def test_samplingpath_oddcase():
x0 = np.array([
0.19833663, 0.49931288, 0.62744967, 0.47308545, 0.48858042, 0.49025685,
0.48481497, 0.49068977, 0.49562456, 0.51102634
])
v0 = np.array([
-0.00053468, -0.00106889, 0.0012165, 0.00737494, 0.00152363,
-0.00164736, 0.00371493, 0.02057758, -0.00260349, 0.01266826
])
L0 = 0.
path = SamplingPath(x0, v0, L0)
for i in range(-10, 11):
if i != 0:
path.extrapolate(i)
def start_path(self, ui, region):
"""Start new trajectory path."""
# print("new direction:", self.scale, self.noutside_regions, self.nrejects, self.naccepts)
v = self.generate_direction(ui, region, scale=self.scale)
assert (v**2).sum() > 0, (v, self.scale)
assert region.inside(ui.reshape((1, -1))).all(), ui
self.path = ContourSamplingPath(SamplingPath(ui, v, 0.0), region)
if self.grad_function is not None:
self.path.gradient = self.grad_function
if not (ui > 0).all() or not (ui < 1).all() or not region.inside(ui.reshape((1, -1))):
assert False, ui
self.direction = +1
self.lasti = 0
self.cache = {0: (True, ui, self.last[1])}
self.deadends = set()
# self.iresets += 1
if self.log:
print()
print("starting new direction", v, 'from', ui)
def start_direction(self, region):
"""Choose a new random direction."""
if self.log:
print("choosing random direction")
ui, Li = self.last
v = generate_random_direction(ui, region, scale=self.scale)
# v = generate_region_random_direction(ui, region, scale=self.scale)
self.nrestarts += 1
if self.sampler is None or True:
samplingpath = SamplingPath(ui, v, Li)
contourpath = ContourSamplingPath(samplingpath, region)
if self.samplername == 'steps':
self.sampler = ClockedStepSampler(contourpath, log=self.log)
self.stepper = DirectJumper(self.sampler, self.nsteps, log=self.log)
elif self.samplername == 'bisect':
self.sampler = ClockedBisectSampler(contourpath, log=self.log)
self.stepper = DirectJumper(self.sampler, self.nsteps, log=self.log)
elif self.samplername == 'nuts':
self.sampler = ClockedNUTSSampler(contourpath, log=self.log)
self.stepper = IntervalJumper(self.sampler, self.nsteps, log=self.log)
else:
assert False
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_samplingpath_cubereflect():
x0 = np.array([0.1, 0.1])
v0 = np.array([0.1, 0.01])
L0 = 0.
path = SamplingPath(x0, v0, L0)
path.add(-1, x0 - v0, v0, 1.0)
def test_samplingpath():
x0 = np.array([0.5, 0.5])
v0 = np.array([0.1, 0.0])
L0 = 0.
path = SamplingPath(x0, v0, L0)
assert path.interpolate(0) == (x0, v0, L0, True)
try:
path.interpolate(1)
assert False
except KeyError:
pass
try:
path.interpolate(-1)
assert False
except KeyError:
pass
path.add(-1, x0 - v0, v0, 1.0)
x1, v1, L1, on_path = path.interpolate(-1)
assert_allclose(x1, x0 - v0)
assert_allclose(v1, v0)
assert_allclose(L1, 1.0)
assert on_path
path.add(4, x0 + 4 * v0, v0, 4.0)
x1, v1, L1, on_path = path.interpolate(1)
assert_allclose(x1, x0 + v0)
assert_allclose(v1, v0)
assert L1 is None, L1
assert on_path
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 test_directjumper():
Lmin = -1.0
us = 0.5 + np.zeros((100, 2))
#Ls = np.zeros(100)
region = make_region(2)
def transform(x):
return x
def loglike(x):
return 0.0
def gradient(x, plot=False):
j = np.argmax(np.abs(x - 0.5))
v = np.zeros(len(x))
v[j] = -1 if x[j] > 0.5 else 1
return v
def nocall(x):
assert False
ui = us[np.random.randint(len(us)), :]
v = np.array([0.01, 0.01])
path = ContourSamplingPath(SamplingPath(ui, v, 0.0), region)
path.gradient = nocall
sampler = ClockedBisectSampler(path)
stepper = DirectJumper(sampler, 4)
assert (stepper.naccepts, stepper.nrejects) == (0, 0), (stepper.naccepts,
stepper.nrejects)
assert stepper.isteps == 0, stepper.isteps
x, L = makejump(stepper, sampler, transform, loglike, Lmin)
assert_allclose(x, [0.54, 0.54])
assert (stepper.naccepts, stepper.nrejects) == (4, 0), (stepper.naccepts,
stepper.nrejects)
assert stepper.isteps == 4, stepper.isteps
print()
print("make reflect")
print()
def loglike(x):
return 0.0 if x[0] < 0.505 else -100
path = ContourSamplingPath(SamplingPath(ui, v, 0.0), region)
path.gradient = gradient
sampler = ClockedBisectSampler(path)
stepper = DirectJumper(sampler, 4)
assert (stepper.naccepts, stepper.nrejects) == (0, 0), (stepper.naccepts,
stepper.nrejects)
assert stepper.isteps == 0, stepper.isteps
x, L = makejump(stepper, sampler, transform, loglike, Lmin)
assert_allclose(x, [0.47, 0.55])
assert (stepper.naccepts, stepper.nrejects) == (4, 0), (stepper.naccepts,
stepper.nrejects)
assert stepper.isteps == 4, stepper.isteps
print()
print("make stuck")
print()
# make stuck
def loglike(x):
return -100
path = ContourSamplingPath(SamplingPath(ui, v, 0.0), region)
path.gradient = gradient
sampler = ClockedBisectSampler(path)
stepper = DirectJumper(sampler, 4)
assert (stepper.naccepts, stepper.nrejects) == (0, 0), (stepper.naccepts,
stepper.nrejects)
assert stepper.isteps == 0, stepper.isteps
x, L = makejump(stepper, sampler, transform, loglike, Lmin)
assert_allclose(x, [0.50, 0.50])
assert (stepper.naccepts, stepper.nrejects) == (0, 4), (stepper.naccepts,
stepper.nrejects)
assert stepper.isteps == 4, stepper.isteps
def move(self, ui, region, ndraw=1, plot=False):
"""Advance by slice sampling on the path."""
if self.interval is None:
v = self.generate_direction(ui, region, scale=self.scale)
self.path = ContourSamplingPath(
SamplingPath(ui, v, 0.0), region)
if not (ui > 0).all() or not (ui < 1).all() or not region.inside(ui.reshape((1, -1))):
assert False, ui
# unit hypercube diagonal gives a reasonable maximum path length
maxlength = len(ui)**0.5
# expand direction until it is surely outside
left = -1
right = +1
while abs(left * self.scale) < maxlength:
xj, vj = self.path.extrapolate(left)
if not (xj > 0).all() or not (xj < 1).all() or not region.inside(xj.reshape((1, -1))):
break
# self.path.add(left, xj, vj, 0.0)
left *= 2
while abs(right * self.scale) < maxlength:
xj, _ = self.path.extrapolate(right)
if not (xj > 0).all() or not (xj < 1).all() or not region.inside(xj.reshape((1, -1))):
break
# self.path.add(right, xj, vj, 0.0)
right *= 2
scale = max(-left, right)
# print("scale %f gave %d %d " % (self.scale, left, right))
if scale < 5:
self.scale /= 1.1
# if scale > 100:
# self.scale *= 1.1
assert self.scale > 1e-10, self.scale
self.interval = (left, right, None)
else:
left, right, mid = self.interval
# we rejected mid, and shrink corresponding side
if mid < 0:
left = mid
elif mid > 0:
right = mid
# shrink direction if outside
while True:
mid = np.random.randint(left, right + 1)
# print("interpolating %d - %d - %d" % (left, mid, right),
# self.path.points)
if mid == 0:
_, xj, _, _ = self.path.points[0]
else:
xj, _ = self.path.extrapolate(mid)
if region.inside(xj.reshape((1, -1))):
self.interval = (left, right, mid)
return xj.reshape((1, -1))
else:
if mid < 0:
left = mid
else:
right = mid
self.interval = (left, right, mid)