]))
|> should.equal(Ok(1.5))
metrics.canberra_distance([1.0, 0.0], [0.0, 2.0], option.Some([0.5, 0.5]))
|> should.equal(Ok(1.0))
// Different sized lists (weights) returns an error
metrics.canberra_distance(
[1.0, 2.0, 3.0],
[1.0, 2.0, 3.0],
option.Some([1.0]),
)
|> should.be_error()
// Try invalid input with weights that are negative
metrics.canberra_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([-7.0, -8.0, -9.0]),
)
|> should.be_error()
}
pub fn braycurtis_distance_test() {
// Empty lists returns an error
metrics.braycurtis_distance([], [], option.None)
|> should.be_error()
// One empty list returns an error
metrics.braycurtis_distance([1.0, 2.0, 3.0], [], option.None)
|> should.be_error()
// One empty list returns an error
metrics.braycurtis_distance([], [1.0, 2.0, 3.0], option.None)
|> should.be_error()
// Different sized lists returns an error
metrics.braycurtis_distance([1.0, 2.0], [1.0, 2.0, 3.0, 4.0], option.None)
|> should.be_error()
// Try different types of valid input
metrics.braycurtis_distance([0.0, 0.0], [0.0, 0.0], option.None)
|> should.equal(Ok(0.0))
metrics.braycurtis_distance([1.0, 2.0], [-2.0, -1.0], option.None)
|> should.equal(Ok(3.0))
metrics.braycurtis_distance([1.0, 0.0], [0.0, 2.0], option.None)
|> should.equal(Ok(1.0))
metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.None)
|> should.equal(Ok(0.4))
metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.Some([1.0, 1.0]))
|> should.equal(Ok(0.4))
metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.Some([0.5, 1.0]))
|> should.equal(Ok(0.375))
metrics.braycurtis_distance([1.0, 2.0], [3.0, 4.0], option.Some([0.25, 0.25]))
|> should.equal(Ok(0.4))
// Different sized lists (weights) returns an error
metrics.braycurtis_distance(
[1.0, 2.0, 3.0],
[1.0, 2.0, 3.0],
option.Some([1.0]),
)
|> should.be_error()
// Try invalid input with weights that are negative
metrics.braycurtis_distance(
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
option.Some([-7.0, -8.0, -9.0]),
)
|> should.be_error()
}

753
test/gleam_community/maths/piecewise_test.gleam
View file

@ -1,753 +0,0 @@
import gleam/float
import gleam/int
import gleam/option
import gleam_community/maths/piecewise
import gleeunit/should
pub fn float_ceiling_test() {
// Round 3. digit AFTER decimal point
piecewise.ceiling(12.0654, option.Some(3))
|> should.equal(12.066)
// Round 2. digit AFTER decimal point
piecewise.ceiling(12.0654, option.Some(2))
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
piecewise.ceiling(12.0654, option.Some(1))
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
piecewise.ceiling(12.0654, option.Some(0))
|> should.equal(13.0)
// Round 1. digit BEFORE decimal point
piecewise.ceiling(12.0654, option.Some(-1))
|> should.equal(20.0)
// Round 2. digit BEFORE decimal point
piecewise.ceiling(12.0654, option.Some(-2))
|> should.equal(100.0)
// Round 3. digit BEFORE decimal point
piecewise.ceiling(12.0654, option.Some(-3))
|> should.equal(1000.0)
}
pub fn float_floor_test() {
// Round 3. digit AFTER decimal point
piecewise.floor(12.0654, option.Some(3))
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
piecewise.floor(12.0654, option.Some(2))
|> should.equal(12.06)
// Round 1. digit AFTER decimal point
piecewise.floor(12.0654, option.Some(1))
|> should.equal(12.0)
// Round 0. digit BEFORE decimal point
piecewise.floor(12.0654, option.Some(0))
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
piecewise.floor(12.0654, option.Some(-1))
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
piecewise.floor(12.0654, option.Some(-2))
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
piecewise.floor(12.0654, option.Some(-3))
|> should.equal(0.0)
}
pub fn float_truncate_test() {
// Round 3. digit AFTER decimal point
piecewise.truncate(12.0654, option.Some(3))
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
piecewise.truncate(12.0654, option.Some(2))
|> should.equal(12.06)
// Round 1. digit AFTER decimal point
piecewise.truncate(12.0654, option.Some(1))
|> should.equal(12.0)
// Round 0. digit BEFORE decimal point
piecewise.truncate(12.0654, option.Some(0))
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
piecewise.truncate(12.0654, option.Some(-1))
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
piecewise.truncate(12.0654, option.Some(-2))
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
piecewise.truncate(12.0654, option.Some(-3))
|> should.equal(0.0)
}
pub fn math_round_to_nearest_test() {
// Try with positive values
piecewise.round(1.5, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(2.0)
piecewise.round(1.75, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(2.0)
piecewise.round(2.0, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(2.0)
piecewise.round(3.5, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(4.0)
piecewise.round(4.5, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(4.0)
// Try with negative values
piecewise.round(-3.5, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(-4.0)
piecewise.round(-4.5, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(-4.0)
// Round 3. digit AFTER decimal point
piecewise.round(12.0654, option.Some(3), option.Some(piecewise.RoundNearest))
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
piecewise.round(12.0654, option.Some(2), option.Some(piecewise.RoundNearest))
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
piecewise.round(12.0654, option.Some(1), option.Some(piecewise.RoundNearest))
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(0), option.Some(piecewise.RoundNearest))
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(-1), option.Some(piecewise.RoundNearest))
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(-2), option.Some(piecewise.RoundNearest))
|> should.equal(0.0)
// Round 3. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(-3), option.Some(piecewise.RoundNearest))
|> should.equal(0.0)
}
pub fn math_round_up_test() {
// Note: Rounding mode "RoundUp" is an alias for the ceiling function
// Try with positive values
piecewise.round(0.45, option.Some(0), option.Some(piecewise.RoundUp))
|> should.equal(1.0)
piecewise.round(0.5, option.Some(0), option.Some(piecewise.RoundUp))
|> should.equal(1.0)
piecewise.round(0.45, option.Some(1), option.Some(piecewise.RoundUp))
|> should.equal(0.5)
piecewise.round(0.5, option.Some(1), option.Some(piecewise.RoundUp))
|> should.equal(0.5)
piecewise.round(0.455, option.Some(2), option.Some(piecewise.RoundUp))
|> should.equal(0.46)
piecewise.round(0.505, option.Some(2), option.Some(piecewise.RoundUp))
|> should.equal(0.51)
// Try with negative values
piecewise.round(-0.45, option.Some(0), option.Some(piecewise.RoundUp))
|> should.equal(-0.0)
piecewise.round(-0.5, option.Some(0), option.Some(piecewise.RoundUp))
|> should.equal(-0.0)
piecewise.round(-0.45, option.Some(1), option.Some(piecewise.RoundUp))
|> should.equal(-0.4)
piecewise.round(-0.5, option.Some(1), option.Some(piecewise.RoundUp))
|> should.equal(-0.5)
piecewise.round(-0.455, option.Some(2), option.Some(piecewise.RoundUp))
|> should.equal(-0.45)
piecewise.round(-0.505, option.Some(2), option.Some(piecewise.RoundUp))
|> should.equal(-0.5)
}
pub fn math_round_down_test() {
// Note: Rounding mode "RoundDown" is an alias for the floor function
// Try with positive values
piecewise.round(0.45, option.Some(0), option.Some(piecewise.RoundDown))
|> should.equal(0.0)
piecewise.round(0.5, option.Some(0), option.Some(piecewise.RoundDown))
|> should.equal(0.0)
piecewise.round(0.45, option.Some(1), option.Some(piecewise.RoundDown))
|> should.equal(0.4)
piecewise.round(0.5, option.Some(1), option.Some(piecewise.RoundDown))
|> should.equal(0.5)
piecewise.round(0.455, option.Some(2), option.Some(piecewise.RoundDown))
|> should.equal(0.45)
piecewise.round(0.505, option.Some(2), option.Some(piecewise.RoundDown))
|> should.equal(0.5)
// Try with negative values
piecewise.round(-0.45, option.Some(0), option.Some(piecewise.RoundDown))
|> should.equal(-1.0)
piecewise.round(-0.5, option.Some(0), option.Some(piecewise.RoundDown))
|> should.equal(-1.0)
piecewise.round(-0.45, option.Some(1), option.Some(piecewise.RoundDown))
|> should.equal(-0.5)
piecewise.round(-0.5, option.Some(1), option.Some(piecewise.RoundDown))
|> should.equal(-0.5)
piecewise.round(-0.455, option.Some(2), option.Some(piecewise.RoundDown))
|> should.equal(-0.46)
piecewise.round(-0.505, option.Some(2), option.Some(piecewise.RoundDown))
|> should.equal(-0.51)
}
pub fn math_round_to_zero_test() {
// Note: Rounding mode "RoundToZero" is an alias for the truncate function
// Try with positive values
piecewise.round(0.5, option.Some(0), option.Some(piecewise.RoundToZero))
|> should.equal(0.0)
piecewise.round(0.75, option.Some(0), option.Some(piecewise.RoundToZero))
|> should.equal(0.0)
piecewise.round(0.45, option.Some(1), option.Some(piecewise.RoundToZero))
|> should.equal(0.4)
piecewise.round(0.57, option.Some(1), option.Some(piecewise.RoundToZero))
|> should.equal(0.5)
piecewise.round(0.4575, option.Some(2), option.Some(piecewise.RoundToZero))
|> should.equal(0.45)
piecewise.round(0.5075, option.Some(2), option.Some(piecewise.RoundToZero))
|> should.equal(0.5)
// Try with negative values
piecewise.round(-0.5, option.Some(0), option.Some(piecewise.RoundToZero))
|> should.equal(0.0)
piecewise.round(-0.75, option.Some(0), option.Some(piecewise.RoundToZero))
|> should.equal(0.0)
piecewise.round(-0.45, option.Some(1), option.Some(piecewise.RoundToZero))
|> should.equal(-0.4)
piecewise.round(-0.57, option.Some(1), option.Some(piecewise.RoundToZero))
|> should.equal(-0.5)
piecewise.round(-0.4575, option.Some(2), option.Some(piecewise.RoundToZero))
|> should.equal(-0.45)
piecewise.round(-0.5075, option.Some(2), option.Some(piecewise.RoundToZero))
|> should.equal(-0.5)
}
pub fn math_round_ties_away_test() {
// Try with positive values
piecewise.round(1.4, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(1.0)
piecewise.round(1.5, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(2.0)
piecewise.round(2.5, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(3.0)
// Try with negative values
piecewise.round(-1.4, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(-1.0)
piecewise.round(-1.5, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(-2.0)
piecewise.round(-2.0, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(-2.0)
piecewise.round(-2.5, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(-3.0)
// Round 3. digit AFTER decimal point
piecewise.round(12.0654, option.Some(3), option.Some(piecewise.RoundTiesAway))
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
piecewise.round(12.0654, option.Some(2), option.Some(piecewise.RoundTiesAway))
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
piecewise.round(12.0654, option.Some(1), option.Some(piecewise.RoundTiesAway))
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(0), option.Some(piecewise.RoundTiesAway))
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
piecewise.round(
12.0654,
option.Some(-1),
option.Some(piecewise.RoundTiesAway),
)
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
piecewise.round(
12.0654,
option.Some(-2),
option.Some(piecewise.RoundTiesAway),
)
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
piecewise.round(
12.0654,
option.Some(-3),
option.Some(piecewise.RoundTiesAway),
)
|> should.equal(0.0)
}
pub fn math_round_ties_up_test() {
// Try with positive values
piecewise.round(1.4, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(1.0)
piecewise.round(1.5, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(2.0)
piecewise.round(2.5, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(3.0)
// Try with negative values
piecewise.round(-1.4, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(-1.0)
piecewise.round(-1.5, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(-1.0)
piecewise.round(-2.0, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(-2.0)
piecewise.round(-2.5, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(-2.0)
// Round 3. digit AFTER decimal point
piecewise.round(12.0654, option.Some(3), option.Some(piecewise.RoundTiesUp))
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
piecewise.round(12.0654, option.Some(2), option.Some(piecewise.RoundTiesUp))
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
piecewise.round(12.0654, option.Some(1), option.Some(piecewise.RoundTiesUp))
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(0), option.Some(piecewise.RoundTiesUp))
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(-1), option.Some(piecewise.RoundTiesUp))
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(-2), option.Some(piecewise.RoundTiesUp))
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
piecewise.round(12.0654, option.Some(-3), option.Some(piecewise.RoundTiesUp))
|> should.equal(0.0)
}
pub fn math_round_edge_cases_test() {
// The default number of digits is 0 if None is provided
piecewise.round(12.0654, option.None, option.Some(piecewise.RoundNearest))
|> should.equal(12.0)
// The default rounding mode is piecewise.RoundNearest if None is provided
piecewise.round(12.0654, option.None, option.None)
|> should.equal(12.0)
}
pub fn float_absolute_value_test() {
piecewise.float_absolute_value(20.0)
|> should.equal(20.0)
piecewise.float_absolute_value(-20.0)
|> should.equal(20.0)
}
pub fn int_absolute_value_test() {
piecewise.int_absolute_value(20)
|> should.equal(20)
piecewise.int_absolute_value(-20)
|> should.equal(20)
}
pub fn float_absolute_difference_test() {
piecewise.float_absolute_difference(20.0, 15.0)
|> should.equal(5.0)
piecewise.float_absolute_difference(-20.0, -15.0)
|> should.equal(5.0)
piecewise.float_absolute_difference(20.0, -15.0)
|> should.equal(35.0)
piecewise.float_absolute_difference(-20.0, 15.0)
|> should.equal(35.0)
piecewise.float_absolute_difference(0.0, 0.0)
|> should.equal(0.0)
piecewise.float_absolute_difference(1.0, 2.0)
|> should.equal(1.0)
piecewise.float_absolute_difference(2.0, 1.0)
|> should.equal(1.0)
piecewise.float_absolute_difference(-1.0, 0.0)
|> should.equal(1.0)
piecewise.float_absolute_difference(0.0, -1.0)
|> should.equal(1.0)
piecewise.float_absolute_difference(10.0, 20.0)
|> should.equal(10.0)
piecewise.float_absolute_difference(-10.0, -20.0)
|> should.equal(10.0)
piecewise.float_absolute_difference(-10.5, 10.5)
|> should.equal(21.0)
}
pub fn int_absolute_difference_test() {
piecewise.int_absolute_difference(20, 15)
|> should.equal(5)
piecewise.int_absolute_difference(-20, -15)
|> should.equal(5)
piecewise.int_absolute_difference(20, -15)
|> should.equal(35)
piecewise.int_absolute_difference(-20, 15)
|> should.equal(35)
}
pub fn float_sign_test() {
piecewise.float_sign(100.0)
|> should.equal(1.0)
piecewise.float_sign(0.0)
|> should.equal(0.0)
piecewise.float_sign(-100.0)
|> should.equal(-1.0)
}
pub fn float_flip_sign_test() {
piecewise.float_flip_sign(100.0)
|> should.equal(-100.0)
piecewise.float_flip_sign(0.0)
|> should.equal(-0.0)
piecewise.float_flip_sign(-100.0)
|> should.equal(100.0)
}
pub fn float_copy_sign_test() {
piecewise.float_copy_sign(100.0, 10.0)
|> should.equal(100.0)
piecewise.float_copy_sign(-100.0, 10.0)
|> should.equal(100.0)
piecewise.float_copy_sign(100.0, -10.0)
|> should.equal(-100.0)
piecewise.float_copy_sign(-100.0, -10.0)
|> should.equal(-100.0)
}
pub fn int_sign_test() {
piecewise.int_sign(100)
|> should.equal(1)
piecewise.int_sign(0)
|> should.equal(0)
piecewise.int_sign(-100)
|> should.equal(-1)
}
pub fn int_flip_sign_test() {
piecewise.int_flip_sign(100)
|> should.equal(-100)
piecewise.int_flip_sign(0)
|> should.equal(-0)
piecewise.int_flip_sign(-100)
|> should.equal(100)
}
pub fn int_copy_sign_test() {
piecewise.int_copy_sign(100, 10)
|> should.equal(100)
piecewise.int_copy_sign(-100, 10)
|> should.equal(100)
piecewise.int_copy_sign(100, -10)
|> should.equal(-100)
piecewise.int_copy_sign(-100, -10)
|> should.equal(-100)
}
pub fn float_minimum_test() {
piecewise.minimum(0.75, 0.5, float.compare)
|> should.equal(0.5)
piecewise.minimum(0.5, 0.75, float.compare)
|> should.equal(0.5)
piecewise.minimum(-0.75, 0.5, float.compare)
|> should.equal(-0.75)
piecewise.minimum(-0.75, 0.5, float.compare)
|> should.equal(-0.75)
}
pub fn int_minimum_test() {
piecewise.minimum(75, 50, int.compare)
|> should.equal(50)
piecewise.minimum(50, 75, int.compare)
|> should.equal(50)
piecewise.minimum(-75, 50, int.compare)
|> should.equal(-75)
piecewise.minimum(-75, 50, int.compare)
|> should.equal(-75)
}
pub fn float_maximum_test() {
piecewise.maximum(0.75, 0.5, float.compare)
|> should.equal(0.75)
piecewise.maximum(0.5, 0.75, float.compare)
|> should.equal(0.75)
piecewise.maximum(-0.75, 0.5, float.compare)
|> should.equal(0.5)
piecewise.maximum(-0.75, 0.5, float.compare)
|> should.equal(0.5)
}
pub fn int_maximum_test() {
piecewise.maximum(75, 50, int.compare)
|> should.equal(75)
piecewise.maximum(50, 75, int.compare)
|> should.equal(75)
piecewise.maximum(-75, 50, int.compare)
|> should.equal(50)
piecewise.maximum(-75, 50, int.compare)
|> should.equal(50)
}
pub fn float_minmax_test() {
piecewise.minmax(0.75, 0.5, float.compare)
|> should.equal(#(0.5, 0.75))
piecewise.minmax(0.5, 0.75, float.compare)
|> should.equal(#(0.5, 0.75))
piecewise.minmax(-0.75, 0.5, float.compare)
|> should.equal(#(-0.75, 0.5))
piecewise.minmax(-0.75, 0.5, float.compare)
|> should.equal(#(-0.75, 0.5))
}
pub fn int_minmax_test() {
piecewise.minmax(75, 50, int.compare)
|> should.equal(#(50, 75))
piecewise.minmax(50, 75, int.compare)
|> should.equal(#(50, 75))
piecewise.minmax(-75, 50, int.compare)
|> should.equal(#(-75, 50))
piecewise.minmax(-75, 50, int.compare)
|> should.equal(#(-75, 50))
}
pub fn float_list_minimum_test() {
// An empty lists returns an error
[]
|> piecewise.list_minimum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> piecewise.list_minimum(float.compare)
|> should.equal(Ok(1.5))
}
pub fn int_list_minimum_test() {
// An empty lists returns an error
[]
|> piecewise.list_minimum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> piecewise.list_minimum(int.compare)
|> should.equal(Ok(1))
}
pub fn float_list_maximum_test() {
// An empty lists returns an error
[]
|> piecewise.list_maximum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> piecewise.list_maximum(float.compare)
|> should.equal(Ok(4.5))
}
pub fn int_list_maximum_test() {
// An empty lists returns an error
[]
|> piecewise.list_maximum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> piecewise.list_maximum(int.compare)
|> should.equal(Ok(4))
}
pub fn float_list_arg_maximum_test() {
// An empty lists returns an error
[]
|> piecewise.arg_maximum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> piecewise.arg_maximum(float.compare)
|> should.equal(Ok([0, 1]))
}
pub fn int_list_arg_maximum_test() {
// An empty lists returns an error
[]
|> piecewise.arg_maximum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> piecewise.arg_maximum(int.compare)
|> should.equal(Ok([0, 1]))
}
pub fn float_list_arg_minimum_test() {
// An empty lists returns an error
[]
|> piecewise.arg_minimum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> piecewise.arg_minimum(float.compare)
|> should.equal(Ok([4]))
}
pub fn int_list_arg_minimum_test() {
// An empty lists returns an error
[]
|> piecewise.arg_minimum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> piecewise.arg_minimum(int.compare)
|> should.equal(Ok([4]))
}
pub fn float_list_extrema_test() {
// An empty lists returns an error
[]
|> piecewise.extrema(float.compare)
|> should.be_error()
// Valid input returns a result
[4.0, 4.0, 3.0, 2.0, 1.0]
|> piecewise.extrema(float.compare)
|> should.equal(Ok(#(1.0, 4.0)))
// Valid input returns a result
[1.0, 4.0, 2.0, 5.0, 0.0]
|> piecewise.extrema(float.compare)
|> should.equal(Ok(#(0.0, 5.0)))
}
pub fn int_list_extrema_test() {
// An empty lists returns an error
[]
|> piecewise.extrema(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> piecewise.extrema(int.compare)
|> should.equal(Ok(#(1, 4)))
// Valid input returns a result
[1, 4, 2, 5, 0]
|> piecewise.extrema(int.compare)
|> should.equal(Ok(#(0, 5)))
}

203
test/gleam_community/maths/predicates_test.gleam
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@ -1,203 +0,0 @@
import gleam/list
import gleam_community/maths/predicates
import gleeunit/should
pub fn float_is_close_test() {
let val = 99.0
let ref_val = 100.0
// We set 'atol' and 'rtol' such that the values are equivalent
// if 'val' is within 1 percent of 'ref_val' +/- 0.1
let rtol = 0.01
let atol = 0.1
predicates.is_close(val, ref_val, rtol, atol)
|> should.be_true()
}
pub fn float_list_all_close_test() {
let val = 99.0
let ref_val = 100.0
let xarr = list.repeat(val, 42)
let yarr = list.repeat(ref_val, 42)
// We set 'atol' and 'rtol' such that the values are equivalent
// if 'val' is within 1 percent of 'ref_val' +/- 0.1
let rtol = 0.01
let atol = 0.1
predicates.all_close(xarr, yarr, rtol, atol)
|> fn(zarr: Result(List(Bool), Nil)) -> Result(Bool, Nil) {
case zarr {
Ok(arr) ->
arr
|> list.all(fn(a) { a })
|> Ok
_ ->
Nil
|> Error
}
}
|> should.equal(Ok(True))
}
pub fn float_is_fractional_test() {
predicates.is_fractional(1.5)
|> should.equal(True)
predicates.is_fractional(0.5)
|> should.equal(True)
predicates.is_fractional(0.3333)
|> should.equal(True)
predicates.is_fractional(0.9999)
|> should.equal(True)
predicates.is_fractional(1.0)
|> should.equal(False)
predicates.is_fractional(999.0)
|> should.equal(False)
}
pub fn int_is_power_test() {
predicates.is_power(10, 10)
|> should.equal(True)
predicates.is_power(11, 10)
|> should.equal(False)
predicates.is_power(4, 2)
|> should.equal(True)
predicates.is_power(5, 2)
|> should.equal(False)
predicates.is_power(27, 3)
|> should.equal(True)
predicates.is_power(28, 3)
|> should.equal(False)
}
pub fn int_is_even_test() {
predicates.is_even(0)
|> should.equal(True)
predicates.is_even(2)
|> should.equal(True)
predicates.is_even(12)
|> should.equal(True)
predicates.is_even(5)
|> should.equal(False)
predicates.is_even(-3)
|> should.equal(False)
predicates.is_even(-4)
|> should.equal(True)
}
pub fn int_is_odd_test() {
predicates.is_odd(0)
|> should.equal(False)
predicates.is_odd(3)
|> should.equal(True)
predicates.is_odd(13)
|> should.equal(True)
predicates.is_odd(4)
|> should.equal(False)
predicates.is_odd(-3)
|> should.equal(True)
predicates.is_odd(-4)
|> should.equal(False)
}
pub fn int_is_perfect_test() {
predicates.is_perfect(6)
|> should.equal(True)
predicates.is_perfect(28)
|> should.equal(True)
predicates.is_perfect(496)
|> should.equal(True)
predicates.is_perfect(1)
|> should.equal(False)
predicates.is_perfect(3)
|> should.equal(False)
predicates.is_perfect(13)
|> should.equal(False)
}
pub fn int_is_prime_test() {
// Test a negative integer, i.e., not a natural number
predicates.is_prime(-7)
|> should.equal(False)
predicates.is_prime(1)
|> should.equal(False)
predicates.is_prime(2)
|> should.equal(True)
predicates.is_prime(3)
|> should.equal(True)
predicates.is_prime(5)
|> should.equal(True)
predicates.is_prime(7)
|> should.equal(True)
predicates.is_prime(11)
|> should.equal(True)
predicates.is_prime(42)
|> should.equal(False)
predicates.is_prime(7919)
|> should.equal(True)
// Test 1st Carmichael number
predicates.is_prime(561)
|> should.equal(False)
// Test 2nd Carmichael number
predicates.is_prime(1105)
|> should.equal(False)
}
pub fn is_between_test() {
predicates.is_between(5.5, 5.0, 6.0)
|> should.equal(True)
predicates.is_between(5.0, 5.0, 6.0)
|> should.equal(False)
predicates.is_between(6.0, 5.0, 6.0)
|> should.equal(False)
}
pub fn is_divisible_test() {
predicates.is_divisible(10, 2)
|> should.equal(True)
predicates.is_divisible(7, 3)
|> should.equal(False)
}
pub fn is_multiple_test() {
predicates.is_multiple(15, 5)
|> should.equal(True)
predicates.is_multiple(14, 5)
|> should.equal(False)
}

328
test/gleam_community/maths/sequences_test.gleam
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@ -1,328 +0,0 @@
import gleam/iterator
import gleam/list
import gleam_community/maths/elementary
import gleam_community/maths/predicates
import gleam_community/maths/sequences
import gleeunit/should
pub fn float_list_linear_space_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
// ---> With endpoint included
let assert Ok(linspace) = sequences.linear_space(10.0, 50.0, 5, True)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[10.0, 20.0, 30.0, 40.0, 50.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = sequences.linear_space(10.0, 20.0, 5, True)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[10.0, 12.5, 15.0, 17.5, 20.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Try with negative stop
// ----> Without endpoint included
let assert Ok(linspace) = sequences.linear_space(10.0, 50.0, 5, False)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[10.0, 18.0, 26.0, 34.0, 42.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = sequences.linear_space(10.0, 20.0, 5, False)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[10.0, 12.0, 14.0, 16.0, 18.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Try with negative stop
let assert Ok(linspace) = sequences.linear_space(10.0, -50.0, 5, False)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[10.0, -2.0, -14.0, -26.0, -38.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = sequences.linear_space(10.0, -20.0, 5, True)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[10.0, 2.5, -5.0, -12.5, -20.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Try with negative start
let assert Ok(linspace) = sequences.linear_space(-10.0, 50.0, 5, False)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[-10.0, 2.0, 14.0, 26.0, 38.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = sequences.linear_space(-10.0, 20.0, 5, True)
let assert Ok(result) =
predicates.all_close(
linspace |> iterator.to_list(),
[-10.0, -2.5, 5.0, 12.5, 20.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// A negative number of points does not work (-5)
sequences.linear_space(10.0, 50.0, -5, True)
|> should.be_error()
}
pub fn float_list_logarithmic_space_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
// ---> With endpoint included
// - Positive start, stop, base
let assert Ok(logspace) = sequences.logarithmic_space(1.0, 3.0, 3, True, 10.0)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[10.0, 100.0, 1000.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, stop, negative base
let assert Ok(logspace) =
sequences.logarithmic_space(1.0, 3.0, 3, True, -10.0)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[-10.0, 100.0, -1000.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, negative stop, base
let assert Ok(logspace) =
sequences.logarithmic_space(1.0, -3.0, 3, True, -10.0)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[-10.0, -0.1, -0.001],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, base, negative stop
let assert Ok(logspace) =
sequences.logarithmic_space(1.0, -3.0, 3, True, 10.0)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[10.0, 0.1, 0.001],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive stop, base, negative start
let assert Ok(logspace) =
sequences.logarithmic_space(-1.0, 3.0, 3, True, 10.0)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[0.1, 10.0, 1000.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// ----> Without endpoint included
// - Positive start, stop, base
let assert Ok(logspace) =
sequences.logarithmic_space(1.0, 3.0, 3, False, 10.0)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[10.0, 46.41588834, 215.443469],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// A negative number of points does not work (-3)
sequences.logarithmic_space(1.0, 3.0, -3, True, 10.0)
|> should.be_error()
}
pub fn float_list_geometric_space_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
// ---> With endpoint included
// - Positive start, stop
let assert Ok(logspace) = sequences.geometric_space(10.0, 1000.0, 3, True)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[10.0, 100.0, 1000.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, negative stop
let assert Ok(logspace) = sequences.geometric_space(10.0, 0.001, 3, True)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[10.0, 0.1, 0.001],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive stop, negative start
let assert Ok(logspace) = sequences.geometric_space(0.1, 1000.0, 3, True)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[0.1, 10.0, 1000.0],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// ----> Without endpoint included
// - Positive start, stop
let assert Ok(logspace) = sequences.geometric_space(10.0, 1000.0, 3, False)
let assert Ok(result) =
predicates.all_close(
logspace |> iterator.to_list(),
[10.0, 46.41588834, 215.443469],
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Test invalid input (start and stop can't be equal to 0.0)
sequences.geometric_space(0.0, 1000.0, 3, False)
|> should.be_error()
sequences.geometric_space(-1000.0, 0.0, 3, False)
|> should.be_error()
// A negative number of points does not work
sequences.geometric_space(-1000.0, 0.0, -3, False)
|> should.be_error()
}
pub fn float_list_arange_test() {
// Positive start, stop, step
sequences.arange(1.0, 5.0, 1.0)
|> iterator.to_list()
|> should.equal([1.0, 2.0, 3.0, 4.0])
sequences.arange(1.0, 5.0, 0.5)
|> iterator.to_list()
|> should.equal([1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5])
sequences.arange(1.0, 2.0, 0.25)
|> iterator.to_list()
|> should.equal([1.0, 1.25, 1.5, 1.75])
// Reverse (switch start/stop largest/smallest value)
sequences.arange(5.0, 1.0, 1.0)
|> iterator.to_list()
|> should.equal([])
// Reverse negative step
sequences.arange(5.0, 1.0, -1.0)
|> iterator.to_list()
|> should.equal([5.0, 4.0, 3.0, 2.0])
// Positive start, negative stop, step
sequences.arange(5.0, -1.0, -1.0)
|> iterator.to_list()
|> should.equal([5.0, 4.0, 3.0, 2.0, 1.0, 0.0])
// Negative start, stop, step
sequences.arange(-5.0, -1.0, -1.0)
|> iterator.to_list()
|> should.equal([])
// Negative start, stop, positive step
sequences.arange(-5.0, -1.0, 1.0)
|> iterator.to_list()
|> should.equal([-5.0, -4.0, -3.0, -2.0])
}

114
test/gleam_community/maths/special_test.gleam
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@ -1,114 +0,0 @@
import gleam/result
import gleam_community/maths/elementary
import gleam_community/maths/predicates
import gleam_community/maths/special
import gleeunit/should
pub fn float_beta_function_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Valid input returns a result
special.beta(-0.5, 0.5)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
special.beta(0.5, 0.5)
|> predicates.is_close(3.1415926535897927, 0.0, tol)
|> should.be_true()
special.beta(0.5, -0.5)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
special.beta(5.0, 5.0)
|> predicates.is_close(0.0015873015873015873, 0.0, tol)
|> should.be_true()
}
pub fn float_error_function_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Valid input returns a result
special.erf(-0.5)
|> predicates.is_close(-0.5204998778130465, 0.0, tol)
|> should.be_true()
special.erf(0.5)
|> predicates.is_close(0.5204998778130465, 0.0, tol)
|> should.be_true()
special.erf(1.0)
|> predicates.is_close(0.8427007929497148, 0.0, tol)
|> should.be_true()
special.erf(2.0)
|> predicates.is_close(0.9953222650189527, 0.0, tol)
|> should.be_true()
special.erf(10.0)
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
}
pub fn float_gamma_function_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Valid input returns a result
special.gamma(-0.5)
|> predicates.is_close(-3.5449077018110318, 0.0, tol)
|> should.be_true()
special.gamma(0.5)
|> predicates.is_close(1.7724538509055159, 0.0, tol)
|> should.be_true()
special.gamma(1.0)
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
special.gamma(2.0)
|> predicates.is_close(1.0, 0.0, tol)
|> should.be_true()
special.gamma(3.0)
|> predicates.is_close(2.0, 0.0, tol)
|> should.be_true()
special.gamma(10.0)
|> predicates.is_close(362_880.0, 0.0, tol)
|> should.be_true()
}
pub fn float_incomplete_gamma_function_test() {
let assert Ok(tol) = elementary.power(10.0, -6.0)
// Invalid input gives an error
// 1st arg is invalid
special.incomplete_gamma(-1.0, 1.0)
|> should.be_error()
// 2nd arg is invalid
special.incomplete_gamma(1.0, -1.0)
|> should.be_error()
// Valid input returns a result
special.incomplete_gamma(1.0, 0.0)
|> result.unwrap(-999.0)
|> predicates.is_close(0.0, 0.0, tol)
|> should.be_true()
special.incomplete_gamma(1.0, 2.0)
|> result.unwrap(-999.0)
|> predicates.is_close(0.864664716763387308106, 0.0, tol)
|> should.be_true()
special.incomplete_gamma(2.0, 3.0)
|> result.unwrap(-999.0)
|> predicates.is_close(0.8008517265285442280826, 0.0, tol)
|> should.be_true()
special.incomplete_gamma(3.0, 4.0)
|> result.unwrap(-999.0)
|> predicates.is_close(1.523793388892911312363, 0.0, tol)
|> should.be_true()
}

549
test/gleam_community/metrics_test.gleam Normal file
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import gleam/float
import gleam/set
import gleam_community/maths
import gleeunit/should
pub fn float_list_norm_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// An empty lists returns 0.0
[]
|> maths.norm(1.0)
|> should.equal(Ok(0.0))
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) =
[1.0, 1.0, 1.0]
|> maths.norm(1.0)
result
|> maths.is_close(3.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[1.0, 1.0, 1.0]
|> maths.norm(-1.0)
result
|> maths.is_close(0.3333333333333333, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -1.0, -1.0]
|> maths.norm(-1.0)
result
|> maths.is_close(0.3333333333333333, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -1.0, -1.0]
|> maths.norm(1.0)
result
|> maths.is_close(3.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -2.0, -3.0]
|> maths.norm(-10.0)
result
|> maths.is_close(0.9999007044905545, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -2.0, -3.0]
|> maths.norm(-100.0)
result
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[-1.0, -2.0, -3.0]
|> maths.norm(2.0)
result
|> maths.is_close(3.7416573867739413, 0.0, tol)
|> should.be_true()
}
pub fn float_list_norm_with_weights_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// An empty lists returns 0.0
[]
|> maths.norm_with_weights(1.0)
|> should.equal(Ok(0.0))
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) =
[#(1.0, 1.0), #(1.0, 1.0), #(1.0, 1.0)]
|> maths.norm_with_weights(1.0)
result
|> maths.is_close(3.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[#(1.0, 0.5), #(1.0, 0.5), #(1.0, 0.5)]
|> maths.norm_with_weights(1.0)
result
|> maths.is_close(1.5, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
[#(1.0, 0.5), #(2.0, 0.5), #(3.0, 0.5)]
|> maths.norm_with_weights(2.0)
result
|> maths.is_close(2.6457513110645907, 0.0, tol)
|> should.be_true()
}
pub fn float_list_manhattan_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Try with valid input (same as Minkowski distance with p = 1)
let assert Ok(result) = maths.manhattan_distance([#(0.0, 1.0), #(0.0, 2.0)])
result
|> maths.is_close(3.0, 0.0, tol)
|> should.be_true()
maths.manhattan_distance([#(1.0, 4.0), #(2.0, 5.0), #(3.0, 6.0)])
|> should.equal(Ok(9.0))
maths.manhattan_distance([#(1.0, 2.0), #(2.0, 3.0)])
|> should.equal(Ok(2.0))
maths.manhattan_distance_with_weights([#(1.0, 2.0, 0.5), #(2.0, 3.0, 1.0)])
|> should.equal(Ok(1.5))
maths.manhattan_distance_with_weights([
#(1.0, 4.0, 1.0),
#(2.0, 5.0, 1.0),
#(3.0, 6.0, 1.0),
])
|> should.equal(Ok(9.0))
maths.manhattan_distance_with_weights([
#(1.0, 4.0, 1.0),
#(2.0, 5.0, 2.0),
#(3.0, 6.0, 3.0),
])
|> should.equal(Ok(18.0))
maths.manhattan_distance_with_weights([
#(1.0, 4.0, -7.0),
#(2.0, 5.0, -8.0),
#(3.0, 6.0, -9.0),
])
|> should.be_error()
}
pub fn float_list_minkowski_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Test order < 1
maths.minkowski_distance([#(0.0, 0.0), #(0.0, 0.0)], -1.0)
|> should.be_error()
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(result) =
maths.minkowski_distance([#(1.0, 1.0), #(1.0, 1.0)], 1.0)
result
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.minkowski_distance([#(0.0, 1.0), #(0.0, 1.0)], 10.0)
result
|> maths.is_close(1.0717734625362931, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.minkowski_distance([#(0.0, 1.0), #(0.0, 1.0)], 100.0)
result
|> maths.is_close(1.0069555500567189, 0.0, tol)
|> should.be_true()
// Euclidean distance (p = 2)
let assert Ok(result) =
maths.minkowski_distance([#(0.0, 1.0), #(0.0, 2.0)], 2.0)
result
|> maths.is_close(2.23606797749979, 0.0, tol)
|> should.be_true()
// Manhattan distance (p = 1)
let assert Ok(result) =
maths.minkowski_distance([#(0.0, 1.0), #(0.0, 2.0)], 1.0)
result
|> maths.is_close(3.0, 0.0, tol)
|> should.be_true()
// Try different valid input
let assert Ok(result) =
maths.minkowski_distance([#(1.0, 4.0), #(2.0, 5.0), #(3.0, 6.0)], 4.0)
result
|> maths.is_close(3.9482220388574776, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.minkowski_distance_with_weights(
[#(1.0, 4.0, 1.0), #(2.0, 5.0, 1.0), #(3.0, 6.0, 1.0)],
4.0,
)
result
|> maths.is_close(3.9482220388574776, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.minkowski_distance_with_weights(
[#(1.0, 4.0, 1.0), #(2.0, 5.0, 2.0), #(3.0, 6.0, 3.0)],
4.0,
)
result
|> maths.is_close(4.6952537402198615, 0.0, tol)
|> should.be_true()
// Try invalid input with weights that are negative
maths.minkowski_distance_with_weights(
[#(1.0, 4.0, -7.0), #(2.0, 5.0, -8.0), #(3.0, 6.0, -9.0)],
2.0,
)
|> should.be_error()
}
pub fn float_list_euclidean_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Empty lists returns an error
maths.euclidean_distance([])
|> should.be_error()
// Try with valid input (same as Minkowski distance with p = 2)
let assert Ok(result) = maths.euclidean_distance([#(0.0, 1.0), #(0.0, 2.0)])
result
|> maths.is_close(2.23606797749979, 0.0, tol)
|> should.be_true()
// Try different valid input
let assert Ok(result) =
maths.euclidean_distance([#(1.0, 4.0), #(2.0, 5.0), #(3.0, 6.0)])
result
|> maths.is_close(5.196152422706632, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.euclidean_distance_with_weights([
#(1.0, 4.0, 1.0),
#(2.0, 5.0, 1.0),
#(3.0, 6.0, 1.0),
])
result
|> maths.is_close(5.196152422706632, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.euclidean_distance_with_weights([
#(1.0, 4.0, 1.0),
#(2.0, 5.0, 2.0),
#(3.0, 6.0, 3.0),
])
result
|> maths.is_close(7.3484692283495345, 0.0, tol)
|> should.be_true()
// Try invalid input with weights that are negative
maths.euclidean_distance_with_weights([
#(1.0, 4.0, -7.0),
#(2.0, 5.0, -8.0),
#(3.0, 6.0, -9.0),
])
|> should.be_error()
}
pub fn mean_test() {
// An empty list returns an error
[]
|> maths.mean()
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> maths.mean()
|> should.equal(Ok(2.0))
}
pub fn median_test() {
// An empty list returns an error
[]
|> maths.median()
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> maths.median()
|> should.equal(Ok(2.0))
[1.0, 2.0, 3.0, 4.0]
|> maths.median()
|> should.equal(Ok(2.5))
}
pub fn variance_test() {
// Degrees of freedom
let ddof = 1
// An empty list returns an error
[]
|> maths.variance(ddof)
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> maths.variance(ddof)
|> should.equal(Ok(1.0))
}
pub fn standard_deviation_test() {
// Degrees of freedom
let ddof = 1
// An empty list returns an error
[]
|> maths.standard_deviation(ddof)
|> should.be_error()
// Valid input returns a result
[1.0, 2.0, 3.0]
|> maths.standard_deviation(ddof)
|> should.equal(Ok(1.0))
}
pub fn jaccard_index_test() {
maths.jaccard_index(set.from_list([]), set.from_list([]))
|> should.equal(0.0)
let set_a = set.from_list([0, 1, 2, 5, 6, 8, 9])
let set_b = set.from_list([0, 2, 3, 4, 5, 7, 9])
maths.jaccard_index(set_a, set_b)
|> should.equal(4.0 /. 10.0)
let set_c = set.from_list([0, 1, 2, 3, 4, 5])
let set_d = set.from_list([6, 7, 8, 9, 10])
maths.jaccard_index(set_c, set_d)
|> should.equal(0.0 /. 11.0)
let set_e = set.from_list(["cat", "dog", "hippo", "monkey"])
let set_f = set.from_list(["monkey", "rhino", "ostrich", "salmon"])
maths.jaccard_index(set_e, set_f)
|> should.equal(1.0 /. 7.0)
}
pub fn sorensen_dice_coefficient_test() {
maths.sorensen_dice_coefficient(set.from_list([]), set.from_list([]))
|> should.equal(0.0)
let set_a = set.from_list([0, 1, 2, 5, 6, 8, 9])
let set_b = set.from_list([0, 2, 3, 4, 5, 7, 9])
maths.sorensen_dice_coefficient(set_a, set_b)
|> should.equal(2.0 *. 4.0 /. { 7.0 +. 7.0 })
let set_c = set.from_list([0, 1, 2, 3, 4, 5])
let set_d = set.from_list([6, 7, 8, 9, 10])
maths.sorensen_dice_coefficient(set_c, set_d)
|> should.equal(2.0 *. 0.0 /. { 6.0 +. 5.0 })
let set_e = set.from_list(["cat", "dog", "hippo", "monkey"])
let set_f = set.from_list(["monkey", "rhino", "ostrich", "salmon", "spider"])
maths.sorensen_dice_coefficient(set_e, set_f)
|> should.equal(2.0 *. 1.0 /. { 4.0 +. 5.0 })
}
pub fn overlap_coefficient_test() {
maths.overlap_coefficient(set.from_list([]), set.from_list([]))
|> should.equal(0.0)
let set_a = set.from_list([0, 1, 2, 5, 6, 8, 9])
let set_b = set.from_list([0, 2, 3, 4, 5, 7, 9])
maths.overlap_coefficient(set_a, set_b)
|> should.equal(4.0 /. 7.0)
let set_c = set.from_list([0, 1, 2, 3, 4, 5])
let set_d = set.from_list([6, 7, 8, 9, 10])
maths.overlap_coefficient(set_c, set_d)
|> should.equal(0.0 /. 5.0)
let set_e = set.from_list(["horse", "dog", "hippo", "monkey", "bird"])
let set_f = set.from_list(["monkey", "bird", "ostrich", "salmon"])
maths.overlap_coefficient(set_e, set_f)
|> should.equal(2.0 /. 4.0)
}
pub fn cosine_similarity_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Two orthogonal vectors (represented by lists)
maths.cosine_similarity([#(-1.0, 1.0), #(1.0, 1.0), #(0.0, -1.0)])
|> should.equal(Ok(0.0))
// Two identical (parallel) vectors (represented by lists)
maths.cosine_similarity([#(1.0, 1.0), #(2.0, 2.0), #(3.0, 3.0)])
|> should.equal(Ok(1.0))
// Two parallel, but oppositely oriented vectors (represented by lists)
maths.cosine_similarity([#(-1.0, 1.0), #(-2.0, 2.0), #(-3.0, 3.0)])
|> should.equal(Ok(-1.0))
// Try with arbitrary valid input
let assert Ok(result) =
maths.cosine_similarity([#(1.0, 4.0), #(2.0, 5.0), #(3.0, 6.0)])
result
|> maths.is_close(0.9746318461970762, 0.0, tol)
|> should.be_true()
// Try valid input with weights
let assert Ok(result) =
maths.cosine_similarity_with_weights([
#(1.0, 4.0, 1.0),
#(2.0, 5.0, 1.0),
#(3.0, 6.0, 1.0),
])
result
|> maths.is_close(0.9746318461970762, 0.0, tol)
|> should.be_true()
// Try with different weights
let assert Ok(result) =
maths.cosine_similarity_with_weights([
#(1.0, 4.0, 1.0),
#(2.0, 5.0, 2.0),
#(3.0, 6.0, 3.0),
])
result
|> maths.is_close(0.9855274566525745, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.cosine_similarity_with_weights([
#(1.0, 1.0, 2.0),
#(2.0, 2.0, 3.0),
#(3.0, 3.0, 4.0),
])
result
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
let assert Ok(result) =
maths.cosine_similarity_with_weights([
#(-1.0, 1.0, 1.0),
#(-2.0, 2.0, 0.5),
#(-3.0, 3.0, 0.33),
])
result
|> maths.is_close(-1.0, 0.0, tol)
|> should.be_true()
// Try invalid input with weights that are negative
maths.cosine_similarity_with_weights([
#(1.0, 4.0, -7.0),
#(2.0, 5.0, -8.0),
#(3.0, 6.0, -9.0),
])
|> should.be_error()
}
pub fn chebyshev_distance_test() {
// Empty lists returns an error
maths.chebyshev_distance([])
|> should.be_error()
// Try different types of valid input
maths.chebyshev_distance([#(1.0, 0.0), #(0.0, 2.0)])
|> should.equal(Ok(2.0))
maths.chebyshev_distance([#(1.0, 2.0), #(0.0, 0.0)])
|> should.equal(Ok(1.0))
maths.chebyshev_distance([#(1.0, -2.0), #(0.0, 0.0)])
|> should.equal(Ok(3.0))
maths.chebyshev_distance([#(-5.0, -1.0), #(-10.0, -12.0), #(-3.0, -3.0)])
|> should.equal(Ok(4.0))
maths.chebyshev_distance([#(1.0, 1.0), #(2.0, 2.0), #(3.0, 3.0)])
|> should.equal(Ok(0.0))
maths.chebyshev_distance_with_weights([
#(-5.0, -1.0, 0.5),
#(-10.0, -12.0, 1.0),
#(-3.0, -3.0, 1.0),
])
|> should.equal(Ok(2.0))
}
pub fn canberra_distance_test() {
// Empty lists returns an error
maths.canberra_distance([])
|> should.be_error()
// Try different types of valid input
maths.canberra_distance([#(0.0, 0.0), #(0.0, 0.0)])
|> should.equal(Ok(0.0))
maths.canberra_distance([#(1.0, -2.0), #(2.0, -1.0)])
|> should.equal(Ok(2.0))
maths.canberra_distance([#(1.0, 0.0), #(0.0, 2.0)])
|> should.equal(Ok(2.0))
maths.canberra_distance([#(1.0, 2.0), #(0.0, 0.0)])
|> should.equal(Ok(1.0 /. 3.0))
maths.canberra_distance_with_weights([#(1.0, 0.0, 1.0), #(0.0, 2.0, 1.0)])
|> should.equal(Ok(2.0))
maths.canberra_distance_with_weights([#(1.0, 0.0, 1.0), #(0.0, 2.0, 0.5)])
|> should.equal(Ok(1.5))
maths.canberra_distance_with_weights([#(1.0, 0.0, 0.5), #(0.0, 2.0, 0.5)])
|> should.equal(Ok(1.0))
// Try invalid input with weights that are negative
maths.canberra_distance_with_weights([
#(1.0, 4.0, -7.0),
#(2.0, 5.0, -8.0),
#(3.0, 6.0, -9.0),
])
|> should.be_error()
}
pub fn braycurtis_distance_test() {
// Empty lists returns an error
maths.braycurtis_distance([])
|> should.be_error()
// Try different types of valid input
maths.braycurtis_distance([#(0.0, 0.0), #(0.0, 0.0)])
|> should.equal(Ok(0.0))
maths.braycurtis_distance([#(1.0, -2.0), #(2.0, -1.0)])
|> should.equal(Ok(3.0))
maths.braycurtis_distance([#(1.0, 0.0), #(0.0, 2.0)])
|> should.equal(Ok(1.0))
maths.braycurtis_distance([#(1.0, 3.0), #(2.0, 4.0)])
|> should.equal(Ok(0.4))
maths.braycurtis_distance_with_weights([#(1.0, 3.0, 1.0), #(2.0, 4.0, 1.0)])
|> should.equal(Ok(0.4))
maths.braycurtis_distance_with_weights([#(1.0, 3.0, 0.5), #(2.0, 4.0, 1.0)])
|> should.equal(Ok(0.375))
maths.braycurtis_distance_with_weights([#(1.0, 3.0, 0.25), #(2.0, 4.0, 0.25)])
|> should.equal(Ok(0.4))
// Try invalid input with weights that are negative
maths.braycurtis_distance_with_weights([
#(1.0, 4.0, -7.0),
#(2.0, 5.0, -8.0),
#(3.0, 6.0, -9.0),
])
|> should.be_error()
}

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test/gleam_community/piecewise_test.gleam Normal file
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import gleam/float
import gleam/int
import gleam_community/maths
import gleeunit/should
pub fn float_ceiling_test() {
// Round 3. digit AFTER decimal point
maths.round_up(12.0654, 3)
|> should.equal(12.066)
// Round 2. digit AFTER decimal point
maths.round_up(12.0654, 2)
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
maths.round_up(12.0654, 1)
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
maths.round_up(12.0654, 0)
|> should.equal(13.0)
// Round 1. digit BEFORE decimal point
maths.round_up(12.0654, -1)
|> should.equal(20.0)
// Round 2. digit BEFORE decimal point
maths.round_up(12.0654, -2)
|> should.equal(100.0)
// Round 3. digit BEFORE decimal point
maths.round_up(12.0654, -3)
|> should.equal(1000.0)
}
pub fn float_floor_test() {
// Round 3. digit AFTER decimal point
maths.round_down(12.0654, 3)
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
maths.round_down(12.0654, 2)
|> should.equal(12.06)
// Round 1. digit AFTER decimal point
maths.round_down(12.0654, 1)
|> should.equal(12.0)
// Round 0. digit BEFORE decimal point
maths.round_down(12.0654, 0)
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
maths.round_down(12.0654, -1)
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
maths.round_down(12.0654, -2)
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
maths.round_down(12.0654, -3)
|> should.equal(0.0)
}
pub fn float_truncate_test() {
// Round 3. digit AFTER decimal point
maths.round_to_zero(12.0654, 3)
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
maths.round_to_zero(12.0654, 2)
|> should.equal(12.06)
// Round 1. digit AFTER decimal point
maths.round_to_zero(12.0654, 1)
|> should.equal(12.0)
// Round 0. digit BEFORE decimal point
maths.round_to_zero(12.0654, 0)
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
maths.round_to_zero(12.0654, -1)
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
maths.round_to_zero(12.0654, -2)
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
maths.round_to_zero(12.0654, -3)
|> should.equal(0.0)
}
pub fn math_round_to_nearest_test() {
// Try with positive values
maths.round_to_nearest(1.5, 0)
|> should.equal(2.0)
maths.round_to_nearest(1.75, 0)
|> should.equal(2.0)
maths.round_to_nearest(2.0, 0)
|> should.equal(2.0)
maths.round_to_nearest(3.5, 0)
|> should.equal(4.0)
maths.round_to_nearest(4.5, 0)
|> should.equal(4.0)
// Try with negative values
maths.round_to_nearest(-3.5, 0)
|> should.equal(-4.0)
maths.round_to_nearest(-4.5, 0)
|> should.equal(-4.0)
// // Round 3. digit AFTER decimal point
maths.round_to_nearest(12.0654, 3)
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
maths.round_to_nearest(12.0654, 2)
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
maths.round_to_nearest(12.0654, 1)
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
maths.round_to_nearest(12.0654, 0)
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
maths.round_to_nearest(12.0654, -1)
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
maths.round_to_nearest(12.0654, -2)
|> should.equal(0.0)
// Round 3. digit BEFORE decimal point
maths.round_to_nearest(12.0654, -3)
|> should.equal(0.0)
}
pub fn math_round_up_test() {
// Try with positive values
maths.round_up(0.45, 0)
|> should.equal(1.0)
maths.round_up(0.5, 0)
|> should.equal(1.0)
maths.round_up(0.45, 1)
|> should.equal(0.5)
maths.round_up(0.5, 1)
|> should.equal(0.5)
maths.round_up(0.455, 2)
|> should.equal(0.46)
maths.round_up(0.505, 2)
|> should.equal(0.51)
// Try with negative values
maths.round_up(-0.45, 0)
|> should.equal(-0.0)
maths.round_up(-0.5, 0)
|> should.equal(-0.0)
maths.round_up(-0.45, 1)
|> should.equal(-0.4)
maths.round_up(-0.5, 1)
|> should.equal(-0.5)
maths.round_up(-0.455, 2)
|> should.equal(-0.45)
maths.round_up(-0.505, 2)
|> should.equal(-0.5)
}
pub fn math_round_down_test() {
// Try with positive values
maths.round_down(0.45, 0)
|> should.equal(0.0)
maths.round_down(0.5, 0)
|> should.equal(0.0)
maths.round_down(0.45, 1)
|> should.equal(0.4)
maths.round_down(0.5, 1)
|> should.equal(0.5)
maths.round_down(0.455, 2)
|> should.equal(0.45)
maths.round_down(0.505, 2)
|> should.equal(0.5)
// Try with negative values
maths.round_down(-0.45, 0)
|> should.equal(-1.0)
maths.round_down(-0.5, 0)
|> should.equal(-1.0)
maths.round_down(-0.45, 1)
|> should.equal(-0.5)
maths.round_down(-0.5, 1)
|> should.equal(-0.5)
maths.round_down(-0.455, 2)
|> should.equal(-0.46)
maths.round_down(-0.505, 2)
|> should.equal(-0.51)
}
pub fn math_round_to_zero_test() {
// Note: Rounding mode "RoundToZero" is an alias for the truncate function
// Try with positive values
maths.round_to_zero(0.5, 0)
|> should.equal(0.0)
maths.round_to_zero(0.75, 0)
|> should.equal(0.0)
maths.round_to_zero(0.45, 1)
|> should.equal(0.4)
maths.round_to_zero(0.57, 1)
|> should.equal(0.5)
maths.round_to_zero(0.4575, 2)
|> should.equal(0.45)
maths.round_to_zero(0.5075, 2)
|> should.equal(0.5)
// Try with negative values
maths.round_to_zero(-0.5, 0)
|> should.equal(0.0)
maths.round_to_zero(-0.75, 0)
|> should.equal(0.0)
maths.round_to_zero(-0.45, 1)
|> should.equal(-0.4)
maths.round_to_zero(-0.57, 1)
|> should.equal(-0.5)
maths.round_to_zero(-0.4575, 2)
|> should.equal(-0.45)
maths.round_to_zero(-0.5075, 2)
|> should.equal(-0.5)
}
pub fn math_round_ties_away_test() {
// Try with positive values
maths.round_ties_away(1.4, 0)
|> should.equal(1.0)
maths.round_ties_away(1.5, 0)
|> should.equal(2.0)
maths.round_ties_away(2.5, 0)
|> should.equal(3.0)
// Try with negative values
maths.round_ties_away(-1.4, 0)
|> should.equal(-1.0)
maths.round_ties_away(-1.5, 0)
|> should.equal(-2.0)
maths.round_ties_away(-2.0, 0)
|> should.equal(-2.0)
maths.round_ties_away(-2.5, 0)
|> should.equal(-3.0)
// Round 3. digit AFTER decimal point
maths.round_ties_away(12.0654, 3)
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
maths.round_ties_away(12.0654, 2)
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
maths.round_ties_away(12.0654, 1)
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
maths.round_ties_away(12.0654, 0)
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
maths.round_ties_away(12.0654, -1)
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
maths.round_ties_away(12.0654, -2)
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
maths.round_ties_away(12.0654, -3)
|> should.equal(0.0)
}
pub fn math_round_ties_up_test() {
// Try with positive values
maths.round_ties_up(1.4, 0)
|> should.equal(1.0)
maths.round_ties_up(1.5, 0)
|> should.equal(2.0)
maths.round_ties_up(2.5, 0)
|> should.equal(3.0)
// Try with negative values
maths.round_ties_up(-1.4, 0)
|> should.equal(-1.0)
maths.round_ties_up(-1.5, 0)
|> should.equal(-1.0)
maths.round_ties_up(-2.0, 0)
|> should.equal(-2.0)
maths.round_ties_up(-2.5, 0)
|> should.equal(-2.0)
// Round 3. digit AFTER decimal point
maths.round_ties_up(12.0654, 3)
|> should.equal(12.065)
// Round 2. digit AFTER decimal point
maths.round_ties_up(12.0654, 2)
|> should.equal(12.07)
// Round 1. digit AFTER decimal point
maths.round_ties_up(12.0654, 1)
|> should.equal(12.1)
// Round 0. digit BEFORE decimal point
maths.round_ties_up(12.0654, 0)
|> should.equal(12.0)
// Round 1. digit BEFORE decimal point
maths.round_ties_up(12.0654, -1)
|> should.equal(10.0)
// Round 2. digit BEFORE decimal point
maths.round_ties_up(12.0654, -2)
|> should.equal(0.0)
// Round 2. digit BEFORE decimal point
maths.round_ties_up(12.0654, -3)
|> should.equal(0.0)
}
pub fn float_absolute_difference_test() {
maths.float_absolute_difference(20.0, 15.0)
|> should.equal(5.0)
maths.float_absolute_difference(-20.0, -15.0)
|> should.equal(5.0)
maths.float_absolute_difference(20.0, -15.0)
|> should.equal(35.0)
maths.float_absolute_difference(-20.0, 15.0)
|> should.equal(35.0)
maths.float_absolute_difference(0.0, 0.0)
|> should.equal(0.0)
maths.float_absolute_difference(1.0, 2.0)
|> should.equal(1.0)
maths.float_absolute_difference(2.0, 1.0)
|> should.equal(1.0)
maths.float_absolute_difference(-1.0, 0.0)
|> should.equal(1.0)
maths.float_absolute_difference(0.0, -1.0)
|> should.equal(1.0)
maths.float_absolute_difference(10.0, 20.0)
|> should.equal(10.0)
maths.float_absolute_difference(-10.0, -20.0)
|> should.equal(10.0)
maths.float_absolute_difference(-10.5, 10.5)
|> should.equal(21.0)
}
pub fn int_absolute_difference_test() {
maths.int_absolute_difference(20, 15)
|> should.equal(5)
maths.int_absolute_difference(-20, -15)
|> should.equal(5)
maths.int_absolute_difference(20, -15)
|> should.equal(35)
maths.int_absolute_difference(-20, 15)
|> should.equal(35)
}
pub fn float_sign_test() {
maths.float_sign(100.0)
|> should.equal(1.0)
maths.float_sign(0.0)
|> should.equal(0.0)
maths.float_sign(-100.0)
|> should.equal(-1.0)
}
pub fn float_flip_sign_test() {
maths.float_flip_sign(100.0)
|> should.equal(-100.0)
maths.float_flip_sign(0.0)
|> should.equal(-0.0)
maths.float_flip_sign(-100.0)
|> should.equal(100.0)
}
pub fn float_copy_sign_test() {
maths.float_copy_sign(100.0, 10.0)
|> should.equal(100.0)
maths.float_copy_sign(-100.0, 10.0)
|> should.equal(100.0)
maths.float_copy_sign(100.0, -10.0)
|> should.equal(-100.0)
maths.float_copy_sign(-100.0, -10.0)
|> should.equal(-100.0)
}
pub fn int_sign_test() {
maths.int_sign(100)
|> should.equal(1)
maths.int_sign(0)
|> should.equal(0)
maths.int_sign(-100)
|> should.equal(-1)
}
pub fn int_flip_sign_test() {
maths.int_flip_sign(100)
|> should.equal(-100)
maths.int_flip_sign(0)
|> should.equal(-0)
maths.int_flip_sign(-100)
|> should.equal(100)
}
pub fn int_copy_sign_test() {
maths.int_copy_sign(100, 10)
|> should.equal(100)
maths.int_copy_sign(-100, 10)
|> should.equal(100)
maths.int_copy_sign(100, -10)
|> should.equal(-100)
maths.int_copy_sign(-100, -10)
|> should.equal(-100)
}
pub fn float_minmax_test() {
maths.minmax(0.75, 0.5, float.compare)
|> should.equal(#(0.5, 0.75))
maths.minmax(0.5, 0.75, float.compare)
|> should.equal(#(0.5, 0.75))
maths.minmax(-0.75, 0.5, float.compare)
|> should.equal(#(-0.75, 0.5))
maths.minmax(-0.75, 0.5, float.compare)
|> should.equal(#(-0.75, 0.5))
}
pub fn int_minmax_test() {
maths.minmax(75, 50, int.compare)
|> should.equal(#(50, 75))
maths.minmax(50, 75, int.compare)
|> should.equal(#(50, 75))
maths.minmax(-75, 50, int.compare)
|> should.equal(#(-75, 50))
maths.minmax(-75, 50, int.compare)
|> should.equal(#(-75, 50))
}
pub fn float_list_minimum_test() {
// An empty lists returns an error
[]
|> maths.list_minimum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> maths.list_minimum(float.compare)
|> should.equal(Ok(1.5))
}
pub fn int_list_minimum_test() {
// An empty lists returns an error
[]
|> maths.list_minimum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> maths.list_minimum(int.compare)
|> should.equal(Ok(1))
}
pub fn float_list_maximum_test() {
// An empty lists returns an error
[]
|> maths.list_maximum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> maths.list_maximum(float.compare)
|> should.equal(Ok(4.5))
}
pub fn int_list_maximum_test() {
// An empty lists returns an error
[]
|> maths.list_maximum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> maths.list_maximum(int.compare)
|> should.equal(Ok(4))
}
pub fn float_list_arg_maximum_test() {
// An empty lists returns an error
[]
|> maths.arg_maximum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> maths.arg_maximum(float.compare)
|> should.equal(Ok([0, 1]))
}
pub fn int_list_arg_maximum_test() {
// An empty lists returns an error
[]
|> maths.arg_maximum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> maths.arg_maximum(int.compare)
|> should.equal(Ok([0, 1]))
}
pub fn float_list_arg_minimum_test() {
// An empty lists returns an error
[]
|> maths.arg_minimum(float.compare)
|> should.be_error()
// Valid input returns a result
[4.5, 4.5, 3.5, 2.5, 1.5]
|> maths.arg_minimum(float.compare)
|> should.equal(Ok([4]))
}
pub fn int_list_arg_minimum_test() {
// An empty lists returns an error
[]
|> maths.arg_minimum(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> maths.arg_minimum(int.compare)
|> should.equal(Ok([4]))
}
pub fn float_list_extrema_test() {
// An empty lists returns an error
[]
|> maths.extrema(float.compare)
|> should.be_error()
// Valid input returns a result
[4.0, 4.0, 3.0, 2.0, 1.0]
|> maths.extrema(float.compare)
|> should.equal(Ok(#(1.0, 4.0)))
// Valid input returns a result
[1.0, 4.0, 2.0, 5.0, 0.0]
|> maths.extrema(float.compare)
|> should.equal(Ok(#(0.0, 5.0)))
}
pub fn int_list_extrema_test() {
// An empty lists returns an error
[]
|> maths.extrema(int.compare)
|> should.be_error()
// Valid input returns a result
[4, 4, 3, 2, 1]
|> maths.extrema(int.compare)
|> should.equal(Ok(#(1, 4)))
// Valid input returns a result
[1, 4, 2, 5, 0]
|> maths.extrema(int.compare)
|> should.equal(Ok(#(0, 5)))
}

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test/gleam_community/sequences_test.gleam Normal file
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import gleam/float
import gleam/list
import gleam/yielder
import gleam_community/maths
import gleeunit/should
pub fn float_list_linear_space_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
// ---> With endpoint included
let assert Ok(linspace) = maths.linear_space(10.0, 50.0, 5, True)
let assert Ok(result) =
maths.all_close(
linspace |> yielder.to_list() |> list.zip([10.0, 20.0, 30.0, 40.0, 50.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = maths.linear_space(10.0, 20.0, 5, True)
let assert Ok(result) =
maths.all_close(
linspace |> yielder.to_list() |> list.zip([10.0, 12.5, 15.0, 17.5, 20.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Try with negative stop
// ----> Without endpoint included
let assert Ok(linspace) = maths.linear_space(10.0, 50.0, 5, False)
let assert Ok(result) =
maths.all_close(
linspace |> yielder.to_list() |> list.zip([10.0, 18.0, 26.0, 34.0, 42.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = maths.linear_space(10.0, 20.0, 5, False)
let assert Ok(result) =
maths.all_close(
linspace |> yielder.to_list() |> list.zip([10.0, 12.0, 14.0, 16.0, 18.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Try with negative stop
let assert Ok(linspace) = maths.linear_space(10.0, -50.0, 5, False)
let assert Ok(result) =
maths.all_close(
linspace
|> yielder.to_list()
|> list.zip([10.0, -2.0, -14.0, -26.0, -38.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = maths.linear_space(10.0, -20.0, 5, True)
let assert Ok(result) =
maths.all_close(
linspace
|> yielder.to_list()
|> list.zip([10.0, 2.5, -5.0, -12.5, -20.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Try with negative start
let assert Ok(linspace) = maths.linear_space(-10.0, 50.0, 5, False)
let assert Ok(result) =
maths.all_close(
linspace |> yielder.to_list() |> list.zip([-10.0, 2.0, 14.0, 26.0, 38.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
let assert Ok(linspace) = maths.linear_space(-10.0, 20.0, 5, True)
let assert Ok(result) =
maths.all_close(
linspace |> yielder.to_list() |> list.zip([-10.0, -2.5, 5.0, 12.5, 20.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// A negative number of points does not work (-5)
maths.linear_space(10.0, 50.0, -5, True)
|> should.be_error()
}
pub fn float_list_logarithmic_space_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
// ---> With endpoint included
// - Positive start, stop, base
let assert Ok(logspace) = maths.logarithmic_space(1.0, 3.0, 3, True, 10.0)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([10.0, 100.0, 1000.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, stop, negative base
let assert Ok(logspace) = maths.logarithmic_space(1.0, 3.0, 3, True, -10.0)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([-10.0, 100.0, -1000.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, negative stop, base
let assert Ok(logspace) = maths.logarithmic_space(1.0, -3.0, 3, True, -10.0)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([-10.0, -0.1, -0.001]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, base, negative stop
let assert Ok(logspace) = maths.logarithmic_space(1.0, -3.0, 3, True, 10.0)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([10.0, 0.1, 0.001]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive stop, base, negative start
let assert Ok(logspace) = maths.logarithmic_space(-1.0, 3.0, 3, True, 10.0)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([0.1, 10.0, 1000.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// ----> Without endpoint included
// - Positive start, stop, base
let assert Ok(logspace) = maths.logarithmic_space(1.0, 3.0, 3, False, 10.0)
let assert Ok(result) =
maths.all_close(
logspace
|> yielder.to_list()
|> list.zip([10.0, 46.41588834, 215.443469]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// A negative number of points does not work (-3)
maths.logarithmic_space(1.0, 3.0, -3, True, 10.0)
|> should.be_error()
}
pub fn float_list_geometric_space_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
// ---> With endpoint included
// - Positive start, stop
let assert Ok(logspace) = maths.geometric_space(10.0, 1000.0, 3, True)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([10.0, 100.0, 1000.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive start, negative stop
let assert Ok(logspace) = maths.geometric_space(10.0, 0.001, 3, True)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([10.0, 0.1, 0.001]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// - Positive stop, negative start
let assert Ok(logspace) = maths.geometric_space(0.1, 1000.0, 3, True)
let assert Ok(result) =
maths.all_close(
logspace |> yielder.to_list() |> list.zip([0.1, 10.0, 1000.0]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// ----> Without endpoint included
// - Positive start, stop
let assert Ok(logspace) = maths.geometric_space(10.0, 1000.0, 3, False)
let assert Ok(result) =
maths.all_close(
logspace
|> yielder.to_list()
|> list.zip([10.0, 46.41588834, 215.443469]),
0.0,
tol,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// Test invalid input (start and stop can't be equal to 0.0)
maths.geometric_space(0.0, 1000.0, 3, False)
|> should.be_error()
maths.geometric_space(-1000.0, 0.0, 3, False)
|> should.be_error()
// A negative number of points does not work
maths.geometric_space(-1000.0, 0.0, -3, False)
|> should.be_error()
}
pub fn float_list_arange_test() {
// Positive start, stop, step
maths.arange(1.0, 5.0, 1.0)
|> yielder.to_list()
|> should.equal([1.0, 2.0, 3.0, 4.0])
maths.arange(1.0, 5.0, 0.5)
|> yielder.to_list()
|> should.equal([1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5])
maths.arange(1.0, 2.0, 0.25)
|> yielder.to_list()
|> should.equal([1.0, 1.25, 1.5, 1.75])
// Reverse (switch start/stop largest/smallest value)
maths.arange(5.0, 1.0, 1.0)
|> yielder.to_list()
|> should.equal([])
// Reverse negative step
maths.arange(5.0, 1.0, -1.0)
|> yielder.to_list()
|> should.equal([5.0, 4.0, 3.0, 2.0])
// Positive start, negative stop, step
maths.arange(5.0, -1.0, -1.0)
|> yielder.to_list()
|> should.equal([5.0, 4.0, 3.0, 2.0, 1.0, 0.0])
// Negative start, stop, step
maths.arange(-5.0, -1.0, -1.0)
|> yielder.to_list()
|> should.equal([])
// Negative start, stop, positive step
maths.arange(-5.0, -1.0, 1.0)
|> yielder.to_list()
|> should.equal([-5.0, -4.0, -3.0, -2.0])
}
pub fn float_list_exponential_space_test() {
let assert Ok(tolerance) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
// ---> With endpoint included
let assert Ok(exp_space) = maths.exponential_space(1.0, 1000.0, 4, True)
let assert Ok(result) =
maths.all_close(
exp_space |> yielder.to_list() |> list.zip([1.0, 10.0, 100.0, 1000.0]),
0.0,
tolerance,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// ---> Without endpoint included
let assert Ok(exp_space) = maths.exponential_space(1.0, 1000.0, 4, False)
let assert Ok(result) =
maths.all_close(
exp_space
|> yielder.to_list()
|> list.zip([
1.0, 5.623413251903491, 31.622776601683793, 177.82794100389228,
]),
0.0,
tolerance,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// A negative number of points does not work (-3)
maths.exponential_space(1.0, 1000.0, -3, True)
|> should.be_error()
}
pub fn float_list_symmetric_space_test() {
let assert Ok(tolerance) = float.power(10.0, -6.0)
// Check that the function agrees, at some arbitrary input
// points, with known function values
let assert Ok(sym_space) = maths.symmetric_space(0.0, 5.0, 5)
sym_space
|> yielder.to_list()
|> should.equal([-5.0, -2.5, 0.0, 2.5, 5.0])
let assert Ok(sym_space) = maths.symmetric_space(0.0, 5.0, 5)
sym_space
|> yielder.to_list()
|> should.equal([-5.0, -2.5, 0.0, 2.5, 5.0])
// Negative center
let assert Ok(sym_space) = maths.symmetric_space(-10.0, 5.0, 5)
sym_space
|> yielder.to_list()
|> should.equal([-15.0, -12.5, -10.0, -7.5, -5.0])
// Uneven number of points
let assert Ok(sym_space) = maths.symmetric_space(0.0, 2.0, 4)
let assert Ok(result) =
maths.all_close(
sym_space
|> yielder.to_list()
|> list.zip([-2.0, -0.6666666666666667, 0.6666666666666665, 2.0]),
0.0,
tolerance,
)
result
|> list.all(fn(x) { x == True })
|> should.be_true()
// A negative number of points does not work (-5)
maths.symmetric_space(0.0, 5.0, -5)
|> should.be_error()
}

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test/gleam_community/special_test.gleam Normal file
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import gleam/float
import gleam/result
import gleam_community/maths
import gleeunit/should
pub fn float_beta_function_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Valid input returns a result
maths.beta(-0.5, 0.5)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.beta(0.5, 0.5)
|> maths.is_close(3.1415926535897927, 0.0, tol)
|> should.be_true()
maths.beta(0.5, -0.5)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.beta(5.0, 5.0)
|> maths.is_close(0.0015873015873015873, 0.0, tol)
|> should.be_true()
}
pub fn float_error_function_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Valid input returns a result
maths.erf(-0.5)
|> maths.is_close(-0.5204998778130465, 0.0, tol)
|> should.be_true()
maths.erf(0.5)
|> maths.is_close(0.5204998778130465, 0.0, tol)
|> should.be_true()
maths.erf(1.0)
|> maths.is_close(0.8427007929497148, 0.0, tol)
|> should.be_true()
maths.erf(2.0)
|> maths.is_close(0.9953222650189527, 0.0, tol)
|> should.be_true()
maths.erf(10.0)
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
}
pub fn float_gamma_function_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Valid input returns a result
maths.gamma(-0.5)
|> maths.is_close(-3.5449077018110318, 0.0, tol)
|> should.be_true()
maths.gamma(0.5)
|> maths.is_close(1.7724538509055159, 0.0, tol)
|> should.be_true()
maths.gamma(1.0)
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
maths.gamma(2.0)
|> maths.is_close(1.0, 0.0, tol)
|> should.be_true()
maths.gamma(3.0)
|> maths.is_close(2.0, 0.0, tol)
|> should.be_true()
maths.gamma(10.0)
|> maths.is_close(362_880.0, 0.0, tol)
|> should.be_true()
}
pub fn float_incomplete_gamma_function_test() {
let assert Ok(tol) = float.power(10.0, -6.0)
// Invalid input gives an error
// 1st arg is invalid
maths.incomplete_gamma(-1.0, 1.0)
|> should.be_error()
// 2nd arg is invalid
maths.incomplete_gamma(1.0, -1.0)
|> should.be_error()
// Valid input returns a result
maths.incomplete_gamma(1.0, 0.0)
|> result.unwrap(-999.0)
|> maths.is_close(0.0, 0.0, tol)
|> should.be_true()
maths.incomplete_gamma(1.0, 2.0)
|> result.unwrap(-999.0)
|> maths.is_close(0.864664716763387308106, 0.0, tol)
|> should.be_true()
maths.incomplete_gamma(2.0, 3.0)
|> result.unwrap(-999.0)
|> maths.is_close(0.8008517265285442280826, 0.0, tol)
|> should.be_true()
maths.incomplete_gamma(3.0, 4.0)
|> result.unwrap(-999.0)
|> maths.is_close(1.523793388892911312363, 0.0, tol)
|> should.be_true()
}