def test_sample():
# test sampling of two overlapping ellipsoids that samples are uniform
# within
rad = 1
shift = 0.75
ndim = 10
cen1 = np.zeros(ndim)
cen2 = np.zeros(ndim)
cen2[0] = shift
sig = np.eye(10) * rad**2
ells = [db.Ellipsoid(cen1, sig), db.Ellipsoid(cen2, sig)]
mu = db.MultiEllipsoid(ells)
R = []
nsim = 100000
rstate = get_rstate()
for i in range(nsim):
R.append(mu.sample(rstate=rstate)[0])
R = np.array(R)
assert (all([mu.contains(_) for _ in R]))
# here I'm checking that all the points are uniformly distributed
# within each ellipsoid
for curc in [cen1, cen2]:
dist1 = (np.sqrt(np.sum((R - curc)**2, axis=1)) / rad)
# radius from 0 to 1
xdist1 = dist1**ndim
# should be uniformly distributed from 0 to 1
xdist1 = xdist1[xdist1 < 1]
pval = scipy.stats.kstest(xdist1,
scipy.stats.uniform(loc=0.0, scale=1).cdf)[1]
assert ((pval > 0.003) & (pval < 0.997))
nhalf = (R[:, 0] > shift / 2.).sum()
print(nhalf, nsim)
assert (np.abs(nhalf - 0.5 * nsim) < 5 * np.sqrt(0.5 * nsim))
def test_overlap():
rstate = get_rstate()
ndim = 2
cen1 = np.array([0, 0])
cen2 = np.array([1, 0])
rad = 0.7
sig = np.eye(ndim) * rad**2
ell1 = db.Ellipsoid(cen1, sig)
ell2 = db.Ellipsoid(cen2, sig)
ell = db.MultiEllipsoid([ell1, ell2])
nsamp = 10000
xs = rstate.uniform(size=(nsamp, ndim))
ind1 = np.sum((xs - cen1[None, :])**2, axis=1) < rad**2
ind2 = np.sum((xs - cen2[None, :])**2, axis=1) < rad**2
for i in range(nsamp):
n1 = int(ind1[i])
n2 = int(ind2[i])
assert ell.overlap(xs[i]) == n1 + n2
assert ell.overlap(xs[i], j=0) == n2
within = ell.within(xs[i])
within2 = []
if n1 == 1:
within2.append(0)
if n2 == 1:
within2.append(1)
within2 = np.array(within2)
assert np.all(within == within2)
def test_mc_logvol():
def capvol(n, r, h):
# see https://en.wikipedia.org/wiki/Spherical_cap
Cn = np.pi**(n / 2.) / scipy.special.gamma(1 + n / 2.)
return (
Cn * r**n *
(1 / 2 - (r - h) / r * scipy.special.gamma(1 + n / 2) /
np.sqrt(np.pi) / scipy.special.gamma(
(n + 1.) / 2) * scipy.special.hyp2f1(1. / 2,
(1 - n) / 2, 3. / 2,
((r - h) / r)**2)))
def sphere_vol(n, r):
Cn = np.pi**(n / 2.) / scipy.special.gamma(1 + n / 2.) * r**n
return Cn
def two_sphere_vol(c1, c2, r1, r2):
D = np.sqrt(np.sum((c1 - c2)**2))
n = len(c1)
if D >= r1 + r2:
return sphere_vol(n, r1) + sphere_vol(n, r2)
# now either one is fully inside or the is overlap
if D + r1 <= r2 or D + r2 <= r1:
#fully inside
return max(sphere_vol(n, r1), sphere_vol(n, r2))
else:
x = 1. / 2 / D * np.sqrt(2 * r1**2 * r2**2 + 2 * D**2 * r1**2 +
2 * D**2 * r2**2 - r1**4 - r2**4 - D**4)
capsize1 = r1 - np.sqrt(r1**2 - x**2)
capsize2 = r2 - np.sqrt(r2**2 - x**2)
V = (sphere_vol(n, r1) + sphere_vol(n, r2) -
capvol(n, r1, capsize1) - capvol(n, r2, capsize2))
return V
rstate = get_rstate()
ndim = 10
cen1 = np.zeros(ndim)
cen2 = np.zeros(ndim)
r1 = 1
r2 = 0.5
sig1 = np.eye(ndim) * r1**2
sig2 = np.eye(ndim) * r2**2
Ds = np.linspace(0, 2, 30)
nsamp = 10000
for D in Ds:
cen2[0] = D
ell = db.MultiEllipsoid(
[db.Ellipsoid(cen1, sig1),
db.Ellipsoid(cen2, sig2)])
lv = ell.monte_carlo_logvol(nsamp, rstate=rstate)[0]
vtrue = two_sphere_vol(cen1, cen2, r1, r2)
assert (np.abs(np.log(vtrue) - lv) < 1e-2)
def test_samples_multi():
rstate = get_rstate()
ndim = 10
cen = np.zeros(ndim) + .5
sig = np.eye(ndim)
ell = db.MultiEllipsoid([db.Ellipsoid(cen, sig)])
nsamp = 10000
X = ell.samples(nsamp, rstate=rstate)
R = np.sqrt(((X - cen[None, :])**2).sum(axis=1))
xdist1 = R**ndim
pval = scipy.stats.kstest(xdist1,
scipy.stats.uniform(loc=0.0, scale=1).cdf)[1]
assert ((pval > 1e-3) and (pval < 1 - 1e-3))
def test_sample(withq, ndim):
# test sampling of two overlapping ellipsoids that samples are uniform
# within
rad = 1
shift = 0.75
cen1 = np.zeros(ndim)
cen2 = np.zeros(ndim)
cen2[0] = shift
sig = np.eye(ndim) * rad**2
ells = [db.Ellipsoid(cen1, sig), db.Ellipsoid(cen2, sig)]
mu = db.MultiEllipsoid(ells)
R = []
nsim = 100000
rstate = get_rstate()
if withq:
for i in range(nsim):
while True:
x, _, q = mu.sample(return_q=True, rstate=rstate)
if rstate.uniform() < 1. / q:
R.append(x)
break
else:
for i in range(nsim):
R.append(mu.sample(rstate=rstate)[0])
R = np.array(R)
assert (all([mu.contains(_) for _ in R]))
assert (all([ells[0].contains(_) or ells[1].contains(_) for _ in R]))
# here I'm checking that all the points are uniformly distributed
# within each ellipsoid
for curc in [cen1, cen2]:
dist1 = (np.sqrt(np.sum((R - curc)**2, axis=1)) / rad)
# radius from 0 to 1
xdist1 = dist1**ndim
# should be uniformly distributed from 0 to 1
xdist1 = xdist1[xdist1 < 1]
pval = scipy.stats.kstest(xdist1,
scipy.stats.uniform(loc=0.0, scale=1).cdf)[1]
assert ((pval > PVAL) & (pval < (1 - PVAL)))
nhalf = (R[:, 0] > shift / 2.).sum()
assert (np.abs(nhalf - 0.5 * nsim) < 5 * np.sqrt(0.5 * nsim))
def computer(fitpts, testpts, bound='multi', bootstrap=None, rstate=None):
""" Compute logvolume and fraction of points covered
given actual live points (fitpts) and test points (testpts)"""
# ndim = fitpts.shape[-1]
cent = fitpts.mean(axis=0)
cov = np.cov(fitpts.T) # ndim)
curb = db.Ellipsoid(cent, cov) # pts)
curb.update(fitpts, rstate=rstate, bootstrap=bootstrap)
if bound == 'multi':
curb = db.MultiEllipsoid([curb])
curb.update(fitpts, rstate=rstate, bootstrap=bootstrap)
if bound not in ['single', 'multi']:
raise RuntimeError('unknown bound', bound)
frac = np.array([curb.contains(_) for _ in testpts]).sum() / len(testpts)
if bound == 'single':
nell = 1
logvol = curb.logvol
else:
nell = len(curb.ells)
logvol = curb.logvol_tot
return logvol, frac, nell