def test_multiply():
x = np.linspace(-2.5, 15, 5)[:, np.newaxis].astype(np.float32)
y = randn(x.size)[:, np.newaxis].astype(np.float32)
gk_x = GaussianKernel(0.1)
x_e1 = FiniteVec.construct_RKHS_Elem(gk_x, x)
x_e2 = FiniteVec.construct_RKHS_Elem(gk_x, y)
x_fv = FiniteVec(gk_x,
np.vstack([x, y]),
prefactors=np.hstack([x_e1.prefactors] * 2),
points_per_split=x.size)
oper_feat_vec = FiniteVec(gk_x, x)
oper = FiniteOp(oper_feat_vec, oper_feat_vec, np.eye(len(x)))
res_e1 = multiply(oper, x_e1)
res_e2 = multiply(oper, x_e2)
res_v = multiply(oper, x_fv)
assert np.allclose(
res_e1.prefactors,
(oper.matr @ oper.inp_feat.inner(x_e1)
).flatten()), "Application of operator to RKHS element failed."
assert np.allclose(
res_v.inspace_points,
np.vstack([res_e1.inspace_points, res_e2.inspace_points])
), "Application of operator to all vectors in RKHS vector failed at inspace points."
assert np.allclose(
res_v.prefactors, np.hstack([
res_e1.prefactors, res_e2.prefactors
])), "Application of operator to all vectors in RKHS vector failed."
assert np.allclose(
multiply(oper, oper).matr, oper.inp_feat.inner(
oper.outp_feat)), "Application of operator to operator failed."
def frank_wolfe_fx(element: FiniteVec, num_samples: np.int32 = 100):
assert (len(element) == 1)
#key = PRNGKey(np.int32(time()))
solution = FiniteVec(element.k,
element.inspace_points[:1, :],
np.zeros(1),
points_per_split=1)
for k in range(num_samples):
def cost(x):
x = x.reshape((1, -1))
return (solution(x) - element(x)).sum()
g_cost = grad(cost)
idx = randint(0, element.points_per_split - 1)
cand = element.inspace_points[idx:idx + 1, :]
#print(cand)
#print(cost(cand), grad(cost)(cand))
res = minimize(__casted_output(cost),
cand,
jac=__casted_output(g_cost))
solution.inspace_points = np.vstack(
[solution.inspace_points, res["x"]])
gamma_k = 1. / (k + 1)
solution.prefactors = np.hstack([(1 - gamma_k) * solution.prefactors,
gamma_k])
solution.points_per_split = solution.points_per_split + 1
return solution
def test_FiniteMap():
gk_x = GaussianKernel(0.1)
x = np.linspace(-2.5, 15, 20)[:, np.newaxis].astype(np.float32)
#x = np.random.randn(20, 1).astype(np.float)
ref_fvec = FiniteVec(gk_x, x, np.ones(len(x)))
ref_elem = FiniteVec.construct_RKHS_Elem(gk_x, x, np.ones(len(x)))
C1 = FiniteMap(ref_fvec, ref_fvec, np.linalg.inv(inner(ref_fvec)))
assert(np.allclose((C1 @ ref_elem).prefactors, 1.))
C2 = FiniteMap(ref_fvec, ref_fvec, [email protected])
assert(np.allclose((C2 @ ref_elem).prefactors, np.sum(C1.matr, 0)))
n_rvs = 50
rv_fvec = FiniteVec(gk_x, random.normal(rng, (n_rvs, 1)) * 5, np.ones(n_rvs))
C3 = FiniteMap(rv_fvec, rv_fvec, np.eye(n_rvs))
assert np.allclose((C3 @ C1).matr, gk_x(rv_fvec.insp_pts, ref_fvec.insp_pts) @ C1.matr, 0.001, 0.001)
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_FiniteOp():
gk_x = GaussianKernel(0.1)
x = np.linspace(-2.5, 15, 20)[:, np.newaxis].astype(np.float)
#x = np.random.randn(20, 1).astype(np.float)
ref_fvec = FiniteVec(gk_x, x, np.ones(len(x)))
ref_elem = FiniteVec.construct_RKHS_Elem(gk_x, x, np.ones(len(x)))
C1 = FiniteOp(ref_fvec, ref_fvec, np.linalg.inv(inner(ref_fvec)))
assert (np.allclose(multiply(C1, ref_elem).prefactors, 1.))
C2 = FiniteOp(ref_fvec, ref_fvec, C1.matr @ C1.matr)
assert (np.allclose(multiply(C2, ref_elem).prefactors, np.sum(C1.matr, 0)))
n_rvs = 50
rv_fvec = FiniteVec(gk_x,
np.random.randn(n_rvs).reshape((-1, 1)) * 5,
np.ones(n_rvs))
C3 = FiniteOp(rv_fvec, rv_fvec, np.eye(n_rvs))
assert (np.allclose(
multiply(C3, C1).matr,
gk_x(rv_fvec.inspace_points, ref_fvec.inspace_points) @ C1.matr),
0.001, 0.001)
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_CovOp(plot=False):
from scipy.stats import multivariate_normal
nsamps = 1000
samps_unif = None
regul_C_ref = 0.0001
D = 1
import pylab as pl
if samps_unif is None:
samps_unif = nsamps
gk_x = GaussianKernel(0.2)
targ = mixt(D, [
multivariate_normal(3 * np.ones(D),
np.eye(D) * 0.7**2),
multivariate_normal(7 * np.ones(D),
np.eye(D) * 1.5**2)
], [0.5, 0.5])
out_samps = targ.rvs(nsamps).reshape([nsamps, 1]).astype(float)
out_fvec = FiniteVec(gk_x, out_samps, np.ones(nsamps))
#gk_x = LaplaceKernel(3)
#gk_x = StudentKernel(0.7, 15)
x = np.linspace(-2.5, 15, samps_unif)[:, np.newaxis].astype(float)
ref_fvec = FiniteVec(gk_x, x, np.ones(len(x)))
ref_elem = ref_fvec.sum()
C_ref = CovOp(
ref_fvec,
regul=0.) # CovOp_compl(out_fvec.k, out_fvec.inspace_points, regul=0.)
inv_Gram_ref = np.linalg.inv(inner(ref_fvec))
assert (np.allclose((inv_Gram_ref @ inv_Gram_ref) / C_ref.inv().matr,
1.,
atol=1e-3))
#assert(np.allclose(multiply(C_ref.inv(), ref_elem).prefactors, np.sum(np.linalg.inv(inner(ref_fvec)), 0), rtol=1e-02))
C_samps = CovOp(out_fvec, regul=regul_C_ref)
unif_obj = multiply(
C_samps.inv(),
FiniteVec.construct_RKHS_Elem(out_fvec.k, out_fvec.inspace_points,
out_fvec.prefactors).normalized())
C_ref = CovOp(ref_fvec, regul=regul_C_ref)
dens_obj = multiply(
C_ref.inv(),
FiniteVec.construct_RKHS_Elem(out_fvec.k, out_fvec.inspace_points,
out_fvec.prefactors)).normalized()
#dens_obj.prefactors = np.sum(dens_obj.prefactors, 1)
#dens_obj.prefactors = dens_obj.prefactors / np.sum(dens_obj.prefactors)
#print(np.sum(dens_obj.prefactors))
#p = np.sum(inner(dens_obj, ref_fvec), 1)
targp = np.exp(targ.logpdf(ref_fvec.inspace_points.squeeze())).squeeze()
estp = np.squeeze(inner(dens_obj, ref_fvec))
estp2 = np.squeeze(
inner(dens_obj.unsigned_projection().normalized(), ref_fvec))
assert (np.abs(targp.squeeze() - estp).mean() < 0.8)
if plot:
pl.plot(ref_fvec.inspace_points.squeeze(),
estp / np.max(estp) * np.max(targp),
"b--",
label="scaled estimate")
pl.plot(ref_fvec.inspace_points.squeeze(),
estp2 / np.max(estp2) * np.max(targp),
"g-.",
label="scaled estimate (uns)")
pl.plot(ref_fvec.inspace_points.squeeze(), targp, label="truth")
#pl.plot(ref_fvec.inspace_points.squeeze(), np.squeeze(inner(unif_obj, ref_fvec)), label="unif")
pl.legend(loc="best")
pl.show()
assert (np.std(np.squeeze(inner(unif_obj.normalized(), out_fvec))) < 0.15)
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))