def test_Cdo_timeseries(plot = False):
raise NotImplementedError()
if plot:
import pylab as pl
x = np.linspace(0, 40, 400).reshape((-1, 1))
y = np.sin(x) + randn(len(x)).reshape((-1, 1)) * 0.2
proc_data = np.hstack([x,y])
if plot:
pl.plot(x.flatten(), y.flatten())
invec = FiniteVec(GaussianKernel(0.5), np.array([y.squeeze()[i:i+10] for i in range(190)]))
outvec = FiniteVec(GaussianKernel(0.5), y[10:200])
refervec = FiniteVec(outvec.k, np.linspace(y[:-201].min() - 2, y[:-201].max() + 2, 5000)[:, None])
cd = Cdo(invec, outvec, refervec, 0.1)
cd = Cmo(invec, outvec, 0.1)
sol2 = np.array([(cd @ FiniteVec(invec.k, y[end-10:end].T)).normalized().get_mean_var() for end in range(200,400) ])
if plot:
pl.plot(x[200:].flatten(), sol2.T[0].flatten())
invec = CombVec(FiniteVec(PeriodicKernel(np.pi, 5), x[:200,:]),
SpVec(SplitDimsKernel([0,1,2],[PeriodicKernel(np.pi, 5), GaussianKernel(0.1)]),
proc_data[:200,:], np.array([200]), use_subtrajectories=True), np.multiply)
outvec = FiniteVec(GaussianKernel(0.5), y[1:-199])
#cd = Cdo(invec, outvec, refervec, 0.1)
cd = Cmo(invec, outvec, 0.1)
#sol = (cd.inp_feat.inner(SpVec(invec.k, proc_data[:230], np.array([230]), use_subtrajectories=True)))
#sol = [(cd.inp_feat.inner(SiEdSpVec(invec.k_obs, y[:end], np.array([end]), invec.k_idx, use_subtrajectories=False ))) for end in range(200,400) ]
#pl.plot(np.array([sol[i][-1] for i in range(len(sol))]))
#sol = np.array([multiply (cd, SpVec(invec.k, proc_data[:end], np.array([end]), use_subtrajectories=False)).normalized().get_mean_var() for end in range(200,400) ])
sol = (cd @ CombVec(FiniteVec(invec.v1.k, x), SpVec(invec.v2.k, proc_data[:400], np.array([400]), use_subtrajectories=True), np.multiply)).normalized().get_mean_var()
print(sol)
return sol2.T[0], sol[0][200:], y[200:]
(true_x1, est_x1, este_x1, true_x2, est_x2, este_x2) = [lambda samps: true_dens(np.hstack([np.repeat(x1, len(samps), 0), samps])),
lambda samps: np.squeeze(inner((cd@ FiniteVec.construct_RKHS_Elem(invec.k, x1)).normalized().pos_proj().normalized(), FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps))))),
lambda samps: np.squeeze(inner((cm@ FiniteVec.construct_RKHS_Elem(invec.k, x1)).normalized().pos_proj().normalized(), FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps))))),
lambda samps: true_dens(np.hstack([np.repeat(x2, len(samps), 0), samps])),
lambda samps: np.squeeze(inner((cd@ FiniteVec.construct_RKHS_Elem(invec.k, x2)).normalized().pos_proj().normalized(), FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps))))),
lambda samps: np.squeeze(inner((cm@ FiniteVec.construct_RKHS_Elem(invec.k, x2)).normalized().pos_proj().normalized(), FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps)))))]
t = np.array((true_x1(refervec.insp_pts), true_x2(refervec.insp_pts)))
e = np.array((est_x1(refervec.insp_pts), est_x2(refervec.insp_pts)))
if plot:
import pylab as pl
(fig, ax) = pl.subplots(1, 3, False, False)
ax[0].plot(refervec.insp_pts, t[0])
ax[0].plot(refervec.insp_pts, e[0], "--", label = "dens")
ax[0].plot(refervec.insp_pts, este_x1(refervec.insp_pts), "-.", label = "emb")
ax[1].plot(refervec.insp_pts, t[1])
ax[1].plot(refervec.insp_pts, e[1], "--", label = "dens")
ax[1].plot(refervec.insp_pts, este_x2(refervec.insp_pts),"-.", label = "emb")
ax[2].scatter(*rvs.T)
fig.legend()
fig.show()
assert(np.allclose(e,t, atol=0.5))
def test_SpVecTraffic():
in_kern = PeriodicKernel(5, 1)
out_kern = GaussianKernel(0.5)
resh_traf = np.random.random_integers(0, 12, 20 * 20 * 2).reshape(
(20, 20, 2))
resh_traf[:, :, 0] = np.arange(20)
regr_inp = resh_traf[:15, :-1, :].reshape((-1, 2))
regr_out = resh_traf[:15, 1:, :].reshape((-1, 2))[:, 1:2]
un, sr = SparseReduce.sum_from_unique(regr_out.flatten())
num_points_per_obs = resh_traf.shape[1] - 1
inp_vec = SpVec(in_kern,
regr_inp,
np.arange(1, regr_inp.shape[0] // num_points_per_obs + 1) *
num_points_per_obs,
gram_reduce=sr)
out_vec = FiniteVec(
out_kern,
un[:, np.newaxis],
)
O = Cmo(inp_vec, out_vec)
test_inp = resh_traf[15:, :10, :].reshape((-1, 2))
invec_inf = SpVec(
in_kern,
test_inp,
np.array([test_inp.shape[0]]),
use_subtrajectories=False) #initial observed trajectory/warmup
print(len(O @ invec_inf))
cur_ro = RolloutSpVec(O, invec_inf, 1)
rval = []
for i in tqdm(range(1, 10)):
new_point = cur_ro.current_outp_emb.point_representant()
rval.append(new_point)
cur_ro.update(new_point)
def test_Cdmo(plot = False):
cent_vals = [True, False]
site_vals = [0., 1.]
def generate_donut(nmeans = 10, nsamps_per_mean = 50):
from scipy.stats import multivariate_normal
from numpy import exp
def pol2cart(theta, rho):
x = (rho * np.cos(theta)).reshape(-1,1)
y = (rho * np.sin(theta)).reshape(-1,1)
return np.concatenate([x, y], axis = 1)
comp_distribution = multivariate_normal(np.zeros(2), np.eye(2)/100)
means = pol2cart(np.linspace(0,2*3.141, nmeans + 1)[:-1], 1)
rvs = comp_distribution.rvs(nmeans * nsamps_per_mean) + np.repeat(means, nsamps_per_mean, 0)
true_dens = lambda samps: exp(location_mixture_logpdf(samps, means, np.ones(nmeans) / nmeans, comp_distribution))
return rvs, means, true_dens
x_vals = [np.zeros((1,1)) + i for i in site_vals]
(rvs, means, true_dens) = generate_donut(500, 10)
regul = CovOp.regul(1, len(rvs)) # we will look at 1 point inputs
invec = FiniteVec(GenGaussKernel(0.3, 1.7), rvs[:, :1])
outvec = FiniteVec(GenGaussKernel(0.3, 1.7), rvs[:, 1:])
refervec = FiniteVec(outvec.k, np.linspace(-4, 4, 10000)[:, None])
C_ref = CovOp(refervec)
maps = {}
for center in cent_vals:
cm = Cmo(invec, outvec, regul, center = center)
maps[center] = {"emb":cm, "dens":C_ref.solve(cm)}
print(np.abs(cm.const_cent_term - maps[center]["dens"].const_cent_term).max())
ests = {map_type:
{cent: np.array([maps[cent][map_type](x).dens_proj()(refervec.insp_pts).squeeze()
for x in x_vals])
for cent in cent_vals}
for map_type in ["emb", "dens"]}
t = np.array([true_dens(np.hstack([np.repeat(x, len(refervec.insp_pts), 0), refervec.insp_pts]))
for x in x_vals])
if plot:
import matplotlib.pyplot as plt
(fig, ax) = plt.subplots(len(site_vals) + 1, 1, False, False)
for i, site in enumerate(site_vals):
ax[i].plot(refervec.insp_pts, t[i], linewidth=2, color="b", label = "true dens", alpha = 0.5)
for map_type in ["emb", "dens"]:
for cent in cent_vals:
if map_type == "emb":
color = "r"
else:
color = "g"
if cent == True:
style = ":"
else:
style= "--"
ax[i].plot(refervec.insp_pts, ests[map_type][cent][i], style, color = color, label = map_type+" "+("cent" if cent else "unc"), alpha = 0.5)
ax[-1].scatter(*rvs.T)
fig.legend()
fig.show()
for cent in cent_vals:
assert(np.allclose(ests["dens"][cent],t, atol=0.5))
def test_Cdmo(plot=False):
def generate_donut(nmeans=10, nsamps_per_mean=50):
from scipy.stats import multivariate_normal
from numpy import exp
def pol2cart(theta, rho):
x = (rho * np.cos(theta)).reshape(-1, 1)
y = (rho * np.sin(theta)).reshape(-1, 1)
return np.concatenate([x, y], axis=1)
comp_distribution = multivariate_normal(np.zeros(2), np.eye(2) / 100)
means = pol2cart(np.linspace(0, 2 * 3.141, nmeans + 1)[:-1], 1)
rvs = comp_distribution.rvs(nmeans * nsamps_per_mean) + np.repeat(
means, nsamps_per_mean, 0)
true_dens = lambda samps: exp(
location_mixture_logpdf(samps, means,
np.ones(nmeans) / nmeans, comp_distribution
))
return rvs, means, true_dens
x1 = np.ones((1, 1))
x2 = np.zeros((1, 1))
(rvs, means, true_dens) = generate_donut(50, 10)
invec = FiniteVec(GaussianKernel(0.5), rvs[:, :1])
outvec = FiniteVec(GaussianKernel(0.5), rvs[:, 1:])
refervec = FiniteVec(outvec.k, np.linspace(-4, 4, 5000)[:, None])
cd = Cdo(invec, outvec, refervec, 0.1)
cm = Cmo(invec, outvec, 0.1)
(true_x1, est_x1, este_x1, true_x2, est_x2, este_x2) = [
lambda samps: true_dens(
np.hstack([np.repeat(x1, len(samps), 0), samps])),
lambda samps: np.squeeze(
inner(
multiply(cd, FiniteVec.construct_RKHS_Elem(invec.k, x1)).
normalized().unsigned_projection().normalized(),
FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps))))),
lambda samps: np.squeeze(
inner(
multiply(cm, FiniteVec.construct_RKHS_Elem(invec.k, x1)).
normalized().unsigned_projection().normalized(),
FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps))))),
lambda samps: true_dens(
np.hstack([np.repeat(x2, len(samps), 0), samps])),
lambda samps: np.squeeze(
inner(
multiply(cd, FiniteVec.construct_RKHS_Elem(invec.k, x2)).
normalized().unsigned_projection().normalized(),
FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps))))),
lambda samps: np.squeeze(
inner(
multiply(cm, FiniteVec.construct_RKHS_Elem(invec.k, x2)).
normalized().unsigned_projection().normalized(),
FiniteVec(refervec.k, samps, prefactors=np.ones(len(samps)))))
]
t = np.array(
(true_x1(refervec.inspace_points), true_x2(refervec.inspace_points)))
e = np.array(
(est_x1(refervec.inspace_points), est_x2(refervec.inspace_points)))
if plot:
import pylab as pl
(fig, ax) = pl.subplots(1, 3, False, False)
ax[0].plot(refervec.inspace_points, t[0])
ax[0].plot(refervec.inspace_points, e[0], "--", label="dens")
ax[0].plot(refervec.inspace_points,
este_x1(refervec.inspace_points),
"-.",
label="emb")
ax[1].plot(refervec.inspace_points, t[1])
ax[1].plot(refervec.inspace_points, e[1], "--", label="dens")
ax[1].plot(refervec.inspace_points,
este_x2(refervec.inspace_points),
"-.",
label="emb")
ax[2].scatter(*rvs.T)
fig.legend()
fig.show()
assert (np.allclose(e, t, atol=0.5))