def test_modeling_4p(self):
exponents = [(0, 1, 1), (0, 1, 2), (1, 4, 0), (1, 3, 0), (1, 4, 1),
(1, 3, 1), (1, 4, 2), (1, 3, 2), (1, 2, 0), (1, 2, 1),
(1, 2, 2), (2, 3, 0), (3, 4, 0), (2, 3, 1), (3, 4, 1),
(4, 5, 0), (2, 3, 2), (3, 4, 2), (1, 1, 0), (1, 1, 1),
(1, 1, 2), (5, 4, 0), (5, 4, 1), (4, 3, 0), (4, 3, 1),
(3, 2, 0), (3, 2, 1), (3, 2, 2), (5, 3, 0), (7, 4, 0),
(2, 1, 0), (2, 1, 1), (2, 1, 2), (9, 4, 0), (7, 3, 0),
(5, 2, 0), (5, 2, 1), (5, 2, 2), (8, 3, 0), (11, 4, 0),
(3, 1, 0), (3, 1, 1)]
points = np.array(
list(zip(*itertools.product([2, 4, 8, 10, 12], repeat=4))))
for expo1, expo2, expo3, expo4 in zip(exponents, exponents[1:],
exponents[2:], exponents[3:]):
termX = CompoundTerm.create(*expo1)
termY = CompoundTerm.create(*expo2)
termZ = CompoundTerm.create(*expo3)
termW = CompoundTerm.create(*expo4)
term = MultiParameterTerm((0, termX), (1, termY), (2, termZ),
(3, termW))
term.coefficient = 10
function = MultiParameterFunction(term)
function.constant_coefficient = 20000
values = function.evaluate(points)
measurements = [
Measurement(Coordinate(p), None, None, v)
for p, v in zip(zip(*points), values)
]
modeler = MultiParameterModeler()
models = modeler.model([measurements])
self.assertEqual(1, len(models))
self.assertApproxFunction(function, models[0].hypothesis.function)
def deserialize_MultiParameterTerm(id_mappings, ioHelper):
new_term = MultiParameterTerm()
new_term.coefficient = ioHelper.readValue()
size = ioHelper.readInt()
for i in range(size):
name = ioHelper.readString()
p = id_mappings.parameter_mapping[name]
prefix = ioHelper.readString()
assert (prefix == 'CompoundTerm')
term = deserialize_CompoundTerm(ioHelper)
new_term.add_parameter_term_pair((p, term))
return new_term
def test_modeling_plus(self):
exponents = [(0, 1, 1), (0, 1, 2), (1, 4, 0), (1, 3, 0), (1, 4, 1), (1, 3, 1), (1, 4, 2), (1, 3, 2),
(1, 2, 0), (1, 2, 1), (1, 2, 2), (2, 3, 0), (3, 4, 0), (2, 3, 1), (3, 4, 1), (4, 5, 0),
(2, 3, 2), (3, 4, 2), (1, 1, 0), (1, 1, 1), (1, 1, 2), (5, 4, 0), (5, 4, 1), (4, 3, 0),
(4, 3, 1), (3, 2, 0), (3, 2, 1), (3, 2, 2), (5, 3, 0), (7, 4, 0), (2, 1, 0), (2, 1, 1),
(2, 1, 2), (9, 4, 0), (7, 3, 0), (5, 2, 0), (5, 2, 1), (5, 2, 2), (8, 3, 0), (11, 4, 0),
(3, 1, 0), (3, 1, 1)]
for expo1, expo2 in zip(exponents, exponents[1:]):
termX = CompoundTerm.create(*expo1)
termY = CompoundTerm.create(*expo2)
term1 = MultiParameterTerm((0, termX))
term1.coefficient = 10
term2 = MultiParameterTerm((1, termY))
term2.coefficient = 20
function = MultiParameterFunction(term1, term2)
function.constant_coefficient = 200
points = [np.array([2, 4, 8, 16, 32, 2, 4, 8, 16, 32, 2, 4, 8, 16, 32, 2, 4, 8, 16, 32, 2, 4, 8, 16, 32]),
np.array([2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32])]
values = function.evaluate(np.array(points))
measurements = [Measurement(Coordinate(p), None, None, v) for p, v in zip(zip(*points), values)]
modeler = MultiParameterModeler()
models = modeler.model([measurements])
self.assertEqual(1, len(models))
self.assertApproxFunction(function, models[0].hypothesis.function)
def create_model(self, measurements: Sequence[Measurement]):
"""
Create a multi-parameter model using the given measurements.
"""
if self.single_parameter_point_selection == 'auto' \
or self.single_parameter_point_selection == 'all':
measurements_sp = self.find_best_measurement_points(measurements)
else:
# use the first base points found for each parameter for modeling of the single parameter functions
measurements_sp = self.find_first_measurement_points(measurements)
# print(coordinates_list)
# model all single parameter experiments using only the selected points from the step before
# parameters = list(range(measurements[0].coordinate.dimensions))
models = self.single_parameter_modeler.model(measurements_sp)
functions = [m.hypothesis.function for m in models]
# check if the number of measurements satisfies the reuqirements of the modeler (>=5)
if len(measurements) < self.min_measurement_points:
warnings.warn("Number of measurements for each parameter needs to be at least 5"
" in order to create a performance model.")
# return None
# get the coordinates for modeling
# coordinates = list(dict.fromkeys(m.coordinate for m in measurements).keys())
# use all available additional points for modeling the multi-parameter models
constantCost = 0
meanModel = 0
for m in measurements:
meanModel += m.value(self.use_median) / float(len(measurements))
for m in measurements:
constantCost += (m.value(self.use_median) - meanModel) * (m.value(self.use_median) - meanModel)
# find out which parameters should be kept
compound_term_pairs = []
for i, function in enumerate(functions):
terms = function.compound_terms
if len(terms) > 0:
compound_term = terms[0]
compound_term.coefficient = 1
compound_term_pairs.append((i, compound_term))
# see if the function is constant
if len(compound_term_pairs) == 0:
constant_function = ConstantFunction()
constant_function.constant_coefficient = meanModel
constant_hypothesis = ConstantHypothesis(constant_function, self.use_median)
constant_hypothesis.compute_cost(measurements)
return Model(constant_hypothesis)
# in case is only one parameter, make a single parameter function
elif len(compound_term_pairs) == 1:
param, compound_term = compound_term_pairs[0]
multi_parameter_function = MultiParameterFunction()
multi_parameter_term = MultiParameterTerm(compound_term_pairs[0])
multi_parameter_term.coefficient = compound_term.coefficient
multi_parameter_function.add_compound_term(multi_parameter_term)
# constant_coefficient = functions[param].get_constant_coefficient()
# multi_parameter_function.set_constant_coefficient(constant_coefficient)
multi_parameter_hypothesis = MultiParameterHypothesis(multi_parameter_function, self.use_median)
multi_parameter_hypothesis.compute_coefficients(measurements)
multi_parameter_hypothesis.compute_cost(measurements)
return Model(multi_parameter_hypothesis)
# create multiplicative multi parameter term
mult = MultiParameterTerm(*compound_term_pairs)
# create additive multi parameter terms
add = [MultiParameterTerm(ctp) for ctp in compound_term_pairs]
# create multi parameter functions
mp_functions = [
# create f1 function a*b
MultiParameterFunction(mult),
# create f4 function a+b
MultiParameterFunction(*add)
]
if not self.allow_combinations_of_sums_and_products:
pass
# add Hypotheses for 2 parameter models
elif len(compound_term_pairs) == 2:
mp_functions += [
# create f2 function a*b+a
MultiParameterFunction(add[0], mult),
# create f3 function a*b+b
MultiParameterFunction(add[1], mult)
]
# add Hypotheses for 3 parameter models
elif len(compound_term_pairs) == 3:
# create multiplicative multi parameter terms
# x*y
mult_x_y = MultiParameterTerm(compound_term_pairs[0], compound_term_pairs[1])
# y*z
mult_y_z = MultiParameterTerm(compound_term_pairs[1], compound_term_pairs[2])
# x*z
mult_x_z = MultiParameterTerm(compound_term_pairs[0], compound_term_pairs[2])
# create multi parameter functions
mp_functions += [
# x*y*z+x
MultiParameterFunction(mult, add[0]),
# x*y*z+y
MultiParameterFunction(mult, add[1]),
# x*y*z+z
MultiParameterFunction(mult, add[2]),
# x*y*z+x*y
MultiParameterFunction(mult, mult_x_y),
# x*y*z+y*z
MultiParameterFunction(mult, mult_y_z),
# x*y*z+x*z
MultiParameterFunction(mult, mult_x_z),
# x*y*z+x*y+z
MultiParameterFunction(mult, mult_x_y, add[2]),
# x*y*z+y*z+x
MultiParameterFunction(mult, mult_y_z, add[0]),
# x*y*z+x*z+y
MultiParameterFunction(mult, mult_x_z, add[1]),
# x*y*z+x+y
MultiParameterFunction(mult, add[0], add[1]),
# x*y*z+x+z
MultiParameterFunction(mult, add[0], add[2]),
# x*y*z+y+z
MultiParameterFunction(mult, add[1], add[2]),
# x*y+z
MultiParameterFunction(mult_x_y, add[2]),
# x*y+z+y
MultiParameterFunction(mult_x_y, add[2], add[1]),
# x*y+z+x
MultiParameterFunction(mult_x_y, add[2], add[0]),
# x*z+y
MultiParameterFunction(mult_x_z, add[1]),
# x*z+y+x
MultiParameterFunction(mult_x_z, add[1], add[0]),
# x*z+y+z
MultiParameterFunction(mult_x_z, add[1], add[2]),
# y*z+x
MultiParameterFunction(mult_y_z, add[0]),
# y*z+x+y
MultiParameterFunction(mult_y_z, add[0], add[1]),
# y*z+x+z
MultiParameterFunction(mult_y_z, add[0], add[2])
]
# create the hypotheses from the functions
hypotheses = [MultiParameterHypothesis(f, self.use_median)
for f in mp_functions]
# select one function as the bestHypothesis for the start
best_hypothesis = copy.deepcopy(hypotheses[0])
best_hypothesis.compute_coefficients(measurements)
best_hypothesis.compute_cost(measurements)
best_hypothesis.compute_adjusted_rsquared(constantCost, measurements)
logging.info(f"hypothesis 0: {best_hypothesis.function} --- smape: {best_hypothesis.SMAPE} "
f"--- ar2: {best_hypothesis.AR2} --- rss: {best_hypothesis.RSS} "
f"--- rrss: {best_hypothesis.rRSS} --- re: {best_hypothesis.RE}")
# find the best hypothesis
for i, hypothesis in enumerate(hypotheses):
hypothesis.compute_coefficients(measurements)
hypothesis.compute_cost(measurements)
hypothesis.compute_adjusted_rsquared(constantCost, measurements)
logging.info(f"hypothesis {i}: {hypothesis.function} --- smape: {hypothesis.SMAPE} "
f"--- ar2: {hypothesis.AR2} --- rss: {hypothesis.RSS} "
f"--- rrss: {hypothesis.rRSS} --- re: {hypothesis.RE}")
term_contribution_big_enough = True
# for all compound terms check if they are smaller than minimum allowed contribution
for term in hypothesis.function.compound_terms:
# ignore this hypothesis, since one of the terms contributes less than epsilon to the function
if term.coefficient == 0 or hypothesis.calc_term_contribution(term, measurements) < self.epsilon:
term_contribution_big_enough = False
break
if not term_contribution_big_enough:
continue
elif self.compare_with_RSS:
if hypotheses[i].RSS < best_hypothesis.RSS:
best_hypothesis = copy.deepcopy(hypotheses[i])
elif hypotheses[i].SMAPE < best_hypothesis.SMAPE:
best_hypothesis = copy.deepcopy(hypotheses[i])
# add the best found hypothesis to the model list
model = Model(best_hypothesis)
logging.info(f"best hypothesis: {best_hypothesis.function} --- smape: {best_hypothesis.SMAPE} "
f"--- ar2: {best_hypothesis.AR2} --- rss: {best_hypothesis.RSS} "
f"--- rrss: {best_hypothesis.rRSS} --- re: {best_hypothesis.RE}")
return model