#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
# pyre-strict
from abc import ABC, abstractmethod
from typing import List, Optional, Tuple, TypeVar, Union
import numpy as np
import torch
from ax.utils.common.docutils import copy_doc
from ax.utils.common.typeutils import checked_cast, not_none
from botorch.test_functions import synthetic as botorch_synthetic
from pyre_extensions import override
T = TypeVar("T")
[docs]class SyntheticFunction(ABC):
_required_dimensionality: int
_domain: List[Tuple[float, float]]
_minimums: Optional[List[Tuple[float, ...]]] = None
_maximums: Optional[List[Tuple[float, ...]]] = None
_fmin: Optional[float] = None
_fmax: Optional[float] = None
@property
def name(self) -> str:
return self.__class__.__name__
def __call__(
self,
*args: Union[int, float, np.ndarray],
**kwargs: Union[int, float, np.ndarray],
) -> Union[float, np.ndarray]:
"""Simplified way to call the synthetic function and pass the argument
numbers directly, e.g. `branin(2.0, 3.0)`.
"""
if kwargs:
if self.required_dimensionality:
assert (
len(kwargs) == self.required_dimensionality or len(kwargs) == 1
), (
f"Function {self.name} expected either "
f"{self.required_dimensionality} arguments "
"or a single numpy array argument."
)
assert not args, (
f"Function {self.name} expected either all anonymous "
"arguments or all keyword arguments."
)
args = list(kwargs.values()) # pyre-ignore[9]
for x in args:
if isinstance(x, np.ndarray):
return self.f(X=x)
assert np.isscalar(
x
), f"Expected numerical arguments or numpy arrays, got {type(x)}."
if isinstance(x, int):
x = float(x)
return checked_cast(float, self.f(np.array(args)))
[docs] def f(self, X: np.ndarray) -> Union[float, np.ndarray]:
"""Synthetic function implementation.
Args:
X (numpy.ndarray): an n by d array, where n represents the number
of observations and d is the dimensionality of the inputs.
Returns:
numpy.ndarray: an n-dimensional array.
"""
assert isinstance(X, np.ndarray), "X must be a numpy (nd)array."
if self.required_dimensionality:
if len(X.shape) == 1:
input_dim = X.shape[0]
elif len(X.shape) == 2:
input_dim = X.shape[1]
else:
raise ValueError(
"Synthetic function call expects input of either 1-d array or "
"n by d array, where n is number of observations and d is "
"dimensionality of the input."
)
assert input_dim == self.required_dimensionality, (
f"Input violates required dimensionality of {self.name}: "
f"{self.required_dimensionality}. Got {input_dim}."
)
X = X.astype(np.float64)
if len(X.shape) == 1:
return self._f(X=X)
else:
return np.array([self._f(X=x) for x in X])
@property
def required_dimensionality(self) -> int:
"""Required dimensionality of input to this function."""
return self._required_dimensionality
@property
def domain(self) -> List[Tuple[float, float]]:
"""Domain on which function is evaluated.
The list is of the same length as the dimensionality of the inputs,
where each element of the list is a tuple corresponding to the min
and max of the domain for that dimension.
"""
return self._domain
@property
def minimums(self) -> List[Tuple[float, ...]]:
"""List of global minimums.
Each element of the list is a d-tuple, where d is the dimensionality
of the inputs. There may be more than one global minimums.
"""
return self.informative_failure_on_none(self._minimums)
@property
def maximums(self) -> List[Tuple[float, ...]]:
"""List of global minimums.
Each element of the list is a d-tuple, where d is the dimensionality
of the inputs. There may be more than one global minimums.
"""
return self.informative_failure_on_none(self._maximums)
@property
def fmin(self) -> float:
"""Value at global minimum(s)."""
return self.informative_failure_on_none(self._fmin)
@property
def fmax(self) -> float:
"""Value at global minimum(s)."""
return self.informative_failure_on_none(self._fmax)
@abstractmethod
def _f(self, X: np.ndarray) -> float:
"""Implementation of the synthetic function. Must be implemented in subclass.
Args:
X: A one-dimensional array with `d` elements, where d is the
dimensionality of the inputs.
Returns:
float: Function value.
"""
...
[docs]class FromBotorch(SyntheticFunction):
def __init__(
self, botorch_synthetic_function: botorch_synthetic.SyntheticTestFunction
) -> None:
self._botorch_function = botorch_synthetic_function
self._required_dimensionality: int = self._botorch_function.dim
self._domain: List[Tuple[float, float]] = self._botorch_function._bounds
self._fmin: Optional[float] = self._botorch_function._optimal_value
@override
@property
def name(self) -> str:
return f"{self.__class__.__name__}_{self._botorch_function.__class__.__name__}"
@override
def _f(self, X: np.ndarray) -> float:
# TODO: support batch evaluation
return float(self._botorch_function(X=torch.from_numpy(X)).item())
[docs]def from_botorch(
botorch_synthetic_function: botorch_synthetic.SyntheticTestFunction,
) -> SyntheticFunction:
"""Utility to generate Ax synthetic functions from BoTorch synthetic functions."""
return FromBotorch(botorch_synthetic_function=botorch_synthetic_function)
[docs]class Hartmann6(SyntheticFunction):
"""Hartmann6 function (6-dimensional with 1 global minimum)."""
_required_dimensionality = 6
_domain: List[Tuple[float, float]] = [(0.0, 1.0) for i in range(6)]
_minimums = [(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573)]
_fmin: float = -3.32237
_fmax = 0.0
_alpha: np.ndarray = np.array([1.0, 1.2, 3.0, 3.2])
_A: np.ndarray = np.array(
[
[10, 3, 17, 3.5, 1.7, 8],
[0.05, 10, 17, 0.1, 8, 14],
[3, 3.5, 1.7, 10, 17, 8],
[17, 8, 0.05, 10, 0.1, 14],
]
)
_P: np.ndarray = 10 ** (-4) * np.array(
[
[1312, 1696, 5569, 124, 8283, 5886],
[2329, 4135, 8307, 3736, 1004, 9991],
[2348, 1451, 3522, 2883, 3047, 6650],
[4047, 8828, 8732, 5743, 1091, 381],
]
)
@override
@copy_doc(SyntheticFunction._f)
def _f(self, X: np.ndarray) -> float:
y = 0.0
for j, alpha_j in enumerate(self._alpha):
t = 0
for k in range(6):
t += self._A[j, k] * ((X[k] - self._P[j, k]) ** 2)
y -= alpha_j * np.exp(-t)
return float(y)
[docs]class Aug_Hartmann6(Hartmann6):
"""Augmented Hartmann6 function (7-dimensional with 1 global minimum)."""
_required_dimensionality = 7
_domain: List[Tuple[float, float]] = [(0.0, 1.0) for i in range(7)]
# pyre-fixme[15]: `_minimums` overrides attribute defined in `Hartmann6`
# inconsistently.
_minimums = [(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573, 1.0)]
_fmin: float = -3.32237
_fmax = 0.0
@override
@copy_doc(SyntheticFunction._f)
def _f(self, X: np.ndarray) -> float:
y = 0.0
alpha_0 = self._alpha[0] - 0.1 * (1 - X[-1])
for j, alpha_j in enumerate(self._alpha):
t = 0
for k in range(6):
t += self._A[j, k] * ((X[k] - self._P[j, k]) ** 2)
if j == 0:
y -= alpha_0 * np.exp(-t)
else:
y -= alpha_j * np.exp(-t)
return float(y)
[docs]class Branin(SyntheticFunction):
"""Branin function (2-dimensional with 3 global minima)."""
_required_dimensionality = 2
_domain: List[Tuple[float, float]] = [(-5.0, 10.0), (0.0, 15.0)]
_minimums: List[Tuple[float, float]] = [
(-np.pi, 12.275),
(np.pi, 2.275),
(9.42478, 2.475),
]
_fmin = 0.397887
_fmax = 308.129
@override
@copy_doc(SyntheticFunction._f)
def _f(self, X: np.ndarray) -> float:
x_1 = X[0]
x_2 = X[1]
return float(
(x_2 - 5.1 / (4 * np.pi**2) * x_1**2 + 5.0 / np.pi * x_1 - 6.0) ** 2
+ 10 * (1 - 1.0 / (8 * np.pi)) * np.cos(x_1)
+ 10
)
[docs]class Aug_Branin(SyntheticFunction):
"""Augmented Branin function (3-dimensional with infinitely many global minima)."""
_required_dimensionality = 3
_domain: List[Tuple[float, float]] = [(-5.0, 10.0), (0.0, 15.0), (0.0, 1.0)]
_minimums: List[Tuple[float, float, float]] = [
(-np.pi, 12.275, 1.0),
(np.pi, 2.275, 1.0),
(9.42478, 2.475, 1.0),
]
_fmin = 0.397887
_fmax = 308.129
@override
@copy_doc(SyntheticFunction._f)
def _f(self, X: np.ndarray) -> float:
x_1 = X[0]
x_2 = X[1]
return float(
(
x_2
- (5.1 / (4 * np.pi**2) - 0.1 * (1 - X[-1])) * x_1**2
+ 5.0 / np.pi * x_1
- 6.0
)
** 2
+ 10 * (1 - 1.0 / (8 * np.pi)) * np.cos(x_1)
+ 10
)
hartmann6 = Hartmann6()
aug_hartmann6 = Aug_Hartmann6()
branin = Branin()
aug_branin = Aug_Branin()
# Synthetic functions constructed from BoTorch.
ackley: SyntheticFunction = from_botorch(
botorch_synthetic_function=botorch_synthetic.Ackley()
)
