def build_experiment(self):
df = pd.DataFrame(doe.ccdesign(len(self.f), (1, 1), face='cci'),
columns=[f.name for f in self.f])
for f in self.f:
df[f.name] = (df[f.name] * f.delta) + f.centre
df[f.name] = myround(df[f.name], f.precision)
self.data = df
def plan_matrix(n, m):
print(f'\nПлан матриці при n = {n}, m = {m}')
y = np.zeros(shape=(n, m))
for i in range(n):
for j in range(m):
y[i][j] = random.randint(y_min, y_max)
no = n - 14 if n > 14 else 1
x_norm = ccdesign(3, center=(0, no))
x_norm = np.insert(x_norm, 0, 1, axis=1)
for i in range(4, 11):
x_norm = np.insert(x_norm, i, 0, axis=1)
l = 1.215
for i in range(len(x_norm)):
for j in range(len(x_norm[i])):
if x_norm[i][j] < -1 or x_norm[i][j] > 1:
x_norm[i][j] = -l if x_norm[i][j] < 0 else l
def add_sq_nums(x):
for i in range(len(x)):
x[i][4] = x[i][1] * x[i][2]
x[i][5] = x[i][1] * x[i][3]
x[i][6] = x[i][2] * x[i][3]
x[i][7] = x[i][1] * x[i][3] * x[i][2]
x[i][8] = x[i][1]**2
x[i][9] = x[i][2]**2
x[i][10] = x[i][3]**2
return x
x_norm = add_sq_nums(x_norm)
x = np.ones(shape=(len(x_norm), len(x_norm[0])), dtype=np.int64)
for i in range(8):
for j in range(1, 4):
x[i][j] = x_range[j -
1][0] if x_norm[i][j] == -1 else x_range[j -
1][1]
for i in range(8, len(x)):
for j in range(1, 3):
x[i][j] = (x_range[j - 1][0] + x_range[j - 1][1]) / 2
dx = [
x_range[i][1] - (x_range[i][0] + x_range[i][1]) / 2 for i in range(3)
]
x[8][1] = l * dx[0] + x[9][1]
x[9][1] = -l * dx[0] + x[9][1]
x[10][2] = l * dx[1] + x[9][2]
x[11][2] = -l * dx[1] + x[9][2]
x[12][3] = l * dx[2] + x[9][3]
x[13][3] = -l * dx[2] + x[9][3]
x = add_sq_nums(x)
print('\nX:\n', x)
print('\nX нормалізоване:\n')
for i in x_norm:
print([round(x, 2) for x in i])
print('\nY:\n', y)
return x, y, x_norm
def generate_samples(num_samples_inside, num_samples_boundary, x_k, delta_k):
"""
Generates samples from both `inside the region` and `on the boundary`.
To sample from the boundary, the *Central Composite* is used.
To sample from the region interior, the *Latin Hypercube Sampling* is used.
Args:
num_samples_inside (int): Number of desired samples inside the region.
num_samples_boundary (int): Number of desired samples on the region boundary.
x_k (vector): Center of the boundary.
delta_k (float): Radius of the boundary.
Returns:
total_samples: list of new samples form the boundary
"""
# 1. Determine the dimension of x_k: used for knowing the random vector dimensions
x_k_dim = x_k.shape[0]
# 2. Sample from boundary: Central Composite
if x_k_dim == 1:
samples_boundary = np.array([[-1.0], [1.0]])
else:
res = [
normalize(v)
for v in ccdesign(x_k_dim, center=[0 for i in range(x_k_dim)])
]
samples_boundary = np.array(res)
samples_boundary = random.choices(delta_k * samples_boundary + x_k,
k=num_samples_boundary)
# 3. Sample from region: Latin Hypercube Sampling
samples_inside = lhs(x_k_dim, samples=num_samples_inside)
scaled_samples_inside = np.vectorize(lambda x: -delta_k + x * delta_k * 2)(
samples_inside)
samples_inside = scaled_samples_inside + x_k
# 4. Add directions to the center point x_k to get new candidate points
total_samples = np.concatenate((np.concatenate(
(samples_boundary, samples_inside)), [[0.0 for i in range(x_k_dim)]]))
for i in range(5):
total_samples = np.concatenate(
(total_samples, [[0.0 for i in range(x_k_dim)]]))
return total_samples
# if __name__ == "__main__":
# x_k = np.array([0.0], dtype=np.float32)
# delta_k = 2.0
# print(generate_samples(5, 3, x_k, delta_k))
def gen_matrix(self):
self.seq = [[1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3], [1, 1],
[2, 2], [3, 3]]
if self.y_only_int == True:
self.y = np.random.randint(self.y_min, self.y_max + 1,
(self.N, self.m))
else:
self.y = np.random.sample(
(self.N, self.m)) * (self.y_max - self.y_min) + self.y_min
self.y_mean = [i.mean() for i in self.y]
self.y_std = [np.std(i) for i in self.y]
delta_x = [np.abs(m[1] - m[0]) / 2 for m in self.x]
x_i_0 = [(m[1] + m[0]) / 2 for m in self.x]
self.extended = ccdesign(3, center=(0, 1))
self.extended_real = np.zeros((15, 3))
for i in range(self.extended.shape[0]):
for j in range(self.extended.shape[1]):
if self.extended[i][j] == 1:
self.extended_real[i][j] = self.x[j][1]
elif self.extended[i][j] == -1:
self.extended_real[i][j] = self.x[j][0]
elif self.extended[i][j] == 0:
self.extended_real[i][j] = x_i_0[j]
elif self.extended[i][j] > 0:
self.extended[i][j] = self.l
self.extended_real[i][j] = self.l * delta_x[j] + x_i_0[j]
else:
self.extended_real[i][j] = -self.l * delta_x[j] + x_i_0[j]
self.extended[i][j] = -self.l
num = self.extended.shape[1]
seq = [[1, 2], [1, 3], [2, 3], [1, 2, 3], [1, 1], [2, 2], [3, 3]]
for i in seq:
app = np.array([1] * self.extended.shape[0])
app_real = np.array([1] * self.extended.shape[0])
for j in i:
app = app * self.extended.T[j - 1]
app_real = app_real * self.extended_real.T[j - 1]
self.extended = np.insert(self.extended, num, app.T, axis=1)
self.extended_real = np.insert(self.extended_real,
num,
app_real.T,
axis=1)
num += 1
def gen_matrix(self):
self.seq = [[1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3], [1, 1],
[2, 2], [3, 3]]
delta_x = [np.abs(m[1] - m[0]) / 2 for m in self.x]
x_i_0 = [(m[1] + m[0]) / 2 for m in self.x]
self.extended = ccdesign(3, center=(0, 0))
# self.extended = np.delete(self.extended, -1, 0)
self.extended_real = np.zeros((14, 3))
for i in range(self.extended.shape[0]):
for j in range(self.extended.shape[1]):
if self.extended[i][j] == 1:
self.extended_real[i][j] = self.x[j][1]
elif self.extended[i][j] == -1:
self.extended_real[i][j] = self.x[j][0]
elif self.extended[i][j] == 0:
self.extended_real[i][j] = x_i_0[j]
elif self.extended[i][j] > 0:
self.extended[i][j] = self.l
self.extended_real[i][j] = self.l * delta_x[j] + x_i_0[j]
else:
self.extended_real[i][j] = -self.l * delta_x[j] + x_i_0[j]
self.extended[i][j] = -self.l
self.y = np.array([[
self.y_func(*self.extended_real[i][:3]) + np.random.rand() * 10 + 5
for j in range(self.m)
] for i in range(self.N)])
self.y_mean = [i.mean() for i in self.y]
self.y_std = [np.std(i) for i in self.y]
num = self.extended.shape[1]
seq = [[1, 2], [1, 3], [2, 3], [1, 2, 3], [1, 1], [2, 2], [3, 3]]
for i in seq:
app = np.array([1] * self.extended.shape[0])
app_real = np.array([1] * self.extended.shape[0])
for j in i:
app = app * self.extended.T[j - 1]
app_real = app_real * self.extended_real.T[j - 1]
self.extended = np.insert(self.extended, num, app.T, axis=1)
self.extended_real = np.insert(self.extended_real,
num,
app_real.T,
axis=1)
num += 1
def sampling(self, nx, xlimits, method='LHS', random_seed=10000):
'''
create nx samples bounded by xlimits using specified method.
xlimits defines lb and ub, in np.array([[LB1, UB1], [LB2, UB2], ...]) format.
method = 'LHS': Latin hypercube sampling, 'CCD': centralized composite design,
'PBD': Plackett-Burman design, 'PB-CCD': Plackett-Burman centralized composite design
'''
n_var = xlimits.shape[0]
# Sampling
if method.lower() == 'lhs':
x = DOE.lhs(n_var,
samples=nx,
criterion='correlation',
random_state=random_seed) * 2.0 - 1.0
elif method.lower() == 'ccd':
if n_var > 8:
raise ValueError(
'number of variables is TOO LARGE for centralized composite design (CCD).'
)
if n_var > 7:
warnings.warn(
'number of variables is TOO LARGE for centralized composite design (CCD).'
)
x = DOE.ccdesign(n_var,
center=(0, 1),
alpha='rotatable',
face='inscribed')
elif method.lower() == 'pbd':
x = DOE.pbdesign(n_var)
elif method.lower() in ['pb-ccd', 'pbccd']:
l = np.sqrt(n_var)
x = DOE.pbdesign(n_var) / l
x = np.append(x, -x / 2.0, axis=0)
for idx in range(0, n_var):
z = np.zeros((1, n_var))
z[0, idx] = 1.0
x = np.append(x, z, axis=0)
z[0, idx] = -1.0
x = np.append(x, z, axis=0)
x = np.append(x, np.zeros((1, n_var)), axis=0)
# Scale
for idx in range(0, xlimits.shape[0]):
x[:, idx] = (x[:, idx] + 1.0) / 2.0 * (
xlimits[idx, 1] - xlimits[idx, 0]) + xlimits[idx, 0]
# Return
return x
def ccd_lhs(self,
ccd_factors,
lhs_factors,
add_samples=5,
seed=None,
center_fill=False):
"""
Get experiments corresponding to a hybrid central composit
and latin hypercube design.
"""
# Run cc design
cc = pd.DataFrame(ccdesign(len(ccd_factors), (0, 1), 'o', 'cci'),
columns=ccd_factors)
cc = Data(cc)
cc.standardize(target=None, scaler='minmax')
# Either fill lh design or a single number
if center_fill:
lh = pd.DataFrame(np.ones((len(cc.data), len(lhs_factors))) * 0.5,
columns=lhs_factors)
else:
lh = pd.DataFrame(lhs(len(lhs_factors),
samples=len(cc.data),
criterion='center',
random_state=seed),
columns=lhs_factors)
lh2 = pd.DataFrame(lhs(self.N,
samples=add_samples,
criterion='center',
random_state=seed),
columns=ccd_factors + lhs_factors)
# Concatenate
design = pd.concat([cc.data, lh], axis=1)
design = pd.concat([design, lh2], axis=0).reset_index(drop=True)
# Reorder
self.design = design.copy()[self.names]
for i in range(len(x)):
x[i][4] = x[i][1] * x[i][2]
x[i][5] = x[i][1] * x[i][3]
x[i][6] = x[i][2] * x[i][3]
x[i][7] = x[i][1] * x[i][3] * x[i][2]
x[i][8] = x[i][1]**2
x[i][9] = x[i][2]**2
x[i][10] = x[i][3]**2
return x
if n > 14:
no = n - 14
else:
no = 1
xn = ccdesign(3, center=(0, no))
xn = np.insert(xn, 0, 1, axis=1)
for i in range(4, 11):
xn = np.insert(xn, i, 0, axis=1)
l = 1.215
for i in range(len(xn)):
for j in range(len(xn[i])):
if xn[i][j] < -1 or xn[i][j] > 1:
if xn[i][j] < 0:
xn[i][j] = -l
else:
xn[i][j] = l
def plan_matrix5(n, m):
print(f'\nГереруємо матрицю планування для n = {n}, m = {m}')
y = np.zeros(shape=(n, m)) # створюємо матрицю з нулів
for i in range(n):
for j in range(m):
y[i][j] = random.randint(y_min, y_max) # заповнюємо цю матрицю ігриками
start = time.time()
if n > 14:
no = n - 14
else:
no = 1
print("Время проверки 1 = ", start-time.time())
x_norm = ccdesign(3, center=(0, no)) # Central-Composite designs
x_norm = np.insert(x_norm, 0, 1, axis=1)
for i in range(4, 11):
x_norm = np.insert(x_norm, i, 0, axis=1)
l = 1.215
# матриця планування з нормовaними значеннями
for i in range(len(x_norm)):
for j in range(len(x_norm[i])):
start = time.time()
if x_norm[i][j] < -1 or x_norm[i][j] > 1:
if x_norm[i][j] < 0:
x_norm[i][j] = -l
else:
x_norm[i][j] = l
print("Время проверки 2 = ", start-time.time())
def add_sq_nums(x): # рахуємо квадратні числа
for i in range(len(x)):
x[i][4] = x[i][1] * x[i][2]
x[i][5] = x[i][1] * x[i][3]
x[i][6] = x[i][2] * x[i][3]
x[i][7] = x[i][1] * x[i][3] * x[i][2]
x[i][8] = x[i][1] ** 2
x[i][9] = x[i][2] ** 2
x[i][10] = x[i][3] ** 2
return x
x_norm = add_sq_nums(x_norm) # додаємо їх в матрицю
x = np.ones(shape=(len(x_norm), len(x_norm[0])), dtype=np.int64) # заповнюємо матрицю одиницями
# матриця планування з натуральними значеннями факторів
for i in range(8):
for j in range(1, 4):
start = time.time()
if x_norm[i][j] == -1:
x[i][j] = x_range[j - 1][0]
else:
x[i][j] = x_range[j - 1][1]
print("Время проверки = ", start-time.time())
for i in range(8, len(x)):
for j in range(1, 3):
x[i][j] = (x_range[j - 1][0] + x_range[j - 1][1]) / 2
dx = [x_range[i][1] - (x_range[i][0] + x_range[i][1]) / 2 for i in range(3)]
x[8][1] = l * dx[0] + x[9][1]
x[9][1] = -l * dx[0] + x[9][1]
x[10][2] = l * dx[1] + x[9][2]
x[11][2] = -l * dx[1] + x[9][2]
x[12][3] = l * dx[2] + x[9][3]
x[13][3] = -l * dx[2] + x[9][3]
x = add_sq_nums(x) # додаємо квадратні числа в матрицю за натуральними значеннями
print('\nX:\n', x)
print('\nX нормоване:\n')
for i in x_norm:
print([round(x, 2) for x in i])
print('\nY:\n', y)
return x, y, x_norm
def plan_matrix5(n, m):
print(f'\nГереруємо матрицю планування для n = {n}, m = {m}')
y = np.zeros(shape=(n, m))
for i in range(n):
for j in range(m):
y[i][j] = random.randint(y_min, y_max)
if n > 14:
no = n - 14
else:
no = 1
x_norm = ccdesign(3, center=(0, no))
x_norm = np.insert(x_norm, 0, 1, axis=1)
for i in range(4, 11):
x_norm = np.insert(x_norm, i, 0, axis=1)
l = 1.215
# матриця планування з нормовaними значеннями
for i in range(len(x_norm)):
for j in range(len(x_norm[i])):
if x_norm[i][j] < -1 or x_norm[i][j] > 1:
if x_norm[i][j] < 0:
x_norm[i][j] = -l
else:
x_norm[i][j] = l
# рахуємо квадратні числа
def add_sq_nums(x):
for i in range(len(x)):
x[i][4] = x[i][1] * x[i][2]
x[i][5] = x[i][1] * x[i][3]
x[i][6] = x[i][2] * x[i][3]
x[i][7] = x[i][1] * x[i][3] * x[i][2]
x[i][8] = x[i][1] ** 2
x[i][9] = x[i][2] ** 2
x[i][10] = x[i][3] ** 2
return x
x_norm = add_sq_nums(x_norm)
x = np.ones(shape=(len(x_norm), len(x_norm[0])), dtype=np.int64)
# матриця планування з натуральними значеннями факторів
for i in range(8):
for j in range(1, 4):
if x_norm[i][j] == -1:
x[i][j] = x_range[j - 1][0]
else:
x[i][j] = x_range[j - 1][1]
for i in range(8, len(x)):
for j in range(1, 3):
x[i][j] = (x_range[j - 1][0] + x_range[j - 1][1]) / 2
dx = [x_range[i][1] - (x_range[i][0] + x_range[i][1]) / 2 for i in range(3)]
x[8][1] = l * dx[0] + x[9][1]
x[9][1] = -l * dx[0] + x[9][1]
x[10][2] = l * dx[1] + x[9][2]
x[11][2] = -l * dx[1] + x[9][2]
x[12][3] = l * dx[2] + x[9][3]
x[13][3] = -l * dx[2] + x[9][3]
x = add_sq_nums(x) # квадратні числа в матрицю за натуральними значеннями
print('\nX:\n', x)
print('\nX нормоване:\n')
for i in x_norm:
print([round(x, 2) for x in i])
print('\nY:\n', y)
return x, y, x_norm
class ExperimentDesigner:
_matrix_designers = {
'fullfactorial2levels': pyDOE2.ff2n,
'fullfactorial3levels': lambda n: pyDOE2.fullfact([3] * n),
'placketburman': pyDOE2.pbdesign,
'boxbehnken': lambda n: pyDOE2.bbdesign(n, 1),
'ccc': lambda n: pyDOE2.ccdesign(n, (0, 3), face='ccc'),
'ccf': lambda n: pyDOE2.ccdesign(n, (0, 3), face='ccf'),
'cci': lambda n: pyDOE2.ccdesign(n, (0, 3), face='cci'),
}
def __init__(self,
factors,
design_type,
responses,
skip_screening=True,
at_edges='distort',
relative_step=.25,
gsd_reduction='auto',
model_selection='brute',
n_folds='loo',
manual_formula=None,
shrinkage=1.0,
q2_limit=0.5,
gsd_span_ratio=0.5):
try:
assert at_edges in ('distort', 'shrink'),\
'unknown action at_edges: {0}'.format(at_edges)
assert relative_step is None or 0 < relative_step < 1,\
'relative_step must be float between 0 and 1 not {}'.format(relative_step)
assert model_selection in ('brute', 'greedy', 'manual'), \
'model_selection must be "brute", "greedy", "manual".'
assert n_folds == 'loo' or (isinstance(n_folds, int) and n_folds > 0), \
'n_folds must be "loo" or positive integer'
assert 0.9 <= shrinkage <= 1, 'shrinkage must be float between 0.9 and 1.0, not {}'.format(
shrinkage)
assert 0 <= q2_limit <= 1, 'q2_limit must be float between 0 and 1, not {}'.format(
q2_limit)
if model_selection == 'manual':
assert isinstance(manual_formula, str), \
'If model_selection is "manual" formula must be provided.'
except AssertionError as e:
raise ValueError(str(e))
self.factors = OrderedDict()
factor_types = list()
for factor_name, f_spec in factors.items():
factor = factor_from_spec(f_spec)
if isinstance(factor, CategoricalFactor) and skip_screening:
raise DesignerError(
'Can\'t perform optimization with categorical '
'variables without prior screening.')
self.factors[factor_name] = factor
logging.debug('Sets factor {}: {}'.format(factor_name, factor))
factor_types.append(f_spec.get('type', 'continuous'))
self.skip_screening = skip_screening
self.step_length = relative_step
self.design_type = design_type
self.responses = responses
self.response_values = None
self.gsd_reduction = gsd_reduction
self.model_selection = model_selection
self.n_folds = n_folds
self.shrinkage = shrinkage
self.q2_limit = q2_limit
self._formula = manual_formula
self._edge_action = at_edges
self._allowed_phases = ['optimization', 'screening']
self._phase = 'optimization' if self.skip_screening else 'screening'
self._n_screening_evaluations = 0
self._factor_types = factor_types
self._gsd_span_ratio = gsd_span_ratio
self._stored_transform = lambda x: x
self._best_experiment = {
'optimal_x': pd.Series([]),
'optimal_y': None,
'weighted_y': None
}
n = len(self.factors)
try:
self._matrix_designers[self.design_type.lower()]
except KeyError:
raise UnsupportedDesign(self.design_type)
if len(self.responses) > 1:
self._desirabilites = {
name: make_desirability_function(factor)
for name, factor in self.responses.items()
}
else:
self._desirabilites = None
def new_design(self):
"""
:return: Experimental design-sheet.
:rtype: pandas.DataFrame
"""
if self._phase == 'screening':
return self._new_screening_design(reduction=self.gsd_reduction)
else:
return self._new_optimization_design()
def write_factor_csv(self, out_file):
factors = list()
idx = pd.Index(['fixed_value', 'current_low', 'current_high'])
for name, factor in self.factors.items():
current_min = None
current_high = None
fixed_value = None
if issubclass(type(factor), NumericFactor):
current_min = factor.current_low
current_high = factor.current_high
elif isinstance(factor, CategoricalFactor):
fixed_value = factor.fixed_value
else:
raise NotImplementedError
data = [fixed_value, current_min, current_high]
factors.append(pd.Series(data, index=idx, name=name))
factors_df = pd.DataFrame(factors)
logging.info('Saving factor settings to {}'.format(out_file))
factors_df.to_csv(out_file)
def update_factors_from_csv(self, csv_file):
factors_df = pd.DataFrame.from_csv(csv_file)
logging.info('Reading factor settings from {}'.format(csv_file))
for name, factor in self.factors.items():
logging.info('Updating factor {}'.format(name))
if issubclass(type(factor), NumericFactor):
current_low = factors_df.loc[name]['current_low']
current_high = factors_df.loc[name]['current_high']
logging.info('Factor: {}. Setting current_low to {}'.format(
name, current_low))
logging.info('Factor: {}. Setting current_high to {}'.format(
name, current_high))
factor.current_low = current_low
factor.current_high = current_high
elif isinstance(factor, CategoricalFactor):
if pd.isnull(factors_df.loc[name]['fixed_value']):
fixed_value = None
logging.info(
'Factor: {}. Had no fixed_value.'.format(name))
else:
fixed_value = factors_df.loc[name]['fixed_value']
logging.info(
'Factor: {}. Setting fixed_value to {}.'.format(
name, fixed_value))
factor.fixed_value = fixed_value
def get_optimal_settings(self, response):
"""
Calculate optimal factor settings given response. Returns calculated
optimum.
If the current phase is 'screening': returns the factor settings of
the best run and updates the current factor settings.
If the current phase is 'optimization': returns the factor settings of
the predicted optimum, but doesn't update current factor settings in
case a validation step is to be run first
:param pandas.DataFrame response: Response sheet.
:returns: Calculated optimum.
:rtype: OptimizationResult
"""
self._response_values = response.copy()
response = response.copy()
# Perform any transformations or weigh together multiple responses:
treated_response, criterion = self.treat_response(response)
if self._phase == 'screening':
# Find the best screening result and update factors accordingly
self._screening_response = treated_response
self._screening_criterion = criterion
return self._evaluate_screening(treated_response, criterion,
self._gsd_span_ratio)
else:
# Predict optimal parameter settings, but don't update factors
return self._predict_optimum_settings(treated_response, criterion)
def _update_best_experiment(self, result):
update = False
if self._best_experiment['optimal_x'].empty:
update = True
elif result['criterion'] == 'maximize':
if result['weighted_response'] > self._best_experiment[
'weighted_y']:
update = True
elif result['criterion'] == 'minimize':
if result['weighted_response'] < self._best_experiment[
'weighted_y']:
update = True
if update:
self._best_experiment['optimal_x'] = result['factor_settings']
self._best_experiment['optimal_y'] = result['response']
self._best_experiment['weighted_y'] = result['weighted_response']
return update
def get_best_experiment(self,
experimental_sheet,
response_sheet,
use_index=1):
"""
Accepts an experimental design and the corresponding response values.
Finds the best experiment and updates self._best_experiment.
Returns the best experiment, to be used in fnc update_factors_from_optimum
"""
assert isinstance(experimental_sheet, pd.core.frame.DataFrame), \
'The input experimental sheet must be a pandas DataFrame'
assert isinstance(response_sheet, pd.core.frame.DataFrame), \
'The input response sheet must be a pandas DataFrame'
assert sorted(experimental_sheet.columns) == sorted(self.factors), \
'The factors of the experimental sheet must match those in the \
pipeline. You input:\n{}\nThey should be:\n{}' .format(
list(experimental_sheet.columns),
list(self.factors.keys()))
assert sorted(response_sheet.columns) == sorted(self.responses), \
'The responses of the response sheet must match those in the \
pipeline. You input:\n{}\nThey should be:\n{}' .format(
list(response_sheet.columns),
list(self.responses.keys()))
response = response_sheet.copy()
treated_response, criterion = self.treat_response(
response, perform_transform=False)
treated_response = treated_response.iloc[:, 0]
if criterion == 'maximize':
optimum_i = treated_response.argsort().iloc[-use_index]
elif criterion == 'minimize':
optimum_i = treated_response.argsort().iloc[use_index - 1]
else:
raise NotImplementedError
optimum_settings = experimental_sheet.iloc[optimum_i]
results = OrderedDict()
optimal_weighted_response = np.array(treated_response.iloc[optimum_i])
optimal_response = response_sheet.iloc[optimum_i]
results['factor_settings'] = optimum_settings
results['weighted_response'] = optimal_weighted_response
results['response'] = optimal_response
results['criterion'] = criterion
results['new_best'] = False
results['old_best'] = self._best_experiment
has_multiple_responses = response_sheet.shape[1] > 1
logging.debug('The best response was found in experiment:\n{}'.format(
optimum_settings.name))
logging.debug('The response values were:\n{}'.format(
response_sheet.iloc[optimum_i]))
if has_multiple_responses:
logging.debug('The weighed response was:\n{}'.format(
treated_response.iloc[optimum_i]))
logging.debug('Will return optimum settings:\n{}'.format(
results['factor_settings']))
logging.debug('And best response:\n{}'.format(results['response']))
if self._update_best_experiment(results):
results['new_best'] = True
return results
def update_factors_from_optimum(self,
optimal_experiment,
tol=0.25,
recovery=False):
"""
Updates the factor settings based on how far the current settings are
from those supplied in optimal_experiment['factor_settings'].
:param OrderedDict optimal_experiment: Output from get_best_experiment
:param float tol: Accepted relative distance to design space edge.
:returns: Calculated optimum.
:rtype: OptimizationResult
"""
are_numeric = np.array(self._factor_types) != 'categorical'
numeric_names = np.array(list(self.factors.keys()))[are_numeric]
numeric_factors = np.array(list(self.factors.values()))[are_numeric]
optimal_x = optimal_experiment['factor_settings']
optimal_y = optimal_experiment['weighted_response']
criterion = optimal_experiment['criterion']
# Get only numeric factors
if recovery:
optimal_x = optimal_x.iloc[optimal_x.index.isin(numeric_names)]
centers = np.array([f.center for f in numeric_factors])
spans = np.array([f.span for f in numeric_factors])
ratios = (optimal_x - centers) / spans
if not recovery:
logging.debug(
'The distance of the factor optimas from the factor centers, '
'expressed as the ratio of the step length:\n{}'.format(
ratios))
if (abs(ratios) < tol).all():
converged = True
if not recovery:
logging.info('Convergence reached.')
else:
converged = False
if not recovery:
logging.info('Convergence not reached. Moves design.')
for ratio, name, factor in zip(ratios, numeric_names,
numeric_factors):
if abs(ratio) < tol:
if not recovery:
logging.debug(
('Factor {} not updated - within tolerance '
'limits.').format(name))
continue
if not recovery:
self._update_numeric_factor(factor, name, ratio)
converged, reached_limits = self._check_convergence(centers,
converged,
criterion,
optimal_y,
numeric_factors,
recovery=recovery)
optimization_results = pd.Series(index=self._design_sheet.columns,
dtype=object)
for name, factor in self.factors.items():
if isinstance(factor, CategoricalFactor):
optimization_results[name] = factor.fixed_value
else:
optimization_results[name] = optimal_x[name]
results = OptimizationResult(optimization_results,
converged,
tol,
reached_limits,
empirically_found=True)
return results
def _predict_optimum_settings(self, response, criterion):
"""
Calculate a model from the response and find the optimum.
:returns: Calculated optimum.
:rtype: OptimizationResult
"""
logging.info('Predicting optimum')
are_numeric = np.array(self._factor_types) != 'categorical'
numeric_names = np.array(list(self.factors.keys()))[are_numeric]
optimal_x, model, prediction = predict_optimum(
self._design_sheet.loc[:, are_numeric],
response.iloc[:, 0].values,
numeric_names,
criterion=criterion,
n_folds=self.n_folds,
model_selection=self.model_selection,
manual_formula=self._formula,
q2_limit=self.q2_limit)
optimization_results = pd.Series(index=self._design_sheet.columns,
dtype=object)
if not optimal_x.empty:
# If Q2 of model was above the limit and if an optimum was found
for name, factor in self.factors.items():
if isinstance(factor, CategoricalFactor):
optimization_results[name] = factor.fixed_value
elif isinstance(factor, OrdinalFactor):
optimization_results[name] = int(np.round(optimal_x[name]))
else:
optimization_results[name] = optimal_x[name]
result = OptimizationResult(optimization_results,
converged=False,
tol=0,
reached_limits=False,
empirically_found=False)
return result
def treat_response(self, response, perform_transform=True):
"""
Perform any specified transformations on the response.
If several responses are defined, combine them into one. The geometric
mean of Derringer and Suich's desirability functions will be used for
optimization, see:
Derringer, G., and Suich, R., (1980), "Simultaneous Optimization
of Several Response Variables," Journal of Quality Technology, 12,
4, 214-219.
Returns a single response variable and the associated maximize/minimize
criterion.
"""
has_multiple_responses = response.shape[1] > 1
for name, spec in self.responses.items():
transform = spec.get('transform', None)
response_values = response[name]
if perform_transform:
if transform == 'log':
logging.debug('Log-transforming response {}'.format(name))
response_values = np.log(response_values)
self._stored_transform = np.log
elif transform == 'box-cox':
response_values, lambda_ = scipy.stats.boxcox(
response_values)
logging.debug('Box-cox transforming response {} '
'(lambda={:.4f})'.format(name, lambda_))
self._stored_transform = _make_stored_boxcox(lambda_)
else:
self._stored_transform = lambda x: x
if has_multiple_responses:
desirability_function = self._desirabilites[name]
response_values = [
desirability_function(value) for value in response_values
]
response[name] = response_values
if has_multiple_responses:
response = np.power(response.product(axis=1),
(1 / response.shape[1]))
response = response.to_frame('combined_response')
criterion = 'maximize'
else:
criterion = list(self.responses.values())[0]['criterion']
return response, criterion
def reevaluate_screening(self):
if self._screening_response is None:
raise DesignerError('screening must be run before re-evaluation')
return self._evaluate_screening(self._screening_response,
self._screening_criterion,
self._gsd_span_ratio,
self._n_screening_evaluations + 1)
def _validate_new_factor_limits(self, factor, factor_name, low_limit,
high_limit):
# If the proposed step change takes us below or above min and max:
logging.debug('Factor {}: Proposed new factor low is {}.'.format(
factor_name, low_limit))
logging.debug('Factor {}: Proposed new factor high is {}.'.format(
factor_name, high_limit))
adjusted_settings = False
if low_limit < factor.min:
nudge = abs(low_limit - factor.min)
logging.debug(
'Factor {}: Minimum allowed setting ({}) would be exceeded by '
'the proposed new factor low.'.format(factor_name, factor.min))
low_limit += nudge
high_limit += nudge
adjusted_settings = True
elif high_limit > factor.max:
nudge = abs(high_limit - factor.max)
logging.debug(
'Factor {}: Maximum allowed setting ({}) would be exceeded by '
'the proposed new factor high.'.format(factor_name,
factor.max))
low_limit -= nudge
high_limit -= nudge
adjusted_settings = True
if adjusted_settings:
logging.debug('Factor {}: Adjusted the proposed new factor '
'settings by {}.'.format(factor_name, nudge))
logging.debug('Factor {}: New factor low is {}.'.format(
factor_name, low_limit))
logging.debug('Factor {}: New factor high is {}.'.format(
factor_name, high_limit))
return (low_limit, high_limit)
def _evaluate_screening(self,
response,
criterion,
span_ratio,
use_index=1):
"""
:param float span_ratio: The ratio of the span between gsd points that will be used in the following optimization design.
"""
self._n_screening_evaluations += 1
logging.info('Evaluating screening results.')
response_series = response.iloc[:, 0]
factor_items = sorted(self.factors.items())
if criterion == 'maximize':
optimum_i = response_series.argsort().iloc[-use_index]
elif criterion == 'minimize':
optimum_i = response_series.argsort().iloc[use_index - 1]
else:
raise NotImplementedError
optimum_design_row = self._design_matrix[optimum_i]
optimum_settings = OrderedDict()
# Update all factors according to current results. For each factor,
# the current_high and current_low will be set to factors level above
# and below the point in the screening design with the best response.
for factor_level, (name, factor) in zip(optimum_design_row,
factor_items):
if isinstance(factor, CategoricalFactor):
factor_levels = np.array(factor.values)
factor.fixed_value = factor_levels[factor_level]
else:
factor_levels = sorted(self._design_sheet[name].unique())
min_ = factor_levels[max([0, factor_level - 1])]
max_ = factor_levels[min(
[factor_level + 1,
len(factor_levels) - 1])]
span = max_ - min_
# Shrink the span a bit
logging.debug('Factor {} span: {}'.format(name, span))
logging.debug('Factor {}: adjusting span with '
'gsd_span_ratio {}'.format(name, span_ratio))
span = span * span_ratio
if isinstance(factor, OrdinalFactor) and span < 2.0:
# Make sure ordinal factors' spans don't shrink to the
# point where there's no spread in the exp. design
logging.debug('Factor {}: span ({}) too small, adjusting '
'to minimal span for ordinal factor.'.format(
name, span))
span = 2.0
logging.debug('Factor {} span: {}'.format(name, span))
# center around best point
best_point = factor_levels[factor_level]
new_low = best_point - span / 2
new_high = best_point + span / 2
if isinstance(factor, OrdinalFactor):
new_low = int(np.round(new_low))
new_high = int(np.round(new_high))
# nudge new high and low so we don't exceed the limits
new_low, new_high = self._validate_new_factor_limits(
factor, name, new_low, new_high)
# update factors
factor.current_low = new_low
factor.current_high = new_high
optimum_settings[name] = factor_levels[factor_level]
logging.info('New settings for factor {}:\n{}'.format(
name, factor))
results = OptimizationResult(pd.Series(optimum_settings),
converged=False,
tol=0,
reached_limits=False,
empirically_found=True)
logging.info('Best screening result was exp no {}'.format(optimum_i))
logging.info('The corresponding response was:\n{}'.format(
self._response_values.iloc[optimum_i]))
if len(self._response_values.columns) > 1:
logging.info('The combined response was:\n{}'.format(
response.iloc[optimum_i]))
logging.info('The factor settings were:\n{}'.format(
results.predicted_optimum))
# update current best experiment
self.get_best_experiment(
self._design_sheet, self._response_values
if len(self._response_values.columns) > 1 else response)
self._phase = 'optimization'
return results
def set_phase(self, phase):
assert phase in self._allowed_phases, 'phase must be one of {}'.format(
self._allowed_phases)
self._phase = phase
def _update_numeric_factor(self, factor, name, ratio):
logging.info('Factor {}: Updating settings.'.format(name))
logging.info('Factor {}: Current settings: {}'.format(name, factor))
step_length = self.step_length if self.step_length is not None \
else abs(ratio)
step = factor.span * step_length * np.sign(ratio)
logging.debug(
'Factor {}: Step by which settings are adjusted is {}.'.format(
name, step))
logging.debug(
'Factor {}: Current span between high and low is {}.'.format(
name, factor.span))
logging.debug('Factor {}: Will shrink the span by {}.'.format(
name, self.shrinkage))
new_span = factor.span * self.shrinkage
logging.debug('Factor {}: New span is {}.'.format(name, new_span))
if isinstance(factor, QuantitativeFactor):
current_low_new = factor.center + step - new_span / 2
current_high_new = factor.center + step + new_span / 2
elif isinstance(factor, OrdinalFactor):
current_low_new = np.round(factor.center + step - new_span / 2)
current_high_new = np.round(factor.center + step + new_span / 2)
else:
raise NotImplementedError
# If the proposed step change takes us below or above min and max:
new_low, new_high = self._validate_new_factor_limits(
factor, name, current_low_new, current_high_new)
factor.current_low = new_low
factor.current_high = new_high
logging.info('Factor {}: New settings: {}'.format(name, factor))
logging.info('Factor {}: Done updating.'.format(name))
def _new_screening_design(self, reduction='auto'):
factor_items = sorted(self.factors.items())
levels = list()
names = list()
dtypes = list()
for name, factor in factor_items:
names.append(name)
if isinstance(factor, CategoricalFactor):
levels.append(factor.values)
dtypes.append(object)
continue
num_levels = factor.screening_levels
spacing = getattr(factor, 'screening_spacing', 'linear')
min_ = factor.min
max_ = factor.max
if not np.isfinite([min_, max_]).all():
raise ValueError(
'Can\'t perform screening with unbounded factors')
space = np.linspace if spacing == 'linear' else np.logspace
values = space(min_, max_, num_levels)
if isinstance(factor, OrdinalFactor):
values = sorted(np.unique(np.round(values)))
dtypes.append(int)
else:
dtypes.append(float)
levels.append(values)
design_matrix = pyDOE2.gsd(
[len(values) for values in levels],
reduction if reduction is not 'auto' else len(levels))
factor_matrix = list()
for i, (values, dtype) in enumerate(zip(levels, dtypes)):
values = np.array(values)[design_matrix[:, i]]
series = pd.Series(values, dtype=dtype)
factor_matrix.append(series)
self._design_matrix = design_matrix
self._design_sheet = pd.concat(factor_matrix, axis=1, keys=names)
return self._design_sheet
def _new_optimization_design(self):
matrix_designer = self._matrix_designers[self.design_type.lower()]
numeric_factors = [(name, factor)
for name, factor in self.factors.items()
if isinstance(factor, NumericFactor)]
numeric_factor_names = [name for name, factor in numeric_factors]
design_matrix = matrix_designer(len(numeric_factors))
mins = np.array([f.min for _, f in numeric_factors])
maxes = np.array([f.max for _, f in numeric_factors])
span = np.array([f.span for _, f in numeric_factors])
centers = np.array([f.center for _, f in numeric_factors])
factor_matrix = design_matrix * (span / 2.0) + centers
# Check if current settings are outside allowed design space.
# Also, for factors that are specified as ordinal, adjust their values
# in the design matrix to be rounded floats
for i, (factor_name, factor) in enumerate(numeric_factors):
if isinstance(factor, OrdinalFactor):
factor_matrix[:, i] = np.round(factor_matrix[:, i])
logging.debug('Current setting {}: {}'.format(factor_name, factor))
if (factor_matrix < mins).any() or (factor_matrix > maxes).any():
logging.warning(('Out of design space factors. Adjusts factors'
'by {}.'.format(self._edge_action + 'ing')))
if self._edge_action == 'distort':
# Simply cap out-of-boundary values at mins and maxes.
capped_mins = np.maximum(factor_matrix, mins)
capped_mins_and_maxes = np.minimum(capped_mins, maxes)
factor_matrix = capped_mins_and_maxes
elif self._edge_action == 'shrink':
raise NotImplementedError
factors = list()
for name, factor in self.factors.items():
if isinstance(factor, CategoricalFactor):
values = np.repeat(factor.fixed_value, len(design_matrix))
factors.append(pd.Series(values))
else:
i = numeric_factor_names.index(name)
dtype = int if isinstance(factor, OrdinalFactor) else float
factors.append(pd.Series(factor_matrix[:, i].astype(dtype)))
self._design_sheet = pd.concat(factors,
axis=1,
keys=self.factors.keys())
return self._design_sheet
def _check_convergence(self,
centers,
converged,
criterion,
prediction,
numeric_factors,
recovery=False):
# It's possible that the optimum is predicted to be at the edge of the allowed
# min or max factor setting. This will produce a high 'ratio' and the algorithm
# is not considered to have converged (above). However, in this situation we
# can't move the space any further and we should stop iterating.
new_centers = np.array([f.center for f in numeric_factors])
if (centers == new_centers).all():
if not recovery:
logging.info(
'The design has not moved since last iteration. Converged.'
)
converged = True
reached_limits = True
if len(self.responses) > 1 and prediction < 1:
reached_limits = False
elif len(self.responses) == 1:
r_spec = list(self.responses.values())[0]
low_limit = self._stored_transform(r_spec.get('low_limit', 1))
high_limit = self._stored_transform(r_spec.get(
'high_limit', 1))
if criterion == 'maximize' and 'low_limit' in r_spec:
reached_limits = prediction >= low_limit
elif criterion == 'minimize' and 'high_limit' in r_spec:
reached_limits = prediction <= high_limit
elif criterion == 'target' and 'low_limit' in r_spec and 'high_limit' in r_spec:
reached_limits = low_limit <= prediction <= high_limit
else:
reached_limits = False
return converged, reached_limits
def run(
self,
seed,
n,
dims,
sample_type,
scale,
scale_factor,
outfile,
x0,
x1,
n_line,
hard_bounds,
):
np.random.seed(seed)
n_samples = n
n_dims = dims
hard_bounds = hard_bounds
sample_type = sample_type
if sample_type == "random":
x = np.random.random((n_samples, n_dims))
elif sample_type == "grid":
subdivision = int(pow(n_samples, 1 / float(n_dims)))
temp = [np.linspace(0, 1.0, subdivision) for i in range(n_dims)]
X = np.meshgrid(*temp)
x = np.stack([xx.flatten() for xx in X], axis=1)
elif sample_type == "lhs":
x = doe.lhs(n_dims, samples=n_samples, random_state=seed)
elif sample_type == "lhd":
_x = doe.lhs(n_dims, samples=n_samples, random_state=seed)
x = norm(loc=0.5, scale=0.125).ppf(_x)
elif sample_type == "star":
_x = doe.doe_star.star(n_dims)[0]
x = 0.5 * (_x + 1.0) # transform to center at 0.5 (range 0-1)
elif sample_type == "ccf" or sample_type == "ccc" or sample_type == "cci":
_x = np.unique(doe.ccdesign(n_dims, face=sample_type), axis=0)
x = 0.5 * (_x + 1.0)
else:
raise ValueError(sample_type +
" is not a valid choice for sample_type!")
scales = process_scale(scale)
if scales is not None:
limits = []
do_log = []
for scale in scales:
limits.append((scale[0], scale[1]))
if len(scale) < 3:
scale.append("linear")
if scale[2] == "log":
do_log.append(True)
else:
do_log.append(False)
x = scale_samples(x, limits, do_log=do_log)
# scale the whole box
x = scale_factor * x
# add x0
if x0 is not None:
x0 = np.atleast_2d(np.load(x0))
if scales is not None:
sa = scale_factor * np.array(scales)[:, :2].astype("float")
center = np.mean(sa, axis=1)
else:
center = scale_factor * 0.5
# Loop over all x0 points
all_x = []
for _x0 in x0:
_x = x + _x0 - center
# replace the first entry with x0 for the random ones
if sample_type == "lhs" or sample_type == "lhd":
_x[0] = _x0
else: # add it for the stencil points
_x = np.insert(_x, 0, _x0, axis=0)
if x1 is not None:
x1 = np.load(x1)
line_range = np.linspace(0, 1, n_line + 1,
endpoint=False)[1:]
line_samples = _x0 + np.outer(line_range, (x1 - _x0))
_x = np.vstack((_x, line_samples))
all_x.append(_x)
x = np.vstack(all_x)
if hard_bounds:
if scales is None:
x = np.clip(x, 0, 1)
else:
for i, dim in enumerate(scales):
x[:, i] = np.clip(x[:, i], dim[0], dim[1])
print(x)
np.save(outfile, x)
def plan_matrix5(n, m):
y = np.zeros(shape=(n, m))
for i in range(n):
for j in range(m):
y[i][j] = random.randint(y_min, y_max)
if n > 14:
no = n - 14
else:
no = 1
x_norm = ccdesign(3, center=(0, no))
x_norm = np.insert(x_norm, 0, 1, axis=1)
for i in range(4, 11):
x_norm = np.insert(x_norm, i, 0, axis=1)
l = 1.215
for i in range(len(x_norm)):
for j in range(len(x_norm[i])):
if x_norm[i][j] < -1 or x_norm[i][j] > 1:
if x_norm[i][j] < 0:
x_norm[i][j] = -l
else:
x_norm[i][j] = l
def add_sq_nums(x):
for i in range(len(x)):
x[i][4] = x[i][1] * x[i][2]
x[i][5] = x[i][1] * x[i][3]
x[i][6] = x[i][2] * x[i][3]
x[i][7] = x[i][1] * x[i][3] * x[i][2]
x[i][8] = x[i][1]**2
x[i][9] = x[i][2]**2
x[i][10] = x[i][3]**2
return x
x_norm = add_sq_nums(x_norm)
x = np.ones(shape=(len(x_norm), len(x_norm[0])), dtype=np.int64)
for i in range(8):
for j in range(1, 4):
if x_norm[i][j] == -1:
x[i][j] = x_range[j - 1][0]
else:
x[i][j] = x_range[j - 1][1]
for i in range(8, len(x)):
for j in range(1, 3):
x[i][j] = (x_range[j - 1][0] + x_range[j - 1][1]) / 2
dx = [
x_range[i][1] - (x_range[i][0] + x_range[i][1]) / 2
for i in range(3)
]
x[8][1] = l * dx[0] + x[9][1]
x[9][1] = -l * dx[0] + x[9][1]
x[10][2] = l * dx[1] + x[9][2]
x[11][2] = -l * dx[1] + x[9][2]
x[12][3] = l * dx[2] + x[9][3]
x[13][3] = -l * dx[2] + x[9][3]
x = add_sq_nums(x)
print('\nМатриця X:\n')
for i in x:
for j in i:
print("{0:5}".format(j), end='|')
print()
print('\nX нормоване:\n')
for i in x_norm:
for j in i:
print("{0:5.3}".format(j), end='|')
print()
print('Y')
for i in y:
for j in i:
print("{0:5.8}".format(j), end='|')
print()
return x, y, x_norm
