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benchmarkfunctions.py
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'''This module contains the following:
BenignEllipse
A moderately conditioned function.
BenignEllipseNoisyThres
A moderately conditioned function with additive noise above a certain
(function value) threshold.
BenignEllipseAddNoise
A moderately conditioned function with additive noise of a specified
strength applied.
BenignEllipseMultNoise
A moderately conditioned function with multiplicative noise of a specified
strength applied.
Ellipse
A badly conditioned function.
EllipseAddNoise
A badly conditioned function with additive noise of a specified
strength applied.
EllipseMultNoise
A badly conditioned function with multiplicative noise of a specified
strength applied.
sphere
The standard spherical quadratic function.
SphereAddNoise
The standard spherical quadratic function with additive noise of a
specified streght applied.
SphereMultNoise
The standard spherical quadratic function with multiplicative noise of a
specified streght applied.
sigmoidal
A sigmoidal function thresholding large values.
'''
import numpy as np
import sys
class BenignEllipse(object):
'''Implements a quadratic function of condition number 1e2.'''
def __init__(self, n):
self.elli_factors = np.zeros(n)
for i in range(n):
self.elli_factors[i] = np.power(1e2, i / (n - 1))
def __call__(self, x):
return np.sqrt(np.dot(x, self.elli_factors * x))
class BenignEllipseNoisyThres(object):
'''Implements a quadratic function of condition number 1e2
with a noise strength proportional to the problem dimension
The noise is applied only above a threshold of 3.5 (function value).'''
def __init__(self, n, rng=np.random.RandomState()):
self.n = n
self.rng = rng
self.elli_factors = np.zeros(n)
for i in range(n):
self.elli_factors[i] = np.power(1e2, i / (n - 1))
def __call__(self, x):
f = np.sqrt(np.dot(x, self.elli_factors * x))
if f > 3.5:
f += (self.rng.randn()*(200/self.n))
return f
class BenignEllipseAddNoise(object):
'''An implementation of a quadratic function of condition number 1e6
on which additive noise is applied.'''
def __init__(self, n, noiseamp, rng=np.random.RandomState()):
self.noiseamp = noiseamp
self.rng = rng
self.elli_factors = np.zeros(n)
for i in range(n):
self.elli_factors[i] = np.power(1e2, i / (n - 1))
def __call__(self, x):
f_no_noise = np.sqrt(np.dot(x, self.elli_factors * x))
return f_no_noise*self.rng.randn()*self.noiseamp
class BenignEllipseMultNoise(object):
'''An implementation of a quadratic function of condition number 1e6
on which multiplicative noise is applied.'''
def __init__(self, n, noiseamp, rng=np.random.RandomState()):
self.noiseamp = noiseamp
self.rng = rng
self.elli_factors = np.zeros(n)
for i in range(n):
self.elli_factors[i] = np.power(1e2, i / (n - 1))
def __call__(self, x):
f_no_noise = np.sqrt(np.dot(x, self.elli_factors * x))
return f_no_noise*sigmoidal(self.rng.randn()*self.noiseamp)
class Ellipse(object):
'''Implements a quadratic function of condition number 1e6.'''
def __init__(self, n):
self.elli_factors = np.zeros(n)
for i in range(n):
self.elli_factors[i] = np.power(1e6, i / (n - 1))
def __call__(self, x):
return np.sqrt(np.dot(x, self.elli_factors * x))
class EllipseAddNoise(object):
'''An implementation of a quadratic function of condition number 1e6
on which additive noise is applied.'''
def __init__(self, n, noiseamp, rng=np.random.RandomState()):
self.noiseamp = noiseamp
self.rng = rng
self.elli_factors = np.zeros(n)
for i in range(n):
self.elli_factors[i] = np.power(1e6, i / (n - 1))
def __call__(self, x):
f_no_noise = np.sqrt(np.dot(x, self.elli_factors * x))
return f_no_noise*self.rng.randn()*self.noiseamp
class EllipseMultNoise(object):
'''An implementation of a quadratic function of condition number 1e6
on which multiplicative noise is applied.'''
def __init__(self, n, noiseamp, rng=np.random.RandomState()):
self.noiseamp = noiseamp
self.rng = rng
self.elli_factors = np.zeros(n)
for i in range(n):
self.elli_factors[i] = np.power(1e6, i / (n - 1))
def __call__(self, x):
f_no_noise = np.sqrt(np.dot(x, self.elli_factors * x))
return f_no_noise*sigmoidal(self.rng.randn()*self.noiseamp)
def sphere(x):
'''Implements a quadratic function of condition number 1e0.'''
return np.sqrt(np.dot(x, x))
class SphereAddNoise(object):
'''An implementation of a quadratic function of condition number 1
on which additive noise is applied.'''
def __init__(self, n, noiseamp, rng=np.random.RandomState()):
self.noiseamp = noiseamp
self.rng = rng
def __call__(self, x):
f_no_noise = np.sqrt(np.dot(x, x))
return f_no_noise*self.rng.randn()*self.noiseamp
class SphereMultNoise(object):
'''An implementation of a quadratic function of condition number 1
on which multiplicative noise is applied.'''
def __init__(self, n, noiseamp, rng=np.random.RandomState()):
self.noiseamp = noiseamp
self.rng = rng
def __call__(self, x):
f_no_noise = np.sqrt(np.dot(x, x))
return f_no_noise*sigmoidal(rng.randn()*self.noiseamp)
def sigmoidal(x):
'''A sigmoidal function thresholding large values.'''
return 2 / (1 + np.exp(-x))