Numba compatible distributions¶
Test each of the Numba compatible distributions.
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import numba as nb
import numpy as np
from matplotlib import pyplot as plt
import laser.core.distributions as distributions
import numba as nb
import numpy as np
from matplotlib import pyplot as plt
import laser.core.distributions as distributions
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def plot_histogram(data: list[tuple[np.ndarray, str, str]], bins: int = 101) -> None:
for d, label, color in data:
plt.hist(d, bins=bins, density=True, alpha=0.6, color=color, label=label)
plt.xlabel('Value')
plt.ylabel('Density')
plt.title('Histogram')
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()
def plot_histogram(data: list[tuple[np.ndarray, str, str]], bins: int = 101) -> None:
for d, label, color in data:
plt.hist(d, bins=bins, density=True, alpha=0.6, color=color, label=label)
plt.xlabel('Value')
plt.ylabel('Density')
plt.title('Histogram')
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()
Beta¶
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NSAMPLES = np.int32(100_000)
traces = []
for alpha, beta, color in [(0.5, 0.5, "red"), (5.0, 1.0, "blue"), (1.0, 3.0, "green"), (2.0, 2.0, "purple"), (2.0, 5.0, "orange")]:
dist = distributions.beta(a=alpha, b=beta)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples, f'Beta({alpha}, {beta})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for alpha, beta, color in [(0.5, 0.5, "red"), (5.0, 1.0, "blue"), (1.0, 3.0, "green"), (2.0, 2.0, "purple"), (2.0, 5.0, "orange")]:
dist = distributions.beta(a=alpha, b=beta)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples, f'Beta({alpha}, {beta})', color))
plot_histogram(traces)
Binomial¶
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NSAMPLES = np.int32(100_000)
traces = []
for p, n, color in [(0.5, 20, "blue"), (0.7, 20, "green"), (0.5, 40, "red")]:
dist = distributions.binomial(n=n, p=p)
distributions.sample_ints(dist, samples := np.zeros(NSAMPLES, dtype=np.int32))
traces.append((samples, f'Binomial({n}, {p})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for p, n, color in [(0.5, 20, "blue"), (0.7, 20, "green"), (0.5, 40, "red")]:
dist = distributions.binomial(n=n, p=p)
distributions.sample_ints(dist, samples := np.zeros(NSAMPLES, dtype=np.int32))
traces.append((samples, f'Binomial({n}, {p})', color))
plot_histogram(traces)
Exponential¶
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NSAMPLES = np.int32(100_000)
traces = []
for lamda, color in [(0.5, "red"), (1.0, "green"), (1.5, "lightblue")]:
dist = distributions.exponential(scale=1/lamda)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[samples < 8], f'Exponential(1/{lamda})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for lamda, color in [(0.5, "red"), (1.0, "green"), (1.5, "lightblue")]:
dist = distributions.exponential(scale=1/lamda)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[samples < 8], f'Exponential(1/{lamda})', color))
plot_histogram(traces)
Gamma¶
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NSAMPLES = np.int32(100_000)
traces = []
for alpha, theta, color in [(1.0, 2.0, "red"), (2.0, 2.0, "orange"), (3.0, 2.0, "yellow"), (5.0, 1.0, "green"), (9.0, 0.5, "black"), (7.5, 1.0, "blue"), (0.5, 1.0, "purple")]:
dist = distributions.gamma(shape=alpha, scale=theta)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[(samples > 0.25) & (samples <= 15)], f'Gamma({alpha}, {theta})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for alpha, theta, color in [(1.0, 2.0, "red"), (2.0, 2.0, "orange"), (3.0, 2.0, "yellow"), (5.0, 1.0, "green"), (9.0, 0.5, "black"), (7.5, 1.0, "blue"), (0.5, 1.0, "purple")]:
dist = distributions.gamma(shape=alpha, scale=theta)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[(samples > 0.25) & (samples <= 15)], f'Gamma({alpha}, {theta})', color))
plot_histogram(traces)
Logistic¶
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NSAMPLES = np.int32(100_000)
traces = []
for mu, s, color in [(5, 2, "blue"), (9, 3, "green"), (9, 4, "red"), (6, 2, "lightblue"), (2, 1, "purple")]:
dist = distributions.logistic(loc=mu, scale=s)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[(samples >= -5) & (samples <= 25)], f'Logistic({mu}, {s})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for mu, s, color in [(5, 2, "blue"), (9, 3, "green"), (9, 4, "red"), (6, 2, "lightblue"), (2, 1, "purple")]:
dist = distributions.logistic(loc=mu, scale=s)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[(samples >= -5) & (samples <= 25)], f'Logistic({mu}, {s})', color))
plot_histogram(traces)
LogNormal¶
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NSAMPLES = np.int32(100_000)
traces = []
for mu, sigma, color in [(0, 1, "blue"), (0, 0.5, "green"), (0, 0.25, "red")]:
dist = distributions.lognormal(mean=mu, sigma=sigma)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[samples <= 3], f'Lognormal({mu}, {sigma})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for mu, sigma, color in [(0, 1, "blue"), (0, 0.5, "green"), (0, 0.25, "red")]:
dist = distributions.lognormal(mean=mu, sigma=sigma)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[samples <= 3], f'Lognormal({mu}, {sigma})', color))
plot_histogram(traces)
Multinomial¶
NegativeBinomial¶
Normal¶
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NSAMPLES = np.int32(100_000)
traces = []
for mu, sigmasq, color in [(0, 0.2, "blue"), (0, 1.0, "red"), (0, 5.0, "orange"), (-2, 0.5, "green")]:
dist = distributions.normal(loc=mu, scale=np.sqrt(sigmasq))
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[(samples >= -5) & (samples <= 5)], f'Normal({mu}, {np.sqrt(sigmasq)})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for mu, sigmasq, color in [(0, 0.2, "blue"), (0, 1.0, "red"), (0, 5.0, "orange"), (-2, 0.5, "green")]:
dist = distributions.normal(loc=mu, scale=np.sqrt(sigmasq))
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[(samples >= -5) & (samples <= 5)], f'Normal({mu}, {np.sqrt(sigmasq)})', color))
plot_histogram(traces)
Poisson¶
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NSAMPLES = np.int32(100_000)
traces = []
for lamda, color in [(1, "orange"), (4, "purple"), (10, "lightblue")]:
dist = distributions.poisson(lam=lamda)
distributions.sample_ints(dist, samples := np.zeros(NSAMPLES, dtype=np.int32))
traces.append((samples[samples <= 20], f'Poisson({lamda})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for lamda, color in [(1, "orange"), (4, "purple"), (10, "lightblue")]:
dist = distributions.poisson(lam=lamda)
distributions.sample_ints(dist, samples := np.zeros(NSAMPLES, dtype=np.int32))
traces.append((samples[samples <= 20], f'Poisson({lamda})', color))
plot_histogram(traces)
Uniform¶
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NSAMPLES = np.int32(100_000)
traces = []
for low, high, color in [(0.0, 1.0, "red"), (0.25, 1.25, "orange"), (0.0, 2.0, "green"), (-1.0, 1.0,"blue"), (2.71828, 3.14159, "indigo"), (1.30, 4.20, "violet")]:
dist = distributions.uniform(low=low, high=high)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples, f'Uniform({low}, {high})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for low, high, color in [(0.0, 1.0, "red"), (0.25, 1.25, "orange"), (0.0, 2.0, "green"), (-1.0, 1.0,"blue"), (2.71828, 3.14159, "indigo"), (1.30, 4.20, "violet")]:
dist = distributions.uniform(low=low, high=high)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples, f'Uniform({low}, {high})', color))
plot_histogram(traces)
Weibull¶
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NSAMPLES = np.int32(100_000)
traces = []
for k, lamda, color in [(0.5, 1.0, "blue"), (1.0, 1.0, "red"), (1.5, 1.0, "purple"), (5.0, 1.0, "green")]:
dist = distributions.weibull(a=k, lam=lamda)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[samples <= 2.5], f'Weibull({k}, {lamda})', color))
plot_histogram(traces)
NSAMPLES = np.int32(100_000)
traces = []
for k, lamda, color in [(0.5, 1.0, "blue"), (1.0, 1.0, "red"), (1.5, 1.0, "purple"), (5.0, 1.0, "green")]:
dist = distributions.weibull(a=k, lam=lamda)
distributions.sample_floats(dist, samples := np.zeros(NSAMPLES, dtype=np.float32))
traces.append((samples[samples <= 2.5], f'Weibull({k}, {lamda})', color))
plot_histogram(traces)
