# Source code for niapy.problems.schaffer

# encoding=utf8

"""Implementations of Schaffer functions."""

import numpy as np
from niapy.problems.problem import Problem

__all__ = ['SchafferN2', 'SchafferN4', 'ExpandedSchaffer']

[docs]class SchafferN2(Problem):
r"""Implementations of Schaffer N. 2 functions.

Date: 2018

Author: Klemen Berkovič

Function:
**Schaffer N. 2 Function**
:math:f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left(  x_1^2 + x_2^2 \right) \right)^2 }

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (420.968746,...,420.968746)

LaTeX formats:
Inline:
$f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$

Equation:
$$f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$$

Domain:
$-100 \leq x_i \leq 100$

Reference:

"""

[docs]    def __init__(self, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize SchafferN2 problem..

Args:
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.

:func:niapy.problems.Problem.__init__

"""
kwargs.pop('dimension', None)
super().__init__(2, lower, upper, *args, **kwargs)

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$'''

def _evaluate(self, x):
return 0.5 + (np.sin(x[0] ** 2 - x[1] ** 2) ** 2 - 0.5) / (1 + 0.001 * (x[0] ** 2 + x[1] ** 2)) ** 2

[docs]class SchafferN4(Problem):
r"""Implementations of Schaffer N. 2 functions.

Date: 2018

Author: Klemen Berkovič

Function:
**Schaffer N. 2 Function**
:math:f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left(  x_1^2 + x_2^2 \right) \right)^2 }

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (420.968746,...,420.968746)

LaTeX formats:
Inline:
$f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$

Equation:
$$f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$$

Domain:
$-100 \leq x_i \leq 100$

Reference:

"""

[docs]    def __init__(self, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize SchafferN4 problem..

Args:
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.

:func:niapy.problems.Problem.__init__

"""
kwargs.pop('dimension', None)
super().__init__(2, lower, upper, *args, **kwargs)

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$'''

def _evaluate(self, x):
return 0.5 + (np.cos(np.sin(x[0] ** 2 - x[1] ** 2)) ** 2 - 0.5) / (1 + 0.001 * (x[0] ** 2 + x[1] ** 2)) ** 2

[docs]class ExpandedSchaffer(Problem):
r"""Implementations of Expanded Schaffer functions.

Date: 2018

Author: Klemen Berkovič

Function:
**Expanded Schaffer Function**
:math:f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (420.968746,...,420.968746)

LaTeX formats:
Inline:
$f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2$

Equation:
$$f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2$$

Domain:
$-100 \leq x_i \leq 100$

Reference:

"""

[docs]    def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Expanded Schaffer problem..

Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.

:func:niapy.problems.Problem.__init__

"""
super().__init__(dimension, lower, upper, *args, **kwargs)

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2$'''

def _evaluate(self, x):
x_next = np.roll(x, -1)
tmp = x ** 2 + x_next ** 2
val = 0.5 + (np.sin(np.sqrt(tmp)) ** 2 - 0.5) / (1 + 0.001 * tmp) ** 2
return np.sum(val)