def __call__(self, design_vars, model=None):
"""
Generate case.
Parameters
----------
design_vars : dict
Dictionary of design variables for which to generate values.
model : Group
The model containing the design variables (not used).
Yields
------
list
list of name, value tuples for the design variables.
"""
if self._seed is not None:
np.random.seed(self._seed)
size = sum([meta['size'] for name, meta in iteritems(design_vars)])
if self._samples is None:
self._samples = size
# generate design
doe = pyDOE2.lhs(size, samples=self._samples,
criterion=self._criterion,
iterations=self._iterations,
random_state=self._seed)
# yield desvar values for doe samples
for row in doe:
retval = []
col = 0
var = 0
for name, meta in iteritems(design_vars):
size = meta['size']
val = np.empty(size)
for k in range(size):
sample = row[col + k]
lower = meta['lower']
if isinstance(lower, np.ndarray):
lower = lower[k]
upper = meta['upper']
if isinstance(upper, np.ndarray):
upper = upper[k]
val[k] = lower + sample * (upper - lower)
retval.append((name, val))
var += 1
col += size
yield retval
def _ese(self, dim, nt):
# Parameters of maximinESE procedure
P0 = lhs(dim, nt, criterion=None)
J = 20
outer_loop = min(int(1.5 * dim), 30)
inner_loop = min(20 * dim, 100)
D0 = pdist(P0)
R0 = np.corrcoef(P0)
corr0 = np.max(np.abs(R0[R0 != 1]))
phip0 = self._PhiP(P0)
P, historic = self._maximinESE(P0,
outer_loop=outer_loop,
inner_loop=inner_loop,
J=J,
tol=1e-3,
p=10,
return_hist=True)
return P
def select_training_points(self, Nsamples=40, method="LH"):
"""Select training points from the chain to train the GPs.
Note: this method does not use the "scale" parameter.
Args:
Nsamples (int): number of samples to use; defualt is 40
method (string): keyword for selecting different ways of
obtaining training points. Currently unused.
"""
#Create LH training samples
x = pyDOE2.lhs(len(self.chain_cov),
samples=Nsamples,
criterion="center",
iterations=5)
#Transform them correctly
x -= 0.5 #center the training points
s = self.scale
w = self.eigenvalues
R = self.rotation_matrix
#Snap the training points to the MCMC chain
samples = np.dot(s * x[:] * np.sqrt(w), R.T)[:] + self.chain_means
self.unrotated_samples = x
self.unsnapped_samples = samples
cov = self.chain_cov
def sqdists(chain, s, cov):
X = chain[:] - s
r = np.linalg.solve(cov, X.T).T
d = np.sum(X * r, axis=1)
return d
indices = np.array([np.argmin(sqdists(self.chain, s, cov)) \
for s in samples])
#Include the max liklihood point
best_ind = np.argmax(self.lnlikes)
self.training_inds = np.append(indices, best_ind)
return
def lhs_of_variables(variables_dict,
number_of_samples,
method='m',
random_seed=None):
# generate a dict with the enumerated values to run for each variable in a latin hypercube experiment
num_factors = len(
variables_dict) # get the number of factors for the experiment
design = pd.DataFrame(pyDOE2.lhs(num_factors,
samples=number_of_samples,
criterion=method,
random_state=random_seed),
columns=variables_dict.keys())
for var in variables_dict:
max_var_value = variables_dict[var][1]
min_var_value = variables_dict[var][0]
design[var] = design[var].apply(
lambda x: (max_var_value - min_var_value) * x + min_var_value)
return design
def _ese(self, dim, nt, fixed_index=[], P0=[]):
"""
Parameters
----------
fixed_index : list
When running an "ese" optimization, we can fix the indexes of
the points that we do not want to modify
"""
# Parameters of maximinESE procedure
if len(fixed_index) == 0:
P0 = lhs(dim, nt, criterion=None, random_state=self.random_state)
else:
P0 = P0
self.random_state = np.random.RandomState()
J = 20
outer_loop = min(int(1.5 * dim), 30)
inner_loop = min(20 * dim, 100)
D0 = pdist(P0)
R0 = np.corrcoef(P0)
corr0 = np.max(np.abs(R0[R0 != 1]))
phip0 = self._PhiP(P0)
P, historic = self._maximinESE(
P0,
outer_loop=outer_loop,
inner_loop=inner_loop,
J=J,
tol=1e-3,
p=10,
return_hist=True,
fixed_index=fixed_index,
)
return P
def latin_hc(filename, num_evals):
num_params = 5
DataDir = "../Data/"
# galsim parameters
para1 = np.linspace(1e4, 1e5, num_evals) # Flux
para2 = np.linspace(0.1, 1., num_evals) # Radius
para3 = np.linspace(-0.5, 0.5, num_evals) # g1
para4 = np.linspace(-0.5, 0.5, num_evals) # g2
para5 = np.linspace(0.2, 0.4, num_evals) # psf fwhm
AllPara = np.vstack([para1, para2, para3, para4, para5])
# AllLabels = [r'Flux', r'Radius', r'Shear g1', r'Shear g2', r'PSF fwhm']
# latin hypercube
lhd = pyDOE.lhs(AllPara.shape[0], samples=num_evals, criterion=None) # c cm corr m
idx = (lhd * num_evals).astype(int)
AllCombinations = np.zeros((num_evals, AllPara.shape[0]))
for i in range(AllPara.shape[0]):
AllCombinations[:, i] = AllPara[i][idx[:, i]]
# Delete row when g1**2 + g2**2 > 1
del_rows = np.where(AllCombinations[:, 2]**2+AllCombinations[:, 3]**2 > 1.)[0]
AllCombinations = np.delete(AllCombinations, del_rows, axis=0)
np.savetxt(DataDir+filename, AllCombinations)
def _compute(self, nt):
"""
Implemented by sampling methods to compute the requested number of sampling points.
The number of dimensions (nx) is determined based on `xlimits.shape[0]`.
Arguments
---------
nt : int
Number of points requested.
Returns
-------
ndarray[nt, nx]
The sampling locations in the unit hypercube.
"""
xlimits = self.options["xlimits"]
nx = xlimits.shape[0]
if isinstance(self.options["random_state"], np.random.RandomState):
self.random_state = self.options["random_state"]
elif isinstance(self.options["random_state"], int):
self.random_state = np.random.RandomState(
self.options["random_state"])
else:
self.random_state = np.random.RandomState()
if self.options["criterion"] != "ese":
return lhs(
nx,
samples=nt,
criterion=self.options["criterion"],
random_state=self.random_state,
)
elif self.options["criterion"] == "ese":
return self._ese(nx, nt)
parser.add_argument("-gamma_lo", help="Lower bound on gamma", default=1)
parser.add_argument("-gamma_hi", help="Upper bound on gamma", default=10)
args = parser.parse_args()
outname = args.outname
ntrain, npts = args.ntrain, args.npts
rhos, rt = args.rhos, args.rt
cosmo = args.cosmo
rs_lo, rs_hi = args.rs_by_rt_lo, args.rs_by_rt_hi
alpha_lo, alpha_hi = args.alpha_lo, args.alpha_hi
beta_lo, beta_hi = args.beta_lo, args.beta_hi
gamma_lo, gamma_hi = args.gamma_lo, args.gamma_hi
r_by_rt = np.logspace(-2, np.log10(2), npts)
ndim = 4
design = lhs(ndim, ntrain, criterion='maximin')
rs_arr = rt * design[:, 0] * (rs_hi - rs_lo) + rs_lo
alpha_arr = design[:, 1] * (alpha_hi - alpha_lo) + alpha_lo
beta_arr = design[:, 2] * (beta_hi - beta_lo) + beta_lo
gamma_arr = design[:, 3] * (gamma_hi - gamma_lo) + gamma_lo
cosmo = cosmology.setCosmology(cosmo)
start = time()
results = np.zeros((ntrain, ndim + npts)).astype('f4')
gen = zip(range(ntrain), rs_arr, alpha_arr, beta_arr, gamma_arr)
for i, rs, alpha, beta, gamma in gen:
if np.mod(i, 100) == 0:
print("...working on i = {0}".format(i))
eval_limit=5,
cache_file=cache_file,
cache_dir='test')
driver = OptimizationDriver(init_problem, **driver_config)
n_dim = 5
### Sampling Example
## Parametric sweep
levels = np.array([1, 1, 4, 1, 1])
design = pyDOE.fullfact(levels)
levels[levels == 1] = 2
ff_scaled = design / (levels - 1)
## Latin Hypercube
lhs_scaled = pyDOE.lhs(n_dim, criterion='center', samples=12)
## Execute Candidates
num_evals = driver.sample(ff_scaled,
design_name='test_s',
cache_file=cache_file)
num_evals = driver.parallel_sample(lhs_scaled,
design_name='test_p',
cache_file=cache_file)
### Optimization Example
## Show humpday optimizers
# for i, f in humpday.OPTIMIZERS:
# print(i, f.__name__)
def execute_ga(self,
x0,
vlb,
vub,
vob,
bits,
pop_size,
max_gen,
random_state,
Pm=None,
Pc=0.5):
"""
Perform the genetic algorithm.
Parameters
----------
x0 : ndarray
Initial design values.
vlb : ndarray
Lower bounds array.
vub : ndarray
Upper bounds array. This includes over-allocation so that every point falls on an
integer value.
vob : ndarray
Outer bounds array. This is purely for bounds check.
bits : ndarray
Number of bits to encode the design space for each element of the design vector.
pop_size : int
Number of points in the population.
max_gen : int
Number of generations to run the GA.
random_state : np.random.RandomState, int
Random state (or seed-number) which controls the seed and random draws.
Pm : float or None
Mutation rate.
Pc : float
Crossover rate.
Returns
-------
ndarray
Best design point.
float
Objective value at best design point.
int
Number of successful function evaluations.
"""
comm = self.comm
nobj = self.nobj
self.lchrom = int(np.sum(bits))
if nobj > 1:
xopt = []
fopt = []
# Needs to be divisible by number of objectives because of tournament selection
# strategy.
if np.mod(pop_size, nobj) > 0:
pop_size += nobj - np.mod(pop_size, nobj)
else:
xopt = copy.deepcopy(vlb)
fopt = np.inf
# Needs to be divisible by two because tournament selection pits one half of the
# population against the other half.
if np.mod(pop_size, 2) == 1:
pop_size += 1
self.npop = int(pop_size)
fitness = np.zeros((self.npop, nobj))
# If mutation rate is not provided as input
if Pm is None:
Pm = (self.lchrom + 1.0) / (2.0 * pop_size * np.sum(bits))
elite = self.elite
new_gen = np.round(
lhs(self.lchrom,
self.npop,
criterion='center',
random_state=random_state))
new_gen[0] = self.encode(x0, vlb, vub, bits)
# Main Loop
nfit = 0
for generation in range(max_gen + 1):
old_gen = copy.deepcopy(new_gen)
x_pop = self.decode(old_gen, vlb, vub, bits)
# Evaluate fitness of points in this generation.
if comm is not None:
# Parallel
# Since GA is random, ranks generate different new populations, so just take one
# and use it on all.
x_pop = comm.bcast(x_pop, root=0)
cases = [((item, ii), None) for ii, item in enumerate(x_pop)
if np.all(item - vob <= 0)]
# Pad the cases with some dummy cases to make the cases divisible amongst the procs.
# TODO: Add a load balancing option to this driver.
extra = len(cases) % comm.size
if extra > 0:
for j in range(comm.size - extra):
cases.append(cases[-1])
results = concurrent_eval(self.objfun,
cases,
comm,
allgather=True,
model_mpi=self.model_mpi)
fitness[:] = np.inf
for result in results:
returns, traceback = result
if returns:
val, success, ii = returns
if success:
fitness[ii, :] = val
nfit += 1
else:
# Print the traceback if it fails
print('A case failed:')
print(traceback)
else:
# Serial
for ii in range(self.npop):
x = x_pop[ii]
if np.any(x - vob > 0):
# Exceeded bounds for integer variables that are over-allocated.
success = False
else:
fitness[ii, :], success, _ = self.objfun(x, 0)
if success:
nfit += 1
else:
fitness[ii, :] = np.inf
# Find Pareto front.
if nobj > 1:
xopt, fopt = self.eval_pareto(x_pop, fitness, xopt, fopt)
# Find best objective.
else:
# Elitism means replace worst performing point with best from
# previous generation.
if elite and generation > 0:
max_index = np.argmax(fitness[:, 0])
old_gen[max_index] = min_gen
x_pop[max_index] = min_x
fitness[max_index, 0] = min_fit
# Find best performing point in this generation.
min_fit = np.min(fitness)
min_index = np.argmin(fitness)
min_gen = old_gen[min_index]
min_x = x_pop[min_index]
if min_fit < fopt:
fopt = min_fit
xopt = min_x
# Evolve new generation.
if nobj > 1:
new_gen, new_obj = self.tournament_multi_obj(old_gen, fitness)
else:
new_gen = self.tournament(old_gen, fitness[:, 0])
new_gen = self.crossover(new_gen, Pc)
new_gen = self.mutate(new_gen, Pm)
return xopt, fopt, nfit
def wrapper():
return pydoe.lhs(self.dim, self.num_pts, iterations=1)
def run_initial_values_benchmark(
self, log_file_name='sellar/results/log_file_initial_values.txt'):
if path.exists(log_file_name):
remove(log_file_name)
s = '################### Running robustness to initial values test ################### \n'
logfile = open(log_file_name, 'a+')
logfile.writelines(s)
logfile.close()
print(s)
test_cases = [('SLSQP', 'full_analytic', False),
('SLSQP', 'semi_analytic_fd', False),
('SLSQP', 'monolythic_fd', True),
('COBYLA', 'derivative_free', False)]
for test_case in test_cases:
optimizer = test_case[0]
derivative_method = test_case[1]
blackbox = test_case[2]
prob_type = 'MDO'
# Number of samples
N = 50
res_num_compute = {'MDF': [], 'IDF': [], 'HYBRID': [], 'NVH': []}
variables = {'x': (0., 10.), 'z1': (-10.0, 10.), 'z2': (0., 10.)}
# DOE
doe = lhs(len(variables.keys()), samples=N, criterion='center')
initial_values = {'x': (0., 10.), 'z': np.zeros(2)}
# Perform an analysis for each sample
for sample in doe:
lower_bound = variables['x'][0]
upper_bound = variables['x'][1]
initial_values['x'] = (upper_bound -
lower_bound) * sample[0] + lower_bound
lower_bound = variables['z1'][0]
upper_bound = variables['z1'][1]
z1 = (upper_bound - lower_bound) * sample[1] + lower_bound
lower_bound = variables['z2'][0]
upper_bound = variables['z2'][1]
z2 = (upper_bound - lower_bound) * sample[2] + lower_bound
initial_values['z'] = np.array([z1, z2])
prob_list = [
MDFProblem(name='MDF',
optimizer=optimizer,
derivative_method=derivative_method,
blackbox=blackbox,
log_file=log_file_name,
print=False),
IDFProblem(name='IDF',
optimizer=optimizer,
derivative_method=derivative_method,
blackbox=blackbox,
log_file=log_file_name,
print=False),
HybridProblem(name='HYBRID',
optimizer=optimizer,
derivative_method=derivative_method,
blackbox=blackbox,
log_file=log_file_name,
print=False),
NVHProblem(name='NVH',
optimizer=optimizer,
derivative_method=derivative_method,
blackbox=blackbox,
log_file=log_file_name,
print=False)
]
self.run_analysis(prob_list, initial_values=initial_values)
for prob in prob_list:
if prob.post_analysis_results['success']:
res_num_compute[prob.name].append(
prob.post_analysis_results['num_compute'])
# Result analysis
for i, (key, value) in enumerate(res_num_compute.items()):
s = '> ---------- Running ' + prob_type + ' using ' + key + ' formulation and ' + \
optimizer + ' optimizer with ' + derivative_method + ' ------------ \n'
max_num_compute = max(value)
min_num_compute = min(value)
mean_num_compute = np.mean(value)
median_num_compute = np.median(value)
percentage_of_success = len(value) / N * 100.
res = 'Max number of evaluations : ' + str(max_num_compute) + '\n' \
'Min number of evaluations : ' + str(min_num_compute) + '\n' \
'Mean number of evaluations : ' + str(mean_num_compute) + '\n' \
'Median number of evaluations : ' + str(median_num_compute) + '\n' \
'Percentage of success : ' + str(percentage_of_success) + '\n'
s += s + res
logfile = open(log_file_name, 'a+')
logfile.writelines(s)
logfile.close()
print(s)
def __data_inverse(self, data_row, num_samples, sampling_method):
"""Generates a neighborhood around a prediction.
For numerical features, perturb them by sampling from a Normal(0,1) and
doing the inverse operation of mean-centering and scaling, according to
the means and stds in the training data. For categorical features,
perturb by sampling according to the training distribution, and making
a binary feature that is 1 when the value is the same as the instance
being explained.
Args:
data_row: 1d numpy array, corresponding to a row
num_samples: size of the neighborhood to learn the linear model
sampling_method: 'gaussian' or 'lhs'
Returns:
A tuple (data, inverse), where:
data: dense num_samples * K matrix, where categorical features
are encoded with either 0 (not equal to the corresponding value
in data_row) or 1. The first row is the original instance.
inverse: same as data, except the categorical features are not
binary, but categorical (as the original data)
"""
is_sparse = sp.sparse.issparse(data_row)
if is_sparse:
num_cols = data_row.shape[1]
data = sp.sparse.csr_matrix((num_samples, num_cols),
dtype=data_row.dtype)
else:
num_cols = data_row.shape[0]
data = np.zeros((num_samples, num_cols))
categorical_features = range(num_cols)
if self.discretizer is None:
instance_sample = data_row
scale = self.scaler.scale_
mean = self.scaler.mean_
if is_sparse:
# Perturb only the non-zero values
non_zero_indexes = data_row.nonzero()[1]
num_cols = len(non_zero_indexes)
instance_sample = data_row[:, non_zero_indexes]
scale = scale[non_zero_indexes]
mean = mean[non_zero_indexes]
if sampling_method == 'gaussian':
data = self.random_state.normal(
0, 1,
num_samples * num_cols).reshape(num_samples, num_cols)
data = np.array(data)
elif sampling_method == 'lhs':
data = lhs(num_cols,
samples=num_samples).reshape(num_samples, num_cols)
means = np.zeros(num_cols)
stdvs = np.array([1] * num_cols)
for i in range(num_cols):
data[:, i] = norm(loc=means[i],
scale=stdvs[i]).ppf(data[:, i])
data = np.array(data)
else:
warnings.warn(
'''Invalid input for sampling_method.
Defaulting to Gaussian sampling.''',
UserWarning)
data = self.random_state.normal(
0, 1,
num_samples * num_cols).reshape(num_samples, num_cols)
data = np.array(data)
if self.sample_around_instance:
data = data * scale + instance_sample
else:
data = data * scale + mean
if is_sparse:
if num_cols == 0:
data = sp.sparse.csr_matrix(
(num_samples, data_row.shape[1]), dtype=data_row.dtype)
else:
indexes = np.tile(non_zero_indexes, num_samples)
indptr = np.array(
range(0,
len(non_zero_indexes) * (num_samples + 1),
len(non_zero_indexes)))
data_1d_shape = data.shape[0] * data.shape[1]
data_1d = data.reshape(data_1d_shape)
data = sp.sparse.csr_matrix(
(data_1d, indexes, indptr),
shape=(num_samples, data_row.shape[1]))
categorical_features = self.categorical_features
first_row = data_row
else:
first_row = self.discretizer.discretize(data_row)
data[0] = data_row.copy()
inverse = data.copy()
for column in categorical_features:
values = self.feature_values[column]
freqs = self.feature_frequencies[column]
inverse_column = self.random_state.choice(values,
size=num_samples,
replace=True,
p=freqs)
binary_column = (inverse_column == first_row[column]).astype(int)
binary_column[0] = 1
inverse_column[0] = data[0, column]
data[:, column] = binary_column
inverse[:, column] = inverse_column
if self.discretizer is not None:
inverse[1:] = self.discretizer.undiscretize(inverse[1:])
inverse[0] = data_row
return data, inverse
result.write(templ.render(x=x, z=z))
fh.write('%f %f %s\n' % (x, z, 'x_%.3f_z_%.3f' % (x, z)))
fh.close()
fh = open('nonapod_inputs_random_500/input_list', 'w')
for i in range(500):
x = random.uniform(min_x, max_x)
z = random.uniform(min_z, max_z)
with open('nonapod_inputs_random_500/x_%.3f_z_%.3f' % (x, z),
'w') as result:
result.write(templ.render(x=x, z=z))
fh.write('%f %f %s\n' % (x, z, 'x_%.3f_z_%.3f' % (x, z)))
fh.close()
# Lastly, the latin hypercube sampling approach:
sample_space_50 = lhs(2, samples=50)
sample_space_500 = lhs(2, samples=500)
# Transform those numbers in [0,1] to values in our space of interest
for arr in [sample_space_50, sample_space_500]:
arr[:, 0] = arr[:, 0] * (max_x - min_x) + min_x
arr[:, 1] = arr[:, 1] * (max_z - min_z) + min_z
fh = open('nonapod_inputs_latin_50/input_list', 'w')
for x, z in sample_space_50:
with open('nonapod_inputs_latin_50/x_%.3f_z_%.3f' % (x, z), 'w') as result:
result.write(templ.render(x=x, z=z))
fh.write('%f %f %s\n' % (x, z, 'x_%.3f_z_%.3f' % (x, z)))
fh.close()
fh = open('nonapod_inputs_latin_500/input_list', 'w')
def checkmethods(self):
pathfile_bladegen = 'D:\\Program Files\\ANSYS Inc\\v180\\aisol\\BladeModeler\\BladeGen'
pathfile_cfturbo = 'C:\\Program Files\\CFturbo 10.3\\cfturbo.exe'
pathfile_workbench = 'D:\\Program Files\\ANSYS Inc\\v180\\Framework\\bin\\Win64\\RunWB2.exe'
pathfile_cfxsolve = 'D:\\Program Files\\ANSYS Inc\\v180\\CFX\\bin\\cfx5solve.exe'
pathfile_cfxmondata = 'D:\\Program Files\\ANSYS Inc\\v180\\CFX\\bin\\cfx5mondata.exe'
pathfile_cfxpost = 'D:\\Program Files\\ANSYS Inc\\v180\\CFX\\bin\\cfx5post.exe'
current_path = os.getcwd()
filepath_results = (current_path + '\\b_results')
if not os.path.isdir(filepath_results):
os.mkdir(filepath_results)
bladegen_bat = 'B1_bat_bladegen.txt'
cfturbo_bat = 'B1_bat_cfturbo.txt'
workbench_bat = 'B2_bat_workbench.txt'
cfxsolve_bat = 'B3_bat_cfxsolve.txt'
cfxmondata_bat = 'B4_bat_cfxmondata.txt'
cfxpost_bat = 'B5_bat_cfxpost.txt'
if os.path.isfile(bladegen_bat):
os.remove(bladegen_bat)
if os.path.isfile(cfturbo_bat):
os.remove(cfturbo_bat)
if os.path.isfile(workbench_bat):
os.remove(workbench_bat)
if os.path.isfile(cfxsolve_bat):
os.remove(cfxsolve_bat)
if os.path.isfile(cfxmondata_bat):
os.remove(cfxmondata_bat)
if os.path.isfile(cfxpost_bat):
os.remove(cfxpost_bat)
# write bladegen basic bat file
bladegen_bat_base = 'A1_bat_bladegen.txt'
fp_bladegen01_bat = open(current_path + '\\' +
bladegen_bat_base).readlines()
fp_bladegen02_bat = open(bladegen_bat, 'w')
try:
for eachline in fp_bladegen01_bat:
fp_bladegen02_bat.write(
eachline.replace('bladegen_set_path', pathfile_bladegen))
finally:
fp_bladegen02_bat.close()
# write cfturbo basic bat file
cfturbo_bat_base = 'A1_bat_cfturbo.txt'
fp_cfturbo01_bat = open(current_path + '\\' +
cfturbo_bat_base).readlines()
fp_cfturbo02_bat = open(cfturbo_bat, 'w')
try:
for eachline in fp_cfturbo01_bat:
fp_cfturbo02_bat.write(
eachline.replace('cfturbo_set_path', pathfile_cfturbo))
finally:
fp_cfturbo02_bat.close()
# write workbench basic bat file
workbench_bat_base = 'A2_bat_workbench.txt'
fp_workbench01_bat = open(current_path + '\\' +
workbench_bat_base).readlines()
fp_workbench02_bat = open(workbench_bat, 'w')
try:
for eachline in fp_workbench01_bat:
fp_workbench02_bat.write(
eachline.replace('workbench_set_path', pathfile_workbench))
finally:
fp_workbench02_bat.close()
# write cfxsolve basic bat file
core_cfx_num = self.core.currentText()
cfxsolve_bat_base = 'A3_bat_cfxsolve.txt'
fp_cfxsolve01_bat = open(current_path + '\\' +
cfxsolve_bat_base).readlines()
fp_cfxsolve02_bat = open(cfxsolve_bat, 'w')
try:
for eachline in fp_cfxsolve01_bat:
fp_cfxsolve02_bat.write(eachline.replace('cfxsolve_set_path', pathfile_cfxsolve) \
.replace('corenum', core_cfx_num))
finally:
fp_cfxsolve02_bat.close()
# write cfxmondata basic bat file
cfxmondata_bat_base = 'A4_bat_cfxmondata.txt'
fp_cfxmondata01_bat = open(current_path + '\\' +
cfxmondata_bat_base).readlines()
fp_cfxmondata02_bat = open(cfxmondata_bat, 'w')
try:
for eachline in fp_cfxmondata01_bat:
fp_cfxmondata02_bat.write(
eachline.replace('cfxmondata_set_path',
pathfile_cfxmondata))
finally:
fp_cfxmondata02_bat.close()
# write cfxpost basic bat file
cfxpost_bat_base = 'A5_bat_cfxpost.txt'
fp_cfxpost01_bat = open(current_path + '\\' +
cfxpost_bat_base).readlines()
fp_cfxpost02_bat = open(cfxpost_bat, 'w')
try:
for eachline in fp_cfxpost01_bat:
fp_cfxpost02_bat.write(
eachline.replace('cfxpost_set_path', pathfile_cfxpost))
finally:
fp_cfxpost02_bat.close()
# write all results
results_file_path = 'pump_performance_data.xlsx'
columns_head = [
'x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7', 'efficiency', 'head',
'power'
]
if self.cb1.currentText() == 'Des':
self.cb2.setEnabled(False)
self.cb3.setEnabled(False)
self.cb4.setEnabled(False)
x = np.array([[60.5, 45.8, 49.7, 54.8, 60.7, 60.0, 65.8]])
pump_performance = objective_pump(x)
all_data = np.hstack((x, pump_performance))
write_results_excel(all_data, results_file_path, columns_head)
elif self.cb1.currentText() == 'Opt':
self.cb2.showPopup()
self.cb3.setEnabled(False)
self.cb4.setEnabled(False)
if self.cb2.currentText() == 'DOE':
self.cb3.showPopup()
self.cb4.setEnabled(False)
self.cb3.setEnabled(True)
if self.cb3.currentText() == 'New':
x_initial = lhs(7, samples=5, criterion='center')
ub_array = np.array(
[70.0, 80.0, 80.0, 80.0, 80.0, 80.0, 68.0])
lb_array = np.array(
[50.0, 40.0, 40.0, 40.0, 40.0, 40.0, 58.0])
x = np.multiply(x_initial,
(ub_array - lb_array)) + lb_array
filename_new_doe = 'DOE_new_design.xlsx'
if not os.path.isdir(filename_new_doe):
write_results_excel(
x, filename_new_doe,
['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7'])
else:
os.rmdir(filename_new_doe)
write_results_excel(
x, filename_new_doe,
['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7'])
pump_performance = objective_pump(x)
all_data = np.hstack((x, pump_performance))
write_results_excel(all_data, results_file_path,
columns_head)
elif self.cb3.currentText() == 'Existed':
filename_existed_doe = 'DOE_existed_design.xlsx'
df = pd.DataFrame(pd.read_excel(filename_existed_doe))
x = df.to_numpy()[..., 1:]
pump_performance = objective_pump(x)
all_data = np.hstack((x, pump_performance))
write_results_excel(all_data, results_file_path,
columns_head)
elif self.cb2.currentText() == 'AI':
self.cb4.showPopup()
self.cb3.setEnabled(False)
self.cb4.setEnabled(True)
f_objective = lambda x: objective_pump(x)
numpop = 20
numiter = 500
functiondim = 2
lb = -32 * np.ones([1, functiondim])
ub = 32 * np.ones([1, functiondim])
echo = 'on'
if self.cb4.currentText() == 'PSO':
from pso_algorithm import pso
xgbest, fgbest, fbest = pso(f_objective, numpop,
functiondim, lb, ub, numiter,
echo)
'''
elif self.cb4.currentText() == 'GSA':
from gsa_algorithm import gsa
[xgbest,fgbest,fbest]=gsa(f_objective,numpop,functiondim,lb,ub,numiter,echo)
elif self.cb4.currentText() == 'GA':
from ga_algorithm import ga
[xgbest,fgbest,fbest]=gsa(f_objective,numpop,functiondim,lb,ub,numiter,echo)
elif self.cb4.currentText() == 'BA':
from ba_algorithm import ba
[xgbest,fgbest,fbest]=ba(f_objective,numpop,functiondim,lb,ub,numiter,echo)
elif self.cb4.currentText() == 'ABC':
from abc_algorithm import abc
[xgbest,fgbest,fbest]=abc(f_objective,numpop,functiondim,lb,ub,numiter,echo)
'''
all_data = np.hstack((xgbest, fgbest))
filename_global_best = 'IA_global_best.xlsx'
write_results_excel(all_data, filename_global_best,
['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'y'])
filename_iteration_best = 'IA_iteration_best.xlsx'
write_results_excel(fbest, filename_iteration_best, ['y'])
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 wrapper():
return pydoe.lhs(self.dim, self.num_pts, iterations=1)
def get_unit_latin_hypercube(dims, n_samples):
return pyDOE2.lhs(n=dims, samples=n_samples, criterion='correlation')
def main():
# num_lhc = 100
# num_evals = np.logspace(2, 4, num=num_lhc)
num_lhc = 1
num_evals = [512]
num_params = 5
verbose = True
np.random.seed(7)
set_name = 'training'
#########################################################################
####### Parameters -- these should follow the following syntax ########
# para = np.linspace(lower_lim, upper_lim, total_eval)
for n in range(num_lhc):
nevals = np.int(num_evals[n])
# cosmology parameters - excluding tau and dark energy
para1 = np.linspace(1e4, 1e5, nevals) # Flux
para2 = np.linspace(0.1, 1., nevals) # Radius
para3 = np.linspace(-0.5, 0.5, nevals) # g1
para4 = np.linspace(-0.5, 0.5, nevals) # g2
para5 = np.linspace(0.2, 0.4, nevals) # psf fwhm
# redshift parameters
if (num_params == 7):
para6 = np.linspace(0.5, 1.5, nevals) # z_m
para7 = np.linspace(0.05, 0.5, nevals) # FWHM
# no other known option yet - can insert other options, or read from text file
elif (num_params > 5):
print("unknown parameter option")
if (num_params == 5):
AllPara = np.vstack([para1, para2, para3, para4, para5])
AllLabels = [
r'Flux', r'Radius', r'Shear g1', r'Shear g2', r'PSF fwhm'
]
elif (num_params == 7):
AllPara = np.vstack(
[para1, para2, para3, para4, para5, para6, para7])
AllLabels = [
r'$\tilde{\omega}_m$', r'$\tilde{\omega}_b$',
r'$\tilde{\sigma}_8$', r'$\tilde{'
r'h}$', r'$\tilde{n}_s$', r'$\tilde{z}_m$', r'$\tilde{FWHM}$'
]
#########################################################################
# latin hypercube
lhd = pyDOE.lhs(AllPara.shape[0], samples=nevals,
criterion=None) # c cm corr m
idx = (lhd * nevals).astype(int)
AllCombinations = np.zeros((nevals, AllPara.shape[0]))
for i in range(AllPara.shape[0]):
AllCombinations[:, i] = AllPara[i][idx[:, i]]
# Delete row when g1**2 + g2**2 > 1
del_rows = np.where(
AllCombinations[:, 2]**2 + AllCombinations[:, 3]**2 > 1.)[0]
AllCombinations = np.delete(AllCombinations, del_rows, axis=0)
# np.savetxt('lhc_'+str(nevals)+'_'+str(num_params)+'_'+set_name+'.txt', AllCombinations)
# if verbose:
# print(lhd)
# lhd = norm(loc=0, scale=1).ppf(lhd) # this applies to both factors here
#
if verbose:
f, a = plt.subplots(AllPara.shape[0],
AllPara.shape[0],
sharex=True,
sharey=True)
plt.subplots_adjust(left=None,
bottom=None,
right=None,
top=None,
wspace=None,
hspace=None)
plt.rcParams.update({'font.size': 4})
for i in range(AllPara.shape[0]):
for j in range(i + 1):
print(i, j)
if (i != j):
a[i, j].scatter(lhd[:, i], lhd[:, j], s=1, alpha=0.7)
a[i, j].grid(True)
a[j, i].set_visible(False)
else:
# a[i,i].set_title(AllLabels[i])
a[i, i].text(0.4, 0.4, AllLabels[i], size='x-large')
hist, bin_edges = np.histogram(lhd[:, i],
density=True,
bins=12)
# a[i,i].bar(hist)
a[i, i].bar(bin_edges[:-1],
hist / hist.max(),
width=0.09,
alpha=0.5)
plt.xlim(0, 1)
plt.ylim(0, 1)
plt.tight_layout()
plt.savefig('../Data/Plots/LatinSq.pdf',
figsize=(5000, 5000),
bbox_inches="tight",
dpi=900)
opt_method = input(
'Which method do you want to choose? design of experiment or intelligent algorithm(DOE/IA): '
)
while opt_method not in choose_opt_method:
opt_method = input(
'Which method do you want to choose? design of experiment or intelligent algorithm(DOE/IA): '
)
if opt_method == choose_opt_method[0]:
print('DOE is choosed')
choose_DOE = ('New', 'Existed')
DOE_opt = input('Is the DOE New or Existed(New or Existed): ')
while DOE_opt not in choose_DOE:
DOE_opt = input('Is the DOE New or Existed(New or Existed): ')
if DOE_opt == choose_DOE[0]:
print('DOE is New')
x_initial = lhs(7, samples=5, criterion='center')
ub_array = np.array([70.0, 80.0, 80.0, 80.0, 80.0, 80.0, 68.0])
lb_array = np.array([50.0, 40.0, 40.0, 40.0, 40.0, 40.0, 58.0])
x = np.multiply(x_initial, (ub_array - lb_array)) + lb_array
filename_new_doe = 'DOE_new_design.xlsx'
if not os.path.isdir(filename_new_doe):
write_results_excel(x, filename_new_doe,
['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7'])
else:
os.rmdir(filename_new_doe)
write_results_excel(x, filename_new_doe,
['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7'])
pump_performance = objective_pump(x)
all_data = np.hstack((x, pump_performance))
write_results_excel(all_data, results_file_path, columns_head)
else:
cache_dir=run_name + '/' + case,
reconnect_cache=False,
write_csv=write_to_csv)
driver = OptimizationDriver(prob.create_problem, **driver_config)
# More information about sampling: https://pythonhosted.org/pyDOE/index.html
if sampling_method is 'fullfact':
# Full factorial parametric sweep
levels = np.array([N_levels] * prob.get_problem_dimen())
design = pyDOE.fullfact(levels)
levels[levels == 1] = 2
samples = design / (levels - 1)
elif sampling_method is 'lhs':
# Latin Hypercube Sampling of design space
samples = pyDOE.lhs(prob.get_problem_dimen(),
criterion='cm',
samples=N_samples)
# Saves sampling values for post-process analysis
if save_samples:
with open(driver.options['cache_dir'] + '/' + case + '_' +
sampling_method + '_samples.csv',
'w',
newline='') as f:
csv_writer = csv.writer(f)
csv_writer.writerows(samples)
# Breaking sampling into small batches to reduce impacts of memory leak
N_samples_per_batch = len(samples) / N_smb
for i in range(N_smb):
start = int(i * N_samples_per_batch)
def lhs(samples: int, attributes: int, *args, **kwargs) -> np.ndarray:
return pyDOE2.lhs(attributes, samples, *args, **kwargs)
def generateTradeStudy(tradeStudy):
fileName = os.getcwd() + '\\Results\\' + tradeStudy.fileName
runHPOP = tradeStudy.runHPOP
epoch = tradeStudy.epoch
a = tradeStudy.a
e = tradeStudy.e
i = tradeStudy.i
RAAN = tradeStudy.RAAN
AoP = tradeStudy.AoP
TA = tradeStudy.TA
Cd = tradeStudy.Cd
Cr = tradeStudy.Cr
DragArea = tradeStudy.DragArea
SunArea = tradeStudy.SunArea
Mass = tradeStudy.Mass
OrbPerCal = tradeStudy.OrbPerCal
GaussQuad = tradeStudy.GaussQuad
SigLvl = tradeStudy.SigLvl
SolFlxFile = tradeStudy.SolFlxFile
AtmDen = tradeStudy.AtmDen
SecondOrderOblateness = tradeStudy.SecondOrderOblateness
numberOfRuns = tradeStudy.numberOfRuns
howToVary = tradeStudy.howToVary
varyCols = tradeStudy.varyCols
varyValues = tradeStudy.varyValues
setSunAreaEqualToDragArea = tradeStudy.setSunAreaEqualToDragArea
np.random.seed(seed=1)
# Generate Additional Columns
Rp = a * (1 - e)
Ra = a * (1 + e)
p = a * (1 - e**2)
rs, vs = coe2rv(GM_earth * 1e-9, p, e, i * np.pi / 180, RAAN * np.pi / 180,
AoP * np.pi / 180, TA * np.pi / 180)
x = rs[0]
y = rs[1]
z = rs[2]
Vx = vs[0]
Vy = vs[1]
Vz = vs[2]
CdAM = Cd * DragArea / Mass
CrAM = Cr * SunArea / Mass
# Generate Dataframe to store all of the runs
data = [
epoch, a, e, i, RAAN, AoP, TA, Rp, Ra, p, x, y, z, Vx, Vy, Vz, Cd, Cr,
DragArea, SunArea, Mass, CdAM, CrAM, OrbPerCal, GaussQuad, SigLvl,
SolFlxFile, AtmDen, SecondOrderOblateness
]
columns = [
'epoch', 'a', 'e', 'i', 'RAAN', 'AoP', 'TA', 'Rp', 'Ra', 'p', 'x', 'y',
'z', 'Vx', 'Vy', 'Vz', 'Cd', 'Cr', 'Drag Area', 'Sun Area', 'Mass',
'Cd*Drag Area/Mass', 'Cr*Sun Area/Mass', 'Orb Per Calc',
'Gaussian Quad', 'Flux Sigma Level', 'SolarFluxFile', 'Density Model',
'2nd Order Oblateness'
]
df = pd.DataFrame(data=data, index=columns).T
df[df.columns[:-3]] = df[df.columns[:-3]].astype(float)
# Grid Search
if howToVary.lower() == 'gridsearch':
# Create grid search of parameters and update the Dataframe
numOfLevels = [len(val) for val in varyValues]
runs = fullfact(numOfLevels).astype(int)
paramdf = pd.DataFrame()
for ii in range(len(runs.T)):
paramdf[varyCols[ii]] = varyValues[ii][runs[:, ii]]
df = pd.concat([df] * len(runs), ignore_index=True)
for col in paramdf.columns:
df[col] = paramdf[col]
# Latin Hypercube
elif howToVary.lower() == 'latinhypercube':
# Generate runs
lhd = lhs(len(varyCols), samples=numberOfRuns)
# lhd = stats.norm(loc=0, scale=1).ppf(lhd) # Convert to a normal distribution
lhd = pd.DataFrame(lhd)
adjustEpoch = False
if 'epoch' in varyCols:
date1 = yydddToDatetime(varyValues[0][0])
date2 = yydddToDatetime(varyValues[0][1])
deltaDays = lhd[0] * (date2 - date1).days
minDate = [varyValues[0][0] for i in range(numberOfRuns)]
varyCols.remove('epoch')
varyValues = varyValues[1:]
lhd = lhd.drop(0, axis=1)
adjustEpoch = True
lhd.columns = varyCols
# Replace string columns with categories
strii = [
ii for ii in range(len(varyValues))
if isinstance(varyValues[ii][0], str)
]
for ii in strii:
lhd.iloc[:, ii] = pd.cut(lhd.iloc[:, ii],
len(varyValues[ii]),
labels=varyValues[ii])
# Replace float columns with values in range
varyValues = np.array(varyValues)
floatii = lhd.dtypes == float
lhsMinMax = varyValues[floatii]
lhsMinMax = np.concatenate(lhsMinMax, axis=0).reshape(-1, 2)
lhd.loc[:, floatii] = lhd.loc[:, floatii] * (
lhsMinMax[:, 1] - lhsMinMax[:, 0]) + lhsMinMax[:, 0]
indxs = [
ii for ii in range(len(varyCols)) if varyCols[ii] in
['Orb Per Calc', 'Gaussian Quad', 'Flux Sigma Level']
]
lhd.iloc[:, indxs] = lhd.iloc[:, indxs].round()
# Create df
df = pd.concat([df] * len(lhd), ignore_index=True)
if adjustEpoch == True:
df['epoch'] = [
adjustDate(yyddd, deltaDay)
for yyddd, deltaDay in zip(minDate, deltaDays)
]
for col in lhd.columns:
df[col] = lhd[col]
# Perturb
elif howToVary.lower() == 'perturb':
# Sample from a normal distribution
rv = stats.norm()
rvVals = rv.rvs((numberOfRuns, len(varyCols)))
# Create perturbation df
pertdf = pd.DataFrame(rvVals) * varyValues
pertdf.columns = varyCols
# Duplicate original df by the number of runs
df = pd.concat([df] * numberOfRuns, ignore_index=True)
if 'epoch' in varyCols:
df['epoch'] = [
adjustDate(yyddd, deltaDay)
for yyddd, deltaDay in zip(df['epoch'], pertdf['epoch'])
]
varyCols.remove('epoch')
varyValues = varyValues[1:]
for col in varyCols:
df[col] = df[col] + pertdf[col]
# Update dependant values
df = updateDf(df, runHPOP, varyCols, setSunAreaEqualToDragArea)
# Convert all columns to floats and round to the 10th decimal, otherwise there are some numerical rounding issues.
cols = [
col for col in df.columns if col not in
['SolarFluxFile', 'Density Model', '2nd Order Oblateness']
]
df[cols] = df[cols].astype(float)
for col in cols:
df[col] = np.round(df[col], 10)
# Add results
df['LT Orbits'] = np.nan
df['LT Years'] = np.nan
df['LT Runtime'] = np.nan
if runHPOP == True:
df['HPOP Years'] = np.nan
df['HPOP Runtime'] = np.nan
df.index.name = 'Run ID'
df = df.reset_index()
df.to_csv(fileName) # Create a new csv to store the results
return df
def run_initial_values_benchmark(self, log_file_name='ema/results/log_file_initial_values.txt'):
if path.exists(log_file_name):
remove(log_file_name)
s = '################### Running robustness to initial values test ################### \n'
logfile = open(log_file_name, 'a+')
logfile.writelines(s)
logfile.close()
print(s)
# Set to true to print detail of each sample
print_option = False
test_cases = [('SLSQP', 'full_analytic', False), ('SLSQP', 'semi_analytic_fd', False)]
for test_case in test_cases:
optimizer = test_case[0]
derivative_method = test_case[1]
blackbox = test_case[2]
prob_type = 'MDO'
# Number of samples
N = 50
res_num_compute = {
'MDF': [],
'IDF': [],
'HYBRID': [],
'NVH': []
}
# Scale to make sure that a solution exist
k_os = 1.
# Bounds of the variables of the DOE
# lower_bound = 0.1
# upper_bound = 1.
variables = {
'N_red': (0.1, 8.),
'J_mot': (1e-6, 1.e-1),
'T_em': (0.1, 100.)
}
# DOE
doe = lhs(len(variables.keys()), samples=N, criterion='center')
# Perform an analysis for each sample
for sample in doe:
initial_values = copy.copy(variables)
for i, (key, value) in enumerate(initial_values.items()):
upper_bound = value[1]
lower_bound = value[0]
initial_values[key] = (upper_bound - lower_bound) * sample[i] + lower_bound
prob_list = [
MDFProblem(name='MDF', optimizer=optimizer, derivative_method=derivative_method,
blackbox=blackbox, log_file=log_file_name, scale=k_os, print=print_option),
IDFProblem(name='IDF', optimizer=optimizer, derivative_method=derivative_method,
blackbox=blackbox, log_file=log_file_name, scale=k_os, print=print_option),
HybridProblem(name='HYBRID', optimizer=optimizer, derivative_method=derivative_method,
blackbox=blackbox, log_file=log_file_name, scale=k_os, print=print_option),
NVHProblem(name='NVH', optimizer=optimizer, derivative_method=derivative_method,
blackbox=blackbox, log_file=log_file_name, scale=k_os, print=print_option)]
self.run_analysis(prob_list, initial_values=initial_values)
for prob in prob_list:
if prob.post_analysis_results['success']:
res_num_compute[prob.name].append(prob.post_analysis_results['num_compute'])
# Result analysis
for i, (key, value) in enumerate(res_num_compute.items()):
s = '> ---------- Running ' + prob_type + ' using ' + \
key + ' formulation and ' + optimizer + ' optimizer with ' + \
derivative_method + ' at scale ' + str(k_os) + ' ------------ \n'
try:
max_num_compute = max(value)
min_num_compute = min(value)
mean_num_compute = np.mean(value)
median_num_compute = np.median(value)
percentage_of_success = len(value) / N * 100.
res = 'Max number of evaluations : ' + str(max_num_compute) + '\n' \
'Min number of evaluations : ' + str(min_num_compute) + '\n' \
'Mean number of evaluations : ' + str(mean_num_compute) + '\n' \
'Median number of evaluations : ' + str(median_num_compute) + '\n' \
'Percentage of success : ' + str(percentage_of_success) + '\n'
s += s + res
except:
s += s + 'All samples failed. \n'
pass
logfile = open(log_file_name, 'a+')
logfile.writelines(s)
logfile.close()
print(s)
def execute_ga(self, x0, vlb, vub, vob, bits, pop_size, max_gen, random_state, Pm=None, Pc=0.5):
"""
Perform the genetic algorithm.
Parameters
----------
x0 : ndarray
Initial design values
vlb : ndarray
Lower bounds array.
vub : ndarray
Upper bounds array. This includes over-allocation so that every point falls on an
integer value.
vob : ndarray
Outer bounds array. This is purely for bounds check.
bits : ndarray
Number of bits to encode the design space for each element of the design vector.
pop_size : int
Number of points in the population.
max_gen : int
Number of generations to run the GA.
random_state : np.random.RandomState, int
Random state (or seed-number) which controls the seed and random draws.
Pm : float or None
Mutation rate
Pc : float
Crossover rate
Returns
-------
ndarray
Best design point
float
Objective value at best design point.
int
Number of successful function evaluations.
"""
comm = self.comm
xopt = copy.deepcopy(vlb)
fopt = np.inf
self.lchrom = int(np.sum(bits))
if np.mod(pop_size, 2) == 1:
pop_size += 1
self.npop = int(pop_size)
fitness = np.zeros((self.npop, ))
# If mutation rate is not provided as input
if Pm is None:
Pm = (self.lchrom + 1.0) / (2.0 * pop_size * np.sum(bits))
elite = self.elite
new_gen = np.round(lhs(self.lchrom, self.npop, criterion='center',
random_state=random_state))
new_gen[0] = self.encode(x0, vlb, vub, bits)
# Main Loop
nfit = 0
for generation in range(max_gen + 1):
old_gen = copy.deepcopy(new_gen)
x_pop = self.decode(old_gen, vlb, vub, bits)
# Evaluate points in this generation.
if comm is not None:
# Parallel
# Since GA is random, ranks generate different new populations, so just take one
# and use it on all.
x_pop = comm.bcast(x_pop, root=0)
cases = [((item, ii), None) for ii, item in enumerate(x_pop)
if np.all(item - vob <= 0)]
# Pad the cases with some dummy cases to make the cases divisible amongst the procs.
# TODO: Add a load balancing option to this driver.
extra = len(cases) % comm.size
if extra > 0:
for j in range(comm.size - extra):
cases.append(cases[-1])
results = concurrent_eval(self.objfun, cases, comm, allgather=True,
model_mpi=self.model_mpi)
fitness[:] = np.inf
for result in results:
returns, traceback = result
if returns:
val, success, ii = returns
if success:
fitness[ii] = val
nfit += 1
else:
# Print the traceback if it fails
print('A case failed:')
print(traceback)
else:
# Serial
for ii in range(self.npop):
x = x_pop[ii]
if np.any(x - vob > 0):
# Exceeded bounds for integer variables that are over-allocated.
success = False
else:
fitness[ii], success, _ = self.objfun(x, 0)
if success:
nfit += 1
else:
fitness[ii] = np.inf
# Elitism means replace worst performing point with best from previous generation.
if elite and generation > 0:
max_index = np.argmax(fitness)
old_gen[max_index] = min_gen
x_pop[max_index] = min_x
fitness[max_index] = min_fit
# Find best performing point in this generation.
min_fit = np.min(fitness)
min_index = np.argmin(fitness)
min_gen = old_gen[min_index]
min_x = x_pop[min_index]
if min_fit < fopt:
fopt = min_fit
xopt = min_x
# Evolve new generation.
new_gen = self.tournament(old_gen, fitness)
new_gen = self.crossover(new_gen, Pc)
new_gen = self.mutate(new_gen, Pm)
return xopt, fopt, nfit
def execute_ga(self, vlb, vub, bits, pop_size, max_gen, random_state):
"""
Perform the genetic algorithm.
Parameters
----------
vlb : ndarray
Lower bounds array.
vub : ndarray
Upper bounds array.
bits : ndarray
Number of bits to encode the design space for each element of the design vector.
pop_size : int
Number of points in the population.
max_gen : int
Number of generations to run the GA.
random_state : np.random.RandomState, int
Random state (or seed-number) which controls the seed and random draws.
Returns
-------
ndarray
Best design point
float
Objective value at best design point.
int
Number of successful function evaluations.
"""
comm = self.comm
xopt = copy.deepcopy(vlb)
fopt = np.inf
self.lchrom = int(np.sum(bits))
if np.mod(pop_size, 2) == 1:
pop_size += 1
self.npop = int(pop_size)
fitness = np.zeros((self.npop, ))
Pc = 0.5
Pm = (self.lchrom + 1.0) / (2.0 * pop_size * np.sum(bits))
elite = self.elite
# TODO: from an user-supplied intial population
# new_gen, lchrom = encode(x0, vlb, vub, bits)
new_gen = np.round(
lhs(self.lchrom,
self.npop,
criterion='center',
random_state=random_state))
# Main Loop
nfit = 0
for generation in range(max_gen + 1):
old_gen = copy.deepcopy(new_gen)
x_pop = self.decode(old_gen, vlb, vub, bits)
# Evaluate points in this generation.
if comm is not None:
# Parallel
# Since GA is random, ranks generate different new populations, so just take one
# and use it on all.
x_pop = comm.bcast(x_pop, root=0)
cases = [((item, ii), None) for ii, item in enumerate(x_pop)]
results = concurrent_eval(self.objfun,
cases,
comm,
allgather=True,
model_mpi=self.model_mpi)
fitness[:] = np.inf
for result in results:
returns, traceback = result
if returns:
val, success, ii = returns
if success:
fitness[ii] = val
nfit += 1
else:
# Print the traceback if it fails
print('A case failed:')
print(traceback)
else:
# Serial
for ii in range(self.npop):
x = x_pop[ii]
fitness[ii], success, _ = self.objfun(x, 0)
if success:
nfit += 1
else:
fitness[ii] = np.inf
# Elitism means replace worst performing point with best from previous generation.
if elite and generation > 0:
max_index = np.argmax(fitness)
old_gen[max_index] = min_gen
x_pop[max_index] = min_x
fitness[max_index] = min_fit
# Find best performing point in this generation.
min_fit = np.min(fitness)
min_index = np.argmin(fitness)
min_gen = old_gen[min_index]
min_x = x_pop[min_index]
if min_fit < fopt:
fopt = min_fit
xopt = min_x
# Evolve new generation.
new_gen = self.tournament(old_gen, fitness)
new_gen = self.crossover(new_gen, Pc)
new_gen = self.mutate(new_gen, Pm)
return xopt, fopt, nfit
nsims = main.nsims
except AttributeError:
nsims = 5
# import parameter ranges table
loginfo("Reading in lhs parameter range data from <" + dir_path +
"\input\lhs\lhs_param_ranges_vvwm.csv>.")
param_ranges = pd.read_csv(
os.path.join(dir_path, "input", "lhs", "lhs_param_ranges_vvwm.csv"))
print(param_ranges)
# create list of input parameter names
param_names = param_ranges["Parameter"].to_list()
# conduct lhs sampling
lhs_design = lhs(n=len(param_names), samples=nsims)
print("LHS Design w/o Uniform: ", "\n", lhs_design.round(2))
for i in range(0, len(param_names)):
lhs_design[:, i] = param_ranges.loc[i, "Min"] + (lhs_design[:, i]) * (
param_ranges.loc[i, "Range"]) #JMS 10-20-20
print("Uniformly Sampled from LHS Design: ", "\n", lhs_design)
# convert to data frame
lhs_df = pd.DataFrame(lhs_design, columns=param_names)
print(round(lhs_df, 3))
# write out
loginfo("Writing simulated parameter data to <" + dir_path +
"\io\lhs_sampled_params_vvwm.csv>.")
lhs_df.to_csv(os.path.join(dir_path, "io", "lhs_sampled_params_vvwm.csv"))
# import parameter ranges table
loginfo("Reading in lhs parameter range data from <" + dir_path +
r"\input\lhs\lhs_param_ranges.csv>.")
param_ranges = pd.read_csv(
os.path.join(dir_path, "input", "lhs", "lhs_param_ranges.csv"))
print(param_ranges)
# create list of input parameter names
param_names = param_ranges["Parameter"].to_list()
# parameter conditions:
# por >= fc (happens automatically), fc >= wp, MaxRate>=MinRate
# conduct lhs sampling
lhs_design = lhs(
n=len(param_names), samples=3 * nsims
) # take 3x as many samples as needed, in case some don't meet conditions
# uniformly sample
for i in range(0, len(param_names)):
lhs_design[:, i] = param_ranges.loc[
i, "Min"] + (lhs_design[:, i]) * (param_ranges.loc[i, "Range"])
# filter on conditions: fc >= wp, MaxRate >= MinRate
lhs_design = lhs_design[np.where(
lhs_design[:, 11] < lhs_design[:, 10])[0]] # fc >= wp
lhs_design = lhs_design[np.where(
lhs_design[:, 6] < lhs_design[:, 5])[0]] # MaxRate >= MinRate
lhs_design = lhs_design[:nsims] # only take first nsims rows meeting condition
# convert to data frame
lhs_df = pd.DataFrame(lhs_design, columns=param_names)
print(round(lhs_df, 3))
def run_doe_benchmark(self, log_file_name='ema/results/log_file_doe.txt'):
if path.exists(log_file_name):
remove(log_file_name)
s = '################### Running robustness to doe test ################### \n'
logfile = open(log_file_name, 'a+')
logfile.writelines(s)
logfile.close()
print(s)
test_cases = [('SLSQP', 'full_analytic', False), ('SLSQP', 'semi_analytic_fd', False),
('SLSQP', 'monolythic_fd', True), ('COBYLA', 'derivative_free', False)]
for test_case in test_cases:
optimizer = test_case[0]
derivative_method = test_case[1]
blackbox = test_case[2]
prob_type = 'MDA'
# Set to true to print detail of each sample
print_option = False
# Number of samples
N = 50
res_num_compute = {
'MDF': [],
'IDF': [],
'HYBRID': [],
'NVH': []
}
# Scale to make sure that a solution exist for IDF and HYBRID
k_os = 2.
variables = {
'F_ema': (7.e4 * 0.5, 7.e4 * 2.),
'N_red': (1., 10.),
'p': (1.59e-3 * 0.5, 1.59e-3 * 2.),
'A_max': (2. * 0.5, 2.* 2.)
}
# DOE
doe = lhs(len(variables.keys()), samples=N, criterion='center')
# Perform an analysis for each sample
for sample in doe:
initial_values = copy.copy(variables)
for i, (key, value) in enumerate(initial_values.items()):
upper_bound = value[1]
lower_bound = value[0]
initial_values[key] = (upper_bound - lower_bound) * sample[i] + lower_bound
prob_list = [
MDFProblem(name='MDF', prob_type=prob_type, optimizer=optimizer,
derivative_method=derivative_method, blackbox=blackbox,
log_file=log_file_name, scale=k_os, print=print_option),
IDFProblem(name='IDF', prob_type=prob_type, optimizer=optimizer,
derivative_method=derivative_method, blackbox=blackbox,
log_file=log_file_name, scale=k_os, print=print_option),
HybridProblem(name='HYBRID', prob_type=prob_type, optimizer=optimizer,
derivative_method=derivative_method, blackbox=blackbox,
log_file=log_file_name, scale=k_os, print=print_option),
NVHProblem(name='NVH', prob_type=prob_type, optimizer=optimizer,
derivative_method=derivative_method, blackbox=blackbox,
log_file=log_file_name, scale=k_os, print=print_option)]
self.run_analysis(prob_list, initial_values=initial_values)
for prob in prob_list:
if prob.post_analysis_results['success']:
res_num_compute[prob.name].append(prob.post_analysis_results['num_compute'])
# Result analysis
for i, (key, value) in enumerate(res_num_compute.items()):
s = '> ---------- Running ' + prob_type + ' using ' + key + ' formulation and ' + \
optimizer + ' optimizer with ' + derivative_method + \
' at scale ' + str(k_os) + ' ------------ \n'
if len(value) == 0:
value = [0.]
max_num_compute = max(value)
min_num_compute = min(value)
mean_num_compute = np.mean(value)
median_num_compute = np.median(value)
percentage_of_success = len(value) / N * 100.
res = 'Max number of evaluations : ' + str(max_num_compute) + '\n' \
'Min number of evaluations : ' + str(min_num_compute) + '\n' \
'Mean number of evaluations : ' + str(mean_num_compute) + '\n' \
'Median number of evaluations : ' + str(median_num_compute) + '\n' \
'Percentage of success : ' + str(percentage_of_success) + '\n'
s += s + res
logfile = open(log_file_name, 'a+')
logfile.writelines(s)
logfile.close()
print(s)
def lhsdesign(n, min_range, max_range, k=5, include_vertices=False):
"""Returns the Latin Hypercube Sampling for a given range of values.
Parameters
----------
n : int
Number of samples of the hypercube.
min_range : np.array
1-by-p or p-by-1 array containing the minimum values for each variable.
max_range : np.array
1-by-p or p-by-1 array containing the maximum values for each variable.
k : int, optional
Number of iterations to attempt to improve the design.
include_vertices : bool
To include or not the vertices of the hypercube in the sample.
Returns
-------
out : np.array
n-by-p array containing the Latin Hypercube Sampling.
Raises
------
ValueError
If ndim of either `min_range` or `max_range` is not 2.
If the `min_range` or `max_range` aren't vectors.
"""
# check input ranges dimensions. If ndim != 1, raise error
if min_range.ndim != 1 or max_range.ndim != 1:
raise ValueError("Input ranges must be 1D arrays.")
else:
# both have ndim == 1, check if they have the same size
if min_range.size != max_range.size:
raise ValueError(
"min_range and max_range must have the same number of elements"
)
# min_range = min_range.reshape(1, -1)
# max_range = max_range.reshape(1, -1)
p = min_range.size
# proceed with normal calculations
slope = np.tile(max_range - min_range, (n, 1))
offset = np.tile(min_range, (n, 1))
# create normalized LH
x_normalized = lhs(p, samples=n, iterations=k, criterion='maximin')
if include_vertices:
vertices = get_vertices(min_range, max_range)
# scale and return the LH
return np.vstack((x_normalized * slope + offset, vertices))
else:
# scale and return the LH
return x_normalized * slope + offset
def DOE(DOE_Seed, LHD_SampleSize, LHD_SamplingStrategy, IDM_path, DPM_path,
LHD_iterations, RandomiseCFGs, Offset, InfoOnly, make_single_files,
DPM_base_name, test_mode):
np.random.seed(DOE_Seed) #fix
print("STARTING\n")
#Load the Import Design Matrix
IDM_f = open(IDM_path, encoding='utf-8')
IDM = []
csvReader = csv.reader(IDM_f, delimiter="\t")
i = 0
for row in csvReader:
if (i >= 1):
IDM.append(row)
i += 1
IDM_f.close()
#Conv numerics to numerics
for row in range(0, len(IDM)):
IDM[row][1] = float(IDM[row][1])
IDM[row][2] = float(IDM[row][2])
IDM[row][3] = float(IDM[row][3])
#Calculate the size of the full-factorial and the number of LHD parameters
Indicator_DPM = [
] #Hold information on the kind of the parameter in the final DPM
Factorials = [] #Hold Factorial series, also that of FactPower
LHD_factors = 0
for row in range(0, len(IDM)):
Indicator_DPM.append(IDM[row][4])
if IDM[row][4] == "LHD":
LHD_factors += 1
elif IDM[row][4] == "Factorial" or IDM[row][4] == "Fact":
val = IDM[row][1]
tmp = [val]
while (val + IDM[row][3] <= IDM[row][2]):
val += IDM[row][3]
tmp.append(val)
tmp = np.asarray(tmp)
#tmp = np.arange(IDM[row][1],IDM[row][2],IDM[row][3])
Factorials.append([IDM[row][0], tmp]) #parname, #items
elif IDM[row][4] == "FactPower":
tmp = []
pw = int(0)
while (IDM[row][1] * IDM[row][3]**pw <= IDM[row][2]):
tmp.append(IDM[row][1] * IDM[row][3]**pw)
pw += 1
Factorials.append([IDM[row][0], np.asarray(tmp)]) #parname, #items
#Calculate the size of the LHD sample part
SampleMult = 1
if LHD_factors == 0:
if (LHD_SampleSize < 0):
SampleMult = round(-LHD_SampleSize) #use as multiplicator
LHD_SampleSize = 0
elif LHD_factors == 1:
print("It is not possible to have a single LHD factor.\n")
print("Instead, consider to make it 'Fact' and add -N 20 (example) \
to multiply the complete setting by 20.")
return "ERROR"
elif LHD_SampleSize < 0: #implies -N argument
LHD_SampleSize *= -LHD_factors
LHD_SampleSize = round(LHD_SampleSize)
#Calculate the size of the overal sample
FactSampleSize = 1
for item in range(len(Factorials)):
FactSampleSize *= Factorials[item][1].size
SampleSize = int(max(1, LHD_SampleSize) * FactSampleSize)
if len(Factorials) > 0:
print ("Factorial design with ",len(Factorials), " factors and ", \
FactSampleSize, "configurations.\n")
if LHD_factors > 0:
print ("Latin Hyper Cube design with ", LHD_factors, " Factors and ",\
LHD_SampleSize, " distinct design points for each\n")
if SampleMult > 1:
print("All is multiplied by ", SampleMult, ". \nNote: This makes only", \
"sense if at least one random factor exists (like seed)\n")
if test_mode > 0 and test_mode < SampleSize:
print("\nTest mode selected. Sample Size is now:", test_mode)
print("Overal sample size is: ", SampleSize * SampleMult)
if (InfoOnly != 0):
print("\nExit. Info only mode.\n")
return "Done"
#Create a reduced form design point matrix of the factorial factors.
Fact_DPM = np.empty([FactSampleSize, len(Factorials)], "float64")
loops = 1
for col in range(0, len(Factorials)):
row = 0
while row < FactSampleSize:
for item in range(Factorials[col][1].size):
loop_count = 0
while loop_count < loops:
Fact_DPM[row][col] = Factorials[col][1][item]
loop_count += 1
row += 1
loops *= Factorials[col][1].size #increase the number of repeated vals
#select sampling method for LHD part
if LHD_SampleSize > 0:
print("Using strategy " + LHD_SamplingStrategy + " for the LHS")
if (LHD_SamplingStrategy == "corr"
or LHD_SamplingStrategy == "correlation"):
print("with " + str(LHD_iterations) + " iterations \n")
#Provide the LHD Matrix as raw
if LHD_SamplingStrategy == "none":
LHD_raw = pyDOE2.lhs(LHD_factors,
samples=LHD_SampleSize,
iterations=LHD_iterations)
else:
LHD_raw = pyDOE2.lhs(LHD_factors,
samples=LHD_SampleSize,
criterion=LHD_SamplingStrategy,
iterations=LHD_iterations)
#Print correlation matrix
a = np.corrcoef(LHD_raw)
print("Correlation Matrix:")
print(a)
#Normalise to values
LHD_DPM = np.copy(LHD_raw)
for row in range(LHD_SampleSize):
LHD_col = 0
for col in range(len(Indicator_DPM)):
if Indicator_DPM[col] == "LHD":
LHD_DPM[row][LHD_col] *= (IDM[col][2] - IDM[col][1]
) #spannwidth
LHD_DPM[row][LHD_col] += IDM[col][1] #add minimum
#Now, correct to step-size
LHD_DPM[row][LHD_col] = round(LHD_DPM[row][LHD_col] /
IDM[col][3])
LHD_DPM[row][LHD_col] *= IDM[col][3]
LHD_col += 1
#Provide a "Header" for the DPM with Parameter Names and ConfigID
DPM_header = [] #header
for row in range(len(IDM)):
DPM_header.insert(row, IDM[row][0])
DPM_header.insert(0, "ABMAT_ConfigID")
Indicator_DPM.insert(0, "ID")
#Define the complete Design Point Matrix, un-normalised, samples*(Pars+1)
DPM = np.empty([SampleSize * SampleMult, len(DPM_header)], "float64")
row = 0
for mult in range(SampleMult): #multiply
for LHD_row in range(max(LHD_SampleSize, 1)):
#loop through LHD and for each design-vector add the complete factorial
#sub-space
for Fact_row in range(FactSampleSize):
LHD_item = 0
Fact_item = 0
for col in range(len(Indicator_DPM)):
if Indicator_DPM[col] == "ID":
DPM[row][
col] = row + 1 #Set the ConfigID, starting with 1#
elif Indicator_DPM[col] == "LHD":
DPM[row][col] = LHD_DPM[LHD_row][LHD_item]
LHD_item += 1
elif Indicator_DPM[col] == "Factorial" or Indicator_DPM[
col] == "FactPower":
DPM[row][col] = Fact_DPM[Fact_row][Fact_item]
Fact_item += 1
elif Indicator_DPM[col] == "Fixed":
DPM[row][col] = IDM[col - 1][1] #Minimum
elif Indicator_DPM[col] == "Random":
DPM[row][col] = IDM[col - 1][2] - IDM[col -
1][1] #Span
DPM[row][col] *= np.random.uniform() #randomise
DPM[row][col] += IDM[col - 1][1] #add minimum
#Now, correct to step-size
DPM[row][col] = round(DPM[row][col] * IDM[col - 1][3])
DPM[row][col] /= IDM[col - 1][3]
else:
print("Error! Unknown Type of Variable: ", \
Indicator_DPM[col] )
row += 1
#mix the order? Is espescially important in case of distributed "packages"
#of simulations and factorial designs, where the simulation time may vary
#with the factorial's values. E.g. scale parameters.
if (RandomiseCFGs == "Yes"):
np.random.shuffle(DPM)
for row in range(SampleSize * SampleMult):
DPM[row][
0] = row + 1 + Offset #Assign the unique configuration ids
"""
Save the DPM to a tab-separated file
"""
os.makedirs(os.path.dirname(DPM_path + "\\"),
exist_ok=True) #Create dir if necessary
sample = range(SampleSize * SampleMult)
if (not make_single_files):
#Save everything to a tsv file.
out_file = DPM_path + "\\DPM_" + DPM_base_name + ".tsv"
DPM_f = open(out_file, 'w', encoding='utf-8', newline='')
csvWriter = csv.writer(DPM_f, delimiter="\t")
csvWriter.writerow(DPM_header)
if test_mode > 0 and test_mode < SampleSize * SampleMult:
sample = random.sample(sample, test_mode)
for row in sample:
csvWriter.writerow(DPM[row])
DPM_f.close()
else:
#create single tsv files for row in range(SampleSize):
if test_mode > 0 and test_mode < SampleSize * SampleMult:
sample = random.sample(sample, test_mode)
print(sample)
for row in sample:
out_file = DPM_path + "\\DPM_" + DPM_base_name + "_" + str(
int(DPM[row][0])) + ".tsv"
DPM_f = open(out_file, 'w', encoding='utf-8', newline='')
csvWriter = csv.writer(DPM_f, delimiter="\t")
csvWriter.writerow(DPM_header)
csvWriter.writerow(DPM[row])
DPM_f.close()
return "DoneA"
def test_notebook_4():
print("\n Notebook4 tested...")
# Define SPM design parameters
d_e = PositiveParameter("d_e", [50, 500], "mm", "External stator diameter")
d_i = PositiveParameter("d_i", [20, 300], "mm", "Internal stator diameter")
e_tooth = PositiveParameter("e_tooth", [3, 60], "mm", "Tooth thikness")
e_yoke = PositiveParameter("e_yoke", [2, 20], "mm", "Yoke thikness")
w_pm = PositiveParameter("w_pm", [2, 20], "mm", "Permanent magnet width")
r_i = PositiveParameter("r_i", [5, 100], "mm", "Rotor internal radius")
j = PositiveParameter("j", [0.1, 1000], "A/m**2",
"Winding current density")
B_R = PositiveParameter("B_R", [1.1], "tesla",
"Permanent magnet remanence")
B_SAT = PositiveParameter("B_SAT", [0.02], "tesla",
"Iron induction saturation")
MU_0 = PositiveParameter("MU_0", [1.26e-6], "H/m", "Vacuum permeability")
t_l = PositiveParameter("t_l", [0.01, 100], "N", "Linear torque")
parameter_set = PositiveParameterSet(d_e, d_i, e_tooth, e_yoke, w_pm, r_i,
j, B_R, B_SAT, MU_0, t_l)
# Perform dimensional analysis on linear torque
pi_set, _ = buckingham_theorem(parameter_set, False)
# Define new parameters for joule losses definition
p_jl = PositiveParameter("p_jl", [0.01, 1000], "W/m",
"Linear joule losses")
RHO_WIND = PositiveParameter("RHO_WIND", [17000], "ohm*m",
"Linear winding resistivity")
s_wind = PositiveParameter("s_wind", [1, 100], "mm**2",
"Winding total cross section")
parameter_set = PositiveParameterSet(d_e, d_i, e_tooth, e_yoke, w_pm, r_i,
j, B_R, B_SAT, MU_0, RHO_WIND, s_wind,
p_jl)
# Perform dimensional analysis on joule losses
pi_set, _ = buckingham_theorem(parameter_set, False)
# Calculate levels
bounds = numpy.array([[30, 150], [10, 100], [750, 3000]])
doe_levels = lhs(3, samples=27, criterion="maximin", random_state=42)
doe = bounds[:, 0] + doe_levels / doe_levels.max(axis=0) * (bounds[:, 1] -
bounds[:, 0])
# Show matrix
doe_data = pandas.DataFrame(doe, columns=["d_e", "h", "omega_max"])
doe_data.to_excel("output.xls")
os.remove("output.xls")
doe_data.head(n=numpy.shape(doe)[0])
# Plot 3D figure
fig = plot.figure()
ax = fig.add_subplot(111, projection="3d")
ax.scatter(doe[:, 0], doe[:, 1], doe[:, 2])
ax.set_xlabel("$D_e$")
ax.set_ylabel("$h$")
ax.set_zlabel("$\omega_{max}$")
doe = pandas.read_excel("notebooks/04_motor_example/output.xls")
# Declare directly the pi_set problem
doePI = doe[[
"pi01", "pi02", "pi03", "pi1", "pi2", "pi3", "pi4", "pi5", "pi6"
]].values
pi1 = PositiveParameter("pi1", [0.1, 1], "", "t_l*b_r**-1*j**-1*d_e**-3")
pi2 = PositiveParameter("pi2", [0.1, 1], "",
"p_j*rho_win**-1*d_e**-2*j**-2")
pi3 = PositiveParameter(
"pi3", [0.1, 1], "",
"p_fe*delta_p**-1*omega_max**1.5*b_r**-2*d_iron**-1*d_e**-2")
pi4 = PositiveParameter("pi4", [0.1, 1], "", "mu_0*j*d_e*b_r**-1")
pi5 = PositiveParameter("pi5", [0.1, 1], "", "d_i*d_e**-1")
pi6 = PositiveParameter("pi6", [0.1, 1], "", "e_tooth*d_e**-1*n")
pi7 = PositiveParameter("pi7", [0.1, 1], "", "e_yoke*d_e**-1*n")
pi8 = PositiveParameter("pi8", [0.1, 1], "", "w_pm*d_e**-1")
pi9 = PositiveParameter("pi9", [0.1, 1], "", "r_i*d_e**-1")
pi_set = PositiveParameterSet(pi1, pi2, pi3, pi4, pi5, pi6, pi7, pi8, pi9)
# Perform sensitivity analysis
pi_sensitivity(pi_set, doePI, useWidgets=False, test_mode=True)
# Perform dependency analysis
pi_dependency(pi_set, doePI, useWidgets=False, test_mode=True)