def test_multi_source_function_wrapper_evaluation_with_multiple_extra_arguments(
):
functions = [
lambda x:
(2 * x, np.array([[1]] * x.shape[0]), np.array([[1]] * x.shape[0])),
lambda x:
(4 * x, np.array([[2]] * x.shape[0]), np.array([[1]] * x.shape[0]))
]
function_input = np.array([[1, 0], [2, 1], [3, 0], [4, 0], [5, 1]])
source_index = -1
msfw = MultiSourceFunctionWrapper(
functions, source_index, extra_output_names=['cost', 'constraint'])
output = msfw.evaluate(function_input)
assert len(output) == function_input.shape[0]
for i, record in enumerate(output):
assert_array_equal(output[i].X, function_input[i])
this_function = functions[function_input[i, source_index]]
this_function_input = np.delete(function_input[i], source_index)
assert_array_equal(output[i].Y, this_function(this_function_input)[0])
assert_array_equal(output[i].cost,
this_function(this_function_input)[1][0])
assert_array_equal(output[i].constraint,
this_function(this_function_input)[2][0])
def test_multi_source_function_wrapper_too_few_outputs_outputs_fails():
functions = [lambda x: 2 * x,
lambda x: 4 * x]
function_input = np.array([[1, 0], [2, 1], [3, 0], [4, 0], [5, 1]])
source_index = -1
msfw = MultiSourceFunctionWrapper(functions, source_index, extra_output_names=['cost'])
with pytest.raises(ValueError):
msfw.evaluate(function_input)
def test_multi_source_function_wrapper_too_many_outputs_outputs_fails():
functions = [lambda x: (2 * x, np.array([[1]] * x.shape[0]), np.array([[1]] * x.shape[0])),
lambda x: (4 * x, np.array([[2]] * x.shape[0]), np.array([[1]] * x.shape[0]))]
function_input = np.array([[1, 0], [2, 1], [3, 0], [4, 0], [5, 1]])
source_index = -1
msfw = MultiSourceFunctionWrapper(functions, source_index)
with pytest.raises(ValueError):
msfw.evaluate(function_input)
def test_multi_source_function_wrapper_evaluation_single_output():
functions = [lambda x: 2 * x, lambda x: 4 * x]
function_input = np.array([[1, 0], [2, 1], [3, 0], [4, 0], [5, 1]])
source_index = -1
msfw = MultiSourceFunctionWrapper(functions, source_index)
output = msfw.evaluate(function_input)
assert len(output) == function_input.shape[0]
for i, record in enumerate(output):
assert_array_equal(output[i].X, function_input[i])
this_function = functions[function_input[i, source_index]]
this_function_input = np.delete(function_input[i], source_index)
assert_array_equal(output[i].Y, this_function(this_function_input))
def test_multi_source_function_wrapper_evaluation_no_cost():
functions = [lambda x: 2 * x, lambda x: 4 * x]
function_input = np.array([[1, 0], [2, 1], [3, 0], [4, 0], [5, 1]])
source_index = -1
msfw = MultiSourceFunctionWrapper(functions, source_index)
output = msfw.evaluate(function_input)
assert len(output) == function_input.shape[0]
for i, record in enumerate(output):
assert_array_equal(output[i].X, function_input[i])
this_function = functions[function_input[i, source_index]]
this_function_input = np.delete(function_input[i], source_index)
assert_array_equal(output[i].Y, this_function(this_function_input))
assert output[i].cost is None
def multi_fidelity_non_linear_sin(high_fidelity_noise_std_deviation=0,
low_fidelity_noise_std_deviation=0):
"""
Two level non-linear sin function where high fidelity is given by:
.. math::
f_{high}(x) = (x - \sqrt{2}) f_{low}(x)^2
and the low fidelity is:
.. math::
f_{low}(x) = \sin(8 \pi x)
Reference:
Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling.
P. Perdikaris, M. Raissi, A. Damianou, N. D. Lawrence and G. E. Karniadakis (2017)
http://web.mit.edu/parisp/www/assets/20160751.full.pdf
"""
parameter_space = ParameterSpace(
[ContinuousParameter("x1", -5, 10),
InformationSourceParameter(2)])
user_function = MultiSourceFunctionWrapper([
lambda x: nonlinear_sin_low(x, low_fidelity_noise_std_deviation),
lambda x: nonlinear_sin_high(x, high_fidelity_noise_std_deviation),
])
return user_function, parameter_space
def multi_fidelity_borehole_function(high_noise_std_deviation=0, low_noise_std_deviation=0):
"""
Two level borehole function.
The Borehole function models water flow through a borehole. Its simplicity and quick evaluation makes it a commonly
used function for testing a wide variety of methods in computer experiments.
See reference for equations:
https://www.sfu.ca/~ssurjano/borehole.html
:param high_noise_std_deviation: Standard deviation of Gaussian observation noise on high fidelity observations.
Defaults to zero.
:param low_noise_std_deviation: Standard deviation of Gaussian observation noise on low fidelity observations.
Defaults to zero.
:return: Tuple of user function object and parameter space
"""
parameter_space = ParameterSpace([
ContinuousParameter('borehole_radius', 0.05, 0.15),
ContinuousParameter('radius_of_influence', 100, 50000),
ContinuousParameter('upper_aquifer_transmissivity', 63070, 115600),
ContinuousParameter('upper_aquifer_head', 990, 1110),
ContinuousParameter('lower_aquifer_transmissivity', 63.1, 116),
ContinuousParameter('lower_aquifer_head', 700, 820),
ContinuousParameter('borehole_length', 1120, 1680),
ContinuousParameter('hydraulic_conductivity', 9855, 12045),
InformationSourceParameter(2)])
user_function = MultiSourceFunctionWrapper([
lambda x: borehole_low(x, low_noise_std_deviation),
lambda x: borehole_high(x, high_noise_std_deviation)])
return user_function, parameter_space
def multi_fidelity_forrester_function(high_fidelity_noise_std_deviation=0, low_fidelity_noise_std_deviation=0):
"""
Two-level multi-fidelity forrester function where the high fidelity is given by:
.. math::
f(x) = (6x - 2)^2 \sin(12x - 4)
and the low fidelity approximation given by:
.. math::
f_{low}(x) = 0.5 f_{high}(x) + 10 (x - 0.5) + 5
:param high_fidelity_noise_std_deviation: Standard deviation of observation noise on high fidelity observations.
Defaults to zero.
:param low_fidelity_noise_std_deviation: Standard deviation of observation noise on low fidelity observations.
Defaults to zero.
:return: Tuple of user function object and parameter space object
"""
parameter_space = ParameterSpace([ContinuousParameter("x", 0, 1), InformationSourceParameter(2)])
user_function = MultiSourceFunctionWrapper(
[
lambda x: forrester_low(x, low_fidelity_noise_std_deviation),
lambda x: forrester(x, high_fidelity_noise_std_deviation),
]
)
return user_function, parameter_space
def test_multi_source_function_wrapper_invalid_input():
# invalid input
with pytest.raises(ValueError):
functions = [lambda x: 2 * x]
function_input = np.array([1, 0])
msfw = MultiSourceFunctionWrapper(functions)
msfw.evaluate(function_input)
# invalid function output
with pytest.raises(ValueError):
functions = [lambda x: np.array([2])]
function_input = np.array([[1, 0]])
msfw = MultiSourceFunctionWrapper(functions)
msfw.evaluate(function_input)
# invalid function output type
with pytest.raises(ValueError):
functions = [lambda x: [2]]
function_input = np.array([[1, 0]])
msfw = MultiSourceFunctionWrapper(functions)
msfw.evaluate(function_input)
def test_multi_source_function_wrapper_invalid_input():
# invalid input
with pytest.raises(ValueError):
functions = [lambda x: 2 * x]
function_input = np.array([1, 0])
msfw = MultiSourceFunctionWrapper(functions)
msfw.evaluate(function_input)
# invalid function output
with pytest.raises(ValueError):
functions = [lambda x: np.array([2])]
function_input = np.array([[1, 0]])
msfw = MultiSourceFunctionWrapper(functions)
msfw.evaluate(function_input)
# invalid function output type
with pytest.raises(ValueError):
functions = [lambda x: [2]]
function_input = np.array([[1, 0]])
msfw = MultiSourceFunctionWrapper(functions)
msfw.evaluate(function_input)