def test_CovOp(plot = False, center = 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), center = center)
out_meanemb = out_fvec.sum()
x = np.linspace(-2.5, 15, samps_unif)[:, np.newaxis].astype(float)
ref_fvec = FiniteVec(gk_x, x, np.ones(len(x)), center = center)
ref_elem = ref_fvec.sum()
C_ref = CovOp(ref_fvec, regul=0., center = center) # CovOp_compl(out_fvec.k, out_fvec.inspace_points, regul=0.)
inv_Gram_ref = np.linalg.inv(inner(ref_fvec))
C_samps = CovOp(out_fvec, regul=regul_C_ref, center = center)
unif_obj = C_samps.solve(out_meanemb).dens_proj()
C_ref = CovOp(ref_fvec, regul=regul_C_ref, center = center)
dens_obj = C_ref.solve(out_meanemb).dens_proj()
targp = np.exp(targ.logpdf(ref_fvec.insp_pts.squeeze())).squeeze()
estp = np.squeeze(inner(dens_obj, ref_fvec))
estp2 = np.squeeze(inner(dens_obj, ref_fvec))
est_sup = unif_obj(x).squeeze()
assert (np.abs(targp.squeeze()-estp).mean() < 0.8), "Estimated density strongly deviates from true density"
if plot:
pl.plot(ref_fvec.insp_pts.squeeze(), estp/np.max(estp) * np.max(targp), "b--", label="scaled estimate")
pl.plot(ref_fvec.insp_pts.squeeze(), estp2/np.max(estp2) * np.max(targp), "g-.", label="scaled estimate (uns)")
pl.plot(ref_fvec.insp_pts.squeeze(), targp, label = "truth")
pl.plot(x.squeeze(), est_sup.squeeze(), label = "support")
#pl.plot(ref_fvec.inspace_points.squeeze(), np.squeeze(inner(unif_obj, ref_fvec)), label="unif")
pl.legend(loc="best")
pl.show()
supp = unif_obj(x).squeeze()
assert (np.std(supp) < 0.15), "Estimated support has high variance, in data points, while it should be almost constant."
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)
