argmin_testfunctions/styblinskitang.rs
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// Copyright 2018-2024 argmin developers
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or
// http://opensource.org/licenses/MIT>, at your option. This file may not be
// copied, modified, or distributed except according to those terms.
//! # Styblinski-Tang test function
//!
//! Defined as
//!
//! `f(x_1, x_2, ..., x_n) = 1/2 * \sum_{i=1}^{n} \left[ x_i^4 - 16 * x_i^2 + 5 * x_i \right]`
//!
//! where `x_i \in [-5, 5]`.
//!
//! The global minimum is at `f(x_1, x_2, ..., x_n) = f(-2.903534, -2.903534, ..., -2.903534) =
//! -39.16616*n`.
use num::{Float, FromPrimitive};
use std::iter::Sum;
/// Styblinski-Tang test function
///
/// Defined as
///
/// `f(x_1, x_2, ..., x_n) = 1/2 * \sum_{i=1}^{n} \left[ x_i^4 - 16 * x_i^2 + 5 * x_i \right]`
///
/// where `x_i \in [-5, 5]`.
///
/// The global minimum is at `f(x_1, x_2, ..., x_n) = f(-2.903534, -2.903534, ..., -2.903534) =
/// -39.16616*n`.
pub fn styblinski_tang<T>(param: &[T]) -> T
where
T: Float + FromPrimitive + Sum,
{
T::from_f64(0.5).unwrap()
* param
.iter()
.map(|x| {
x.powi(4) - T::from_f64(16.0).unwrap() * x.powi(2) + T::from_f64(5.0).unwrap() * *x
})
.sum()
}
/// Derivative of Styblinski-Tang test function
pub fn styblinski_tang_derivative<T>(param: &[T]) -> Vec<T>
where
T: Float + FromPrimitive + Sum,
{
let n2 = T::from_f64(2.0).unwrap();
let n2_5 = T::from_f64(2.5).unwrap();
let n16 = T::from_f64(16.0).unwrap();
param
.iter()
.map(|x| n2 * x.powi(3) - n16 * *x + n2_5)
.collect()
}
/// Derivative of Styblinski-Tang test function
///
/// This is the const generics version, which requires the number of parameters to be known
/// at compile time.
pub fn styblinski_tang_derivative_const<const N: usize, T>(param: &[T; N]) -> [T; N]
where
T: Float + FromPrimitive + Sum,
{
let n0 = T::from_f64(0.0).unwrap();
let n2 = T::from_f64(2.0).unwrap();
let n2_5 = T::from_f64(2.5).unwrap();
let n16 = T::from_f64(16.0).unwrap();
let mut out = [n0; N];
param
.iter()
.zip(out.iter_mut())
.map(|(x, o)| *o = n2 * x.powi(3) - n16 * *x + n2_5)
.count();
out
}
/// Hessian of Styblinski-Tang test function
pub fn styblinski_tang_hessian<T>(param: &[T]) -> Vec<Vec<T>>
where
T: Float + FromPrimitive + Sum,
{
let n0 = T::from_f64(0.0).unwrap();
let n6 = T::from_f64(6.0).unwrap();
let n16 = T::from_f64(16.0).unwrap();
let n = param.len();
let mut out = vec![vec![n0; n]; n];
param
.iter()
.enumerate()
.map(|(i, x)| out[i][i] = n6 * x.powi(2) - n16)
.count();
out
}
/// Hessian of Styblinski-Tang test function
///
/// This is the const generics version, which requires the number of parameters to be known
/// at compile time.
pub fn styblinski_tang_hessian_const<const N: usize, T>(param: &[T; N]) -> [[T; N]; N]
where
T: Float + FromPrimitive + Sum,
{
let n0 = T::from_f64(0.0).unwrap();
let n6 = T::from_f64(6.0).unwrap();
let n16 = T::from_f64(16.0).unwrap();
let mut out = [[n0; N]; N];
param
.iter()
.enumerate()
.map(|(i, x)| out[i][i] = n6 * x.powi(2) - n16)
.count();
out
}
#[cfg(test)]
mod tests {
use super::*;
use approx::assert_relative_eq;
use finitediff::FiniteDiff;
use proptest::prelude::*;
use std::f32;
#[test]
fn test_styblinski_tang_optimum() {
assert_relative_eq!(
styblinski_tang(&[-2.903534_f32, -2.903534_f32, -2.903534_f32]),
-117.49849,
epsilon = f32::EPSILON
);
assert_relative_eq!(
styblinski_tang(&[-2.903534_f64, -2.903534_f64, -2.903534_f64]),
-117.4984971113142,
epsilon = f64::EPSILON
);
let deriv = styblinski_tang_derivative(&[-2.903534_f64, -2.903534_f64, -2.903534_f64]);
for i in 0..3 {
assert_relative_eq!(deriv[i], 0.0, epsilon = 1e-5, max_relative = 1e-2);
}
}
proptest! {
#[test]
fn test_styblinski_tang_derivative_finitediff(a in -5.0..5.0,
b in -5.0..5.0,
c in -5.0..5.0,
d in -5.0..5.0,
e in -5.0..5.0,
f in -5.0..5.0,
g in -5.0..5.0,
h in -5.0..5.0) {
let param = [a, b, c, d, e, f, g, h];
let derivative = styblinski_tang_derivative(¶m);
let derivative_fd = Vec::from(param).central_diff(&|x| styblinski_tang(&x));
for i in 0..derivative.len() {
assert_relative_eq!(
derivative[i],
derivative_fd[i],
epsilon = 1e-5,
max_relative = 1e-2
);
}
}
}
proptest! {
#[test]
fn test_styblinski_tang_derivative_const_finitediff(a in -5.0..5.0,
b in -5.0..5.0,
c in -5.0..5.0,
d in -5.0..5.0,
e in -5.0..5.0,
f in -5.0..5.0,
g in -5.0..5.0,
h in -5.0..5.0) {
let param = [a, b, c, d, e, f, g, h];
let derivative = styblinski_tang_derivative_const(¶m);
let derivative_fd = Vec::from(param).central_diff(&|x| styblinski_tang(&x));
for i in 0..derivative.len() {
assert_relative_eq!(
derivative[i],
derivative_fd[i],
epsilon = 1e-5,
max_relative = 1e-2
);
}
}
}
proptest! {
#[test]
fn test_styblinski_tang_hessian_finitediff(a in -5.0..5.0,
b in -5.0..5.0,
c in -5.0..5.0,
d in -5.0..5.0,
e in -5.0..5.0,
f in -5.0..5.0,
g in -5.0..5.0,
h in -5.0..5.0) {
let param = [a, b, c, d, e, f, g, h];
let derivative = styblinski_tang_hessian(¶m);
let derivative_fd = Vec::from(param).central_hessian(&|x| styblinski_tang_derivative(&x));
for i in 0..derivative.len() {
for j in 0..derivative[i].len() {
assert_relative_eq!(
derivative[i][j],
derivative_fd[i][j],
epsilon = 1e-5,
max_relative = 1e-2
);
}
}
}
}
proptest! {
#[test]
fn test_styblinski_tang_hessian_const_finitediff(a in -5.0..5.0,
b in -5.0..5.0,
c in -5.0..5.0,
d in -5.0..5.0,
e in -5.0..5.0,
f in -5.0..5.0,
g in -5.0..5.0,
h in -5.0..5.0) {
let param = [a, b, c, d, e, f, g, h];
let derivative = styblinski_tang_hessian_const(¶m);
let derivative_fd = Vec::from(param).central_hessian(&|x| styblinski_tang_derivative(&x));
for i in 0..derivative.len() {
for j in 0..derivative[i].len() {
assert_relative_eq!(
derivative[i][j],
derivative_fd[i][j],
epsilon = 1e-5,
max_relative = 1e-2
);
}
}
}
}
}