def sample(self, mesh):
pos = np.zeros((self.n_point, 3), dtype=np.float32)
ori = np.zeros((self.n_point, 3), dtype=np.float32)
sa = mesh.area_total / float(self.n_point)
# 点を1個生成する面積
error = 0.0
count = 0
for i in range(mesh.n_face):
tmp = mesh.area_face[i]
# 面iの面積
# 面iにまく点の数nptを計算
npt = 0
tmp /= sa
tmp2 = tmp
while (tmp >= 1): # 対象の三角形に何点生成するか
npt += 1
tmp -= 1
error += tmp2 - npt
# 小数部分をまとめる
if (error >= 1): # 小数部分が1より大きければ生成する点数を増加
npt += 1
error -= 1
for j in range(npt): # 各点の座標値を計算
vec, self.seed = sobol.i4_sobol(2, self.seed)
r1 = np.sqrt(vec[0])
r2 = vec[1]
for k in range(3): # Osadaの方法
pos[ count ][ k ] = \
( 1.0-r1 ) * mesh.vert[ mesh.face[ i ][ 0 ] ][ k ] + \
r1 * ( 1.0 - r2 ) * mesh.vert[ mesh.face[ i ][ 1 ] ][ k ] + \
r1 * ( r2 * mesh.vert[ mesh.face[ i ][ 2 ] ][ k ] )
ori[count] = mesh.norm_face[i]
# 点の向きは面の法線
count += 1
if (count != self.n_point): # 生成する点の数が不足していたら追加
vec, self.seed = sobol.i4_sobol(2, self.seed)
r1 = np.sqrt(vec[0])
r2 = vec[1]
for k in range(3): # Osadaの方法
pos[ self.n_point - 1 ][ k ] = \
( 1.0-r1 ) * mesh.vert[ mesh.face[ mesh.n_face - 1 ][ 0 ] ][ k ] + \
r1 * ( 1.0 - r2 ) * mesh.vert[ mesh.face[ mesh.n_face - 1 ][ 1 ] ][ k ] + \
r1 * ( r2 * mesh.vert[ mesh.face[ mesh.n_face - 1 ][ 2 ] ][ k ] )
ori[self.n_point - 1] = mesh.norm_face[mesh.n_face - 1]
# 点の向きは面の法線
count += 1
return np.hstack([pos, ori])
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 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 generate_sobol_seq(dim, n, seed):
seed = seed
out = []
for i in range(n):
cur_out, seed = i4_sobol(dim, seed)
out.append(cur_out)
return np.array(out)
def __call__(self, number_of_samples,
dimension,
start=0):
samples = np.zeros((number_of_samples, dimension))
for sample in range(number_of_samples):
samples[sample,: ] = sobol.i4_sobol(dimension, start + sample)[0]
return samples
def choose_sampling_method(N, k, rl):
x = np.zeros((N, k))
if rl == "R":
x = np.random.random((N, k))
elif rl == "S":
x = cp.dist.sobol_lib.sobol(k, N).T
elif rl == "L":
x = cp.latin_hypercube(k, N).T
elif rl == "sobol":
seed = 123
for i in range(N):
r, seed = i4_sobol(k, seed)
x[i, :] = r
return x
def get_sobol(N):
import sobol
limit_rho_up = 10.
limit_tau_up = 1.
limit_gamma_up = 4.
limit_rho_dn = 2.
limit_tau_dn = 0.1
limit_gamma_dn = 1.
parameterLowerLimits = numpy.array([limit_rho_dn, limit_gamma_dn, limit_tau_dn])
parameterUpperLimits = numpy.array([limit_rho_up, limit_gamma_up, limit_tau_up])
Q = numpy.zeros( (N, 3) )
for i in range(N):
rho, gamma, tau = sobol.i4_sobol(3,i)[0] * (parameterUpperLimits - parameterLowerLimits) +parameterLowerLimits
Q[i,0] = rho
Q[i,1] = gamma
Q[i,2] = tau
return Q
def generate_particles(domain, particles_per_cell = 30, seed = 112):
total_particles = domain["nx"] * domain["ny"] * particles_per_cell
particles = []
# Particle format is: x, y, visc, xvel, yvel
for _ in xrange(total_particles):
xy, seed = sobol.i4_sobol(2, seed)
xy = xy * 2 # This needs to be xmax and xmin, because the sobol returns from 0 - 1.
# Custom rheology
visc = 0.1 if xy[0] > 1. else 0.5
particles.append([xy[0], xy[1], visc, 0., 0.])
particles = np.array(particles)
return particles
def generate_particles(domain, particles_per_cell=30, seed=112):
total_particles = domain["nx"] * domain["ny"] * particles_per_cell
particles = []
# Particle format is: x, y, visc, xvel, yvel
for _ in xrange(total_particles):
xy, seed = sobol.i4_sobol(2, seed)
xy = xy * 2 # This needs to be xmax and xmin, because the sobol returns from 0 - 1.
# Custom rheology
visc = 0.1 if xy[0] > 1. else 0.5
particles.append([xy[0], xy[1], visc, 0., 0.])
particles = np.array(particles)
return particles
def get_sobol(N):
import sobol
limit_rho_up = 10.
limit_tau_up = 1.
limit_gamma_up = 4.
limit_rho_dn = 2.
limit_tau_dn = 0.1
limit_gamma_dn = 1.
parameterLowerLimits = numpy.array(
[limit_rho_dn, limit_gamma_dn, limit_tau_dn])
parameterUpperLimits = numpy.array(
[limit_rho_up, limit_gamma_up, limit_tau_up])
Q = numpy.zeros((N, 3))
for i in range(N):
rho, gamma, tau = sobol.i4_sobol(3, i)[0] * (
parameterUpperLimits - parameterLowerLimits) + parameterLowerLimits
Q[i, 0] = rho
Q[i, 1] = gamma
Q[i, 2] = tau
return Q
def generate_sobol_points(M, dim):
points = []
for i in range(M):
points.append(sobol.i4_sobol(dim, i)[0])
return np.array(points)
def sobol_test05():
"""
sobol_test05 tests i4_sobol.
"""
print(''
'SOBOL_TEST05'
' I4_SOBOL computes the next element of a Sobol sequence.'
''
' In this test, we demonstrate how the SEED can be'
' manipulated to skip ahead in the sequence, or'
' to come back to any part of the sequence.'
'')
target = np.array([
[ 0, 1, 0.000000, 0.000000, 0.000000],
[ 1, 2, 0.500000, 0.500000, 0.500000],
[ 2, 3, 0.750000, 0.250000, 0.750000],
[ 3, 4, 0.250000, 0.750000, 0.250000],
[ 4, 5, 0.375000, 0.375000, 0.625000],
[100, 101, 0.4140625, 0.2578125, 0.3046875],
[101, 102, 0.9140625, 0.7578125, 0.8046875],
[102, 103, 0.6640625, 0.0078125, 0.5546875],
[103, 104, 0.1640625, 0.5078125, 0.0546875],
[104, 105, 0.2265625, 0.4453125, 0.7421875],
[ 3, 4, 0.250000, 0.750000, 0.250000],
[ 4, 5, 0.375000, 0.375000, 0.625000],
[ 5, 6, 0.875000, 0.875000, 0.125000],
[ 6, 7, 0.625000, 0.125000, 0.375000],
[ 7, 8, 0.125000, 0.625000, 0.875000],
[ 98, 99, 0.7890625, 0.3828125, 0.1796875],
[ 99, 100, 0.2890625, 0.8828125, 0.6796875],
[100, 101, 0.4140625, 0.2578125, 0.3046875],
[101, 102, 0.9140625, 0.7578125, 0.8046875],
[102, 103, 0.6640625, 0.0078125, 0.5546875]])
results = np.full_like(target, np.nan)
dim_num = 3
print(''
' Using dimension DIM_NUM = %d\n' % dim_num)
seed = 0
print(''
' Seed Seed I4_SOBOL'
' In Out'
'')
for i in range(5):
[r, seed_out] = i4_sobol(dim_num, seed)
out = '%6d %6d ' % (seed, seed_out)
for j in range(1, dim_num + 1):
out += '%10f ' % r[j - 1]
print(out)
results[i, :] = [seed, seed_out] + list(r)
seed = seed_out
print(''
' Jump ahead by increasing SEED:'
'')
seed = 100
print(''
' Seed Seed I4_SOBOL'
' In Out'
'')
for i in range(5):
[r, seed_out] = i4_sobol(dim_num, seed)
out = '%6d %6d ' % (seed, seed_out)
for j in range(1, dim_num + 1):
out += '%10f ' % r[j - 1]
print(out)
results[5 + i, :] = [seed, seed_out] + list(r)
seed = seed_out
print(''
' Jump back by decreasing SEED:'
'')
seed = 3
print(''
' Seed Seed I4_SOBOL'
' In Out'
'')
for i in range(5):
[r, seed_out] = i4_sobol(dim_num, seed)
out = '%6d %6d ' % (seed, seed_out)
for j in range(1, dim_num + 1):
out += '%10f ' % r[j - 1]
print(out)
results[10 + i, :] = [seed, seed_out] + list(r)
seed = seed_out
print(''
' Jump back by decreasing SEED:'
'')
seed = 98
print(''
' Seed Seed I4_SOBOL'
' In Out'
'')
for i in range(5):
[r, seed_out] = i4_sobol(dim_num, seed)
out = '%6d %6d ' % (seed, seed_out)
for j in range(1, dim_num + 1):
out += '%10f ' % r[j - 1]
print(out)
results[15 + i, :] = [seed, seed_out] + list(r)
seed = seed_out
assert np.all(target == results)
return
def sobol_test04():
"""
sobol_test04 tests i4_sobol.
"""
print('\nSOBOL_TEST04'
' I4_SOBOL returns the next element'
' of a Sobol sequence.'
'\n In this test, we call I4_SOBOL repeatedly.')
dim_max = 4
target = {
2: np.array([
[ 0, 1, 0.000000, 0.000000],
[ 1, 2, 0.500000, 0.500000],
[ 2, 3, 0.750000, 0.250000],
[ 3, 4, 0.250000, 0.750000],
[ 4, 5, 0.375000, 0.375000],
# ......................
[106, 107, 0.9765625, 0.1953125],
[107, 108, 0.4765625, 0.6953125],
[108, 109, 0.3515625, 0.0703125],
[109, 110, 0.8515625, 0.5703125],
[110, 111, 0.6015625, 0.3203125]]),
3: np.array([
[ 0, 1, 0.000000, 0.000000, 0.000000],
[ 1, 2, 0.500000, 0.500000, 0.500000],
[ 2, 3, 0.750000, 0.250000, 0.750000],
[ 3, 4, 0.250000, 0.750000, 0.250000],
[ 4, 5, 0.375000, 0.375000, 0.625000],
# ......................
[106, 107, 0.9765625, 0.1953125, 0.4921875],
[107, 108, 0.4765625, 0.6953125, 0.9921875],
[108, 109, 0.3515625, 0.0703125, 0.1171875],
[109, 110, 0.8515625, 0.5703125, 0.6171875],
[110, 111, 0.6015625, 0.3203125, 0.8671875]]),
4: np.array([
[ 0, 1, 0.000000, 0.000000, 0.000000, 0.000000],
[ 1, 2, 0.500000, 0.500000, 0.500000, 0.500000],
[ 2, 3, 0.750000, 0.250000, 0.750000, 0.250000],
[ 3, 4, 0.250000, 0.750000, 0.250000, 0.750000],
[ 4, 5, 0.375000, 0.375000, 0.625000, 0.125000],
# ......................
[106, 107, 0.9765625, 0.1953125, 0.4921875, 0.6640625],
[107, 108, 0.4765625, 0.6953125, 0.9921875, 0.1640625],
[108, 109, 0.3515625, 0.0703125, 0.1171875, 0.7890625],
[109, 110, 0.8515625, 0.5703125, 0.6171875, 0.2890625],
[110, 111, 0.6015625, 0.3203125, 0.8671875, 0.5390625]])}
for dim_num in range(2, dim_max + 1):
seed = 0
qs = prime_ge(dim_num)
print('\n Using dimension DIM_NUM = %d' % dim_num)
print('\n Seed Seed I4_SOBOL'
' In Out\n')
results = np.full((111, 2 + dim_num), np.nan)
for i in range(111):
[r, seed_out] = i4_sobol(dim_num, seed)
if (i < 5 or 105 < i):
out = '%6d %6d ' % (seed, seed_out)
for j in range(dim_num):
out += '%10f ' % r[j]
print(out)
elif (i == 6):
print(' ......................')
results[i, :] = [seed, seed_out] + list(r)
seed = seed_out
assert np.all(target[dim_num][0:5, :] == results[0:5, :]), "Start of array doesn't match"
assert np.all(target[dim_num][5:10, :] == results[106:111, :]), "End of array doesn't match"
return
def sample(self, N):
""" Returns an array of <N> sobol samples. """
return np.array([i4_sobol(self.dim, i)[0] for i in range(N)])
def main():
"""."""
im_gt = np.squeeze(imread('charlie-chaplin.jpg'))
rho_limits = [0.01, 10]
gamma_limits = [0.01, 2]
tau_limits = [0.01, 10]
param_lb = np.array([rho_limits[0], gamma_limits[0], tau_limits[0]])
param_ub = np.array([rho_limits[1], gamma_limits[1], tau_limits[1]])
sample_size = 2000
Q = np.zeros((sample_size, 3))
for i in range(sample_size):
rho, gamma, tau = sobol.i4_sobol(3, i)[0] * (param_ub - param_lb) + param_lb
Q[i, 0] = rho
Q[i, 1] = gamma
Q[i, 2] = tau
P = []
E = []
# Get initial set of parameters P and corresponding MSEs E
for i in range(20):
print i
P.append(np.array([Q[i, 0], Q[i, 1], Q[i, 2]]))
im_pred = kernel_ridge_regression(
kernel_fct='Exponential', rho=Q[i, 0], gamma=Q[i, 1], tau=Q[i, 2])
mse = compute_mse(im_pred, im_gt)
E.append(mse)
E_best = np.min(E)
# Iterate improving hyperparameters
for j in range(10):
print 'Iteration hyperparameter improvement: {}'.format(j)
u_best = -np.inf
theta_best = None
for i in range(sample_size):
M = matern_kernel(P)
theta = np.array([Q[i, 0], Q[i, 1], Q[i, 2]])
m = get_m(P, theta)
E_i, var_msea = compute_msea(E, M, m)
gamma = (E_best - E_i) / np.sqrt(var_msea)
u = np.sqrt(var_msea)*(gamma*stats.norm.cdf(gamma) +
stats.norm.pdf(gamma))
if u > u_best:
u_best = u
theta_best = theta.copy()
P.append(theta_best)
im_pred = kernel_ridge_regression(kernel_fct='Exponential',
rho=theta_best[0], gamma=theta_best[1], tau=theta_best[2])
mse = compute_mse(im_pred, im_gt)
E.append(mse)
if mse < E_best:
E_best = mse
print 'E_best improved: {}'.format(E_best)
return 0
def __init__(self,
n,
rho,
boundary,
holes=[],
maxIterations=100,
fracTol=1.0e-3,
tessellationFileName=None,
nNodePerh=2.01,
offset=(0.0, 0.0),
rejecter=None):
assert n > 0
# Did we get passed a function or a constant for the density?
if type(rho) == type(1.0):
def rhofunc(posi):
return rho
else:
rhofunc = rho
self.rhofunc = rhofunc
# Build a polytope PLC version of the boundary.
plc = poly.polytope.PLC2d()
plc_coords = poly.vector_of_double()
edges = boundary.edges
vertices = boundary.vertices()
plc.facets.resize(len(edges))
for i, edge in enumerate(edges):
plc.facets[i].append(edge.first)
plc.facets[i].append(edge.second)
assert len(plc.facets[i]) == 2
for p in vertices:
plc_coords.append(p[0])
plc_coords.append(p[1])
assert len(plc_coords) == 2 * len(vertices)
# Add any holes to the boundary PLC.
plc.holes.resize(len(holes))
for ihole, hole in enumerate(holes):
offlast = len(plc_coords) / 2
edges = hole.edges
vertices = hole.vertices()
plc.holes[ihole].resize(len(edges))
for i, edge in enumerate(edges):
plc.holes[ihole][i].append(offlast + edge.first)
plc.holes[ihole][i].append(offlast + edge.second)
assert len(plc.holes[ihole][i]) == 2
for p in vertices:
plc_coords.append(p[0])
plc_coords.append(p[1])
assert len(plc_coords) % 2 == 0
# Initialize the desired number of generators in the boundary using the Sobol sequence.
generators = poly.vector_of_double()
seed = 0
length = max(boundary.xmax.x - boundary.xmin.x,
boundary.xmax.y - boundary.xmin.y)
while len(generators) < 2 * n:
[coords, seed] = i4_sobol(2, seed)
p = boundary.xmin + length * Vector2d(coords[0], coords[1])
ihole = 0
use = boundary.contains(p, False)
if use:
while use and ihole < len(holes):
use = not holes[ihole].contains(p, False)
ihole += 1
if use:
generators.append(p.x)
generators.append(p.y)
assert len(generators) == 2 * n
# Iterate the points toward centroidal relaxation.
self.tessellation = poly.polytope.Tessellation2d()
tessellator = poly.polytope.BoostTessellator2d()
iteration = 0
maxDelta = 2.0 * fracTol
while iteration < maxIterations and maxDelta > fracTol:
tessellator.tessellate(points=generators,
PLCpoints=plc_coords,
geometry=plc,
mesh=self.tessellation)
new_generators = self.computeWeightedCentroids(self.tessellation)
assert len(new_generators) == len(generators)
maxDelta = 0.0
for i in xrange(len(generators) / 2):
deltai = sqrt((generators[2 * i] - new_generators[2 * i])**2 +
(generators[2 * i + 1] -
new_generators[2 * i + 1])**2)
maxDelta = max(maxDelta, deltai / length)
generators[2 * i] = 0.5 * (generators[2 * i] +
new_generators[2 * i])
generators[2 * i + 1] = 0.5 * (generators[2 * i + 1] +
new_generators[2 * i + 1])
iteration += 1
print "CentroidalGenerator2d: Iteration %i, maxDelta=%g" % (
iteration, maxDelta)
# If requested, write out the final tessellation to a silo file.
if tessellationFileName:
poly.polytope.writeTessellation2d(mesh=self.tessellation,
filePrefix=tessellationFileName,
nodeFields=None,
edgeFields=None,
faceFields=None,
cellFields=None,
cycle=iteration)
# Now we can fill out the usual Spheral generator info.
assert len(self.tessellation.cells) == n
self.x, self.y, self.m, self.H = [], [], [], []
centroids = self.computeWeightedCentroids(self.tessellation)
masses = self.computeMasses(self.tessellation)
areas = self.computeAreas(self.tessellation)
assert len(centroids) == 2 * n
assert len(masses) == n
assert len(areas) == n
for i in xrange(n):
self.x.append(centroids[2 * i] + offset[0])
self.y.append(centroids[2 * i + 1] + offset[1])
self.m.append(masses[i])
hi = nNodePerh * sqrt(areas[i] / pi)
assert hi > 0.0
self.H.append(SymTensor2d(1.0 / hi, 0.0, 0.0, 1.0 / hi))
assert len(self.x) == n
assert len(self.y) == n
assert len(self.m) == n
assert len(self.H) == n
# If the user provided a "rejecter", give it a pass
# at the nodes.
if rejecter:
self.x, self.y, self.m, self.H = rejecter(self.x, self.y, self.m,
self.H)
# Have the base class break up the serial node distribution
# for parallel cases.
NodeGeneratorBase.__init__(self, True, self.x, self.y, self.m, self.H)
return
def forward(self, input, h_t, c_t, h_t2, c_t2):
h_t, c_t = self.lstm1(input, (h_t, c_t))
h_t2, c_t2 = self.lstm2(h_t, (h_t2, c_t2))
output = self.linear(h_t2)
return [output, h_t, c_t, h_t2, c_t2]
criterion = nn.L1Loss()
backprop_stepss = []
import sobol
number_of_samples = 30
parameterUpperLimits = np.array([20])
parameterLowerLimits = np.array([100])
for i in range(number_of_samples):
x = sobol.i4_sobol(1, i)[0] * (parameterUpperLimits -
parameterLowerLimits) + parameterLowerLimits
backprop_stepss.append(x)
backprop_stepss = np.concatenate(backprop_stepss, axis=0)
def lstm_network(backprop_steps, train_data_input):
if use_gpu:
power_lstm = Sequence()
power_lstm.double()
power_lstm.cuda()
optimizer = optim.Adam(power_lstm.parameters(), lr=0.01)
for epoch in range(0, 25):
if use_gpu:
h_t = Variable(
def i4_sobol_generate(dim_num, n, skip):
r = np.full((n, dim_num), np.nan)
for j in range(n):
seed = j + skip
r[j, 0:dim_num], next_seed = i4_sobol(dim_num, seed)
return r
def gpo(self, sm, sys, thSys):
#=====================================================================
# Initalisation
#=====================================================================
# Set initial settings
sm.calcGradientFlag = False
sm.calcHessianFlag = False
self.nPars = thSys.nParInference
self.filePrefix = thSys.filePrefix
runNextIter = True
self.iter = 0
# Check algorithm settings and set to default if needed
setSettings(self, "gpo")
# Make a grid to evaluate the EI on
l = np.array(self.lowerBounds[0:thSys.nParInference], dtype=np.float64)
u = np.array(self.upperBounds[0:thSys.nParInference], dtype=np.float64)
# Allocate vectors
AQ = np.zeros((self.maxIter + 1, 1))
mumax = np.zeros((self.maxIter + 1))
thp = np.zeros((self.maxIter + 1, self.nPars))
obp = np.zeros((self.maxIter + 1, 1))
thhat = np.zeros((self.maxIter, self.nPars))
thhatHessian = np.zeros((self.maxIter, self.nPars, self.nPars))
obmax = np.zeros((self.maxIter + 1, 1))
hyperParams = np.zeros((self.maxIter, 3 + self.nPars))
xhatf = np.zeros((self.maxIter + 1, sys.T))
#=====================================================================
# Pre-run using random sampling to estimate hyperparameters
#=====================================================================
# Pre allocate vectors
thPre = np.zeros((self.preIter, self.nPars))
obPre = np.zeros((self.preIter, 1))
#=====================================================================
# Main loop
#=====================================================================
# Pre-compute hypercube points if required
if (self.preSamplingMethod == "latinHyperCube"):
lhd = lhs(self.nPars, samples=self.preIter)
for kk in range(0, self.preIter):
# Sampling parameters using uniform sampling or Latin hypercubes
if (self.preSamplingMethod == "latinHyperCube"):
# Sample parameters using a Latin hypercube over the parameter
# bounds
thPre[kk, :] = l + (u - l) * lhd[kk, :]
elif (self.preSamplingMethod == "sobol"):
# Sample parameters using a Sobol sequence over the parameter
# bounds
thPre[kk, :] = l + (u - l) * i4_sobol(self.nPars, 100 + kk)[0]
else:
# Draw parameters uniform over the parameter bounds
thPre[kk, :] = l + (u - l) * np.random.random(self.nPars)
# Evaluate the objective function in the parameters
thSys.storeParameters(thPre[kk, :], sys)
obPre[kk], tmp1 = self.evaluateObjectiveFunction(sm, sys, thSys)
# Transform and save the parameters
thSys.transform()
thPre[kk, :] = thSys.returnParameters()[0:thSys.nParInference]
# Write out progress if requested
if (self.verbose):
print("gpo: Pre-iteration: " + str(kk) + " of " + str(self.preIter) + " completed, sampled " +
str(np.round(thPre[kk, :], 3)) + " with " + str(np.round(obPre[kk], 2)) + ".")
#=====================================================================
# Fit the GP regression
#=====================================================================
# Remove nan values for the objective function
idxNotNaN = ~np.isnan(obPre)
thPre = thPre[(idxNotNaN).any(axis=1)]
obPre = obPre[(idxNotNaN).any(axis=1)]
# Specify the kernel ( Matern52 with ARD plus bias kernel to compensate
# for non-zero mean )
kernel = GPy.kern.Matern52(
input_dim=self.nPars, ARD=True) + GPy.kern.Bias(input_dim=self.nPars)
# Normalize the objective function evaluations
ynorm = (obPre - np.mean(obPre)) / np.sqrt(np.var(obPre))
# Create the model object
m = GPy.models.GPRegression(thPre, ynorm, kernel, normalizer=False)
#=====================================================================
# Update hyperparameters
#=====================================================================
# Set constraints on hyperparameters
m.Gaussian_noise.variance.constrain_bounded(0.01, 10.0)
m.kern.Mat52.lengthscale.constrain_bounded(0.01, 10.0)
m.kern.Mat52.variance.constrain_bounded(0.01, 25.0)
# Run empirical Bayes to estimate the hyperparameters
m.optimize('bfgs', max_iters=200)
m.optimize_restarts(num_restarts=10, robust=True)
self.GaussianNoiseVariance = np.array(
m.Gaussian_noise.variance, copy=True)
#=====================================================================
# Write to output
#=====================================================================
self.thPre = thPre
self.obPre = obPre
self.m = m
#=====================================================================
# Main loop
#=====================================================================
# Save the initial parameters
thSys.storeParameters(self.initPar, sys)
thp[self.iter, :] = thSys.returnParameters()
thSys.transform()
while (runNextIter):
# Store the parameter
thSys.storeParameters(thp[self.iter, :], sys)
thSys.transform()
#------------------------------------------------------------------
# Evalute the objective function
#------------------------------------------------------------------
obp[self.iter], xhatf[self.iter,
:] = self.evaluateObjectiveFunction(sm, sys, thSys)
# Collect the sampled data (if the objective is finite)
idxNotNaN = ~np.isnan(obp[range(self.iter), :])
x = np.vstack((thPre, thp[(idxNotNaN).any(axis=1)]))
y = np.vstack((obPre, obp[(idxNotNaN).any(axis=1)]))
#------------------------------------------------------------------
# Fit the GP to the sampled data
#------------------------------------------------------------------
ynorm = (y - np.mean(y)) / np.sqrt(np.var(y))
self.ynormMean = np.mean(y)
self.ynormVar = np.var(y)
m = GPy.models.GPRegression(x, ynorm, kernel, normalizer=False)
#------------------------------------------------------------------
# Re-estimate the hyperparameters
#------------------------------------------------------------------
if (np.remainder(self.iter + 1, self.EstimateHyperparametersInterval) == 0):
# Set constraints on hyperparameters
m.Gaussian_noise.variance.constrain_bounded(0.01, 10.0)
m.kern.Mat52.lengthscale.constrain_bounded(0.01, 10.0)
m.kern.Mat52.variance.constrain_bounded(0.01, 25.0)
# Run empirical Bayes to estimate the hyperparameters
m.optimize('bfgs', max_iters=200)
m.optimize_restarts(num_restarts=10, robust=True)
# Save the current noise variance
self.GaussianNoiseVariance = np.array(
m.Gaussian_noise.variance, copy=True)
else:
# Overload current noise estimate (sets to 1.0 every time we
# add data otherwise)
m.Gaussian_noise.variance = self.GaussianNoiseVariance
# Save all the hyperparameters
hyperParams[self.iter, 0] = np.array(
m.Gaussian_noise.variance, copy=True)
hyperParams[self.iter, 1] = np.array(
m.kern.bias.variance, copy=True)
hyperParams[self.iter, 2] = np.array(
m.kern.Mat52.variance, copy=True)
hyperParams[self.iter, range(
3, 3 + self.nPars)] = np.array(m.kern.Mat52.lengthscale, copy=True)
#------------------------------------------------------------------
# Find the maximum expected value of the GP over the sampled parameters
#------------------------------------------------------------------
Mup, ys2 = m.predict(x)
mumax[self.iter] = np.max(Mup)
#------------------------------------------------------------------
# Compute the next point in which to sample the posterior
#------------------------------------------------------------------
# Optimize the AQ function
aqThMax, aqMax, ierror = solve(self.AQfunction, l, u, user_data=(
m, mumax[self.iter], self.epsilon), maxf=1000, maxT=1000)
# Jitter the parameter estimates
if (self.jitterParameters == True):
flag = 0.0
while (flag == 0.0):
z = np.random.multivariate_normal(np.zeros(self.nPars), self.jitteringCovariance[
range(self.nPars), :][:, range(self.nPars)])
flag = self.checkProposedParameters(aqThMax + z)
thSys.storeParameters(aqThMax + z, sys)
aqThMax += z
# Set the new point and save the estimate of the AQ
thp[self.iter + 1, :] = aqThMax
AQ[self.iter + 1] = -aqMax
# Update counter
self.iter += 1
#------------------------------------------------------------------
# Check exit conditions
#------------------------------------------------------------------
# AQ function criteria
if (AQ[self.iter] < self.tolLevel):
print("GPO: reaches tolLevel, so exiting...")
runNextIter = False
# Max iteration criteria
if (self.iter == self.maxIter):
print("GPO: reaches maxIter, so exiting...")
runNextIter = False
#------------------------------------------------------------------
# Estimate the current parameters by maximizing the GP
#------------------------------------------------------------------
if ((self.EstimateThHatEveryIteration == True) | (runNextIter == False)):
thhatCurrent, obmaxCurrent, ierror = solve(
self.MUeval, l, u, user_data=m, algmethod=1, maxf=1000, maxT=1000)
thhat[self.iter - 1, :] = thhatCurrent
obmax[self.iter - 1, :] = obmaxCurrent
print((thhatCurrent, obmaxCurrent))
if (self.EstimateHessianEveryIteration == True):
self.estimateHessian(thhatCurrent)
thhatHessian[self.iter - 1, :, :] = self.invHessianEstimate
#------------------------------------------------------------------
# Print output to console
#------------------------------------------------------------------
if (self.verbose):
if (self.EstimateThHatEveryIteration == True):
parm = ["%.4f" % v for v in thhat[self.iter - 1, :]]
print(
"##############################################################################################")
print("Iteration: " + str(self.iter) + " with current parameters: " +
str(parm) + " and AQ: " + str(np.round(AQ[self.iter], 2)))
print(
"##############################################################################################")
else:
parm = ["%.4f" % v for v in thp[self.iter - 1, :]]
print(
"##############################################################################################")
print("Iteration: " + str(self.iter) + " sampled objective function at parameters: " +
str(parm) + " with value: " + str(np.round(obp[self.iter - 1], 2)))
print(
"##############################################################################################")
#=====================================================================
# Generate output
#=====================================================================
tmp = range(self.iter - 1)
self.ob = obmax[tmp]
self.th = thhat[tmp, :]
self.thhat = thhat[self.iter - 1, :]
self.thHessian = thhatHessian
self.thhatHessian = thhatHessian[self.iter - 1, :, :]
self.aq = AQ[range(self.iter)]
self.obp = obp[tmp]
self.thp = thp[range(self.iter), :]
self.m = m
self.x = x
self.y = y
self.xhatf = xhatf
self.ynorm = ynorm
self.hp = hyperParams
def __init__(self,
ndim,
n,
rho,
boundary,
gradrho,
holes,
centroidFrac,
maxIterations,
fracTol,
tessellationBaseDir,
tessellationFileName,
nNodePerh,
randomseed,
maxNodesPerDomain,
seedPositions,
enforceConstantMassPoints,
cacheFileName):
assert ndim in (2,3)
assert n > 0
# Load our handy aliases.
if ndim == 2:
import Spheral2d as sph
else:
import Spheral3d as sph
# Did we get passed a function or a constant for the density?
if type(rho) in (float, int):
def rhofunc(posi):
return rho
rhomax = rho
else:
rhofunc = rho
rhomax = None
self.rhofunc = rhofunc
# Some useful geometry.
box = boundary.xmax - boundary.xmin
length = box.maxElement()
boundvol = boundary.volume
for hole in holes:
boundvol -= hole.volume
if boundvol <= 0.0:
# The holes were not entirely contained in the bounding volume, so we punt.
boundvol = 0.5*boundary.volume
boxvol = 1.0
for idim in xrange(ndim):
boxvol *= box[idim]
fracOccupied = min(1.0, boxvol/boundvol)
assert fracOccupied > 0.0 and fracOccupied <= 1.0
# If there is an pre-existing cache file, load it instead of doing all the work.
if not self.restoreState(cacheFileName):
# Create a temporary NodeList we'll use store and update positions.
eos = sph.GammaLawGasMKS(2.0, 2.0)
WT = sph.TableKernel(sph.NBSplineKernel(7), 1000)
hmax = 2.0*(boundvol/pi*n)**(1.0/ndim)
nodes = sph.makeFluidNodeList("tmp generator nodes",
eos,
hmin = 1e-10,
hmax = hmax,
kernelExtent = WT.kernelExtent,
hminratio = 1.0,
nPerh = nNodePerh,
topGridCellSize = 2.0*WT.kernelExtent*hmax)
# Make a first pass looking for the maximum density (roughly).
pos = nodes.positions()
mass = nodes.mass()
rhof = nodes.massDensity()
H = nodes.Hfield()
imin, imax = self.globalIDRange(n)
nlocal = imax - imin
nodes.numInternalNodes = nlocal
# If the user provided the starting or seed positions, use 'em.
if seedPositions is not None:
hi = min(hmax, 2.0 * (boundvol/(pi*n))**(1.0/ndim))
assert hi > 0.0
nlocal = len(seedPositions)
assert mpi.allreduce(nlocal, mpi.SUM) == n
nodes.numInternalNodes = nlocal
for i in xrange(nlocal):
pos[i] = seedPositions[i]
rhoi = rhofunc(pos[i])
rhof[i] = rhoi
mass[i] = rhoi * boundvol/n # Not actually correct, but mass will be updated in centroidalRelaxNodes
H[i] = sph.SymTensor.one / hi
else:
# If necessary probe for a maximum density statistically.
rangen = random.Random(randomseed + mpi.rank)
if not rhomax:
rhomax = 0.0
nglobal = 0
while nglobal < n:
p = boundary.xmin + length*sph.Vector(rangen.random(), rangen.random(), rangen.random())
use = boundary.contains(p, False)
if use:
ihole = 0
while use and ihole < len(holes):
use = not holes[ihole].contains(p, True)
ihole += 1
if use:
rhomax = max(rhomax, rhofunc(p))
i = 1
else:
i = 0
nglobal += mpi.allreduce(i, mpi.SUM)
rhomax = mpi.allreduce(rhomax, mpi.MAX)
print "MedialGenerator: selected a maximum density of ", rhomax
# It's a bit tricky to properly use the Sobol sequence in parallel. We handle this by searching for the lowest
# seeds that give us the desired number of points.
seeds = []
seed = 0
while mpi.allreduce(len(seeds), mpi.SUM) < n:
localseed = seed + mpi.rank
[coords, newseed] = i4_sobol(ndim, localseed)
p = boundary.xmin + length*sph.Vector(*tuple(coords))
use = boundary.contains(p, False)
if use:
ihole = 0
while use and ihole < len(holes):
use = not holes[ihole].contains(p, True)
ihole += 1
if use:
rhoi = rhofunc(p)
if rangen.random() < rhoi/rhomax:
seeds.append(localseed)
seed += mpi.procs
# Drop the highest value seeds to ensure we have the correct number of total points.
nglobal = mpi.allreduce(len(seeds), mpi.SUM)
assert n + mpi.procs >= nglobal
seeds.sort()
seeds = [-1] + seeds
while mpi.allreduce(len(seeds), mpi.SUM) > n + mpi.procs:
maxseed = mpi.allreduce(seeds[-1], mpi.MAX)
assert maxseed > -1
if seeds[-1] == maxseed:
seeds = seeds[:-1]
seeds = seeds[1:]
# Load balance the number of seeds per domain.
if len(seeds) > nlocal:
extraseeds = seeds[nlocal:]
else:
extraseeds = []
extraseeds = mpi.allreduce(extraseeds, mpi.SUM)
seeds = seeds[:nlocal]
for iproc in xrange(mpi.procs):
ngrab = max(0, nlocal - len(seeds))
ntaken = mpi.bcast(ngrab, root=iproc)
if mpi.rank == iproc:
seeds += extraseeds[:ngrab]
extraseeds = extraseeds[ntaken:]
assert len(extraseeds) == 0
assert len(seeds) == nlocal
assert mpi.allreduce(len(seeds), mpi.SUM) == n
# Initialize the desired number of generators in the boundary using the Sobol sequence.
hi = min(hmax, 2.0 * (boundvol/(pi*n))**(1.0/ndim))
assert hi > 0.0
for i, seed in enumerate(seeds):
[coords, newseed] = i4_sobol(ndim, seed)
p = boundary.xmin + length*sph.Vector(*tuple(coords))
rhoi = rhofunc(p)
pos[i] = p
rhof[i] = rhoi
mass[i] = rhoi * boundvol/n # Not actually correct, but mass will be updated in centroidalRelaxNodes
H[i] = sph.SymTensor.one / hi
# Each domain has independently generated the correct number of points, but they are randomly distributed.
# Before going further it's useful to try and spatially collect the points by domain.
# We'll use the Spheral Peano-Hilbert space filling curve implementation to do this.
if mpi.procs > 1:
db = sph.DataBase()
db.appendNodeList(nodes)
maxNodes = max(maxNodesPerDomain, 2*n/mpi.procs)
redistributor = sph.PeanoHilbertOrderRedistributeNodes(2.0)
redistributor.redistributeNodes(db)
# If we're in parallel we need the parallel boundary.
if mpi.procs > 1:
boundaries = [sph.TreeDistributedBoundary.instance()]
else:
boundaries = []
# Iterate the points toward centroidal relaxation.
vol, surfacePoint = centroidalRelaxNodes([(nodes, boundary, holes)],
W = WT,
rho = rhofunc,
gradrho = gradrho,
boundaries = boundaries,
fracTol = fracTol,
centroidFrac = centroidFrac,
maxIterations = maxIterations,
tessellationBaseDir = tessellationBaseDir,
tessellationFileName = tessellationFileName)
# Store the values the descendent generators will need.
self.vol, self.surface, self.pos, self.m, self.H = [], [], [], [], []
for i in xrange(nodes.numInternalNodes):
self.vol.append(vol(0,i))
self.surface.append(surfacePoint(0,i))
self.pos.append(sph.Vector(pos[i]))
self.m.append(vol(0,i) * rhofunc(pos[i]))
self.H.append(sph.SymTensor(H[i]))
assert mpi.allreduce(len(self.vol), mpi.SUM) == n
assert mpi.allreduce(len(self.surface), mpi.SUM) == n
assert mpi.allreduce(len(self.pos), mpi.SUM) == n
assert mpi.allreduce(len(self.m), mpi.SUM) == n
assert mpi.allreduce(len(self.H), mpi.SUM) == n
# If requested, enforce constant mass points.
if enforceConstantMassPoints:
msum = mpi.allreduce(sum([0.0] + self.m), mpi.SUM)
self.m = [msum/n]*len(self.pos)
# If requested, we can store the state of the generator such that it can be
# later restored without going through all that work.
if cacheFileName:
self.dumpState(cacheFileName)
return
def gpo(self, sm, sys, thSys):
#=====================================================================
# Initalisation
#=====================================================================
# Set initial settings
sm.calcGradientFlag = False
sm.calcHessianFlag = False
self.nPars = thSys.nParInference
self.filePrefix = thSys.filePrefix
runNextIter = True
self.iter = 0
# Check algorithm settings and set to default if needed
setSettings(self, "gpo")
# Make a grid to evaluate the EI on
l = np.array(self.lowerBounds[0:thSys.nParInference], dtype=np.float64)
u = np.array(self.upperBounds[0:thSys.nParInference], dtype=np.float64)
# Allocate vectors
AQ = np.zeros((self.maxIter + 1, 1))
mumax = np.zeros((self.maxIter + 1))
thp = np.zeros((self.maxIter + 1, self.nPars))
obp = np.zeros((self.maxIter + 1, 1))
thhat = np.zeros((self.maxIter, self.nPars))
thhatHessian = np.zeros((self.maxIter, self.nPars, self.nPars))
obmax = np.zeros((self.maxIter + 1, 1))
hyperParams = np.zeros((self.maxIter, 3 + self.nPars))
xhatf = np.zeros((self.maxIter + 1, sys.T))
#=====================================================================
# Pre-run using random sampling to estimate hyperparameters
#=====================================================================
# Pre allocate vectors
thPre = np.zeros((self.preIter, self.nPars))
obPre = np.zeros((self.preIter, 1))
#=====================================================================
# Main loop
#=====================================================================
# Pre-compute hypercube points if required
if (self.preSamplingMethod == "latinHyperCube"):
lhd = lhs(self.nPars, samples=self.preIter)
for kk in range(0, self.preIter):
# Sampling parameters using uniform sampling or Latin hypercubes
if (self.preSamplingMethod == "latinHyperCube"):
# Sample parameters using a Latin hypercube over the parameter
# bounds
thPre[kk, :] = l + (u - l) * lhd[kk, :]
elif (self.preSamplingMethod == "sobol"):
# Sample parameters using a Sobol sequence over the parameter
# bounds
thPre[kk, :] = l + (u - l) * i4_sobol(self.nPars, 100 + kk)[0]
else:
# Draw parameters uniform over the parameter bounds
thPre[kk, :] = l + (u - l) * np.random.random(self.nPars)
# Evaluate the objective function in the parameters
thSys.storeParameters(thPre[kk, :], sys)
obPre[kk], tmp1 = self.evaluateObjectiveFunction(sm, sys, thSys)
# Transform and save the parameters
thSys.transform()
thPre[kk, :] = thSys.returnParameters()[0:thSys.nParInference]
# Write out progress if requested
if (self.verbose):
print("gpo: Pre-iteration: " + str(kk) + " of " +
str(self.preIter) + " completed, sampled " +
str(np.round(thPre[kk, :], 3)) + " with " +
str(np.round(obPre[kk], 2)) + ".")
#=====================================================================
# Fit the GP regression
#=====================================================================
# Remove nan values for the objective function
idxNotNaN = ~np.isnan(obPre)
thPre = thPre[(idxNotNaN).any(axis=1)]
obPre = obPre[(idxNotNaN).any(axis=1)]
# Specify the kernel ( Matern52 with ARD plus bias kernel to compensate
# for non-zero mean )
kernel = GPy.kern.Matern52(
input_dim=self.nPars,
ARD=True) + GPy.kern.Bias(input_dim=self.nPars)
# Normalize the objective function evaluations
ynorm = (obPre - np.mean(obPre)) / np.sqrt(np.var(obPre))
# Create the model object
m = GPy.models.GPRegression(thPre, ynorm, kernel, normalizer=False)
#=====================================================================
# Update hyperparameters
#=====================================================================
# Set constraints on hyperparameters
m.Gaussian_noise.variance.constrain_bounded(0.01, 10.0)
m.kern.Mat52.lengthscale.constrain_bounded(0.01, 10.0)
m.kern.Mat52.variance.constrain_bounded(0.01, 25.0)
# Run empirical Bayes to estimate the hyperparameters
m.optimize('bfgs', max_iters=200)
m.optimize_restarts(num_restarts=10, robust=True)
self.GaussianNoiseVariance = np.array(m.Gaussian_noise.variance,
copy=True)
#=====================================================================
# Write to output
#=====================================================================
self.thPre = thPre
self.obPre = obPre
self.m = m
#=====================================================================
# Main loop
#=====================================================================
# Save the initial parameters
thSys.storeParameters(self.initPar, sys)
thp[self.iter, :] = thSys.returnParameters()
thSys.transform()
while (runNextIter):
# Store the parameter
thSys.storeParameters(thp[self.iter, :], sys)
thSys.transform()
#------------------------------------------------------------------
# Evalute the objective function
#------------------------------------------------------------------
obp[self.iter], xhatf[
self.iter, :] = self.evaluateObjectiveFunction(sm, sys, thSys)
# Collect the sampled data (if the objective is finite)
idxNotNaN = ~np.isnan(obp[range(self.iter), :])
x = np.vstack((thPre, thp[(idxNotNaN).any(axis=1)]))
y = np.vstack((obPre, obp[(idxNotNaN).any(axis=1)]))
#------------------------------------------------------------------
# Fit the GP to the sampled data
#------------------------------------------------------------------
ynorm = (y - np.mean(y)) / np.sqrt(np.var(y))
self.ynormMean = np.mean(y)
self.ynormVar = np.var(y)
m = GPy.models.GPRegression(x, ynorm, kernel, normalizer=False)
#------------------------------------------------------------------
# Re-estimate the hyperparameters
#------------------------------------------------------------------
if (np.remainder(self.iter + 1,
self.EstimateHyperparametersInterval) == 0):
# Set constraints on hyperparameters
m.Gaussian_noise.variance.constrain_bounded(0.01, 10.0)
m.kern.Mat52.lengthscale.constrain_bounded(0.01, 10.0)
m.kern.Mat52.variance.constrain_bounded(0.01, 25.0)
# Run empirical Bayes to estimate the hyperparameters
m.optimize('bfgs', max_iters=200)
m.optimize_restarts(num_restarts=10, robust=True)
# Save the current noise variance
self.GaussianNoiseVariance = np.array(
m.Gaussian_noise.variance, copy=True)
else:
# Overload current noise estimate (sets to 1.0 every time we
# add data otherwise)
m.Gaussian_noise.variance = self.GaussianNoiseVariance
# Save all the hyperparameters
hyperParams[self.iter, 0] = np.array(m.Gaussian_noise.variance,
copy=True)
hyperParams[self.iter, 1] = np.array(m.kern.bias.variance,
copy=True)
hyperParams[self.iter, 2] = np.array(m.kern.Mat52.variance,
copy=True)
hyperParams[self.iter, range(3, 3 + self.nPars)] = np.array(
m.kern.Mat52.lengthscale, copy=True)
#------------------------------------------------------------------
# Find the maximum expected value of the GP over the sampled parameters
#------------------------------------------------------------------
Mup, ys2 = m.predict(x)
mumax[self.iter] = np.max(Mup)
#------------------------------------------------------------------
# Compute the next point in which to sample the posterior
#------------------------------------------------------------------
# Optimize the AQ function
aqThMax, aqMax, ierror = solve(self.AQfunction,
l,
u,
user_data=(m, mumax[self.iter],
self.epsilon),
maxf=1000,
maxT=1000)
# Jitter the parameter estimates
if (self.jitterParameters == True):
flag = 0.0
while (flag == 0.0):
z = np.random.multivariate_normal(
np.zeros(self.nPars), self.jitteringCovariance[
range(self.nPars), :][:, range(self.nPars)])
flag = self.checkProposedParameters(aqThMax + z)
thSys.storeParameters(aqThMax + z, sys)
aqThMax += z
# Set the new point and save the estimate of the AQ
thp[self.iter + 1, :] = aqThMax
AQ[self.iter + 1] = -aqMax
# Update counter
self.iter += 1
#------------------------------------------------------------------
# Check exit conditions
#------------------------------------------------------------------
# AQ function criteria
if (AQ[self.iter] < self.tolLevel):
print("GPO: reaches tolLevel, so exiting...")
runNextIter = False
# Max iteration criteria
if (self.iter == self.maxIter):
print("GPO: reaches maxIter, so exiting...")
runNextIter = False
#------------------------------------------------------------------
# Estimate the current parameters by maximizing the GP
#------------------------------------------------------------------
if ((self.EstimateThHatEveryIteration == True) |
(runNextIter == False)):
thhatCurrent, obmaxCurrent, ierror = solve(self.MUeval,
l,
u,
user_data=m,
algmethod=1,
maxf=1000,
maxT=1000)
thhat[self.iter - 1, :] = thhatCurrent
obmax[self.iter - 1, :] = obmaxCurrent
print((thhatCurrent, obmaxCurrent))
if (self.EstimateHessianEveryIteration == True):
self.estimateHessian(thhatCurrent)
thhatHessian[self.iter - 1, :, :] = self.invHessianEstimate
#------------------------------------------------------------------
# Print output to console
#------------------------------------------------------------------
if (self.verbose):
if (self.EstimateThHatEveryIteration == True):
parm = ["%.4f" % v for v in thhat[self.iter - 1, :]]
print(
"##############################################################################################"
)
print("Iteration: " + str(self.iter) +
" with current parameters: " + str(parm) +
" and AQ: " + str(np.round(AQ[self.iter], 2)))
print(
"##############################################################################################"
)
else:
parm = ["%.4f" % v for v in thp[self.iter - 1, :]]
print(
"##############################################################################################"
)
print("Iteration: " + str(self.iter) +
" sampled objective function at parameters: " +
str(parm) + " with value: " +
str(np.round(obp[self.iter - 1], 2)))
print(
"##############################################################################################"
)
#=====================================================================
# Generate output
#=====================================================================
tmp = range(self.iter - 1)
self.ob = obmax[tmp]
self.th = thhat[tmp, :]
self.thhat = thhat[self.iter - 1, :]
self.thHessian = thhatHessian
self.thhatHessian = thhatHessian[self.iter - 1, :, :]
self.aq = AQ[range(self.iter)]
self.obp = obp[tmp]
self.thp = thp[range(self.iter), :]
self.m = m
self.x = x
self.y = y
self.xhatf = xhatf
self.ynorm = ynorm
self.hp = hyperParams