def get_samples(self, init_points_count, criterion='center'):
"""
Generates required amount of sample points
:param init_points_count: Number of samples to generate
:param criterion: For details of the effect of this parameter, please refer to pyDOE.lhs documentation
Default: 'center'
:returns: Generated samples
"""
samples = np.empty((init_points_count, self.space.dimensionality))
# Use random design to fill non-continuous variables
random_design = RandomDesign(self.space)
random_design.fill_noncontinous_variables(samples)
if self.space.has_continuous():
bounds = self.space.get_continuous_bounds()
lower_bound = np.asarray(bounds)[:,0].reshape(1, len(bounds))
upper_bound = np.asarray(bounds)[:,1].reshape(1, len(bounds))
diff = upper_bound - lower_bound
from pyDOE import lhs
X_design_aux = lhs(len(self.space.get_continuous_bounds()), init_points_count, criterion=criterion)
I = np.ones((X_design_aux.shape[0], 1))
X_design = np.dot(I, lower_bound) + X_design_aux * np.dot(I, diff)
samples[:, self.space.get_continuous_dims()] = X_design
return samples
def generateCentroids(self):
if self.dimensions<self.centre_num:
centres = lhs(self.dimensions, samples=self.centre_num, criterion=self.criterion)
else:
centres = lhs(self.dimensions, criterion=self.criterion)
centres = centres[:self.centre_num]
for i, centre in enumerate(centres):
centres[i] = map(lambda x: x*self.hyper_cube_length, centre)
std = sqrt(self.variance)
weight = 1
self.weights = [1 for i in xrange(self.centre_num)]
self.centroids = [Centroid(centre, i, std, weight) for i, centre in enumerate(centres)]
def get_lhd_corr_points(var_lower, var_upper):
"""Compute a latin hypercube design with min correlation.
Compute a list of (n+1) points in the given box, where n is the
dimension of the space. The selected points are picked according
to a random latin hypercube design with minimum correlation
criterion. This function relies on the library pyDOE.
Parameters
----------
var_lower : List[float]
List of lower bounds of the variables.
var_upper : List[float]
List of upper bounds of the variables.
Returns
-------
List[List[float]]
List of points in the latin hypercube design.
"""
assert(len(var_lower)==len(var_upper))
n = len(var_lower)
if (n == 1):
# For unidimensional problems, simply take the two endpoints
# of the interval as starting points
return [var_lower, var_upper]
# Otherwise, generate the LHD
lhd = pyDOE.lhs(n, n+1, 'correlation')
node_pos = [[var_lower[i] + (var_upper[i] - var_lower[i])*lhd_point[i]
for i in range(n)] for lhd_point in lhd]
return node_pos
def get_design_sites(dim, n_sample, x_lb, x_ub, sampling_method="lhs"):
x_lb = atleast_2d(x_lb)
x_ub = atleast_2d(x_ub)
x_lb = x_lb.T if size(x_lb, 0) != 1 else x_lb
x_ub = x_ub.T if size(x_ub, 0) != 1 else x_ub
if sampling_method == "lhs":
# Latin Hyper Cube Sampling: Get evenly distributed sampling in R^dim
samples = lhs(dim, samples=n_sample) * (x_ub - x_lb) + x_lb
elif sampling_method == "uniform":
samples = np.random.rand(n_sample, dim) * (x_ub - x_lb) + x_lb
elif sampling_method == "sobol":
seed = mod(int(time.time()) + os.getpid(), int(1e6))
samples = np.zeros((n_sample, dim))
for i in range(n_sample):
samples[i, :], seed = i4_sobol(dim, seed)
samples = samples * (x_ub - x_lb) + x_lb
elif sampling_method == "halton":
sequencer = Halton(dim)
samples = sequencer.get(n_sample) * (x_ub - x_lb) + x_lb
return samples
def sampleHypercube(n_dim, n_samp, rand_set_id=0, crit='m', iterations=5,
rdata_dir='~/cowen/data/random'):
"""Load (if file exists) or generate samples from within hypercube using
Latin hypercube sampling
Requires pyDOE to generate new samples.
"""
fname = samplesFilename(n_dim=n_dim,
n_samp=n_samp,
rand_set_id=rand_set_id,
crit=crit,
iterations=iterations)
rdata_dir = os.path.expandvars(os.path.expanduser(rdata_dir))
fpath = os.path.join(rdata_dir, fname)
if os.path.exists(fpath):
samps = fileio.from_file(fpath)
else:
logging.info('File not found. Generating new set of samples & saving'
' result to "%s"', fpath)
import pyDOE
mkdir(rdata_dir)
# Set a deterministic random state based upon the critical hypercube
# sampling parameters specified
n_bad_seeds(n_dim, n_samp, rand_set_id)
samps = pyDOE.lhs(n=n_dim, samples=n_samp, criterion=crit,
iterations=iterations)
fileio.to_file(samps, fpath)
return samps
def sample(self): # sample with max expected improvement
self.opt_ini_guess = lhs(self.p, 10) # samples for internal max expectation
self.opt_ini_guess = self.opt_ini_guess*(self.bounds[:, 1]-self.bounds[:, 0])+self.bounds[:, 0]
p = self.opt_ini_guess.shape[1] # problem size
n = self.opt_ini_guess.shape[0] # number of optimization runs
# test_lambdas = np.array([int(self.p)*[0.01],
# int(self.p)*[0.1],
# int(self.p)*[1.0],
# int(self.p)*[10.0]])
# self.concentrated_likelihood(test_lambdas) # only for CL-opt eq 4 ego (jones '98)
self.SI = np.diag(np.ones(self.bounds.shape[0])*
self.irl_list[self.X.shape[0]-self.num_ini_guess]) # only for IRL ego
self.fit()
func = lambda x: - self.f(x)
result_x = np.zeros((n, p))
result_f = np.zeros((n, 1))
for i, x0 in enumerate(self.opt_ini_guess):
res = opt.minimize(func, x0=x0, bounds=self.bounds, method='slsqp', tol=1e-5,
options={'eps': 1e-8, 'iprint': 2, 'disp': False, 'maxiter': 100})
result_f[i] = res.fun
result_x[i] = res.x
if np.any(np.isnan(res.x)==True):
wait = 1
if np.abs(np.min(result_f, axis=0)) < 1e-3:
return np.zeros((1,1)) # terminate if no improvement
return result_x[np.argmin(result_f, axis=0)]
def generate_points(self):
"""Generate a matrix with the initial sample points,
scaled to the unit cube
:return: Latin hypercube design in the unit cube
"""
return pydoe.lhs(self.dim, self.npts, self.criterion)
def generate_prameter_samples(n,p):
''' generates Latin-Hypercubesamples with pyDOE and
transforms bounds.
Parameters
-------
n: int
number of samples
p: 5,7
number of parameters
Returns
-------
lh: 2D array
of parameter samples
'''
if p==7:
b=np.array([0.75,200,0.95,1.5,50,0.05,1.5])
a=np.array([0.25,1.5,0.05,0.25,10,0.01,0.7])
elif p==5 :
b=np.array([0.05,200,1.5,50,1.5])
a=np.array([0.01,1.5,0.25,10,0.7])
else:
return 1
lh = pyDOE.lhs(p, samples=n)
#upper and lower bound of parameters un MIT-gcm-PO4-DOP
lh = lh*(b-a)+a
return lh
def create_macros_LHS(self,
number_of_macros=None,
criterion=None,
iterations=None,
batch_size = None,
append_default=False):
try:
import pyDOE
except ImportError:
raise ImportError(
'The pyDOE package must be install to use this class')
if batch_size is not None:
return _batch(self.create_macros_LHS(number_of_macros,
criterion,
iterations), n = batch_size)
if number_of_macros is None:
number_of_macros = self.number_of_macros
if self.seed is not None:
np.random.seed(self.seed)
factors = sum([e.n_factors for e in self
if isinstance(e, SetValue_random)])
lhs_matrix = pyDOE.lhs(factors, number_of_macros,
criterion=criterion,
iterations=iterations)
macro_list = []
for macro_idx in range(number_of_macros):
macro = []
lhs_idx = 0
for elem in self:
if isinstance(elem, SetValue_random):
lhs_val = lhs_matrix[macro_idx, lhs_idx:lhs_idx +
elem.n_factors]
mcr = elem.get_macro(macro_idx,
lower_tail_probability=lhs_val)
lhs_idx += elem.n_factors
else:
mcr = elem.get_macro(macro_idx)
if self.counter_token:
mcr = mcr.replace(self.counter_token, str(macro_idx))
if len(mcr) > 0:
macro.extend(mcr.split('\n'))
macro_list.append(macro)
if append_default is not None:
macro = []
for elem in self:
mcr = elem.get_macro(number_of_macros)
if self.counter_token:
mcr = mcr.replace(self.counter_token, str(number_of_macros))
if len(mcr) > 0:
macro.extend(mcr.split('\n'))
macro_list.append(macro)
return macro_list
def LHS_TITAN(num_sample,min1,range1,min2,range2):
#number of random dimension
randoms=2
lhd = pylhs.lhs(randoms, num_sample)
lhs=np.zeros((num_sample,randoms))
lhs[:,0]=lhd[:,0]*range1+min1
lhs[:,1]=lhd[:,1]*range2+min2
fp = open(os.path.join(os.getcwd(),'titan/input_Coulomb.py'),'r')
simdata = fp.read()
fp.close
fpp = open(os.path.join(os.getcwd(),'titan/exec_script'),'r')
simdatap = fpp.read()
fpp.close
internal=1111
bed=2222
jubnumber=55555
dircs_name='LHS'
#delete the folders if they are already exist
for i in range(0,num_sample):
dirname=os.path.join(os.getcwd(),dircs_name+str(i))
if (os.path.isdir(dirname)):
st.rmtree(os.path.join(os.getcwd(),dircs_name+str(i)))
#creates the folder for simulation
for i in range(0,num_sample):
st.copytree('titan',os.path.join(os.getcwd(),dircs_name+str(i)))
#replace the sample value with initial value in the list of input
for i in range(0,num_sample):
print lhs[i,:]
rep_internal="{:.2f}".format(lhs[i,0])
rp_simdata = simdata.replace(str(internal),rep_internal)
rep_bed="{:.2f}".format(lhs[i,1])
rp_simdata = rp_simdata.replace(str(bed),rep_bed)
fp = open(os.path.join(os.getcwd(),dircs_name+str(i)+'/input_Coulomb.py'),'w')
fp.write(rp_simdata)
fp.flush()
fp.close
# print i
#modifying the job name in the slurm scripts for each sample
for i in range(0,num_sample):
rep_jubnumber="{:.0f}".format(i)
rp_simdatap = simdatap.replace(str(jubnumber),rep_jubnumber)
fpp = open(os.path.join(os.getcwd(),dircs_name+str(i)+'/exec_script'),'w')
fpp.write(rp_simdatap)
fpp.flush()
fpp.close
#writing the LHS design points to a .csv
np.savetxt('Design_Points.csv', lhs, delimiter=',')
def generate_macros(self, batch_size = None):
try:
import pyDOE
except ImportError:
raise ImportError('The pyDOE package must be install to use this class')
self.lhd = pyDOE.lhs(self.LHS_factors, samples=self.number_of_macros)
return super(LatinHyperCubeMacroGenerator,self).generate_macros(batch_size)
def run_test_1():
x = lhs(2,2)
print x
plt.figure(1)
plt.plot(x[:,0],x[:,1],'ro')
#plt.axis([-.5,1.5,-.5,1.5])
plt.grid(True)
plt.show()
def _centered_latin_hypercube(center, schlinge, lb, ub, samples):
samples = max(samples, len(center))
design = lhs(len(lb), samples)
diameter = (ub - lb) / 2
_lb = center - diameter * schlinge
_ub = center + diameter * schlinge
lb = np.maximum(lb, _lb)
ub = np.minimum(ub, _ub)
return design * (ub - lb) + lb
def save_samples():
n = 100
dim = 2
path = 'LHC_test_samples_2d.txt'
xDoe = lhs(dim,n)
fid = open(path,'wt')
for xline in xDoe:
for x in xline:
fid.write('%.6f\t'%x)
fid.write('\n')
fid.close()
def latin_hypercube(pkeys, kind='dpm', nrvs=25, tb=.65, force_normal=False):
""" sample random parameter sets to explore global minima (called by
Optimizer method __hop_around__())
"""
nparams = len(pkeys)
design = lhs(nparams, samples=nrvs, criterion='center')
bounds = get_bounds(kind=kind)
# reverse V_brake boundaries to get max negative val
bounds['ssv'] = (bounds['ssv'][1], bounds['ssv'][0])
pmax = np.array([bounds[pk][-1] for pk in pkeys])
design = pmax * design
samplesLH = {p: design[:, i] for i, p in enumerate(pkeys)}
return samplesLH
def get_samples(self, point_count):
bounds = self.parameter_space.get_bounds()
X_design_aux = pyDOE.lhs(len(bounds), point_count, criterion='center')
ones = np.ones((X_design_aux.shape[0], 1))
lower_bound = np.asarray(bounds)[:, 0].reshape(1, len(bounds))
upper_bound = np.asarray(bounds)[:, 1].reshape(1, len(bounds))
diff = upper_bound - lower_bound
X_design = np.dot(ones, lower_bound) + X_design_aux * np.dot(ones, diff)
samples = self.parameter_space.round(X_design)
return samples
def sampleNonpara(num,cz):
#read the variable table, "variable"
data_set_temp = np.genfromtxt('./variable.csv',
skip_header=1,
dtype=str,
delimiter=',')
#generate the data set under cz
climate = ['1A','2A','2B','3A','3B','3C','4A','4B','4C','5A','5B','6A','6B','7A','8A']
ind = climate.index(cz)
data_set = []
k = 1
for row in data_set_temp:
temp = [str(k)]
temp.append(row[0])#the measure's name
temp.append(row[1])#the argument's name
temp.append(float(row[ind+2]))#the minimum value
temp.append(float(row[ind+19]))#the maximum value
data_set.append(temp)
k += 1
names = []
bounds = []
for row in data_set:
names.append(row[0])
temp = []
temp.append(row[3])
temp.append(row[4])
bounds.append(temp)
#set the variables and ranges of variables
problem = {
'num_vars': len(data_set),
'names': names,
'bounds': bounds
}
#select the samples
sample_temp = doe.lhs(len(data_set), samples=num)
param_values = []
for row1 in sample_temp:
temp = []
for ind,row in enumerate(bounds):
temp.append((row[1]-row[0])*row1[ind]+row[0])
param_values.append(temp)
return data_set,problem,param_values
def generate_macros(self, batch_size = None):
try:
import pyDOE
except ImportError:
raise ImportError('The pyDOE package must be install to use this class')
# Only generate LHS values if user requested more than macros, since the
# first macro is allways the mean value
if self.number_of_macros > 1:
# Create the Latin hyper cube sample matrix. This is used by the
# individual macro generator functions when macros are created.
self.lhd = pyDOE.lhs(self.LHS_factors, samples=self.number_of_macros-1,
criterion = self.criterion,
iterations = self.iterations)
return super(LatinHyperCubeMacroGenerator,self).generate_macros(batch_size)
def verify_random_samples(model, sampler, sample_type, param_min, param_max,
num_samples, savefile, parallel):
# recreate the samples
if num_samples == None:
num_samples = sampler.num_samples
param_left = np.repeat([param_min], num_samples, 0)
param_right = np.repeat([param_max], num_samples, 0)
samples = (param_right-param_left)
if sample_type == "lhs":
samples = samples * pyDOE.lhs(param_min.shape[-1], num_samples)
elif sample_type == "random" or "r":
np.random.seed(1)
samples = samples * np.random.random(param_left.shape)
samples = samples + param_left
# evalulate the model at the samples directly
data = model(samples)
# evaluate the model at the samples
# reset the random seed
if sample_type == "random" or "r":
np.random.seed(1)
(my_samples, my_data) = sampler.user_samples(samples, savefile,
parallel)
# make sure that the samples are within the boundaries
assert np.all(my_samples <= param_right)
assert np.all(my_samples >= param_left)
if len(data.shape) == 1:
data = np.expand_dims(data, axis=1)
if len(samples.shape) == 1:
samples = np.expan_dims(samples, axis=1)
# compare the samples
nptest.assert_array_equal(samples, my_samples)
# compare the data
nptest.assert_array_equal(data, my_data)
# did num_samples get updated?
assert samples.shape[0] == sampler.num_samples
assert num_samples == sampler.num_samples
# did the file get correctly saved?
if comm.rank == 0:
mdat = sio.loadmat(savefile)
nptest.assert_array_equal(samples, mdat['samples'])
nptest.assert_array_equal(data, mdat['data'])
comm.Barrier()
def define_points(self, runs=None):
"""
Method to define the points to be evaluated based on the results from
distribution given by the array method and the bound defined by the
add_variable method.
For dummy, levels means nothing"""
self.n_var = 0
self.n_var_2 = 0
for variable in self.variables:
if variable['levels'] == self.levels:
self.n_var += 1
elif variable['levels'] == 2:
self.n_var_2 += 1
else:
raise Exception('A variable has a number of levels that is ' +
'not the default or 2')
if self.driver == 'Taguchi':
self.Taguchi()
elif self.driver == 'Full Factorial':
self.FullFactorial()
elif self.driver == 'Random':
self.runs = runs
self.Random(runs)
elif self.driver == 'Latin Hypercube':
self.runs = runs
self.array = lhs(len(self.variables), samples=runs,
criterion='center')
self.domain = {}
for j in range(self.n_var+self.n_var_2):
upper = self.variables[j]['upper']
lower = self.variables[j]['lower']
levels = self.variables[j]['levels']
type = self.variables[j]['type']
dummy = []
for i in range(self.runs):
scale = self.array[i][j]
if type == int and (scale*(upper-lower) % (levels-1.) != 0):
raise Exception('The bounds of the defined integer are ' +
'not compatible with number of levels.')
else:
dummy.append(lower + scale*(upper-lower) / (levels-1.))
self.domain[self.variables[j]['name']] = dummy
def random_samples(self, sample_type, param_min, param_max,
savefile, num_samples=None, criterion='center', parallel=False):
"""
Sampling algorithm with three basic options
* ``random`` (or ``r``) generates ``num_samples`` samples in
``lam_domain`` assuming a Lebesgue measure.
* ``lhs`` generates a latin hyper cube of samples.
Note: This function is designed only for generalized rectangles and
assumes a Lebesgue measure on the parameter space.
:param string sample_type: type sampling random (or r),
latin hypercube(lhs), regular grid (rg), or space-filling
curve(TBD)
:param param_min: minimum value for each parameter dimension
:type param_min: :class:`numpy.ndarray` (ndim,)
:param param_max: maximum value for each parameter dimension
:type param_max: :class:`numpy.ndarray` (ndim,)
:param string savefile: filename to save samples and data
:param int num_samples: N, number of samples (optional)
:param string criterion: latin hypercube criterion see
`PyDOE <http://pythonhosted.org/pyDOE/randomized.html>`_
:param bool parallel: Flag for parallel implementation. Uses
lowercase ``mpi4py`` methods if ``samples.shape[0]`` is not
divisible by ``size``. Default value is ``False``.
:rtype: tuple
:returns: (``parameter_samples``, ``data_samples``) where
``parameter_samples`` is np.ndarray of shape (num_samples, ndim)
and ``data_samples`` is np.ndarray of shape (num_samples, mdim)
"""
# Create N samples
if num_samples == None:
num_samples = self.num_samples
param_left = np.repeat([param_min], num_samples, 0)
param_right = np.repeat([param_max], num_samples, 0)
samples = (param_right-param_left)
if sample_type == "lhs":
samples = samples * lhs(param_min.shape[-1],
num_samples, criterion)
elif sample_type == "random" or "r":
samples = samples * np.random.random(param_left.shape)
samples = samples + param_left
return self.user_samples(samples, savefile, parallel)
def verify_random_sample_set(sampler, sample_type, input_sample_set,
num_samples):
test_sample_set = input_sample_set
np.random.seed(1)
# recreate the samples
if num_samples is None:
num_samples = sampler.num_samples
input_domain = input_sample_set.get_domain()
if input_domain is None:
input_domain = np.repeat([[0, 1]], input_sample_set.get_dim(), axis=0)
input_left = np.repeat([input_domain[:, 0]], num_samples, 0)
input_right = np.repeat([input_domain[:, 1]], num_samples, 0)
input_values = (input_right - input_left)
if sample_type == "lhs":
input_values = input_values * pyDOE.lhs(input_sample_set.get_dim(),
num_samples, 'center')
elif sample_type == "random" or "r":
input_values = input_values * np.random.random(input_left.shape)
input_values = input_values + input_left
test_sample_set.set_values(input_values)
# reset the random seed
np.random.seed(1)
# create the sample set from the domain
print sample_type
my_sample_set = sampler.random_sample_set(sample_type, input_sample_set,
num_samples=num_samples)
# make sure that the samples are within the boundaries
assert np.all(my_sample_set._values <= input_right)
assert np.all(my_sample_set._values >= input_left)
# compare the samples
if comm.size == 0:
nptest.assert_array_equal(test_sample_set._values,
my_sample_set._values)
def initial_design(design,bounds,data_init):
"""
:param design: the choice of designs
:param bounds: the boundary of initial points
:param data_init: the number of initial points
"""
if design == 'random':
X_design = samples_multidimensional_uniform(bounds, data_init)
elif design == 'latin':
try:
from pyDOE import lhs
import numpy as np
# Genretate point in unit hypercube
X_design_aux = lhs(len(bounds),data_init, criterion='center')
# Normalize to the give box constrains
lB = np.asarray(bounds)[:,0].reshape(1,len(bounds))
uB = np.asarray(bounds)[:,1].reshape(1,len(bounds))
diff = uB-lB
I = np.ones((X_design_aux.shape[0],1))
X_design = np.dot(I,lB) + X_design_aux*np.dot(I,diff)
except:
print("Cannot find pyDOE library, please install it to use a Latin hypercube to initialize the model.")
return X_design
def sampleMeta(num,cz):
#read the variable table, "variable"
data_set_temp = np.genfromtxt('./variable.csv',
skip_header=1,
dtype=str,
delimiter=',')
#generate the data set under cz
climate = ['1A','2A','2B','3A','3B','3C','4A','4B','4C','5A','5B','6A','6B','7A','8A']
ind = climate.index(cz)
data_set = []
k = 1
num_sens = 0
for row in data_set_temp:
temp = [str(k)]
temp.append(row[0])#the measure's name
temp.append(row[1])#the argument's name
temp.append(float(row[ind+2]))#the minimum value
temp.append(float(row[ind+19]))#the maximum value
data_set.append(temp)
num_sens += 1
k += 1
#select the samples
sample_temp = doe.lhs(num_sens, samples=num*num_sens)
param_values = []
for row1 in sample_temp:
temp = []
num_doe = 0
for row in data_set:
temp.append((row[4]-row[3])*row1[num_doe]+row[3])
num_doe += 1
param_values.append(temp)
return data_set,param_values
def generate_latin_hypercube(gf, num_samples, basename):
# The number of parameters
ndim = (len(gf.builder.global_params) +
(len(gf.data) * len(gf.builder.local_params)))
# Generate a latin hypercube of the parameters
lh = lhs(ndim, samples=num_samples, criterion='center')
# For each sample...
for samp_ix in range(num_samples):
# ...initialize the vector of initial values
p0 = np.zeros(ndim)
# For each parameter...
for p_ix in range(ndim):
# ...get the prior...
pr = gf.priors[p_ix]
# ...and use the inverse CDF of the prior distribution to convert
# the percentile value on [0, 1] to an initial value
percentile = lh[samp_ix, p_ix]
p0[p_ix] = pr.inverse_cdf(percentile)
print("Saving position:")
print(p0)
filename = '%s.%dof%d.lhs' % (basename, samp_ix+1, num_samples)
with open(filename, 'w') as f:
cPickle.dump(p0, f)
return
def design_lhs_exp(variables, maps, offsets=None, samples=int(1e4), project_linear=True):
""" Design an LHS experiment """
design = lhs(len(variables), samples=samples, criterion="m", iterations=100)
z_design = np.zeros_like(design)
print "Computing LHS design..."
if project_linear:
print " using linear re-projection for log variables"
else:
print " using original variable coordinate"
for i, v in enumerate(variables):
dist, a, b = v[3]
if project_linear: # Re-sample in linear space
if v[0].startswith("ln"):
## 9/4/2014
## This is an experimental correction to re-project the
## logarithmic variables into their normal coordinate
## system. It should only effect the sampling, and hopefully
## improve it by forcing it to even things out over the
## actually range we care about
a = np.exp(a)
b = np.exp(b)
offsets[i] = np.exp(offsets[i])
elif v[0].startswith("log"):
## 10/26/2014
## In accordance with above, but for log10 vars
a = 10.0 ** a
b = 10.0 ** b
offsets[i] = 10.0 ** offsets[i]
if offsets:
## These corrections with "offsets" re-center the interval
## so that the left endpoint is 0. I found that if arbitrary
## lower/upper limits were used, sometimes the PPF routines
## would really mess up in inverting the CDF.
a, b = a - offsets[i], b - offsets[i]
if dist == "uniform":
design[:, i] = uniform(a, b).ppf(design[:, i])
elif dist == "normal":
design[:, i] = norm(a, b).ppf(design[:, i])
elif dist == "loguniform":
design[:, i] = loguni_ppf(design[:, i], a, b)
else:
raise ValueError("no dist defined for %s" % dist)
if offsets:
## Project back in to the correct limits
design[:, i] += offsets[i]
a, b = a + offsets[i], b + offsets[i]
if project_linear:
if v[0].startswith("ln"):
## 9/4/2014
## Second half of correction
a = np.log(a)
b = np.log(b)
design[:, i] = np.log(design[:, i])
elif v[0].startswith("log"):
## 10/26/2014
a = np.log10(a)
b = np.log10(b)
design[:, i] = np.log10(design[:, i])
z_design[:, i] = maps[i](design[:, i], a, b)
design = design.T # in x-coords
z_design = z_design.T
return design, z_design
lb = 0.0 #left boundary
rb = 1.0 #right boundary
N_f = 1000 #number of interior points
layers = [1, 400, 1]
#constant in the exact solution and RHS
k = 4
###########################
#Dirichlet data
u_left = 0
u_right = 0
# generate the collocation points
X_f = lb + (rb - lb) * lhs(1, N_f)
model = PhysicsInformedNN(lb, u_left, rb, u_right, X_f, layers, k)
start_time = time.time()
model.train(1000)
elapsed = time.time() - start_time
print('Training time: %.4f' % (elapsed))
# test data
nPred = 1001
X_star = np.linspace(lb, rb, nPred)[np.newaxis]
X_star = X_star.T
u_pred, f_u_pred = model.predict(X_star)
noise = 0.00
u_train = u_train + noise*np.std(u_train)*np.random.randn(u_train.shape[0], u_train.shape[1])
# For solution
N0 = Exact_sol.shape[0]
N_b = Exact_sol.shape[1]
N_f = 2000
idx_x = np.random.choice(x_sol.shape[0], N0, replace=False)
x0_train = x_sol[idx_x,:]
u0_train = Exact_sol[idx_x,0:1]
idx_t = np.random.choice(t_sol.shape[0], N_b, replace=False)
tb_train = t_sol[idx_t,:]
X_f_train = lb_sol + (ub_sol-lb_sol)*lhs(2, N_f)
# Layers
u_layers = [2, 50, 50, 50, 50, 1]
pde_layers = [3, 100, 100, 1]
layers = [2, 50, 50, 50, 50, 1]
# Model
model = DeepHPM(t_train, x_train, u_train,
x0_train, u0_train, tb_train, X_f_train,
u_layers, pde_layers,
layers,
lb_idn, ub_idn,
lb_sol, ub_sol)
f = 10.0 * (1.0 - x) * np.sin(3.0 * np.pi * (x - 0.01))
return f
# Exact solution
def u(x):
u = (0.65479E-3+(-0.115342E-1)*x+0.659469E-2*x**2+0.176577E-2*x**3+ \
(-0.65479E-3)*np.cos(0.942478E1*x)+0.119273E-3*x*np.cos(0.942478E1*x)+ \
0.121116E-2*np.sin(0.942478E1*x)+(-0.126178E-2)*x*np.sin(0.942478E1*x))
return u
# Boundary condtions data
X_u = np.array([0.0, 0.0, 1.0, 1.0])[:, None]
y_u = np.array([0.0, 0.0, 0.0, 0.0])[:, None]
# Forcing training data
X_f = lb + (ub - lb) * lhs(D, N_f)
y_f = f(X_f) + noise_f * np.random.randn(N_f, D)
# Test data
nn = 500
X_star = np.linspace(lb, ub, nn)[:, None]
u_star = u(X_star)
f_star = f(X_star)
# Compute required kernels
k_uu, k_uu1, k_uu2, k_uu3, k_uf, \
k_u1u1, k_u1u2, k_u1u3, k_u1f, \
k_u2u2, k_u2u3, k_u2f, \
k_u3u3, k_u3f, \
k_ff = Beam_kernels()
def create_new_individuals(design, problem, pop_size=None):
"""Create new individuals to the population.
The individuals can be created randomly, by LHS design, or can be passed by the
user.
Design does not apply in case of EvoNN and EvoDN2 problem, where neural networks
are created as individuals.
Parameters
----------
design : str, optional
Describe the method of creation of new individuals.
"RandomDesign" creates individuals randomly.
"LHSDesign" creates individuals using Latin hypercube sampling.
"EvoNN" creates Artificial Neural Networks as individuals.
"EvoDN2" creates Deep Neural Networks.
problem : baseProblem
An object of the class Problem
pop_size : int, optional
Number of individuals in the population. If none, some default population
size based on number of objectives is chosen.
Returns
-------
individuals : list
A list of individuals.
"""
if pop_size is None:
#pop_size_options = [50, 105, 120, 126, 132, 112, 156, 90, 275]
pop_size_options = np.ones(problem.num_of_objectives) * 50
pop_size = pop_size_options[problem.num_of_objectives - 2]
if design == "RandomDesign":
lower_limits = np.asarray(problem.get_variable_lower_bounds())
upper_limits = np.asarray(problem.get_variable_upper_bounds)
individuals = np.random.random((pop_size, problem.n_of_variables))
# Scaling
individuals = individuals * (upper_limits -
lower_limits) + lower_limits
return individuals
elif design == "LHSDesign":
lower_limits = np.asarray(problem.get_variable_lower_bounds())
upper_limits = np.asarray(problem.get_variable_upper_bounds())
individuals = lhs(problem.n_of_variables, samples=pop_size)
# Scaling
individuals = individuals * (upper_limits -
lower_limits) + lower_limits
return individuals
elif design == "EvoNN":
"""Create a population of neural networks for the EvoNN algorithm.
Individuals are 2d arrays representing the weight matrices of the NNs.
One extra row is added for bias.
"""
w_low = problem.params["w_low"]
w_high = problem.params["w_high"]
in_nodes = problem.num_of_variables
num_nodes = problem.params["num_nodes"]
prob_omit = problem.params["prob_omit"]
individuals = np.random.uniform(w_low,
w_high,
size=(pop_size, in_nodes, num_nodes))
# Randomly set some weights to zero
zeros = np.random.choice(np.arange(individuals.size),
ceil(individuals.size * prob_omit))
individuals.ravel()[zeros] = 0
# Set bias
individuals = np.insert(individuals, 0, 1, axis=1)
return individuals
elif design == "EvoDN2":
"""Create a population of deep neural networks (DNNs) for the EvoDN2 algorithm.
Each individual is a list of subnets, and each subnet contains a random amount
of layers and
nodes per layer. The subnets are evolved via evolutionary algorithms, and they
converge
on the final linear layer of the DNN.
"""
individuals = []
for i in range(problem.params["pop_size"]):
nets = []
for j in range(problem.params["num_subnets"]):
layers = []
num_layers = np.random.randint(1, problem.params["max_layers"])
in_nodes = len(problem.subsets[j])
for k in range(num_layers):
out_nodes = random.randint(2, problem.params["max_nodes"])
net = np.random.uniform(
problem.params["w_low"],
problem.params["w_high"],
size=(in_nodes, out_nodes),
)
# Randomly set some weights to zero
zeros = np.random.choice(
np.arange(net.size),
ceil(net.size * problem.params["prob_omit"]),
)
net.ravel()[zeros] = 0
# Add bias
net = np.insert(net, 0, 1, axis=0)
in_nodes = out_nodes
layers.append(net)
nets.append(layers)
individuals.append(nets)
return individuals
elif design == "BioGP":
return problem.create_individuals()
def estimate(self, start_time, final_time, measurement_variable_list, global_start=0, seed=None, use_initial_values=True):
'''Estimate the parameters of the model.
The estimation of the parameters is based on the data in the
``'Measured'`` key in the measurements dictionary attribute,
the parameter_data dictionary attribute, and any exodata inputs.
An optional global start algorithm where multiple estimations are
preformed with different initial guesses within the ranges of each
free parameter provided. It is implemented as tested in
Blum et al. (2019). The algorithm uses latin hypercube sampling
to choose the initial parameter guess values for each iteration and
the iteration with the lowest estimation problem objective value is
chosen. A user-provided guess is included by default using initial
values given to parameter data of the model, though this option can be
turned off to use only sampled initial guesses.
Blum, D.H., Arendt, K., Rivalin, L., Piette, M.A., Wetter, M., and
Veje, C.T. (2019). "Practical factors of envelope model setup and
their effects on the performance of model predictive control for
building heating, ventilating, and air conditioning systems."
Applied Energy 236, 410-425.
https://doi.org/10.1016/j.apenergy.2018.11.093
Parameters
----------
start_time : string
Start time of estimation period.
Setting to 'continue' will result in error.
final_time : string
Final time of estimation period.
measurement_variable_list : list
List of strings defining for which variables defined in the
measurements dictionary attirubute the estimation will
try to minimize the error.
global_start : int, optional
Number of iterations of a global start algorithm.
If 0, the global start algorithm is disabled and the values in
the parameter_data dictionary are used as initial guesses.
Default is 0.
seed : numeric or None, optional
Specific seed of the global start algorithm for the random selection
of initial value guesses.
Default is None.
use_initial_values : boolean, optional
True to include initial parameter values in the estimation iterations.
Default is True.
Yields
------
Updates the ``'Value'`` key for each estimated parameter in the
parameter_data attribute.
'''
# Check for free parameters
free = False;
for key in self.parameter_data.keys():
if self.parameter_data[key]['Free'].get_base_data():
free = True;
break
else:
free = False;
if not free:
# If none free raise error
raise ValueError('No parameters set as "Free" in parameter_data dictionary. Cannot run parameter estimation.');
# Check for measurements
for meas in measurement_variable_list:
if meas not in self.measurements.keys():
raise ValueError('Measurement {0} defined in measurement_variable_list not defined in measurements dictionary.'.format(meas))
# Check for continue
if start_time == 'continue':
raise ValueError('"continue" is not a valid entry for start_time for parameter estimation problems.')
# Perform parameter estimation
self._set_time_interval(start_time, final_time);
self.measurement_variable_list = measurement_variable_list;
# Without global start
if not global_start:
self._estimate_method._estimate(self);
# With global start
else:
# Detect free parameters
free_pars = [];
for par in self.parameter_data.keys():
if self.parameter_data[par]['Free'].display_data():
free_pars.append(par)
# Create lhs sample for all parameters
np.random.seed(seed) # Random seed for LHS initialization
n_free_pars = len(free_pars);
lhs = doe.lhs(n_free_pars, samples=global_start, criterion='c');
# Scale and store lhs samples for parameters between min and max bounds
par_vals = dict();
for par, i in zip(free_pars, range(n_free_pars)):
par_min = self.parameter_data[par]['Minimum'].display_data();
par_max = self.parameter_data[par]['Maximum'].display_data();
par_vals[par] = (lhs[:,i]*(par_max-par_min)+par_min).tolist();
# Add initial value guesses if wanted
if use_initial_values:
par_vals[par].append(self.parameter_data[par]['Value'].display_data())
# Estimate for each sample
J = float('inf');
par_best = dict();
glo_est_data = dict()
if use_initial_values:
iterations = range(global_start+1)
else:
iterations = range(global_start)
for i in iterations:
# Create dictionary to save all estimation iteration data
glo_est_data[i] = dict()
# Set lhs sample values for each parameter
for par in par_vals.keys():
# Use latin hypercube selections
self.parameter_data[par]['Value'].set_data(par_vals[par][i]);
glo_est_data[i][par] = par_vals[par][i]
# Make estimate for iteration
self._estimate_method._estimate(self);
# Validate estimate for iteration
self.validate(start_time, final_time, 'validate', plot = 0);
# Save RMSE for initial_guess
for key in self.RMSE:
glo_est_data[i]['RMSE_{0}'.format(key)] = self.RMSE[key].display_data();
# If solve succeeded, compare objective and if less, save best par values
solver_message = self._estimate_method.opt_problem.get_optimization_statistics()[0]
J_curr = self._estimate_method.opt_problem.get_optimization_statistics()[2]
glo_est_data[i]['Message'] = solver_message
glo_est_data[i]['J'] = J_curr
if ((J_curr < J) and (J_curr > 0.0)) or ((J_curr < J) and (solver_message == 'Solve_Succeeded')):
J = J_curr;
for par in free_pars:
par_best[par] = self.parameter_data[par]['Value'].display_data();
# Save all estimates
glo_est_data['J_Best'] = J
self.glo_est_data = glo_est_data
# Set best parameters in model if found
if par_best:
for par in par_vals.keys():
self.parameter_data[par]['Value'].set_data(par_best[par]);
def _generate(self, n_dimensions: int, n_points: int) -> np.ndarray:
return pyDOE.lhs(n_dimensions, samples=n_points)
# -*- coding: utf-8 -*-
"""
Created on Sat Feb 16 19:56:37 2019
@author: akhil
"""
import numpy as np
from pyDOE import lhs
#import torch
N = 500
x = 50 + 4*lhs(1,N)
y = 50 + 4*lhs(1,N)
xstar = (x-np.mean(x))/np.std(x)
ystar = (y-np.mean(y))/np.std(y)
fxy = np.cos(np.pi*xstar)*np.cos(np.pi*ystar)
layers = 2
dim = 2
nsperlayer = 50
def generate_params_layer1():
inputs = 2
weights = np.random.normal(0,2/(inputs + nsperlayer),(dim,nsperlayer))
bias1 = np.random.random_sample((1,nsperlayer))
bias = np.repeat(bias1,N,axis = 0)
return weights, bias
TXY_kesi_H_train=np.hstack((TXY_kesi_train,H_train)) np.random.shuffle(TXY_kesi_H_train) TXY_kesi_train=TXY_kesi_H_train[:,0:23] H_train=TXY_kesi_H_train[:,23:24] ############################################################################ #提取配点数据 Nf=1000000 #随机取点 lb=np.array([0,x.min(),y.min()]) ub=np.array([t.max(),x.max(),y.max()]) TXY_f_train=lb + (ub-lb)*lhs(3, Nf) TXY_kesi_f=np.hstack((TXY_f_train,np.zeros((Nf,n_eigen)))) kesi_f=np.random.randn(Nf,n_eigen) #随机数数组 TXY_kesi_f[:,3:(n_eigen+3)]=kesi_f np.random.shuffle(TXY_kesi_f) n_colloc=TXY_kesi_f.shape[0] ############################################################################ #提取边界数据 N_boun1=100000 X_boun_col=x[0]*np.ones((N_boun1,1)) Y_boun_col=y[0]+(y[50]-y[0])*lhs(1, N_boun1)
def sample_pspace(model, param_list=None, bounds=None, samples=100, seed=None):
"""
A DataFrame where each row represents a location in the parameter
space, locations distributed to exercise the full range of values
that each parameter can take on.
This is useful for quick and dirty application of tests to a bunch
of locations in the sample space. Kind-of a fuzz-testing for
the model.
Uses latin hypercube sampling, with random values within
the sample bins. The LHS sampler shuffles the bins each time,
so a subsequent call will yield a different sample from the
parameter space.
When a variable has both upper and lower bounds, use a uniform
sample between those bounds.
When a variable has only one bound, use an exponential distribution
with the scale set to be the difference between the bound and the
current model value (1 if they are the same)
When the variable has neither bound, use a normal distribution centered
on the current model value, with scale equal to the absolute value
of the model value (1 if that magnitude is 0)
Parameters
----------
model: pysd.Model object
param_list: None or list of strings
The real names of parameters to include in the explored parameter
space.
If None, uses all of the constants in the model except TIME STEP,
INITIAL TIME, etc.
bounds: DataFrame, string filename, or None
A range test matrix as used for bounds checking.
If None, creates one from the model
These bounds can also place artificial limits on the
parameter space you want to explore, even if the theoretical
bounds on the variable are infinite.
samples: int
How many samples to include in the iterator?
Returns
-------
lhs : pandas DataFrame
distribution-weighted latin hypercube samples
Note
----
Executes the model by 1 time-step to get the current value of parameters.
"""
if param_list is None:
doc = model.doc()
param_list = sorted(
list(
set(doc[doc['Type'] == 'constant']['Real Name']) -
{'FINAL TIME', 'INITIAL TIME', 'TIME STEP', 'TIME STEP'}))
if isinstance(bounds, _pd.DataFrame):
bounds = bounds.set_index('Real Name')
elif bounds is None:
bounds = create_bounds_test_matrix(model).set_index('Real Name')
elif isinstance(bounds, str):
if bounds.split('.')[-1] in ['xls', 'xlsx']:
bounds = _pd.read_excel(bounds,
sheet_name='Bounds',
index_col='Real Name')
elif bounds.split('.')[-1] == 'csv':
bounds = _pd.read_csv(bounds,
index_col='Real Name',
encoding='UTF-8')
elif bounds.split('.')[-1] == 'tab':
bounds = _pd.read_csv(bounds,
sep='\t',
index_col='Real Name',
encoding='UTF-8')
else:
raise ValueError('Unknown file type: bounds')
else:
raise ValueError('Unknown type: bounds')
if seed is not None:
_np.random.seed(seed)
unit_lhs = _pd.DataFrame(_pyDOE.lhs(n=len(param_list), samples=samples),
columns=param_list) # raw latin hypercube sample
res = model.run(return_timestamps=[model.components.initial_time()])
lhs = _pd.DataFrame(index=unit_lhs.index)
for param in param_list:
lower, upper = bounds[['Min', 'Max']].loc[param]
value = res[param].iloc[0]
if lower == upper:
lhs[param] = lower
elif _np.isfinite(lower) and _np.isfinite(
upper): # np.isfinite(0)==True
scale = upper - lower
lhs[param] = _dist.uniform(lower, scale).ppf(unit_lhs[param])
elif _np.isfinite(lower) and _np.isinf(upper):
if lower == value:
scale = 1
else:
scale = value - lower
lhs[param] = _dist.expon(lower, scale).ppf(unit_lhs[param])
elif _np.isinf(lower) and _np.isfinite(
upper): # np.isinf(-np.inf)==True
if upper == value:
scale = 1
else:
scale = upper - value
lhs[param] = upper - _dist.expon(0, scale).ppf(unit_lhs[param])
elif _np.isinf(lower) and _np.isinf(upper): # np.isinf(-np.inf)==True
if value == 0:
scale = 1
else:
scale = abs(value)
lhs[param] = _dist.norm(value, scale).ppf(unit_lhs[param])
else:
raise ValueError('Problem with lower: %s or upper: %s bounds' %
(lower, upper))
return lhs
ub = 1.0 * np.ones(D)
noise_f = 0.01
# Forcing term
def f(x):
f = -(np.pi**2) * np.sin(np.pi * x) - 5 * np.sqrt(2) * np.sin(
np.pi * x)
return f
# Exact solution
def u(x):
u = np.sin(np.pi * x)
return u
# Boundary condtions data
X_u = lb + (ub - lb) * lhs(D, N_u)
y_u = u(X_u)
# Forcing training data
X_f = lb + (ub - lb) * lhs(D, N_f)
y_f = f(X_f) + noise_f * np.random.randn(N_f, D)
# Test data
nn = 500
X_star = np.linspace(lb, ub, nn)
u_star = u(X_star)
f_star = f(X_star)
# Compute required kernels
k_uu, k_uf, k_ff = Helmholtz_kernels()
# flux = 0 bc
X_l = np.hstack((xx[:, 0].flatten()[:,None],
tt[:, 0].flatten()[:,None]))
X_r = np.hstack((xx[:, -1].flatten()[:,None],
tt[:, -1].flatten()[:,None]))
# Doman bounds
lb = X_star.min(0)
ub = X_star.max(0)
# Measurement data
X_U_meas = X_star
U_meas = U_star
# Collocation points
N_f = 10000
X_f_train = lb + (ub-lb)*lhs(X_U_meas.shape[1], N_f)
X_f_train = np.vstack((X_f_train, X_U_meas))
# =============================================================================
# train model
# =============================================================================
model = PhysicsInformedNN(X_U_meas, U_meas, X_f_train, X_l, X_r, layers, lb, ub, scale_factor)
model.train()
# =============================================================================
# result
# =============================================================================
f = open("stdout_ADO.txt", "a+")
elapsed = time.time() - start_time
f.write('Training time: %.4f \n' % (elapsed))
def verify_create_random_discretization(model, sampler, sample_type, input_domain,
num_samples, savefile):
np.random.seed(1)
# recreate the samples
if num_samples is None:
num_samples = sampler.num_samples
input_sample_set = sample_set(input_domain.shape[0])
input_sample_set.set_domain(input_domain)
input_left = np.repeat([input_domain[:, 0]], num_samples, 0)
input_right = np.repeat([input_domain[:, 1]], num_samples, 0)
input_values = (input_right-input_left)
if sample_type == "lhs":
input_values = input_values * pyDOE.lhs(input_sample_set.get_dim(),
num_samples, 'center')
elif sample_type == "random" or "r":
input_values = input_values * np.random.random(input_left.shape)
input_values = input_values + input_left
input_sample_set.set_values(input_values)
# evalulate the model at the samples directly
output_values = (model(input_sample_set._values))
if len(output_values.shape) == 1:
output_sample_set = sample_set(1)
else:
output_sample_set = sample_set(output_values.shape[1])
output_sample_set.set_values(output_values)
# reset the random seed
np.random.seed(1)
comm.barrier()
# create the random discretization using a specified input domain
my_discretization = sampler.create_random_discretization(sample_type,
input_domain, savefile, num_samples=num_samples, globalize=True)
#comm.barrier()
my_num = my_discretization.check_nums()
# make sure that the samples are within the boundaries
assert np.all(my_discretization._input_sample_set._values <= input_right)
assert np.all(my_discretization._input_sample_set._values >= input_left)
if comm.size == 0:
# compare the samples
nptest.assert_array_equal(input_sample_set._values,
my_discretization._input_sample_set._values)
# compare the data
nptest.assert_array_equal(output_sample_set._values,
my_discretization._output_sample_set._values)
# did num_samples get updated?
assert my_num == sampler.num_samples
# did the file get correctly saved?
saved_disc = bet.sample.load_discretization(savefile)
# compare the samples
nptest.assert_array_equal(my_discretization._input_sample_set.get_values(),
saved_disc._input_sample_set.get_values())
# compare the data
nptest.assert_array_equal(my_discretization._output_sample_set.get_values(),
saved_disc._output_sample_set.get_values())
# reset the random seed
np.random.seed(1)
my_sample_set = sample_set(input_domain.shape[0])
my_sample_set.set_domain(input_domain)
#comm.barrier()
# create the random discretization using an initialized sample_set
my_discretization = sampler.create_random_discretization(sample_type,
my_sample_set, savefile, num_samples=num_samples,
globalize=True)
my_num = my_discretization.check_nums()
# make sure that the samples are within the boundaries
assert np.all(my_discretization._input_sample_set._values <= input_right)
assert np.all(my_discretization._input_sample_set._values >= input_left)
if comm.size == 0:
# compare the samples
nptest.assert_array_equal(input_sample_set._values,
my_discretization._input_sample_set._values)
# compare the data
nptest.assert_array_equal(output_sample_set._values,
my_discretization._output_sample_set._values)
# reset the random seed
np.random.seed(1)
# recreate the samples to test default choices with unit hypercube domain
if num_samples is None:
num_samples = sampler.num_samples
my_dim = input_domain.shape[0]
input_sample_set = sample_set(my_dim)
input_sample_set.set_domain(np.repeat([[0.0, 1.0]], my_dim, axis=0))
input_left = np.repeat([input_domain[:, 0]], num_samples, 0)
input_right = np.repeat([input_domain[:, 1]], num_samples, 0)
input_values = (input_right - input_left)
if sample_type == "lhs":
input_values = input_values * pyDOE.lhs(input_sample_set.get_dim(),
num_samples, 'center')
elif sample_type == "random" or "r":
input_values = input_values * np.random.random(input_left.shape)
input_values = input_values + input_left
input_sample_set.set_values(input_values)
# reset random seed
np.random.seed(1)
comm.barrier()
# create the random discretization using a specified input_dim
my_discretization = sampler.create_random_discretization(sample_type,
my_dim, savefile, num_samples=num_samples, globalize=True)
#comm.barrier()
my_num = my_discretization.check_nums()
# make sure that the samples are within the boundaries
assert np.all(my_discretization._input_sample_set._values <= input_right)
assert np.all(my_discretization._input_sample_set._values >= input_left)
if comm.size == 0:
# compare the samples
nptest.assert_array_equal(input_sample_set._values,
my_discretization._input_sample_set._values)
# compare the data
nptest.assert_array_equal(output_sample_set._values,
my_discretization._output_sample_set._values)
import numpy as np
from pyDOE import lhs
from kriging import kriging
from true_function import true_function
from ga import ga
from exp_imp import EGO
k = 2
n = 5*2
# sampling plan
X = lhs(k, samples=n)
y = np.zeros((n, 1))
# find true values
for i in range(k):
y[i] = true_function(X[i], 1)
# create kriging model
kr = kriging(k, X, y)
# train model
kr.train()
# plot prediction
kr.plot_2d()
E = EGO(kr)
MinExpImp = 1e14
infill = 0
parser.add_argument('--num_dim', type=int, required=True)
parser.add_argument('--num_parallels', type=int, required=True)
parser.add_argument('--num_montecarlo', type=int, required=True)
parser.add_argument('--num_speculative_iter', type=int, required=True)
parser.add_argument('--max_gp_samples', type=int, required=True)
args = parser.parse_args()
# set config
num_dim = args.num_dim
num_parallels = args.num_parallels
num_montecarlo = args.num_montecarlo
num_speculative_iter = args.num_speculative_iter
max_gp_samples = args.max_gp_samples
# generate initial simplex using Latin hypercube sampling
initial_simplex = 10 * lhs(num_dim, samples=num_dim + 1) - 5
# optimize
nm = NelderMead(
benchmark,
speculative_exec=True,
num_montecarlo=num_montecarlo,
num_speculative_iter=num_speculative_iter,
num_parallels=num_parallels,
max_gp_samples=max_gp_samples)
x, fx, k = nm.optimize(initial_simplex, min_diam=1e-4) # the results of NM (x, fx, # of iters)
steps = nm.f.count # # of eval steps
evals = len(nm.f.keys) # # of evaluations
# the result of NM method
print('x:\t%s' % (x))
np.random.seed(1234)
if __name__ == "__main__":
N = 12
D = 1
lb = -1.0 * np.ones(D)
ub = 2.0 * np.ones(D)
noise = 0.0
def f(x):
return x * np.sin(np.pi * x)
# Training data
X = lb + (ub - lb) * lhs(D, N)
y = f(X) + noise * np.random.randn(N, D)
# Test data
nn = 200
X_star = np.linspace(lb, ub, nn)[:, None]
y_star = f(X_star)
# Define model
model = GPRegression(X, y)
# Train
model.train()
# Predict
y_pred, y_var = model.predict(X_star)
def create_macros_LHS(
self,
number_of_macros=None,
criterion=None, # noqa
iterations=None,
batch_size=None,
append_default=False,
):
"""Generate AnyScript macros for Latin Hyper Cube Studies studies.
Generates AnyScript macros for parameter studies using Latin hyper cube
sampling. The macros added with the `SetValue_random` are created with
with Latin Hypercube Sampling (LHS) of the parameter space. The number
of generated macros determines the number of LHS samples.
The method uses the pyDOE package to generate the LHS data.
Parameters
----------
number_of_macros : int (Optional)
The number of macro to create.
batch_size : int (Optional)
If specified the function will return a generator which creates macros in
batches.
criterion : {None, 'c', 'm', 'cm', 'corr'}
A a string that specifies how points are sampled
(see: http://pythonhosted.org/pyDOE/randomized.html)
`None` (Default) points are randomizes within the intervals.
"center" or "c" center the points within the sampling intervals
"maximin" or "m": maximize the minimum distance between points, but place
the point in a randomized location within its interval
"centermaximin" or "cm": same as “maximin”, but centered within the intervals
"corr" minimize the maximum correlation coefficient
iterations : int
Specifies how many iterations are used to accomplished the selected criterion
append_default : bool
If True a macro with default (mean) values is appended to the returned list
of returned macros
Returns
-------
list or generator
A list macros or a generator which creates macros in batches
Examples
--------
>>> np.random.seed(1)
>>> from scipy.stats.distributions import logistic, norm
>>> log_dist = logistic( loc= [1,3,4],scale = [0.1,0.5,1] )
>>> norm_dist = norm( loc= [0,0,0],scale = [0.1,0.5,1] )
>>> cmd = [SetValue_random('Main.MyVar1', log_dist), SetValue_random('Main.MyVar2', norm_dist) ]
>>> mg = AnyMacro(cmd, number_of_macros = 3)
>>> mg.create_macros_LHS()
[['classoperation Main.MyVar1 "Set Value" --value="{0.0928967116493,-0.591418725401,-0.484696993931}"',
'classoperation Main.MyVar2 "Set Value" --value="{1.01049414425,2.46211329129,5.73806916203}"'],
['classoperation Main.MyVar1 "Set Value" --value="{-0.0166741228961,0.707722119582,-0.294180629253}"',
'classoperation Main.MyVar2 "Set Value" --value="{1.11326829265,2.66016732923,4.28054911097}"'],
['classoperation Main.MyVar1 "Set Value" --value="{-0.20265197275,0.114947152258,0.924796936287}"',
'classoperation Main.MyVar2 "Set Value" --value="{0.806864877696,4.4114188826,2.93941843565}"']]
""" # noqa
try:
import pyDOE
except ImportError:
raise ImportError("The pyDOE package must be install to use this class")
if batch_size is not None:
return _batch(
self.create_macros_LHS(number_of_macros, criterion, iterations),
n=batch_size,
)
if number_of_macros is None:
number_of_macros = self.number_of_macros
if self.seed is not None:
np.random.seed(self.seed)
factors = sum([e.n_factors for e in self if isinstance(e, SetValue_random)])
lhs_matrix = pyDOE.lhs(
factors, number_of_macros, criterion=criterion, iterations=iterations
)
macro_list = []
for macro_idx in range(number_of_macros):
macro = []
lhs_idx = 0
for elem in self:
if isinstance(elem, SetValue_random):
lhs_val = lhs_matrix[macro_idx, lhs_idx : lhs_idx + elem.n_factors]
mcr = elem.get_macro(macro_idx, lower_tail_probability=lhs_val)
lhs_idx += elem.n_factors
else:
mcr = elem.get_macro(macro_idx)
if self.counter_token:
mcr = mcr.replace(self.counter_token, str(macro_idx))
if len(mcr) > 0:
macro.extend(mcr.split("\n"))
macro_list.append(macro)
if append_default:
macro = []
for elem in self:
mcr = elem.get_macro(number_of_macros)
if self.counter_token:
mcr = mcr.replace(self.counter_token, str(number_of_macros))
if len(mcr) > 0:
macro.extend(mcr.split("\n"))
macro_list.append(macro)
return macro_list
@author: Paris
"""
import numpy as np
import matplotlib.pyplot as plt
from pyDOE import lhs
if __name__ == "__main__":
# N is the number of training points.
# D_in is input dimension
# D_out is output dimension.
N, D_in, D_out = 64, 1, 1
# Create random input and output data
X = lhs(D_in, N)
y = 5 * X + np.random.randn(N, D_out)
# Randomly initialize weights
w = np.random.randn(D_in, D_out)
learning_rate = 1e-3
for it in range(10000):
# Forward pass: compute predicted y
y_pred = np.matmul(X, w)
# Compute and print loss
loss = np.sum((y_pred - y)**2)
print("Iteration: %d, loss: %f" % (it, loss))
# Backprop to compute gradients of W with respect to loss
def LHS_UQ(num_sample,min1,range1,min2,range2):
#number of random dimension
randoms=2
lhd = pylhs.lhs(randoms, num_sample)
lhs=np.zeros((num_sample,randoms))
lhs[:,0]=lhd[:,0]*range1+min1
lhs[:,1]=lhd[:,1]*range2+min2
fp = open(os.path.join(os.getcwd(),'puffin/puffin.inp'),'r')
simdata = fp.read()
fp.close
water_w=0.33
temp=1111
dircs_name='LHS'
#delete the folders if they are already exist
for i in range(0,num_sample):
dirname=os.path.join(os.getcwd(),dircs_name+str(i))
if (os.path.isdir(dirname)):
st.rmtree(os.path.join(os.getcwd(),dircs_name+str(i)))
#creates the folder for simulation
for i in range(0,num_sample):
st.copytree('puffin',os.path.join(os.getcwd(),dircs_name+str(i)))
#replace the sample value with initial value in the list of input
for i in range(0,num_sample):
# print lhs[i,:]
rep_water_w="{:.4f}".format(lhs[i,0])
rp_simdata = simdata.replace(str(water_w),rep_water_w)
rep_temp="{:.0f}".format(lhs[i,1])
rp_simdata = rp_simdata.replace(str(temp), rep_temp)
fp = open(os.path.join(os.getcwd(),dircs_name+str(i)+'/puffin.inp'),'w')
fp.write(rp_simdata)
fp.flush()
fp.close
# print i
# runs the code for each sample and generates the figures
for i in range(0,num_sample):
path=dircs_name+str(i)
os.chdir(path)
os.system('./puffin>output')
os.system('gnuplot field.gnu')
image = sprcs.Popen(["display", "./conc.jpg"])
time.sleep(1)
image.kill()
os.chdir('..')
# print i
particle_flux=np.zeros(num_sample)
eruption_height=np.zeros(num_sample)
# reading the result of simulations from the output file
for i in range(0,num_sample):
dirname=os.path.join(os.getcwd(),dircs_name+str(i))
fp = open(os.path.join(dirname,'output'),'r')
for line in fp:
if line.find("PARTICLE FLUX AT HB")>-1:
info = line.split()
particle_flux[i] = float(info[4])
if line.find("ERUPTION PLUME HEIGHT")>-1:
info = line.split()
eruption_height[i]=float(info[3])
h_mean=sum(eruption_height)/num_sample
h_std=np.sqrt(sum(np.square(eruption_height))/num_sample-h_mean*h_mean)
particle_flux_mean=sum(particle_flux)/num_sample
particle_flux_std=np.sqrt(sum(np.square(particle_flux))/num_sample-particle_flux_mean*particle_flux_mean)
output=np.vstack((lhs[:,0],lhs[:,1],eruption_height,particle_flux)).T
np.savetxt("lhs_output.csv", output, delimiter=",")
print ("Results of the experiment:")
print ("eruption height for the samples: ",eruption_height)
print ("mean of height: ",h_mean)
print ("standard deviation of height: ",h_std)
print ("particle flux for the samples: ",particle_flux)
print ("mean of particle flux: %e"%particle_flux_mean)
print ("standard deviation of particle flux: %e" %particle_flux_std)
f_u_star = self.sess.run(self.f_u_pred, tf_dict)
return u_star, f_u_star
if __name__ == "__main__":
N_b = 800 # number of boundary points
N_f = 1000 # number of collocation points
layers = [2, 20, 20, 20, 1] #number of neurons in each layer
num_train_its = 1000 #number of training iterations
layers = [2, 200, 200, 200, 1]
LB_Plate = np.array([0.0, 0.0])
UB_Plate = np.array([2.0, 1.0])
X_f = LB_Plate + (UB_Plate - LB_Plate) * lhs(
2, N_f) #Generating collocation points
#define model parameters
m = 1
#mode number
k = 4
#wave number
#solve for the constants A1 and A2 in the exact solution
kx = np.sqrt(k**2 - (m * np.pi)**2)
alpha = -k**2
LHS = np.array([[1j * kx, -1j * kx],
[(k - kx) * np.exp(-2 * 1j * kx),
(k + kx) * np.exp(2 * 1j * kx)]])
RHS = np.array([[1], [0]])
def sample_pspace(model, param_list=None, bounds=None, samples=100, seed=None):
"""
A DataFrame where each row represents a location in the parameter
space, locations distributed to exercise the full range of values
that each parameter can take on.
This is useful for quick and dirty application of tests to a bunch
of locations in the sample space. Kind-of a fuzz-testing for
the model.
Uses latin hypercube sampling, with random values within
the sample bins. The LHS sampler shuffles the bins each time,
so a subsequent call will yield a different sample from the
parameter space.
When a variable has both upper and lower bounds, use a uniform
sample between those bounds.
When a variable has only one bound, use an exponential distribution
with the scale set to be the difference between the bound and the
current model value (1 if they are the same)
When the variable has neither bound, use a normal distribution centered
on the current model value, with scale equal to the absolute value
of the model value (1 if that magnitude is 0)
Parameters
----------
model: pysd.Model object
param_list: None or list of strings
The real names of parameters to include in the explored parameter
space.
If None, uses all of the constants in the model except TIME STEP,
INITIAL TIME, etc.
bounds: DataFrame, string filename, or None
A range test matrix as used for bounds checking.
If None, creates one from the model
These bounds can also place artificial limits on the
parameter space you want to explore, even if the theoretical
bounds on the variable are infinite.
samples: int
How many samples to include in the iterator?
Returns
-------
lhs : pandas DataFrame
distribution-weighted latin hypercube samples
Note
----
Executes the model by 1 time-step to get the current value of parameters.
"""
if param_list is None:
doc = model.doc()
param_list = sorted(list(set(doc[doc['Type'] == 'constant']['Real Name']) -
{'FINAL TIME', 'INITIAL TIME', 'TIME STEP', 'TIME STEP'}))
if isinstance(bounds, _pd.DataFrame):
bounds = bounds.set_index('Real Name')
elif bounds is None:
bounds = create_bounds_test_matrix(model).set_index('Real Name')
elif isinstance(bounds, str):
if bounds.split('.')[-1] in ['xls', 'xlsx']:
bounds = _pd.read_excel(bounds, sheetname='Bounds', index_col='Real Name')
elif bounds.split('.')[-1] == 'csv':
bounds = _pd.read_csv(bounds, index_col='Real Name', encoding='UTF-8')
elif bounds.split('.')[-1] == 'tab':
bounds = _pd.read_csv(bounds, sep='\t', index_col='Real Name', encoding='UTF-8')
else:
raise ValueError('Unknown file type: bounds')
else:
raise ValueError('Unknown type: bounds')
if seed is not None:
_np.random.seed(seed)
unit_lhs = _pd.DataFrame(_pyDOE.lhs(n=len(param_list), samples=samples),
columns=param_list) # raw latin hypercube sample
res = model.run(return_timestamps=[model.components.initial_time()])
lhs = _pd.DataFrame(index=unit_lhs.index)
for param in param_list:
lower, upper = bounds[['Min', 'Max']].loc[param]
value = res[param].iloc[0]
if lower == upper:
lhs[param] = lower
elif _np.isfinite(lower) and _np.isfinite(upper): # np.isfinite(0)==True
scale = upper - lower
lhs[param] = _dist.uniform(lower, scale).ppf(unit_lhs[param])
elif _np.isfinite(lower) and _np.isinf(upper):
if lower == value:
scale = 1
else:
scale = value - lower
lhs[param] = _dist.expon(lower, scale).ppf(unit_lhs[param])
elif _np.isinf(lower) and _np.isfinite(upper): # np.isinf(-np.inf)==True
if upper == value:
scale = 1
else:
scale = upper - value
lhs[param] = upper - _dist.expon(0, scale).ppf(unit_lhs[param])
elif _np.isinf(lower) and _np.isinf(upper): # np.isinf(-np.inf)==True
if value == 0:
scale = 1
else:
scale = abs(value)
lhs[param] = _dist.norm(value, scale).ppf(unit_lhs[param])
else:
raise ValueError('Problem with lower: %s or upper: %s bounds' % (lower, upper))
return lhs
X_lb = np.hstack(
(T[:, 0:1], X[:, 0:1]
)) #Lower Boundary condition value of X (x = -1) and T (t = 0...0.99)
u_lb = Exact[:, 0:
1] #Bound Condition value of the field u at (x = 11) and T (t = 0...0.99)
X_ub = np.hstack(
(T[:, -1:], X[:, -1:]
)) #Uppe r Boundary condition value of X (x = 1) and T (t = 0...0.99)
u_ub = Exact[:,
-1:] #Bound Condition value of the field u at (x = 11) and T (t = 0...0.99)
X_b = np.vstack((X_lb, X_ub))
u_b = np.vstack((u_lb, u_ub))
X_f = lb + (ub - lb) * lhs(2, N_f) #Factors generated using LHS
idx = np.random.choice(X_i.shape[0], N_i, replace=False)
X_i = X_i[idx, :] #Randomly Extract the N_u number of x and t values.
u_i = u_i[idx, :] #Extract the N_u number of field values
idx = np.random.choice(X_b.shape[0], N_b, replace=False)
X_b = X_b[idx, :] #Randomly Extract the N_u number of x and t values.
u_b = u_b[idx, :] #Extract the N_u number of field values
training_data = {'X_i': X_i, 'u_i': u_i, 'X_b': X_b, 'u_b': u_b, 'X_f': X_f}
# %%
loss = model, input_dict = npde.main.setup(NN_parameters, NPDE_parameters,
PDE_parameters, training_data,