def test_region_mean_distances():
np.random.seed(1)
points = np.random.uniform(0.4, 0.6, size=(10000, 2))
#points[:,1] *= 0.5
mask = np.abs((points[:, 0] - 0.5)**2 +
(points[:, 1] - 0.5)**2 - 0.08**2) < 0.02**2
print('circle:', mask.sum())
points = points[mask]
mask = points[:, 0] < 0.5
print('half-circle:', mask.sum())
points = points[mask]
transformLayer = AffineLayer(wrapped_dims=[])
transformLayer.optimize(points, points)
region = MLFriends(points, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
print("enlargement factor:", region.enlarge, 1 / region.enlarge)
region.create_ellipsoid()
meandist = region.compute_mean_pair_distance()
t = transformLayer.transform(region.u)
d = 0
N = 0
for i in range(len(t)):
for j in range(i):
d += ((t[i, :] - t[j, :])**2).sum()**0.5
#print(i, j, t[i,:], t[j,:], ((t[i,:] - t[j,:])**2).sum())
N += 1
print((meandist, d, N, t))
assert np.isclose(meandist, d / N), (meandist, d, N)
def prepare_problem(problemname, ndim, nlive, sampler):
loglike, grad, volume, warmup = get_problem(problemname, ndim=ndim)
if hasattr(sampler, 'set_gradient'):
sampler.set_gradient(grad)
np.random.seed(1)
us = np.random.uniform(size=(nlive, ndim))
if ndim > 1:
transformLayer = AffineLayer()
else:
transformLayer = ScalingLayer()
transformLayer.optimize(us, us)
region = MLFriends(us, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid(minvol=1.0)
Ls = np.array([loglike(u) for u in us])
ncalls = 0
nok = 0
i = 0
while True:
if i % int(nlive * 0.2) == 0:
minvol = (1 - 1. / nlive)**i
nextTransformLayer = transformLayer.create_new(us,
region.maxradiussq,
minvol=minvol)
nextregion = MLFriends(us, nextTransformLayer)
nextregion.maxradiussq, nextregion.enlarge = nextregion.compute_enlargement(
nbootstraps=30)
if nextregion.estimate_volume() <= region.estimate_volume():
region = nextregion
transformLayer = region.transformLayer
region.create_ellipsoid(minvol=minvol)
# replace lowest likelihood point
j = np.argmin(Ls)
Lmin = float(Ls[j])
while True:
u, v, logl, nc = sampler.__next__(region, Lmin, us, Ls, transform,
loglike)
ncalls += nc
if logl is not None:
break
us[j, :] = u
region.u[j, :] = u
region.unormed[j, :] = region.transformLayer.transform(u)
Ls[j] = logl
i = i + 1
#print(i, Lmin, volume(Lmin, ndim))
if np.isfinite(volume(Lmin, ndim)):
nok += 1
if nok > 2 * nlive + 1000:
break
return region, i, Lmin, us, Ls, transform, loglike
def test_affine_transform(plot=False):
np.random.seed(1)
corrs = [0, 0.6, 0.95, 0.999]
for corr in corrs:
for scaleratio in [1]: #, 0.001]:
covmatrix = np.array([[1., corr], [corr, 1.]])
# should draw uniformly sampled points
points = genpoints_following_cov(covmatrix, size=400)
print('settings: corr:', corr, 'scaleratio:', scaleratio,
'covmatrix:', covmatrix.flatten(), points.shape)
points[:, 0] = points[:, 0] * 0.01 * scaleratio + 0.5
points[:, 1] = points[:, 1] * 0.01 + 0.5
layer = AffineLayer()
layer.optimize(points, points)
points3 = layer.untransform(
genpoints_following_cov(np.diag([1, 1]), size=400))
#print('cov:', layer.cov, 'covmatrix:', covmatrix, 'ratio:', layer.cov / covmatrix)
tpoints = layer.transform(points)
assert tpoints.shape == points.shape, (tpoints.shape, points.shape)
points2 = layer.untransform(tpoints)
assert tpoints.shape == points2.shape, (tpoints.shape,
points2.shape)
if plot and scaleratio == 1:
plt.figure(figsize=(9, 4))
plt.subplot(1, 2, 1)
plt.scatter(points[:, 0], points[:, 1])
plt.scatter(points2[:, 0], points2[:, 1], marker='x')
plt.scatter(points3[:, 0], points3[:, 1], marker='+')
plt.subplot(1, 2, 2)
plt.scatter(tpoints[:, 0], tpoints[:, 1])
lo, hi = plt.xlim()
lo2, hi2 = plt.ylim()
lo, hi = min(lo, lo2), max(hi, hi2)
plt.xlim(lo, hi)
plt.ylim(lo, hi)
plt.savefig("testtransform_affine_corr%s_scale%s.pdf" %
(corr, scaleratio),
bbox_inches='tight')
plt.close()
assert (points2 == points).all(), (points, tpoints, points2)
# transform a single point
points = points[0]
tpoints = layer.transform(points)
assert tpoints.shape == points.shape, (tpoints.shape, points.shape)
points2 = layer.untransform(tpoints)
assert tpoints.shape == points2.shape, (tpoints.shape,
points2.shape)
assert (points2 == points).all(), (points, tpoints, points2)
def make_region(ndim):
us = np.random.uniform(size=(1000, ndim))
if ndim > 1:
transformLayer = AffineLayer()
else:
transformLayer = ScalingLayer()
transformLayer.optimize(us, us)
region = MLFriends(us, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid(minvol=1.0)
return region
def test_ellipsoids():
tpoints = np.random.uniform(0.4, 0.6, size=(1000, 1))
tregion = WrappingEllipsoid(tpoints)
print(tregion.variable_dims)
tregion.enlarge = tregion.compute_enlargement(nbootstraps=30)
tregion.create_ellipsoid()
for umax in 0.6, 0.5:
print()
print(umax)
points = np.random.uniform(0.4, 0.6, size=(1000, 3))
points = points[points[:, 0] < umax]
tpoints = points * 10
tpoints[:, 0] = np.floor(tpoints[:, 0])
print(points, tpoints)
transformLayer = AffineLayer(wrapped_dims=[])
transformLayer.optimize(points, points)
region = MLFriends(points, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid()
inside = region.inside(points)
assert inside.shape == (len(points), ), (inside.shape, points.shape)
assert inside.all()
region = RobustEllipsoidRegion(points, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid()
inside = region.inside(points)
assert inside.shape == (len(points), ), (inside.shape, points.shape)
assert inside.all()
region = SimpleRegion(points, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid()
inside = region.inside(points)
assert inside.shape == (len(points), ), (inside.shape, points.shape)
assert inside.all()
tregion = WrappingEllipsoid(tpoints)
print(tregion.variable_dims)
tregion.enlarge = tregion.compute_enlargement(nbootstraps=30)
tregion.create_ellipsoid()
inside = tregion.inside(tpoints)
assert inside.shape == (len(tpoints), ), (inside.shape, tpoints.shape)
assert inside.all()
def test_region_sampling_affine(plot=False):
np.random.seed(1)
upoints = np.random.uniform(size=(1000, 2))
upoints[:, 1] *= 0.5
transformLayer = AffineLayer(wrapped_dims=[])
transformLayer.optimize(upoints, upoints)
region = MLFriends(upoints, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
print("enlargement factor:", region.enlarge, 1 / region.enlarge)
region.create_ellipsoid()
nclusters = transformLayer.nclusters
assert nclusters == 1
assert np.allclose(region.unormed, region.transformLayer.transform(
upoints)), "transform should be reproducible"
assert region.inside(
upoints).all(), "live points should lie near live points"
if plot:
plt.plot(upoints[:, 0], upoints[:, 1], 'x ')
for method in region.sampling_methods:
points, nc = method(nsamples=400)
plt.plot(points[:, 0],
points[:, 1],
'o ',
label=str(method.__name__))
plt.legend(loc='best')
plt.savefig('test_regionsampling_affine.pdf', bbox_inches='tight')
plt.close()
for method in region.sampling_methods:
print("sampling_method:", method)
newpoints = method(nsamples=4000)
lo1, lo2 = newpoints.min(axis=0)
hi1, hi2 = newpoints.max(axis=0)
assert 0 <= lo1 < 0.1, (method.__name__, newpoints, lo1, hi1, lo2, hi2)
assert 0 <= lo2 < 0.1, (method.__name__, newpoints, lo1, hi1, lo2, hi2)
assert 0.95 < hi1 <= 1, (method.__name__, newpoints, lo1, hi1, lo2,
hi2)
assert 0.45 <= hi2 < 0.55, (method.__name__, newpoints, lo1, hi1, lo2,
hi2)
assert region.inside(newpoints).all()
region.maxradiussq = 1e-90
assert np.allclose(region.unormed, region.transformLayer.transform(
upoints)), "transform should be reproducible"
assert region.inside(
upoints).all(), "live points should lie very near themselves"
def test_region_ellipsoid(plot=False):
np.random.seed(1)
points = np.random.uniform(0.4, 0.6, size=(1000, 2))
points[:, 1] *= 0.5
transformLayer = AffineLayer(wrapped_dims=[])
transformLayer.optimize(points, points)
region = MLFriends(points, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
print("enlargement factor:", region.enlarge, 1 / region.enlarge)
region.create_ellipsoid()
nclusters = transformLayer.nclusters
assert nclusters == 1
bpts = np.random.uniform(size=(100, 2))
mask = region.inside_ellipsoid(bpts)
d = (bpts - region.ellipsoid_center)
mask2 = np.einsum('ij,jk,ik->i', d, region.ellipsoid_invcov,
d) <= region.enlarge
assert_allclose(mask, mask2)
def test_reversible_gradient(plot=False):
def loglike(x):
x, y = x.transpose()
return -0.5 * (x**2 + ((y - 0.5) / 0.2)**2)
def transform(u):
return u
Lmin = -0.5
for i in [84] + list(range(1, 100)):
print("setting seed = %d" % i)
np.random.seed(i)
points = np.random.uniform(size=(10000, 2))
L = loglike(points)
mask = L > Lmin
points = points[mask, :][:100, :]
active_u = points
active_values = L[mask][:100]
transformLayer = AffineLayer(wrapped_dims=[])
transformLayer.optimize(points, points)
region = MLFriends(points, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid()
nclusters = transformLayer.nclusters
assert nclusters == 1
assert np.allclose(region.unormed,
region.transformLayer.transform(
points)), "transform should be reproducible"
assert region.inside(
points).all(), "live points should lie near live points"
if i == 84:
v = np.array([0.03477044, -0.01977415])
reflpoint = np.array([0.09304075, 0.29114574])
elif i == 4:
v = np.array([0.03949306, -0.00634806])
reflpoint = np.array([0.9934771, 0.55358031])
else:
v = np.random.normal(size=2)
v /= (v**2).sum()**0.5
v *= 0.04
j = np.random.randint(len(active_u))
reflpoint = np.random.normal(active_u[j, :], 0.04)
if not (reflpoint < 1).all() and not (reflpoint > 0).all():
continue
bpts = region.transformLayer.transform(reflpoint).reshape((1, -1))
tt = get_sphere_tangents(region.unormed, bpts)
t = region.transformLayer.untransform(tt * 1e-3 +
region.unormed) - region.u
# compute new vector
normal = t / norm(t, axis=1).reshape((-1, 1))
print("reflecting at ", reflpoint, "with direction", v)
mask_forward1, angles, anglesnew = get_reflection_angles(normal, v)
if mask_forward1.any():
j = np.argmin(
((region.unormed[mask_forward1, :] - bpts)**2).sum(axis=1))
k = np.arange(len(normal))[mask_forward1][j]
angles_used = angles[k]
normal_used = normal[k, :]
print("chose normal", normal_used, k)
#chosen_point = region.u[k,:]
vnew = -(v - 2 * angles_used * normal_used)
assert vnew.shape == v.shape
mask_forward2, angles2, anglesnew2 = get_reflection_angles(
normal, vnew)
#j2 = np.argmin(((region.unormed[mask_forward2,:] - bpts)**2).sum(axis=1))
#chosen_point2 = region.u[mask_forward2,:][0,:]
#assert j2 == j, (j2, j)
assert mask_forward2[k]
#assert_allclose(chosen_point, chosen_point2)
#for m, a, b, m2, a2, b2 in zip(mask_forward1, angles, anglesnew, mask_forward2, angles2, anglesnew2):
# if m != m2:
# print(' ', m, a, b, m2, a2, b2)
#print("using normal", normal)
#print("changed v from", v, "to", vnew)
#angles2 = -(normal * (vnew / norm(vnew))).sum(axis=1)
#mask_forward2 = angles < 0
if plot:
plt.figure(figsize=(5, 5))
plt.title('%d' % mask_forward1.sum())
plt.plot((reflpoint + v)[0], (reflpoint + v)[1],
'^',
color='orange')
plt.plot((reflpoint + vnew)[:, 0], (reflpoint + vnew)[:, 1],
'^ ',
color='lime')
plt.plot(reflpoint[0], reflpoint[1], '^ ', color='r')
plt.plot(region.u[:, 0], region.u[:, 1], 'x ', ms=2, color='k')
plt.plot(region.u[mask_forward1, 0],
region.u[mask_forward1, 1],
'o ',
ms=6,
mfc='None',
mec='b')
plt.plot(region.u[mask_forward2, 0],
region.u[mask_forward2, 1],
's ',
ms=8,
mfc='None',
mec='g')
plt.xlim(0, 1)
plt.ylim(0, 1)
plt.savefig('test_flatnuts_reversible_gradient_%d.png' % i,
bbox_inches='tight')
plt.close()
assert mask_forward1[k] == mask_forward2[k], (mask_forward1[k],
mask_forward2[k])
print("reflecting at ", reflpoint, "with direction", v)
# make that step, then try to go back
j = np.arange(len(normal))[mask_forward1][0]
normal = normal[j, :]
angles = (normal * (v / norm(v))).sum()
v2 = v - 2 * angle(normal, v) * normal
print("reflecting with", normal, "new direction", v2)
#newpoint = reflpoint + v2
#angles2 = (normal * (v2 / norm(v2))).sum()
v3 = v2 - 2 * angle(normal, v2) * normal
print("re-reflecting gives direction", v3)
assert_allclose(v3, v)
print()
print("FORWARD:", v, reflpoint)
samplingpath = SamplingPath(reflpoint - v, v, active_values[0])
contourpath = ContourSamplingPath(samplingpath, region)
normal = contourpath.gradient(reflpoint)
if normal is not None:
assert normal.shape == v.shape, (normal.shape, v.shape)
print("BACKWARD:", v, reflpoint)
v2 = -(v - 2 * angle(normal, v) * normal)
normal2 = contourpath.gradient(reflpoint)
assert_allclose(normal, normal2)
normal2 = normal
v3 = -(v2 - 2 * angle(normal2, v2) * normal2)
assert_allclose(v3, v)
def test_detailed_balance():
def loglike(x):
x, y = x.transpose()
return -0.5 * (x**2 + ((y - 0.5) / 0.2)**2)
def transform(u):
return u
Lmin = -0.5
for i in range(1, 100):
print()
print("---- seed=%d ----" % i)
print()
np.random.seed(i)
points = np.random.uniform(size=(10000, 2))
L = loglike(points)
mask = L > Lmin
points = points[mask, :][:400, :]
active_u = points
active_values = L[mask][:400]
transformLayer = AffineLayer(wrapped_dims=[])
transformLayer.optimize(points, points)
region = MLFriends(points, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid()
nclusters = transformLayer.nclusters
assert nclusters == 1
assert np.allclose(region.unormed,
region.transformLayer.transform(
points)), "transform should be reproducible"
assert region.inside(
points).all(), "live points should lie near live points"
v = np.random.normal(size=2)
v /= (v**2).sum()**0.5
v *= 0.04
print("StepSampler ----")
print("FORWARD SAMPLING FROM", 0, active_u[0], v, active_values[0])
samplingpath = SamplingPath(active_u[0], v, active_values[0])
problem = dict(loglike=loglike, transform=transform, Lmin=Lmin)
sampler = ClockedStepSampler(ContourSamplingPath(samplingpath, region))
check_starting_point(sampler, active_u[0], active_values[0], **problem)
sampler.expand_onestep(fwd=True, **problem)
sampler.expand_onestep(fwd=True, **problem)
sampler.expand_onestep(fwd=True, **problem)
sampler.expand_onestep(fwd=True, **problem)
sampler.expand_onestep(fwd=False, **problem)
sampler.expand_to_step(4, **problem)
sampler.expand_to_step(-4, **problem)
check_starting_point(sampler, active_u[0], active_values[0], **problem)
starti, startx, startv, startL = max(sampler.points)
print()
print("BACKWARD SAMPLING FROM", starti, startx, startv, startL)
samplingpath2 = SamplingPath(startx, -startv, startL)
sampler2 = ClockedStepSampler(
ContourSamplingPath(samplingpath2, region))
check_starting_point(sampler2, startx, startL, **problem)
sampler2.expand_to_step(starti, **problem)
check_starting_point(sampler2, startx, startL, **problem)
starti2, startx2, startv2, startL2 = max(sampler2.points)
assert_allclose(active_u[0], startx2)
assert_allclose(v, -startv2)
starti, startx, startv, startL = min(sampler.points)
print()
print("BACKWARD SAMPLING FROM", starti, startx, startv, startL)
samplingpath3 = SamplingPath(startx, startv, startL)
sampler3 = ClockedStepSampler(
ContourSamplingPath(samplingpath3, region))
check_starting_point(sampler3, startx, startL, **problem)
sampler3.expand_to_step(-starti, **problem)
check_starting_point(sampler3, startx, startL, **problem)
starti3, startx3, startv3, startL3 = max(sampler3.points)
assert_allclose(active_u[0], startx3)
assert_allclose(v, startv3)
print()
print("BisectSampler ----")
log = dict(log=True)
print("FORWARD SAMPLING FROM", 0, active_u[0], v, active_values[0])
samplingpath = SamplingPath(active_u[0], v, active_values[0])
sampler = ClockedBisectSampler(
ContourSamplingPath(samplingpath, region), **log)
check_starting_point(sampler, active_u[0], active_values[0], **problem)
sampler.expand_to_step(10, **problem)
check_starting_point(sampler, active_u[0], active_values[0], **problem)
starti, startx, startv, startL = max(sampler.points)
print()
print("BACKWARD SAMPLING FROM", starti, startx, startv, startL)
samplingpath2 = SamplingPath(startx, -startv, startL)
sampler2 = ClockedBisectSampler(
ContourSamplingPath(samplingpath2, region), **log)
check_starting_point(sampler2, startx, startL, **problem)
sampler2.expand_to_step(starti, **problem)
check_starting_point(sampler2, startx, startL, **problem)
starti2, startx2, startv2, startL2 = max(sampler2.points)
if gap_free_path(sampler, 0, starti, **problem) and gap_free_path(
sampler2, 0, starti2, **problem):
assert_allclose(active_u[0], startx2)
assert_allclose(v, -startv2)
starti, startx, startv, startL = min(sampler.points)
print()
print("BACKWARD SAMPLING FROM", starti, startx, startv, startL)
samplingpath3 = SamplingPath(startx, -startv, startL)
sampler3 = ClockedBisectSampler(
ContourSamplingPath(samplingpath3, region), **log)
check_starting_point(sampler3, startx, startL, **problem)
sampler3.expand_to_step(starti, **problem)
check_starting_point(sampler3, startx, startL, **problem)
starti3, startx3, startv3, startL3 = min(sampler3.points)
if gap_free_path(sampler, 0, starti, **problem) and gap_free_path(
sampler3, 0, starti3, **problem):
assert_allclose(active_u[0], startx3)
assert_allclose(v, -startv3)
print()
print("NUTSSampler ----")
print("FORWARD SAMPLING FROM", 0, active_u[0], v, active_values[0])
samplingpath = SamplingPath(active_u[0], v, active_values[0])
np.random.seed(i)
sampler = ClockedNUTSSampler(ContourSamplingPath(samplingpath, region))
sampler.get_independent_sample(**problem)
def evaluate_warmed_sampler(problemname,
ndim,
nlive,
nsteps,
sampler,
seed=1,
region_class=RobustEllipsoidRegion):
loglike, grad, volume, warmup = get_problem(problemname, ndim=ndim)
if hasattr(sampler, 'set_gradient'):
sampler.set_gradient(grad)
np.random.seed(seed)
def multi_loglike(xs):
return np.asarray([loglike(x) for x in xs])
us = np.array([warmup(ndim) for i in range(nlive)])
Ls = np.array([loglike(u) for u in us])
vol0 = volume(Ls.min(), ndim)
nwarmup = 3 * nlive
if ndim > 1:
transformLayer = AffineLayer()
else:
transformLayer = ScalingLayer()
transformLayer.optimize(us, us)
region = region_class(us, transformLayer)
region.maxradiussq, region.enlarge = region.compute_enlargement(
nbootstraps=30)
region.create_ellipsoid(minvol=vol0)
assert region.ellipsoid_center is not None
sampler.region_changed(Ls, region)
Lsequence = []
stepsequence = []
ncalls = 0
for i in tqdm.trange(nsteps + nwarmup):
if i % int(nlive * 0.2) == 0:
minvol = (1 - 1. / nlive)**i * vol0
with warnings.catch_warnings(), np.errstate(all='raise'):
try:
nextTransformLayer = transformLayer.create_new(
us, region.maxradiussq, minvol=minvol)
nextregion = region_class(us, nextTransformLayer)
nextregion.maxradiussq, nextregion.enlarge = nextregion.compute_enlargement(
nbootstraps=30)
if isinstance(nextregion, RobustEllipsoidRegion
) or nextregion.estimate_volume(
) <= region.estimate_volume():
nextregion.create_ellipsoid(minvol=minvol)
region = nextregion
transformLayer = region.transformLayer
assert region.ellipsoid_center is not None
sampler.region_changed(Ls, region)
except Warning as w:
print("not updating region because: %s" % w)
except FloatingPointError as e:
print("not updating region because: %s" % e)
except np.linalg.LinAlgError as e:
print("not updating region because: %s" % e)
# replace lowest likelihood point
j = np.argmin(Ls)
Lmin = float(Ls[j])
while True:
u, v, logl, nc = sampler.__next__(region, Lmin, us, Ls, transform,
multi_loglike)
if i > nwarmup:
ncalls += nc
if logl is not None:
assert np.isfinite(u).all(), u
assert np.isfinite(v).all(), v
assert np.isfinite(logl), logl
break
if i > nwarmup:
Lsequence.append(Lmin)
stepsequence.append(quantify_step(us[sampler.starti, :], u))
us[j, :] = u
Ls[j] = logl
Lsequence = np.asarray(Lsequence)
return Lsequence, ncalls, np.array(stepsequence)