def test_raw_runner_ito_1d(self):
T = 0.5
sde = Ito1D(particles=30000,
x0=0.0,
drift=drift,
diffusion=diffusion,
sigma=1,
t0=0.0,
dt=1e-2,
T=T)
job = Job(sde=sde,
pdf=Simple1DHistogram(bins=100),
mode=Job.RAW,
settings={})
result, execution_time = run(job, processes=3)
pdf = result.distributions[-1]
print(f"Parallel Execution Time: {execution_time}")
x = np.linspace(pdf.lower_bound, pdf.upper_bound, 1000)
y = pdf(x)
plt.figure(figsize=(20, 10))
plt.plot(x, y, label="Approximation")
sb.distplot(np.random.normal(0, np.sqrt(T), size=10000), label="True")
plt.show()
def test_virus_model(self):
global has_been_sick
has_been_sick = None
T = 200
dt = 1e-1
sde = Exp1D(particles=50000,
x0=1.0,
drift=covid_drift,
diffusion=covid_diffusion,
lam=1.0,
t0=0.0,
dt=dt,
T=T)
job = Job(sde=sde,
pdf=Simple1DHistogram(bins=50),
mode=Job.Video,
settings={"steps_per_frame": 5})
result, execution_time = run(job, processes=4)
tdplot = make_time_1dx_distplot_video(result.distributions,
fps=10,
dt=dt,
steps_per_frame=5,
save=True)
tdplot = three_dee_plot(result.distributions, dt=dt, steps_per_frame=5)
plt.show()
def test_cool_accuracy_plot(self):
T = 1
dt = 1e-2
processes = 2
dim = (4, 4)
_N = np.logspace(3, 6, 4)
_bins = np.array([5, 50, 200, 500]) # , 200, 500])
X, Y = np.meshgrid(_N, _bins)
Z = np.concatenate([X.reshape(-1, 1), Y.reshape(-1, 1)], axis=1)
results = []
for n, b in Z:
N = int(n / processes)
bins = int(b)
sde = Ito1D(particles=N,
x0=0.0,
drift=drift,
diffusion=diffusion,
sigma=1,
t0=0.0,
dt=dt,
T=T)
job = Job(sde=sde,
pdf=Simple1DHistogram(bins=bins),
mode=Job.RAW,
settings={})
result, execution_time = run(job, processes=processes)
pdf = result.distributions[-1]
x = np.linspace(pdf.lower_bound, pdf.upper_bound, 10000)
normal = Normal(mu=0, sigma=np.sqrt(T))
kl_div = relative_entropy_1d(domain=x, p=normal, q=pdf)
print(
f"Parallel Execution Time: {execution_time} -- {n} -- {bins} -- {kl_div}"
)
results.append(kl_div)
results = np.array(results).reshape(*dim)
plt.figure(figsize=(10, 6))
plt.title(f"KL-divergence heatmap", fontsize=20)
print("results", results)
ax = sb.heatmap(results, annot=True, yticklabels=_bins, xticklabels=_N)
plt.ylabel("Bins", fontsize=15)
plt.xlabel("N", fontsize=15)
plt.tight_layout()
plt.savefig("../images/kl-heatmap.png", bbox_inches="tight")
plt.show()
def test_cool_sparseness_plot(self):
dt = 1e-1
processes = 2
_N = 100000
bins = 50
_T = [1, 10, 100, 1000] # 1000, 10000]
results = []
for T in _T:
N = int(_N / processes)
sde = Ito1D(particles=N,
x0=0.0,
drift=drift,
diffusion=diffusion,
sigma=1,
t0=0.0,
dt=dt,
T=T)
job = Job(sde=sde,
pdf=Simple1DHistogram(bins=bins),
mode=Job.RAW,
settings={})
result, execution_time = run(job, processes=processes)
pdf = result.distributions[-1]
x = np.linspace(-np.sqrt(T) * 3, np.sqrt(T) * 3, 100000)
normal = Normal(mu=0, sigma=np.sqrt(T))
kl_div = relative_entropy_1d(domain=x, p=normal, q=pdf)
print(
f"Parallel Execution Time: {execution_time} -- {_N} -- {bins} -- {kl_div}"
)
results.append(kl_div)
results = np.array(results)
plt.figure(figsize=(10, 6))
plt.title(f"KL-divergence sparseness effect", fontsize=20)
print("results", results)
ax = sb.lineplot(_T, results)
plt.ylabel("KL-divergence", fontsize=15)
plt.xlabel("T", fontsize=15)
plt.tight_layout()
# plt.savefig("../images/kl-heatmap.png", bbox_inches="tight")
plt.show()
def test_performance_1(self):
T = 1
dt = 1e-1
processes = 4
N = int(1e6) # int(1e8 / 6)
bins = 50
sde = Ito1D(particles=N,
x0=0.0,
drift=drift,
diffusion=diffusion,
sigma=1,
t0=0.0,
dt=dt,
T=T)
job = Job(sde=sde,
pdf=Simple1DHistogram(bins=bins),
mode=Job.RAW,
settings={})
result, execution_time = run(job, processes=processes)
pdf = result.distributions[-1]
print(f"Parallel Execution Time: {execution_time}")
x = np.linspace(pdf.lower_bound, pdf.upper_bound, 10000)
y = pdf(x)
normal = Normal(mu=0, sigma=np.sqrt(T))
print(
f"Expected -- approximation: {expected_1d(domain=x, pdf=pdf)} | true: {expected_1d(domain=x, pdf=normal)}"
)
print(
f"Variance -- approximation: {variance_1d(domain=x, pdf=pdf)} | true: {variance_1d(domain=x, pdf=normal)}"
)
print(
f"Relative Entropy: {relative_entropy_1d(domain=x, p=normal, q=pdf)}"
)
plt.figure(figsize=(10, 6))
plt.title(f"T={T} dt={dt} N={N * processes} B={bins}", fontsize=20)
plt.plot(x, y, label="Approximation")
p = normal(x)
sb.lineplot(x, p, label="True")
plt.legend(fontsize=14)
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)
plt.tight_layout()
plt.savefig("../images/many-bins-many-particles.png")
plt.show()
def test_video_runner_exp1d(self):
sde = Exp1D(particles=10000,
x0=0.0,
drift=drift,
diffusion=diffusion,
lam=1,
t0=0.0,
dt=1e-2,
T=2.0)
job = Job(sde=sde,
pdf=Simple1DHistogram(bins=100),
mode=Job.Video,
settings={"steps_per_frame": 5})
result, _ = run(job, 2)
result = result.distributions
make_time_1dx_distplot_video(result,
fps=10,
dt=1e-2,
steps_per_frame=5)