def testMaxOfGLFunction(self):
"""Tests limits of the optimizer; not robust enough to find global max
amongst many local minima
Optimizer should return 5.0625 +/- tolerance at x=2.5"""
# Start right of a local min
result = twiddle(objFunction=GLFunction,
args=(),
initialGuess=1,
domain=(0.5, 2.5))
self.assertTrue(
abs(result['parameter'] - 2.5) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = 2.5" % result['parameter'])
self.assertTrue(
abs(result['score'] - 5.0625) <= 0.00001,
"Optimizer returned a max value of %r, but expected 5.0625" %
result['score'])
# Start at a local max
result = twiddle(objFunction=GLFunction,
args=(),
initialGuess=1.25,
domain=(0.5, 2.5))
self.assertFalse(
abs(result['parameter'] - 2.5) <= 0.00001,
"Optimizer found the max at the correct x = 2.5 but should not have"
)
self.assertFalse(
abs(result['score'] - 5.0625) <= 0.00001,
"Optimizer found the global max value of 5.0625 but should not have"
)
def testMaxOfGLFunction(self):
"""Tests limits of the optimizer; not robust enough to find global max
amongst many local minima
Optimizer should return 5.0625 +/- tolerance at x=2.5"""
# Start right of a local min
optimizedThreshold, optimizedScore = twiddle(objFunction=GLFunction,
args = (),
initialGuess = 1,
domain = (0.5, 2.5))
self.assertTrue(abs(optimizedThreshold - 2.5) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = 2.5" % optimizedThreshold)
self.assertTrue(abs(optimizedScore - 5.0625) <= 0.00001,
"Optimizer returned a max value of %r, but expected 5.0625"
% optimizedScore)
# Start at a local max
optimizedThreshold, optimizedScore = twiddle(objFunction=GLFunction,
args = (),
initialGuess = 1.25,
domain = (0.5, 2.5))
self.assertFalse(abs(optimizedThreshold - 2.5) <= 0.00001,
"Optimizer found the max at the correct x = 2.5 but should not have")
self.assertFalse(abs(optimizedScore - 5.0625) <= 0.00001,
"Optimizer found the global max value of 5.0625 but should not have")
def testMaxOfSine(self):
"""Tests ability to distinguish between several local/global maxima
Optimizer should return 1.0 at x={pi/2, 3pi/2}"""
# Start left of local max pi/2
optimizedThreshold, optimizedScore = twiddle(objFunction=sine,
args = (),
initialGuess = math.pi*(0.5 - 0.1),
domain = (0, 2*math.pi))
self.assertTrue(abs(optimizedThreshold - math.pi/2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (optimizedThreshold, math.pi/2))
self.assertTrue(abs(optimizedScore - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" % optimizedScore)
# Start right of local max pi/2
optimizedThreshold, optimizedScore = twiddle(objFunction=sine,
args = (),
initialGuess = math.pi*(0.5 + 0.1),
domain = (0, 2*math.pi))
self.assertTrue(abs(optimizedThreshold - math.pi/2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (optimizedThreshold, math.pi/2))
self.assertTrue(abs(optimizedScore - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" % optimizedScore)
# Start left of local min
optimizedThreshold, optimizedScore = twiddle(objFunction=sine,
args = (),
initialGuess = math.pi*(1.5 - 0.1),
domain = (0, 2*math.pi))
self.assertTrue(abs(optimizedThreshold - math.pi/2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (optimizedThreshold, math.pi/2))
self.assertTrue(abs(optimizedScore - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" % optimizedScore)
# Start right of local min
optimizedThreshold, optimizedScore = twiddle(objFunction=sine,
args = (),
initialGuess = math.pi*(1.5 + 0.1),
domain = (0, 3*math.pi))
self.assertTrue(abs(optimizedThreshold - math.pi*5/2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (optimizedThreshold, math.pi*5/2))
self.assertTrue(abs(optimizedScore - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" % optimizedScore)
def testMaxOfNegativeXSquared(self):
"""Tests ability to locate the single local/global max
Optimizer should return 0 at x=0"""
# Start arbitrarily w/in domain
optimizedThreshold, optimizedScore = twiddle(objFunction=negativeXSquared,
args = (),
initialGuess = 42,
domain = (-50, 50))
self.assertTrue(abs(optimizedThreshold - 0.0) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of \
the maximum location x = 0.0" % optimizedThreshold)
self.assertTrue(abs(optimizedScore - 0) <= math.sqrt(0.00001),
"Optimizer returned a max value of %r, but expected 0" % optimizedScore)
def testMaxOfXSquared(self):
"""Tests ability to locate the max constrained by domain boundaries
Optimizer should return 100 at x=10"""
# Start right of global min
optimizedThreshold, optimizedScore = twiddle(objFunction=xSquared,
args = (),
initialGuess = 1,
domain = (0, 10))
self.assertTrue(abs(optimizedThreshold - 10.0) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of \
the maximum location x = 10.0" % optimizedThreshold)
self.assertTrue(abs(optimizedScore - 100) <= math.sqrt(0.00001),
"Optimizer returned a max value of %r, but expected 100"
% optimizedScore)
def testMaxOfXSquared(self):
"""Tests ability to locate the max constrained by domain boundaries
Optimizer should return 100 at x=10"""
# Start right of global min
result = twiddle(objFunction=xSquared,
args=(),
initialGuess=1,
domain=(0, 10))
self.assertTrue(
abs(result['parameter'] - 10.0) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of \
the maximum location x = 10.0" % result['parameter'])
self.assertTrue(
abs(result['score'] - 100) <= math.sqrt(0.00001),
"Optimizer returned a max value of %r, but expected 100" %
result['score'])
def testMaxOfNegativeXSquared(self):
"""Tests ability to locate the single local/global max
Optimizer should return 0 at x=0"""
# Start arbitrarily w/in domain
result = twiddle(objFunction=negativeXSquared,
args=(),
initialGuess=42,
domain=(-50, 50))
self.assertTrue(
abs(result['parameter'] - 0.0) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of \
the maximum location x = 0.0" % result['parameter'])
self.assertTrue(
abs(result['score'] - 0) <= math.sqrt(0.00001),
"Optimizer returned a max value of %r, but expected 0" %
result['score'])
def testMaxOfSine(self):
"""Tests ability to distinguish between several local/global maxima
Optimizer should return 1.0 at x={pi/2, 3pi/2}"""
# Start left of local max pi/2
result = twiddle(objFunction=sine,
args=(),
initialGuess=math.pi * (0.5 - 0.1),
domain=(0, 2 * math.pi))
self.assertTrue(
abs(result['parameter'] - math.pi / 2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (result['parameter'], math.pi / 2))
self.assertTrue(
abs(result['score'] - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" %
result['score'])
# Start right of local max pi/2
result = twiddle(objFunction=sine,
args=(),
initialGuess=math.pi * (0.5 + 0.1),
domain=(0, 2 * math.pi))
self.assertTrue(
abs(result['parameter'] - math.pi / 2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (result['parameter'], math.pi / 2))
self.assertTrue(
abs(result['score'] - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" %
result['score'])
# Start left of local min
result = twiddle(objFunction=sine,
args=(),
initialGuess=math.pi * (1.5 - 0.1),
domain=(0, 2 * math.pi))
self.assertTrue(
abs(result['parameter'] - math.pi / 2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (result['parameter'], math.pi / 2))
self.assertTrue(
abs(result['score'] - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" %
result['score'])
# Start right of local min
result = twiddle(objFunction=sine,
args=(),
initialGuess=math.pi * (1.5 + 0.1),
domain=(0, 3 * math.pi))
self.assertTrue(
abs(result['parameter'] - math.pi * 5 / 2) <= 0.00001,
"Optimizer returned x = %r, which is not within the tolerance of the \
maximum location x = %r" % (result['parameter'], math.pi * 5 / 2))
self.assertTrue(
abs(result['score'] - 1.0) <= 0.00001,
"Optimizer returned max value of %r, but expected 1.0" %
result['score'])
