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_rollout(self, variant):
peep = 0
pip = 1
use_noise = False
loss_fn = lambda x, y: (jnp.abs(x - y)).mean()
loss = jnp.array(0.)
duration = 0.87
dt = 0.03
tt = jnp.linspace(0, duration, int(duration / dt))
variant_rollout = variant(rollout, static_argnums=(6,))
value, _ = jax.value_and_grad(variant_rollout)(self.controller, self.sim,
tt, use_noise, peep, pip,
loss_fn, loss)
print('test_rollout loss:' + str(value))
self.assertTrue(jnp.allclose(float(value), 11.748882))
def test_jvp_jit(self):
f_dex = primitive(
dex.eval(r'\x:((Fin 10) => Float) y:((Fin 10) => Float). '
'for i. x.i * x.i + 2.0 * y.i'))
def f_jax(x, y):
return x**2 + 2 * y
x = jnp.arange(10.)
y = jnp.linspace(-0.2, 0.5, num=10)
u = jnp.linspace(0.1, 0.3, num=10)
v = jnp.linspace(2.0, -5.0, num=10)
def jvp_dex(args, tangents):
return jax.jvp(f_dex, args, tangents)
def jvp_jax(args, tangents):
return jax.jvp(f_jax, args, tangents)
output_dex, tangent_dex = jax.jit(jvp_dex)((x, y), (u, v))
output_jax, tangent_jax = jax.jit(jvp_jax)((x, y), (u, v))
np.testing.assert_allclose(output_dex, output_jax)
np.testing.assert_allclose(tangent_dex, tangent_jax)
def test_float_weights_should_give_close_output(self, weight_prec):
inputs = random.uniform(self.rng_key, shape=(2, 3))
model, state = self.init_model_with_1_layer(
inputs, num_features=4, weight_prec=weight_prec)
float_weights = jnp.linspace(-1 / 3, 1 / 3, num=12).reshape((3, 4))
exp_output_without_quant = jnp.matmul(inputs, float_weights)
state = state.unfreeze()
state['params']['kernel'] = float_weights
state = flax.core.freeze(state)
outputs_with_quant = model.apply(state, inputs, padding_mask=None)
onp.testing.assert_raises(AssertionError, onp.testing.assert_array_equal,
outputs_with_quant, exp_output_without_quant)
test_utils.assert_all_close_prec(exp_output_without_quant,
outputs_with_quant, weight_prec)
def test_non_conjugate_rv(n):
key = jr.PRNGKey(123)
f = posterior = Prior(kernel=RBF()) * Bernoulli()
x = jnp.sort(jr.uniform(key, shape=(n, 1), minval=-1.0, maxval=1.0), axis=0)
y = 0.5 * jnp.sign(jnp.cos(3 * x + jr.normal(key, shape=x.shape) * 0.05)) + 0.5
D = Dataset(X=x, y=y)
sample_points = jnp.linspace(-1.0, 1.0, num=n).reshape(-1, 1)
hyperparams = {"lengthscale": jnp.array([1.0]), "variance": jnp.array([1.0])}
params = complete(hyperparams, posterior, x.shape[0])
rv = random_variable(f, params, D)
assert isinstance(rv, Callable)
fstar = rv(sample_points)
assert isinstance(fstar, tfd.ProbitBernoulli)
def generate_dataset(n_i, n_b, n_cx, n_ct): x_i = jnp.linspace(*domain[:, 0], n_i).reshape((-1, 1)) t_i = jnp.zeros_like(x_i) u_i = u0_fn(x_i, t_i) v_i = v0_fn(x_i, t_i) x_l = jnp.ones((n_b, 1))*domain[0, 0] x_r = jnp.ones((n_b, 1))*domain[1, 0] t_b = jnp.linspace(*domain[:, 1], n_b).reshape((-1, 1)) u_l = ul_fn(x_l, t_b) u_r = ur_fn(x_r, t_b) v_l = vl_fn(x_l, t_b) v_r = vr_fn(x_r, t_b) x_c = jnp.linspace(*domain[:, 0], n_cx).reshape((-1, 1)) t_c = jnp.linspace(*domain[:, 1], n_ct).reshape((-1, 1)) xt_c = tensor_grid([x_c, t_c]) dirichlet = dataset_Dirichlet(jnp.vstack([x_i, x_l, x_r]), jnp.vstack([t_i, t_b, t_b]), jnp.vstack([u_i, u_l, u_r]), jnp.vstack([v_i, v_l, v_r])) collocation = dataset_Collocation(xt_c[:, 0:1], xt_c[:, 1:2]) return dirichlet, collocation
def plot_vi_gp(obj, mu, Sigma, X, y):
gp = GaussianProcess(GaussianLinearKernel(0., 0., 0., 0., 0., 0.), X, y)
xlim, = obj.boundaries
x_gt = np.linspace(xlim[0], xlim[1], 100)
xx = np.linspace(xlim[0] - 2, xlim[1] + 2, 200)
plt.plot(x_gt, obj.evaluate_without_noise(x_gt), c='c')
plt.title(f"Gaussian Process Regression")
mu = mu.flatten()
for _ in range(500):
sample_gp_parameter = onp.random.multivariate_normal(mu, Sigma)
gp.set_kernel_parameters(*sample_gp_parameter)
function_sample = gp.get_sample(xx.reshape((-1, 1)))
plt.plot(xx, function_sample, alpha=0.3, c='C0')
plt.scatter(gp.array_dataset,
gp.array_objective_function_values,
c='m',
marker="+",
zorder=1000,
s=(30, ))
plt.pause(0.01)
plt.show()
def meshgrid(height, width, is_homogeneous=True):
"""Construct a 2D meshgrid.
Args:
height: height of the grid
width: width of the grid
is_homogeneous: whether to return in homogeneous coordinates
Returns:
x,y grid coordinates [batch, 2 (3 if homogeneous), height, width]
"""
x_t = jnp.matmul(
jnp.ones(shape=[height, 1]),
jnp.transpose(jnp.expand_dims(jnp.linspace(-1.0, 1.0, width), 1),
[1, 0]))
y_t = jnp.matmul(jnp.expand_dims(jnp.linspace(-1.0, 1.0, height), 1),
jnp.ones(shape=[1, width]))
x_t = (x_t + 1.0) * 0.5 * jnp.array(width - 1, dtype='float32')
y_t = (y_t + 1.0) * 0.5 * jnp.array(height - 1, dtype='float32')
if is_homogeneous:
ones = jnp.ones_like(x_t)
coords = jnp.stack([x_t, y_t, ones], axis=0)
else:
coords = jnp.stack([x_t, y_t], axis=0)
# coords = jnp.tile(jnp.expand_dims(coords, 0), [batch, 1, 1, 1])
return coords
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
def generate_data():
T = 1000
tec = jnp.cumsum(15. * random.normal(random.PRNGKey(0), shape=(T, )))
TEC_CONV = -8.4479745e6 # mTECU/Hz
freqs = jnp.linspace(121e6, 168e6, 24)
phase = tec[:, None] / freqs * TEC_CONV
Y = jnp.concatenate([jnp.cos(phase), jnp.sin(phase)], axis=1)
Y_obs = Y + 0.75 * random.normal(random.PRNGKey(1), shape=Y.shape)
# Y_obs[500:550:2, :] += 3. * random.normal(random.PRNGKey(1),shape=Y[500:550:2, :].shape)
Sigma = 0.5**2 * jnp.eye(48)
Omega = jnp.diag(jnp.array([30.]))**2
mu0 = jnp.zeros(1)
Gamma0 = jnp.diag(jnp.array([200.]))**2
amp = jnp.ones_like(phase)
return Gamma0, Omega, Sigma, T, Y_obs, amp, mu0, tec, freqs
def create_grid(
samples_per_dim, value_range = (-1.0, 1.0)
):
"""Creates a tensor with equidistant entries from -1 to +1 in each dim.
Args:
samples_per_dim: Number of points to have along each dimension.
value_range: In each dimension, points will go from range[0] to range[1]
Returns:
A tensor of shape [samples_per_dim] + [len(samples_per_dim)].
"""
s = [jnp.linspace(value_range[0], value_range[1], n) for n in samples_per_dim]
pe = jnp.stack(jnp.meshgrid(*s, sparse=False, indexing="ij"), axis=-1)
return jnp.array(pe)
def test_CP():
from pOP import CP as pCP
x = np.linspace(0, 2, num=10)
z = (x - x[0]) * 2. / (x[-1] - x[0]) - 1.
cp1 = CP(0., 2., np.array([], dtype=np.int32), 5)
cp2 = CP(0., 2., np.array([], dtype=np.int32), 10)
Fc1 = cp1.H(x, 0, False)
Fc2 = cp2.H(x, 3, False)
z = z.reshape(10, 1)
Fp1 = pCP(z, 4)
Fp2 = pCP(z, 9, d=3)
assert (np.linalg.norm(Fc1 - Fp1, ord='fro') < 1e-14)
assert (np.linalg.norm(Fc2 - Fp2, ord='fro') < 1e-14)
def test_mean_and_var_mid():
t0 = 0.0
t1 = 3.0
y0 = np.linspace(0.1, 0.9, D)
num_samples = 500
vals = onp.zeros((num_samples, D))
for i in range(num_samples):
rng = random.PRNGKey(i)
bm = make_brownian_motion(t0, np.zeros(y0.shape), t1, rng)
vals[i, :] = bm(t1 / 2.0)
print(np.mean(vals), np.var(vals))
assert np.allclose(np.mean(vals), 0.0, atol=1e-1, rtol=1e-1)
assert np.allclose(np.var(vals), t1 / 2.0, atol=1e-1, rtol=1e-1)
def test_exponential_global_convolution(self):
init_fn, apply_fn = neural_xc.exponential_global_convolution(
num_channels=2,
grids=jnp.linspace(-1, 1, 5),
minval=0.1,
maxval=2.)
output_shape, init_params = init_fn(random.PRNGKey(0),
input_shape=(-1, 5, 1))
output = apply_fn(init_params, jnp.array(np.random.rand(1, 5, 1)))
self.assertEqual(output_shape, (-1, 5, 2))
self.assertLen(init_params, 1)
self.assertEqual(init_params[0].shape, (2, ))
self.assertEqual(output.shape, (1, 5, 2))
def test_broadcast_kde_cdf_shape(n_samples):
bw = 0.1
precision = 10
x = objax.random.normal((n_samples,), generator=generator)
lb, ub = get_domain_extension(x, 10)
support = np.linspace(lb, ub, precision)
factor = normalization_factor(x, bw)
quantiles = broadcast_kde_cdf(support, x, factor)
# checks
chex.assert_shape(quantiles, (precision,))
def test_fwd_back():
# Run a system forwards then backwards,
# and check that we end up in the same place.
D = 10
t0 = 0.1
t1 = 2.2
y0 = np.linspace(0.1, 0.9, D)
def f(y, t):
return -np.sqrt(t) - y + 0.1 - np.mean((y + 0.2)**2)
ys = odeint(f, y0, np.array([t0, t1]), atol=1e-8, rtol=1e-8)
rys = odeint(f, ys[-1], np.array([t1, t0]), atol=1e-8, rtol=1e-8)
assert np.allclose(y0, rys[-1])
def generate_dataset(n_i, n_b, n_cx, n_ct, n_dx, n_dt):
x_i = jnp.linspace(*domain[:, 0], n_i).reshape((-1, 1))
t_i = jnp.zeros_like(x_i)
u_i = u0_fn(x_i, t_i)
v_i = v0_fn(x_i, t_i)
x_l = jnp.ones((n_b, 1)) * domain[0, 0]
x_r = jnp.ones((n_b, 1)) * domain[1, 0]
t_b = jnp.linspace(*domain[:, 1], n_b).reshape((-1, 1))
u_l = ul_fn(x_l, t_b)
u_r = ur_fn(x_r, t_b)
v_l = vl_fn(x_l, t_b)
v_r = vr_fn(x_r, t_b)
x_c = jnp.linspace(*domain[:, 0], n_cx).reshape((-1, 1))
t_c = jnp.linspace(*domain[:, 1], n_ct).reshape((-1, 1))
xt_c = tensor_grid([x_c, t_c])
data = loadmat(data_file)
u_d, v_d, x_d, t_d = data["u_snapshots"], data["v_snapshots"], data[
"x"], data["t"].T
u_d = u_d[1:-1:(len(x_d) // n_dx), 1:-1:(len(t_d) // n_dt)].reshape(
(-1, 1))
v_d = v_d[1:-1:(len(x_d) // n_dx), 1:-1:(len(t_d) // n_dt)].reshape(
(-1, 1))
x_d = x_d[1:-1:(len(x_d) // n_dx)]
t_d = t_d[1:-1:(len(t_d) // n_dt)]
xt_d = tensor_grid([x_d, t_d])
dirichlet = dataset_Dirichlet(jnp.vstack([x_i, x_l, x_r, xt_d[:, 0:1]]),
jnp.vstack([t_i, t_b, t_b, xt_d[:, 1:2]]),
jnp.vstack([u_i, u_l, u_r, u_d]),
jnp.vstack([v_i, v_l, v_r, v_d]))
collocation = dataset_Collocation(jnp.vstack([xt_c[:, 0:1], xt_d[:, 0:1]]),
jnp.vstack([xt_c[:, 1:2], xt_d[:, 1:2]]))
return dirichlet, collocation
def test_complex_odeint(self):
# https://github.com/google/jax/issues/3986
def dy_dt(y, t, alpha):
return alpha * y
def f(y0, ts, alpha):
return odeint(dy_dt, y0, ts, alpha).real
alpha = 3 + 4j
y0 = 1 + 2j
ts = jnp.linspace(0., 1., 11)
tol = 1e-1 if jtu.num_float_bits(np.float64) == 32 else 1e-3
jtu.check_grads(f, (y0, ts, alpha), modes=["rev"], order=2, atol=tol, rtol=tol)
def test_get_atomic_chain_potential_exponential_coulomb(self):
potential = utils.get_atomic_chain_potential(
grids=jnp.linspace(-10, 10, 201),
locations=jnp.array([0., 1.]),
nuclear_charges=jnp.array([2, 1]),
interaction_fn=utils.exponential_coulomb)
# -2 * 1.071295 * jnp.exp(-np.abs(10) / 2.385345) - 1.071295 * jnp.exp(
# -np.abs(11) / 2.385345) = -0.04302427
self.assertAlmostEqual(float(potential[0]), -0.04302427)
# -2 * 1.071295 * jnp.exp(-np.abs(0) / 2.385345) - 1.071295 * jnp.exp(
# -np.abs(1) / 2.385345) = -2.84702559
self.assertAlmostEqual(float(potential[100]), -2.84702559)
# -2 * 1.071295 * jnp.exp(-np.abs(10) / 2.385345) - 1.071295 * jnp.exp(
# -np.abs(9) / 2.385345) = -0.05699946
self.assertAlmostEqual(float(potential[200]), -0.05699946)
def test_shape(self, num_classes):
resolutions = [8, 4]
channels = [1, 2]
batch_size = 2
model = models.CNNClassifier(num_classes,
resolutions,
channels,
axis_name=None)
resolution = resolutions[0]
shape = [batch_size, resolution, resolution, 1, channels[0]]
inputs = jnp.linspace(-1, 1, np.prod(shape)).reshape(shape)
params = model.init(_JAX_RANDOM_KEY, inputs, train=False)
outputs = model.apply(params, inputs, train=False)
self.assertEqual(outputs.shape, (batch_size, num_classes))
def test_get_xc_potential(self):
grids = jnp.linspace(-5, 5, 10001)
# We use the form of 3d LDA exchange functional as an example. So the
# correlation contribution is 0.
# exchange energy = -0.73855 \int n^(4 / 3) dx
# exchange potential should be -0.73855 * (4 / 3) n^(1 / 3)
# by taking functional derivative on exchange energy.
xc_energy_density_fn = lambda density: -0.73855 * density ** (1 / 3)
density = jnp.exp(-(grids - 1) ** 2)
np.testing.assert_allclose(
scf.get_xc_potential(
density,
xc_energy_density_fn=xc_energy_density_fn,
grids=grids),
-0.73855 * (4 / 3) * density ** (1 / 3))
def piecewise_constant_pdf(key, bins, weights, num_samples, randomized):
"""Piecewise-Constant PDF sampling.
Args:
key: jnp.ndarray(float32), [2,], random number generator.
bins: jnp.ndarray(float32), [batch_size, num_bins + 1].
weights: jnp.ndarray(float32), [batch_size, num_bins].
num_samples: int, the number of samples.
randomized: bool, use randomized samples.
Returns:
z_samples: jnp.ndarray(float32), [batch_size, num_samples].
"""
eps = 1e-5
# Get pdf
weights += eps # prevent nans
pdf = weights / weights.sum(axis=-1, keepdims=True)
cdf = jnp.cumsum(pdf, axis=-1)
cdf = jnp.concatenate([jnp.zeros(list(cdf.shape[:-1]) + [1]), cdf], axis=-1)
# Take uniform samples
if randomized:
u = random.uniform(key, list(cdf.shape[:-1]) + [num_samples])
else:
u = jnp.linspace(0., 1., num_samples)
u = jnp.broadcast_to(u, list(cdf.shape[:-1]) + [num_samples])
# Invert CDF. This takes advantage of the fact that `bins` is sorted.
mask = (u[Ellipsis, None, :] >= cdf[Ellipsis, :, None])
def minmax(x):
x0 = jnp.max(jnp.where(mask, x[Ellipsis, None], x[Ellipsis, :1, None]), -2)
x1 = jnp.min(jnp.where(~mask, x[Ellipsis, None], x[Ellipsis, -1:, None]), -2)
x0 = jnp.minimum(x0, x[Ellipsis, -2:-1])
x1 = jnp.maximum(x1, x[Ellipsis, 1:2])
return x0, x1
bins_g0, bins_g1 = minmax(bins)
cdf_g0, cdf_g1 = minmax(cdf)
denom = (cdf_g1 - cdf_g0)
denom = jnp.where(denom < eps, 1., denom)
t = (u - cdf_g0) / denom
z_samples = bins_g0 + t * (bins_g1 - bins_g0)
# Prevent gradient from backprop-ing through samples
return lax.stop_gradient(z_samples)
def plot_loss(ax, paths=None):
x, y = np.meshgrid(np.arange(xmin, xmax + xstep, xstep),
np.arange(ymin, ymax + ystep, ystep))
z = x + y
ax.contourf(x,
y,
z,
alpha=0.15,
levels=np.linspace(0., 10., 100),
cmap=plt.cm.jet,
antialiased=True,
extend='both')
path_lines = []
path_points = []
if paths is not None:
for path, alpha in zip(paths, ALPHAS):
pathx, pathy = path
ax.quiver(pathx[:-1],
pathy[:-1],
pathx[1:] - pathx[:-1],
pathy[1:] - pathy[:-1],
scale_units='xy',
angles='xy',
scale=1,
color='gray',
alpha=0.75)
line, = ax.plot([], [],
'',
label=alpha,
lw=2,
alpha=0.5,
color='darkviolet')
point, = ax.plot([], [],
'o',
markersize=12,
alpha=0.7,
color='darkviolet')
path_lines.append(line)
path_points.append(point)
ax.set_xlabel('$J_x$')
ax.set_ylabel('$J_y$')
ax.set_xlim((xmin, xmax))
ax.set_ylim((ymin, ymax))
return path_lines, path_points
def make_networks(
spec: specs.EnvironmentSpec,
policy_layer_sizes: Sequence[int] = (300, 200),
critic_layer_sizes: Sequence[int] = (400, 300),
vmin: float = -150.,
vmax: float = 150.,
num_atoms: int = 51,
) -> D4PGNetworks:
"""Creates networks used by the agent."""
action_spec = spec.actions
num_dimensions = np.prod(action_spec.shape, dtype=int)
critic_atoms = jnp.linspace(vmin, vmax, num_atoms)
def _actor_fn(obs):
network = hk.Sequential([
utils.batch_concat,
networks_lib.LayerNormMLP(policy_layer_sizes, activate_final=True),
networks_lib.NearZeroInitializedLinear(num_dimensions),
networks_lib.TanhToSpec(action_spec),
])
return network(obs)
def _critic_fn(obs, action):
network = hk.Sequential([
utils.batch_concat,
networks_lib.LayerNormMLP(
layer_sizes=[*critic_layer_sizes, num_atoms]),
])
value = network([obs, action])
return value, critic_atoms
policy = hk.without_apply_rng(hk.transform(_actor_fn))
critic = hk.without_apply_rng(hk.transform(_critic_fn))
# Create dummy observations and actions to create network parameters.
dummy_action = utils.zeros_like(spec.actions)
dummy_obs = utils.zeros_like(spec.observations)
dummy_action = utils.add_batch_dim(dummy_action)
dummy_obs = utils.add_batch_dim(dummy_obs)
return D4PGNetworks(
policy_network=networks_lib.FeedForwardNetwork(
lambda rng: policy.init(rng, dummy_obs), policy.apply),
critic_network=networks_lib.FeedForwardNetwork(
lambda rng: critic.init(rng, dummy_obs, dummy_action),
critic.apply))
def test_get_hartree_energy(self, interaction_fn):
grids = jnp.linspace(-5, 5, 11)
dx = utils.get_dx(grids)
density = utils.gaussian(grids=grids, center=1., sigma=1.)
# Compute the expected Hartree energy by nested for loops.
expected_hartree_energy = 0.
for x_0, n_0 in zip(grids, density):
for x_1, n_1 in zip(grids, density):
expected_hartree_energy += 0.5 * n_0 * n_1 * interaction_fn(
x_0 - x_1) * dx ** 2
self.assertAlmostEqual(
float(scf.get_hartree_energy(
density=density, grids=grids, interaction_fn=interaction_fn)),
float(expected_hartree_energy))
def test_swsft_forward_spins_channels_matches_swsft_forward(self):
transformer = _get_transformer()
resolution = 16
n_channels = 2
spins = (0, 1)
shape = (resolution, resolution, len(spins), n_channels)
sphere_set = jnp.linspace(-1, 1, np.prod(shape)).reshape(shape)
coefficients = transformer.swsft_forward_spins_channels(
sphere_set, spins)
for channel in range(n_channels):
for spin in spins:
# Slices must match swsft_forward().
sliced = transformer.swsft_forward(
sphere_set[Ellipsis, spin, channel], spin)
self.assertAllClose(coefficients[Ellipsis, spin, channel],
sliced)
def test_conjugate():
key = jr.PRNGKey(123)
kern = to_spectral(RBF(), 10)
posterior = Prior(kernel=kern) * Gaussian()
x = jnp.linspace(-1.0, 1.0, 20).reshape(-1, 1)
y = jnp.sin(x)
params = initialise(key, posterior)
config = get_defaults()
unconstrainer, constrainer = build_all_transforms(params.keys(), config)
params = unconstrainer(params)
mll = marginal_ll(posterior, transform=constrainer)
assert isinstance(mll, Callable)
neg_mll = marginal_ll(posterior, transform=constrainer, negative=True)
assert neg_mll(params, x, y) == jnp.array(-1.0) * mll(params, x, y)
nmll = neg_mll(params, x, y)
assert nmll.shape == ()
def set_axhlines(ax, ys):
"""Paint len(ys) segmented horizontal lines onto plot given by ax."""
try:
ns = len(ys)
except TypeError:
ys = [ys]
ns = len(ys)
grid = np.linspace(0, 1, num=ns + 1)
for i, y in enumerate(ys):
ax.axhline(y,
xmin=grid[i],
xmax=grid[i + 1],
color="k",
linestyle="--",
linewidth=2.5)
def test_get_hartree_potential(self, interaction_fn):
grids = jnp.linspace(-5, 5, 11)
dx = utils.get_dx(grids)
density = utils.gaussian(grids=grids, center=1., sigma=1.)
# Compute the expected Hartree energy by nested for loops.
expected_hartree_potential = np.zeros_like(grids)
for i, x_0 in enumerate(grids):
for x_1, n_1 in zip(grids, density):
expected_hartree_potential[i] += np.sum(
n_1 * interaction_fn(x_0 - x_1)) * dx
np.testing.assert_allclose(
scf.get_hartree_potential(
density=density, grids=grids, interaction_fn=interaction_fn),
expected_hartree_potential)
def test_get_xc_potential_hartree(self):
grids = jnp.linspace(-5, 5, 10001)
density = utils.gaussian(grids=grids, center=1., sigma=1.)
def half_hartree_potential(density):
return 0.5 * scf.get_hartree_potential(
density=density,
grids=grids,
interaction_fn=utils.exponential_coulomb)
np.testing.assert_allclose(
scf.get_xc_potential(
density=density,
xc_energy_density_fn=half_hartree_potential,
grids=grids),
scf.get_hartree_potential(
density, grids=grids, interaction_fn=utils.exponential_coulomb))