def create_training_points_irregular_transformed(n_target, noise_level):
""" create array of training points
Discard any training points where turbines are
not in the correct order and any training points where
turbines are closer than 2D
Maximin design in the transformed space
Parameters
----------
n_target: int
target number of training points
noise_level: float
Level of gaussian noise to be added to
simulator
Returns
-------
X_train: ndarray of shape(variable,6)
array containing valid training points
X_train_tran: ndarray of shape(variable,6)
array containing valid transformed training points
y_train: ndarray of shape(variable,)
value of CT* at test points
n_train: int
number of valid training points
"""
X_train_tran = dp.maximin_reconstruction(n_target, 6)
X_train = np.zeros((len(X_train_tran), 6))
X_train[:, 0] = expon(scale=10).ppf(X_train_tran[:, 0])
X_train[:, 1] = norm(0, 2.5).ppf(X_train_tran[:, 1])
X_train[:, 2] = expon(scale=10).ppf(X_train_tran[:, 2])
X_train[:, 3] = norm(0, 2.5).ppf(X_train_tran[:, 3])
X_train[:, 4] = expon(scale=10).ppf(X_train_tran[:, 4])
X_train[:, 5] = norm(0, 2.5).ppf(X_train_tran[:, 5])
# exclude training points where turbine 1 is closer than 2D
X_train_dist = np.sqrt(X_train[:, 0]**2 + X_train[:, 1]**2)
X_train_real = X_train[X_train_dist > 2]
X_train_tran = X_train_tran[X_train_dist > 2]
# exclude training points where turbine 2 is more important"
# than turbine 1 using distance = sqrt(10*x_1^2 + y_1^2)
X_train_sig = calculate_distance(X_train_real[:, 2],
X_train_real[:, 3]) \
- calculate_distance(X_train_real[:, 0], X_train_real[:, 1])
X_train_real = X_train_real[X_train_sig > 0]
X_train_tran = X_train_tran[X_train_sig > 0]
# exclude training points where turbine 3 is more important
# than turbine 2 using distance = sqrt(10*x_1^2 + y_1^2)
X_train_sig = calculate_distance(X_train_real[:, 4],
X_train_real[:, 5]) \
- calculate_distance(X_train_real[:, 2], X_train_real[:, 3])
X_train_real = X_train_real[X_train_sig > 0]
X_train_tran = X_train_tran[X_train_sig > 0]
# run simulations to find data points
y_train = np.zeros(len(X_train_real))
for i in range(len(X_train_real)):
y_train[i] = simulator6d_halved(X_train_real[i, :], noise_level)
n_train = len(X_train_real)
X_train = X_train_real
return X_train, X_train_tran, y_train, n_train
def create_testing_points_transformed():
""" create array of testing points
Discard any training points where turbines are
not in the correct order and any training points where
turbines are closer than 2D
X_test is tranformed by the cdf of probability distributions
expon(scale=10) in the x direction and norm(0, 2.5) in the y
direction
Parameters
----------
noise_level: float
Level of gaussian noise to be added to
simulator
Returns
-------
X_test: ndarray of shape(variable,6)
array containing valid test points
X_test_tran: ndarray of shape(varaible,6)
array containing valid transformed test points
y_test: ndarray of shape(variable,)
value of CT* at test points
"""
X_test = lhs(6, 10000)
X_test[:, 0] = 30 * X_test[:, 0]
X_test[:, 1] = 10 * X_test[:, 1] - 5
X_test[:, 2] = 30 * X_test[:, 2]
X_test[:, 3] = 10 * X_test[:, 3] - 5
X_test[:, 4] = 30 * X_test[:, 4]
X_test[:, 5] = 10 * X_test[:, 5] - 5
# exclude test points where turbine 1 is closer than 2D
X_test_dist = np.sqrt(X_test[:, 0]**2 + X_test[:, 1]**2)
X_test_real = X_test[X_test_dist > 2]
# exclude test points where turbine 2 is more "important" than turbine 1
# using distance = sqrt(x_1^2 + k*y_1^2)
X_test_sig = calculate_distance(X_test_real[:, 2],
X_test_real[:, 3]) \
- calculate_distance(X_test_real[:, 0], X_test_real[:, 1])
X_test_real = X_test_real[X_test_sig > 0]
# exclude test points where turbine 3 is more "important" than turbine 2
# using distance = sqrt(x_1^2 + k*y_1^2)
X_test_sig = calculate_distance(X_test_real[:, 4],
X_test_real[:, 5]) \
- calculate_distance(X_test_real[:, 2], X_test_real[:, 3])
X_test_real = X_test_real[X_test_sig > 0]
y_test = np.zeros(len(X_test_real))
for i in range(len(X_test_real)):
y_test[i] = simulator6d_halved(X_test_real[i, :])
X_test = X_test_real
X_test_tran = np.zeros((len(X_test_real), 6))
X_test_tran[:, 0] = expon(scale=10).cdf(X_test_real[:, 0])
X_test_tran[:, 2] = expon(scale=10).cdf(X_test_real[:, 2])
X_test_tran[:, 4] = expon(scale=10).cdf(X_test_real[:, 4])
X_test_tran[:, 1] = norm(0, 2.5).cdf(X_test_real[:, 1])
X_test_tran[:, 3] = norm(0, 2.5).cdf(X_test_real[:, 3])
X_test_tran[:, 5] = norm(0, 2.5).cdf(X_test_real[:, 5])
return X_test, X_test_tran, y_test
def validlhs_regular():
from pyDOE import lhs as lhsd
n_samples = 0
while n_samples != 300:
lhs = lhsd(6, 2800)
#expand x, y coordinates to their real values
lhs[:, 0] = expon(scale=10).ppf(lhs[:, 0])
lhs[:, 1] = norm(0, 2.5).ppf(lhs[:, 1])
lhs[:, 2] = expon(scale=10).ppf(lhs[:, 2])
lhs[:, 3] = norm(0, 2.5).ppf(lhs[:, 3])
lhs[:, 4] = expon(scale=10).ppf(lhs[:, 4])
lhs[:, 5] = norm(0, 2.5).ppf(lhs[:, 5])
#exclude points where turbine 2 is closer than turbine 1
valid_1_2 = calculate_distance(lhs[:, 2],
lhs[:, 3]) \
- calculate_distance(lhs[:, 0], lhs[:, 1])
lhs = lhs[valid_1_2 > 0]
#exclude points where turbine 3 is closer than turbine 2
valid_2_3 = calculate_distance(lhs[:, 4],
lhs[:, 5]) \
- calculate_distance(lhs[:, 2], lhs[:, 3])
lhs = lhs[valid_2_3 > 0]
#exclude points where turbines are closer than 2D to origin
dist_1 = np.sqrt(lhs[:, 0]**2 + lhs[:, 1]**2)
lhs = lhs[dist_1 > 2]
dist_2 = np.sqrt(lhs[:, 2]**2 + lhs[:, 3]**2)
lhs = lhs[dist_2 > 2]
dist_3 = np.sqrt(lhs[:, 4]**2 + lhs[:, 5]**2)
lhs = lhs[dist_3 > 2]
#exclude points where turbines are closer than 2D from
#each other
dist_1_2 = np.sqrt((lhs[:, 0] - lhs[:, 2])**2 +
(lhs[:, 1] - lhs[:, 3])**2)
lhs = lhs[dist_1_2 > 2]
dist_2_3 = np.sqrt((lhs[:, 2] - lhs[:, 4])**2 +
(lhs[:, 3] - lhs[:, 5])**2)
lhs = lhs[dist_2_3 > 2]
dist_3_1 = np.sqrt((lhs[:, 4] - lhs[:, 0])**2 +
(lhs[:, 5] - lhs[:, 1])**2)
lhs = lhs[dist_3_1 > 2]
n_samples = len(lhs)
print(n_samples)
#return to transformed coordinates
lhs[:, 0] = expon(scale=10).cdf(lhs[:, 0])
lhs[:, 1] = norm(0, 2.5).cdf(lhs[:, 1])
lhs[:, 2] = expon(scale=10).cdf(lhs[:, 2])
lhs[:, 3] = norm(0, 2.5).cdf(lhs[:, 3])
lhs[:, 4] = expon(scale=10).cdf(lhs[:, 4])
lhs[:, 5] = norm(0, 2.5).cdf(lhs[:, 5])
# replace lhs points with nearest regular arrays
X_reg_tran = np.loadtxt('regular_arrays_no_rot_transformed.txt')
min_dist = np.zeros(len(X_reg_tran))
for i in range(len(lhs)):
diff = np.linalg.norm(X_reg_tran - lhs[i, :], axis=1)
lhs[i, :] = X_reg_tran[np.argmin(diff), :]
return lhs
def validlhs():
from pyDOE import lhs as lhsd
n_samples = 0
while n_samples != 300:
lhs = lhsd(6, 2800)
#expand x, y coordinates to their real values
lhs[:, 0] = expon(scale=10).ppf(lhs[:, 0])
lhs[:, 1] = norm(0, 2.5).ppf(lhs[:, 1])
lhs[:, 2] = expon(scale=10).ppf(lhs[:, 2])
lhs[:, 3] = norm(0, 2.5).ppf(lhs[:, 3])
lhs[:, 4] = expon(scale=10).ppf(lhs[:, 4])
lhs[:, 5] = norm(0, 2.5).ppf(lhs[:, 5])
#exclude points where turbine 2 is closer than turbine 1
valid_1_2 = calculate_distance(lhs[:, 2],
lhs[:, 3]) \
- calculate_distance(lhs[:, 0], lhs[:, 1])
lhs = lhs[valid_1_2 > 0]
#exclude points where turbine 3 is closer than turbine 2
valid_2_3 = calculate_distance(lhs[:, 4],
lhs[:, 5]) \
- calculate_distance(lhs[:, 2], lhs[:, 3])
lhs = lhs[valid_2_3 > 0]
#exclude points where turbines are closer than 2D to origin
dist_1 = np.sqrt(lhs[:, 0]**2 + lhs[:, 1]**2)
lhs = lhs[dist_1 > 2]
dist_2 = np.sqrt(lhs[:, 2]**2 + lhs[:, 3]**2)
lhs = lhs[dist_2 > 2]
dist_3 = np.sqrt(lhs[:, 4]**2 + lhs[:, 5]**2)
lhs = lhs[dist_3 > 2]
#exclude points where turbines are closer than 2D from
#each other
dist_1_2 = np.sqrt((lhs[:, 0] - lhs[:, 2])**2 +
(lhs[:, 1] - lhs[:, 3])**2)
lhs = lhs[dist_1_2 > 2]
dist_2_3 = np.sqrt((lhs[:, 2] - lhs[:, 4])**2 +
(lhs[:, 3] - lhs[:, 5])**2)
lhs = lhs[dist_2_3 > 2]
dist_3_1 = np.sqrt((lhs[:, 4] - lhs[:, 0])**2 +
(lhs[:, 5] - lhs[:, 1])**2)
lhs = lhs[dist_3_1 > 2]
n_samples = len(lhs)
print(n_samples)
#return to transformed coordinates
lhs[:, 0] = expon(scale=10).cdf(lhs[:, 0])
lhs[:, 1] = norm(0, 2.5).cdf(lhs[:, 1])
lhs[:, 2] = expon(scale=10).cdf(lhs[:, 2])
lhs[:, 3] = norm(0, 2.5).cdf(lhs[:, 3])
lhs[:, 4] = expon(scale=10).cdf(lhs[:, 4])
lhs[:, 5] = norm(0, 2.5).cdf(lhs[:, 5])
return lhs
def create_testing_points(noise_level):
""" create array of testing points
Discard any training points where turbines are
not in the correct order and any training points where
turbines are closer than 2D
Parameters
----------
noise_level: float
Level of gaussian noise to be added to
simulator
Returns
-------
X_test_real: ndarray of shape(variable,6)
array containing valid test points
y_test: ndarray of shape(variable,)
value of CT* at test points
"""
X_test = lhs(6, 1000, 'maximin')
X_test[:, 0] = 30 * X_test[:, 0]
X_test[:, 1] = 10 * X_test[:, 1] - 5
X_test[:, 2] = 30 * X_test[:, 2]
X_test[:, 3] = 10 * X_test[:, 3] - 5
X_test[:, 4] = 30 * X_test[:, 4]
X_test[:, 5] = 10 * X_test[:, 5] - 5
# exclude test points where turbine 1 is closer than 2D
X_test_dist = np.sqrt(X_test[:, 0]**2 + X_test[:, 1]**2)
X_test_real = X_test[X_test_dist > 2]
# exclude test points where turbine 2 is more "important" than turbine 1
# using distance = sqrt(x_1^2 + k*y_1^2)
X_test_sig = calculate_distance(X_test_real[:, 2],
X_test_real[:, 3]) \
- calculate_distance(X_test_real[:, 0], X_test_real[:, 1])
X_test_real = X_test_real[X_test_sig > 0]
# exclude test points where turbine 3 is more "important" than turbine 2
# using distance = sqrt(x_1^2 + k*y_1^2)
X_test_sig = calculate_distance(X_test_real[:, 4],
X_test_real[:, 5]) \
- calculate_distance(X_test_real[:, 2], X_test_real[:, 3])
X_test_real = X_test_real[X_test_sig > 0]
y_test = np.zeros(len(X_test_real))
for i in range(len(X_test_real)):
y_test[i] = simulator6d_halved(X_test_real[i, :], noise_level)
return X_test_real, y_test