def compare_pdf_Oscillator():
smpl = np.genfromtxt("map_samples2D.txt")
ndim = 2
tf = 25
nsteps = 1000
u_init = [0, 0]
noise = Noise([0, tf])
lam = noise.get_eigenvalues(ndim)
mean = np.zeros(ndim)
cov = np.diag(lam)
domain = [[-a, a] for a in 6.0 * np.sqrt(np.diag(cov))]
inputs = GaussianInputs(mean, cov, domain)
weights = inputs.pdf(smpl[:, 0:-1])
x_d = np.linspace(-3, 3, 500)
#weights = weights/weights
pdf_scipy = stats.gaussian_kde(smpl[:, -1], weights=weights)
pdf_numba = KDE_Numba(smpl[:, -1], weights=weights)
pdf_kdepy = FFTKDE(bw=pdf_numba.bw).fit(smpl[:, -1], weights)
plt.semilogy(x_d, pdf_scipy(x_d), lw=3)
plt.semilogy(x_d, pdf_numba(x_d), '--')
plt.semilogy(x_d, pdf_kdepy(x_d), '--', lw=0.5)
plt.xlim(-3, 3)
plt.ylim(1e-8, 1e2)
plt.show()
def main():
ndim = 2
np.random.seed(3)
tf = 25
nsteps = 1000
u_init = [0, 0]
noise = Noise([0, tf])
oscil = Oscillator(noise, tf, nsteps, u_init)
my_map = BlackBox(map_def, args=(oscil, ))
n_init = 4
n_iter = 80
mean, cov = np.zeros(ndim), np.ones(ndim)
domain = [[-6, 6]] * ndim
inputs = GaussianInputs(domain, mean, cov)
X = inputs.draw_samples(n_init, "lhs")
Y = my_map.evaluate(X)
o = OptimalDesign(X,
Y,
my_map,
inputs,
fix_noise=True,
noise_var=0.0,
normalize_Y=True)
m_list = o.optimize(n_iter,
acquisition="US",
num_restarts=10,
parallel_restarts=True)
# Compute true pdf
filename = "map_samples{:d}D.txt".format(ndim)
try:
smpl = np.genfromtxt(filename)
pts = smpl[:, 0:-1]
yy = smpl[:, -1]
except:
pts = inputs.draw_samples(n_samples=100, sample_method="grd")
yy = my_map.evaluate(pts, parallel=True, include_noise=False)
np.savetxt(filename, np.column_stack((pts, yy)))
pdf = custom_KDE(yy, weights=inputs.pdf(pts))
for ii in np.arange(0, n_iter + 1, 10):
pb, pp, pm = model_pdf(m_list[ii], inputs, pts=pts)
plot_pdf(pdf,
pb, [pm, pp],
filename="pdfs%.4d.pdf" % (ii),
xticks=[-3, 0, 3],
yticks=[-8, -3, 2])
plot_smp(m_list[ii],
inputs,
n_init,
filename="smps%.4d.pdf" % (ii),
xticks=[-6, 0, 6],
yticks=[-5, 0, 5],
cmapticks=[-2, -1, 0, 1, 2])
def run(casename):
fh = Dataset("../data/" + casename + ".nc", mode="r")
lons = fh.variables["lon"][:]
lats = fh.variables["lat"][:]
depths = fh.variables["elevation"][:]
# Rescale data and flip depths to have anomalies as minima
lons = MinMaxScaler().fit_transform(lons.reshape(-1, 1))
lats = MinMaxScaler().fit_transform(lats.reshape(-1, 1))
tmp = StandardScaler().fit_transform(depths.reshape(-1, 1))
depths = -tmp.reshape(depths.shape)
if casename in ["cuba", "challenger", "izu", "izu2", "izu3"]:
depths = -depths
domain = [[0, 1], [0, 1]]
inputs = UniformInputs(domain)
inputs = GaussianInputs(domain, [0.5, 0.5], [0.01, 0.01])
noise_var = 0.0
interpolant = interpolate.interp2d(lons, lats, depths, kind="cubic")
my_map = BlackBox(map_def, args=(interpolant, ), noise_var=noise_var)
idx_max = np.unravel_index(depths.argmin(), depths.shape)
true_xmin = [lons[idx_max[1]], lats[idx_max[0]]]
true_ymin = np.min(depths)
record_time = np.linspace(0, 15, 226)
n_trials = 50
n_jobs = 40
pts = inputs.draw_samples(n_samples=int(1e5), sample_method="uni")
yy = my_map.evaluate(pts, parallel=True, include_noise=False)
y_list = [yy] * len(record_time)
pt_list = [custom_KDE(yy, weights=inputs.pdf(pts))] * len(record_time)
true_ymin_list = [true_ymin] * len(record_time)
true_xmin_list = [true_xmin] * len(record_time)
metric = [(rmse, dict(pts=pts, y_list=y_list, t_list=record_time)),
(mll, dict(pts=pts, y_list=y_list, t_list=record_time)),
(log_pdf, dict(pts=pts, pt_list=pt_list, t_list=record_time)),
(distmin_model,
dict(true_xmin_list=true_xmin_list, t_list=record_time)),
(regret_tmap,
dict(true_ymin_list=true_ymin_list,
tmap=my_map,
t_list=record_time))]
X_pose = (0, 0, np.pi / 4)
planner = PathPlanner(inputs.domain, look_ahead=0.2, turning_radius=0.02)
acq_list = ["US_IW", "US_LW", "IVR_IW", "IVR_LW"]
for acq in acq_list:
print("Benchmarking " + acq)
b = BenchmarkerPath(my_map, acq, planner, X_pose, record_time, inputs,
metric)
result = b.run_benchmark(n_trials,
n_jobs=n_jobs,
filename=casename + "_" + acq)
def run(function, prefix):
noise_var = 1e-3
b = augment(function)(noise_var=noise_var, rescale_X=True)
my_map, inputs, true_ymin, true_xmin = b.my_map, b.inputs, b.ymin, b.xmin
# Use Gaussian prior
domain = inputs.domain
mean = np.zeros(inputs.input_dim) + 0.5
cov = np.ones(inputs.input_dim) * 0.01
inputs = GaussianInputs(domain, mean, cov)
record_time = np.linspace(0, 15, 226)
n_trials = 50
n_jobs = 20
pts = inputs.draw_samples(n_samples=int(1e5), sample_method="uni")
yy = my_map.evaluate(pts, parallel=True, include_noise=False)
y_list = [yy] * len(record_time)
pt_list = [custom_KDE(yy, weights=inputs.pdf(pts))] * len(record_time)
true_ymin_list = [true_ymin] * len(record_time)
true_xmin_list = [true_xmin] * len(record_time)
metric = [(rmse, dict(pts=pts, y_list=y_list, t_list=record_time)),
(mll, dict(pts=pts, y_list=y_list, t_list=record_time)),
(log_pdf, dict(pts=pts, pt_list=pt_list, t_list=record_time)),
(distmin_model,
dict(true_xmin_list=true_xmin_list, t_list=record_time)),
(regret_tmap,
dict(true_ymin_list=true_ymin_list,
tmap=my_map,
t_list=record_time))]
X_pose = (0, 0, np.pi / 4)
planner = PathPlanner(inputs.domain, look_ahead=0.2, turning_radius=0.02)
acq_list = ["US_IW", "US_LW", "IVR_IW", "IVR_LW"]
for acq in acq_list:
print("Benchmarking " + acq)
b = BenchmarkerPath(my_map, acq, planner, X_pose, record_time, inputs,
metric)
result = b.run_benchmark(n_trials,
n_jobs=n_jobs,
filename=prefix + acq)
def main():
ndim = 2
tf = 25
nsteps = 1000
u_init = [0, 0]
noise = Noise([0, tf])
oscil = Oscillator(noise, tf, nsteps, u_init)
mean, cov = np.zeros(ndim), np.ones(ndim)
domain = [[-6, 6]] * ndim
inputs = GaussianInputs(domain, mean, cov)
prefix = "oscill_"
noise_var = 1e-3
my_map = BlackBox(map_def, args=(oscil, ), noise_var=noise_var)
n_init = 3
n_iter = 80
n_trials = 100
n_jobs = 30
# Compute true pdf
filename = "map_samples{:d}D.txt".format(ndim)
try:
smpl = np.genfromtxt(filename)
pts = smpl[:, 0:-1]
yy = smpl[:, -1]
except:
pts = inputs.draw_samples(n_samples=100, sample_method="grd")
yy = my_map.evaluate(pts, parallel=True, include_noise=False)
np.savetxt(filename, np.column_stack((pts, yy)))
weights = inputs.pdf(pts)
pt = custom_KDE(yy, weights=weights)
metric = [("log_pdf", dict(pt=pt, pts=pts))]
acq_list = ["US", "US_LW", "IVR_IW", "IVR_LW"]
for acq in acq_list:
print("Benchmarking " + acq)
b = Benchmarker(my_map, acq, n_init, n_iter, inputs, metric)
result = b.run_benchmark(n_trials, n_jobs, filename=prefix + acq)
b = BenchmarkerLHS(my_map, n_init, n_iter, inputs, metric)
result = b.run_benchmark(n_trials, n_jobs, filename=prefix + "LHS")
def main():
ndim = 3
np.random.seed(2)
tf = 4000
dt = 0.01
nsteps = int(tf/dt)
u_init = [0, 0.01, 0.01]
pre = PRE(tf, nsteps, u_init)
u, t = pre.solve()
plot_observable(t, u[:,2], ylabel="z",
xticks=[0,2000,4000], yticks=[-0.5,0,0.5,1])
plot_trajectory(t, u)
# Do PCA
iostep = 100
tsnap = t[::iostep]
usnap = u[::iostep]
lam, psi, usnap_mean = comp_pca(usnap, ndim)
print("PCA Eigenvalues:", lam)
n_init = 3
n_iter = 50
mean = np.zeros(ndim)
cov = np.diag(lam)
a_bnds = 4.0
domain = [ [-a, a] for a in a_bnds*np.sqrt(np.diag(cov)) ]
inputs = GaussianInputs(domain, mean, cov)
my_map = BlackBox(map_def, args=(psi,usnap_mean))
X = inputs.draw_samples(n_init, "lhs")
Y = my_map.evaluate(X)
o = OptimalDesign(X, Y, my_map, inputs,
fix_noise=True,
noise_var=0.0,
normalize_Y=True)
m_list = o.optimize(n_iter,
acquisition="EI",
num_restarts=10,
parallel_restarts=True)
def main():
# Generate data for PCA
tf = 2000
dt = 0.01
nsteps = int(tf / dt)
u_init = [0, 0.01, 0.01]
pre = PRE(tf, nsteps, u_init)
u, t = pre.solve()
# Do PCA
ndim = 2
iostep = 100
tsnap = t[::iostep]
usnap = u[::iostep]
lam, psi, usnap_mean = comp_pca(usnap, ndim)
print("PCA Eigenvalues:", lam)
# Set up black box
mean = np.zeros(ndim)
cov = np.diag(lam)
a_bnds = 4.0
domain = [[-a, a] for a in a_bnds * np.sqrt(np.diag(cov))]
inputs = GaussianInputs(domain, mean, cov)
noise_var = 1e-3
my_map = BlackBox(map_def, args=(psi, usnap_mean), noise_var=noise_var)
# Do Benchmark
prefix = "prec2d_"
n_init = 3
n_iter = 100
n_trials = 100
n_jobs = 40
metric = [("regret_tmap", dict(tmap=my_map, true_ymin=0.0)),
("regret_obs", dict(true_ymin=0.0))]
acq_list = [
"EI", "PI", "LCB", "LCB_LW", "IVR", "IVR_BO", "IVR_LW", "IVR_LWBO"
]
for acq in acq_list:
print("Benchmarking " + acq)
b = Benchmarker(my_map, acq, n_init, n_iter, inputs, metric)
result = b.run_benchmark(n_trials, n_jobs, filename=prefix + acq)
def plot_likelihood_ratio(function, n_GMM, filename):
my_map, inputs = function.my_map, function.inputs
mu = np.random.randn(inputs.input_dim)
cov = 4*np.random.randn(inputs.input_dim)**2
inputs = GaussianInputs(inputs.domain, mu=mu, cov=cov)
ngrid = 10
pts = inputs.draw_samples(n_samples=ngrid, sample_method="grd")
ndim = pts.shape[-1]
grd = pts.reshape( (ngrid,)*ndim + (ndim,) ).T
X, Y = grd[0], grd[1]
# Compute map
yy = my_map.evaluate(pts)
# Compute GPy model
model = GPy.models.GPRegression(pts, yy, normalizer=True)
likelihood = Likelihood(model, inputs)
x_new = np.random.rand(2, inputs.input_dim)
print(likelihood._evaluate_raw(x_new))
print(likelihood._jacobian_raw(x_new))
g = GradientChecker(lambda x: likelihood._evaluate_gmm(x),
lambda x: likelihood._jacobian_gmm(x),
x_new, 'x')
assert(g.checkgrad())
yy = model.predict(pts)[0].flatten()
dyy_dx, _ = model.predictive_gradients(pts)
dyy_dx = dyy_dx[:,:,0]
ZZ = yy.reshape( (ngrid,)*ndim ).T
# Compute likelihood ratio
x, y = custom_KDE(yy, weights=inputs.pdf(pts)).evaluate()
fnTn = scipy.interpolate.interp1d(x, y)
fx = inputs.pdf(pts).flatten()
fy = fnTn(yy).flatten()
w = fx/fy
ZL = w.reshape( (ngrid,)*ndim ).T
# Compute gradient of likelihood ratio
dy_dx = np.gradient(y,x)
fnTn_dx = scipy.interpolate.interp1d(x, dy_dx)
tmp = -fx / fy**2 * fnTn_dx(yy)
dw_dx = tmp[:,None] * dyy_dx
plt.figure()
plt.plot(x,y)
plt.plot(x,fnTn(x), '-.')
from scipy.interpolate import InterpolatedUnivariateSpline
spl = InterpolatedUnivariateSpline(x, y)
plt.plot(x, spl(x), '--')
plt.figure()
plt.semilogy(x,dy_dx)
plt.semilogy(x,fnTn_dx(x), '-.')
plt.semilogy(x, spl.derivative()(x), '--')
plt.show(); exit()
def main():
np.random.seed(2)
casename = "izu3"
fh = Dataset("../benchmarks/bathymetry/data/" + casename + ".nc", mode="r")
lons = fh.variables["lon"][:]
lats = fh.variables["lat"][:]
depths = fh.variables["elevation"][:]
# Rescale data and flip depths to have anomalies as minima
lons = MinMaxScaler().fit_transform(lons.reshape(-1, 1))
lats = MinMaxScaler().fit_transform(lats.reshape(-1, 1))
tmp = StandardScaler().fit_transform(depths.reshape(-1, 1))
depths = -tmp.reshape(depths.shape)
if casename in ["cuba", "challenger", "izu", "izu2"]: depths = -depths
domain = [ [0, 1], [0, 1] ]
#inputs = UniformInputs(domain)
inputs = GaussianInputs(domain, [0.5,0.5], [0.01,0.01])
noise_var = 0.0
interpolant = interpolate.interp2d(lons, lats, depths, kind="cubic")
my_map = BlackBox(map_def, args=(interpolant,), noise_var=noise_var)
# Set up path-planner
record_time = np.linspace(0,2,31)
#record_time = np.linspace(0,4,61)
#record_time = np.linspace(0,10,151)
my_map.kwargs["time"] = record_time[0]
X_pose = (0,0,np.pi/4); X = X_pose[0:2]
Y_pose = my_map.evaluate(X); print(Y_pose);
p = PathPlanner(inputs.domain,
look_ahead=0.2,
turning_radius=0.02)
# Run mission
# o = OptimalPathStatic(X_pose, Y_pose, my_map, inputs)
o = OptimalPath(X_pose, Y_pose, my_map, inputs)#, static=True)
m_list, p_list, s_list = o.optimize(record_time,
path_planner=p,
acquisition="US")
# Plot stuff
ngrid = 50
pts = inputs.draw_samples(n_samples=ngrid, sample_method="grd")
ndim = pts.shape[-1]
grd = pts.reshape( (ngrid,)*ndim + (ndim,) ).T
X, Y = grd[0], grd[1]
yy = my_map.evaluate(pts, include_noise=False)
ZZt = yy.reshape( (ngrid,)*ndim ).T
r_list = [ np.array(p.make_itinerary(path,1000)[0]) for path in p_list ]
for ii in range(0, len(m_list)):
model = m_list[ii]
stamp = model.X[-1,-1]*np.ones(len(pts))
yy = model.predict( np.hstack((pts, stamp[:,None])) )[0]
ZZ = yy.reshape( (ngrid,)*ndim ).T
fig = plt.figure(figsize=(10,4))
plt.subplot(121)
plt.contourf(X, Y, ZZ);
for rr in r_list[0:ii+1]:
plt.plot(rr[:,0], rr[:,1], 'r-')
plt.plot(model.X[:,0],model.X[:,1],'ro')
plt.xlim(0,1); plt.ylim(0,1)
plt.axis('equal');
plt.subplot(122)
plt.contourf(X, Y, ZZt);
plt.xlim(0,1); plt.ylim(0,1)
plt.axis('equal');
plt.show();