Algebraic Functions

Examples using classic mathematical test functions.

---

Basic Algebraic Functions

import numpy as np
from surfaces.test_functions.algebraic import (
    SphereFunction,
    RastriginFunction,
    RosenbrockFunction,
    AckleyFunction,
)

# Create functions
sphere = SphereFunction(n_dim=5)
rastrigin = RastriginFunction(n_dim=5)
rosenbrock = RosenbrockFunction(n_dim=5)
ackley = AckleyFunction()  # Fixed 2D

# Evaluate at random points
for func in [sphere, rastrigin, rosenbrock, ackley]:
    space = func.search_space
    sample = {k: np.random.choice(v) for k, v in space.items()}
    result = func(sample)
    print(f"{func.__class__.__name__}: {result:.4f}")

---

Comparing Function Landscapes

"""Compare difficulty of different algebraic functions."""

import numpy as np
from surfaces.test_functions.algebraic import SphereFunction, RastriginFunction

def random_search(func, n_iter=1000, seed=42):
    np.random.seed(seed)
    space = func.search_space
    best = float('inf')
    for _ in range(n_iter):
        sample = {k: np.random.choice(v) for k, v in space.items()}
        result = func(sample)
        best = min(best, result)
    return best

sphere = SphereFunction(n_dim=10)
rastrigin = RastriginFunction(n_dim=10)

print("Random search (1000 iterations):")
print(f"  Sphere: {random_search(sphere):.6f}")
print(f"  Rastrigin: {random_search(rastrigin):.6f}")

---

Scaling with Dimension

"""Test how functions scale with dimensionality."""

import numpy as np
from surfaces.test_functions.algebraic import RastriginFunction
import time

for n_dim in [2, 5, 10, 20, 50]:
    func = RastriginFunction(n_dim=n_dim)
    space = func.search_space

    start = time.time()
    for _ in range(1000):
        sample = {k: np.random.choice(v) for k, v in space.items()}
        func(sample)
    elapsed = time.time() - start

    print(f"n_dim={n_dim:2d}: {elapsed*1000:.1f}ms for 1000 evals")