def generate_distribution_plot(title, subtitle, numpy_rand, f, x0, xf, N,
*args):
print('Numpy exponential random generator mean: ', np.mean(numpy_rand))
print('NumPy std error:', np.std(numpy_rand) / np.sqrt(N) * 100, '%')
t0 = current_milli_time()
rand = sample(f, x0, xf, N, *args)
tf = current_milli_time()
print('\nMC exponential random generator mean: ', np.mean(rand))
print('MCRand std error:', np.std(rand) / np.sqrt(N) * 100, '%')
print('Elapsed time: %.4f ms' % (tf - t0, ))
x = np.linspace(x0, xf, N)
plt.hist(numpy_rand,
bins=30,
density=True,
color=(0, 0, 1, 0.8),
label='NumPy sample')
plt.hist(rand,
bins=30,
density=True,
color=(0, 1, 0, 0.5),
label='MCRand sample')
plt.plot(x, exponential(x), color='r', label='PDF')
plt.text(2, 0.95, subtitle, size=15)
plt.title(title)
plt.xlabel('Sample number')
plt.ylabel('Probability')
plt.legend()
plt.show()
def rayleigh_test():
print('\n\n---------- RAYLEIGH DISTRIBUTION TEST ----------\n')
x0 = 0
xf = 4
sigma = 1
N = 10**5
t0 = current_milli_time()
numpy_rand = np.random.rayleigh(scale=sigma, size=N)
tf = current_milli_time()
print('Numpy rayleigh random generator mean: ', np.mean(numpy_rand))
print('NumPy std error:', np.std(numpy_rand) / np.sqrt(N) * 100, '%')
print('Elapsed time: %.4f ms' % (tf - t0, ))
t0 = current_milli_time()
rand = sample(rayleigh, x0, xf, N, sigma)
tf = current_milli_time()
print('\nMC rayleigh random generator mean: ', np.mean(rand))
print('MCRand std error:', np.std(rand) / np.sqrt(N) * 100, '%')
print('Elapsed time: %.4f ms' % (tf - t0, ))
x = np.linspace(x0, xf, N)
plt.hist(numpy_rand,
bins=30,
density=True,
color=(0, 0, 1, 0.8),
label='NumPy sample')
plt.hist(rand,
bins=30,
density=True,
color=(0, 1, 0, 0.5),
label='MCRand sample')
plt.plot(x,
rayleigh(x, sigma),
color='r',
label=r'Rayleigh PDF $\sigma=%.2f$' % sigma)
plt.text(2.5,
0.3,
r'$PDF(x)=\frac{x\cdot\exp(-\frac{x^2}{2\sigma^2})}{\sigma^2}$',
size=15)
plt.title('Rayleigh distribution test')
plt.xlabel('Sample number')
plt.ylabel('Probability')
plt.legend()
plt.show()
def invented_test():
print('\n\n---------- MODIFIED RAYLEIGH DISTRIBUTION TEST ----------\n')
x0 = -4
xf = 4
sigma = 1
N = 10**5
t0 = current_milli_time()
rand = sample(invented, x0, xf, N, sigma)
tf = current_milli_time()
print('\nMC invented random generator mean: ', np.mean(rand))
print('Elapsed time: %.4f ms' % (tf - t0, ))
x = np.linspace(x0, xf, N)
plt.figure(figsize=(12, 5))
plt.hist(rand,
bins=40,
density=True,
color=(0, 1, 0, 0.5),
label='MCRand sample')
plt.plot(x,
invented(x, sigma),
color='r',
label=r'Modified Rayleigh PDF $\sigma=%.2f$' % sigma)
plt.text(
-4.5,
0.3,
r'$PDF(x)=\frac{x^2\exp(-\frac{x^2}{2\sigma^2})}{2.506628\cdot\sigma^2}$',
size=15)
plt.title('Modified Rayleigh distribution test')
plt.xlabel('Sample number')
plt.ylabel('Probability')
plt.xlim(-5, 5)
plt.ylim(0, 0.35)
plt.legend()
plt.show()
def symmetric_maxwell_boltzmann_test():
print(
'\n\n---------- SYMMETRIC MAXWELL-BOLTZMANN DISTRIBUTION TEST ----------\n'
)
x0 = -10
xf = 10
sigma = 2
N = 10**5
t0 = current_milli_time()
rand = sample(symmetric_maxwell_boltzmann, x0, xf, N, sigma)
tf = current_milli_time()
print('\nMC Symmetric Maxwell-Boltzmann random generator mean: ',
np.mean(rand))
print('Elapsed time: %.4f ms' % (tf - t0, ))
x = np.linspace(x0, xf, N)
plt.figure(figsize=(12, 6))
plt.hist(rand,
bins=40,
density=True,
color=(0, 1, 0, 0.5),
label='MCRand sample')
plt.plot(x,
symmetric_maxwell_boltzmann(x, sigma),
color='r',
label=r'Maxwell-Boltzmann PDF $\sigma=%.2f$' % sigma)
plt.text(
-10.5,
0.135,
r'$PDF(x)=\sqrt{\frac{1}{2\pi}}\cdot\frac{x^2\exp(-\frac{x^2}{2\sigma^2})}{\sigma^3}$',
size=15)
plt.title('Symmetric Maxwell-Boltmann distribution test')
plt.xlabel('Sample number')
plt.ylabel('Probability')
plt.legend()
plt.show()
def test_sample_shape(shape):
rands = sample(uniform_function, 0, 1, shape)
rands.shape = tuple(shape)
def test_bounds_are_valid(bounds, raises):
if raises:
with pytest.raises(ValueError):
sample(uniform_function, bounds[0], bounds[1], (5, 4))
else:
sample(uniform_function, bounds[0], bounds[1], (5, 4))
def gaussian_test():
print('---------- GAUSSIAN TEST ----------\n')
x0 = -5
xf = 5
N = 50000
sigma = 1
mu = 0
print('sigma=%.2f, mu=%.2f\n' % (sigma, mu))
t0 = current_milli_time()
numpy_rand = np.random.normal(mu, sigma, N)
tf = current_milli_time()
print('NumPy gaussian random generator mean: ', np.mean(numpy_rand))
print('NumPy std error:', np.std(numpy_rand) / np.sqrt(N) * 100, '%')
print('Elapsed time: %.4f ms' % (tf - t0, ))
t0 = current_milli_time()
rand = sample(gaussian, x0, xf, N, mu, sigma)
tf = current_milli_time()
print('\nMC gaussian random generator mean: ', np.mean(rand))
print('MCRand std error:', np.std(rand) / np.sqrt(N) * 100, '%')
print('Elapsed time: %.4f ms' % (tf - t0, ))
x = np.linspace(x0, xf, N)
plt.figure(figsize=(9, 6))
plt.hist(numpy_rand,
bins=30,
density=True,
color=(0, 0, 1, 0.8),
label='NumPy sample')
plt.hist(rand,
bins=30,
density=True,
color=(0, 1, 0, 0.5),
label='MCRand sample')
plt.plot(x,
gaussian(x, mu, sigma),
color='r',
label=r'Gaussian PDF $\mu=%.2f$, $\sigma=%.2f$' % (mu, sigma))
plt.text(
-5.3,
0.45,
r'PDF(x)=$\frac{1}{\sqrt{2\pi\sigma^2}}\cdot e^{-\frac{(x-\mu)^2}{2\sigma^2}}$',
size=15)
# (1/(np.sqrt(2*np.pi*sigma**2))) * np.exp(-(x-mu)**2/(2*sigma**2))
plt.title('Gaussian distribution test')
plt.xlabel('Sample number')
plt.ylabel('Probability')
plt.ylim(0, 0.5)
plt.legend()
plt.show()
def cauchy_test():
print('\n\n---------- CAUCHY DISTRIBUTION TEST ----------\n')
x0 = -10
xf = 10
N = 10**5
x0_cauchy = 0
gamma = 1
t0 = current_milli_time()
s = np.random.standard_cauchy(size=N)
numpy_cauchy = s[(s > -10) &
(s < 10)] # truncate distribution so it plots well
tf = current_milli_time()
print('NumPy Cauchy random generator mean: ', np.mean(numpy_cauchy))
print('NumPy std error:', np.std(numpy_cauchy) / np.sqrt(N) * 100, '%')
print('Elapsed time: %.4f ms' % (tf - t0, ))
t0 = current_milli_time()
rand = sample(cauchy, x0, xf, N, x0_cauchy, gamma)
tf = current_milli_time()
print('\nMC Cauchy random generator mean: ', np.mean(rand))
print('MCRand std error:', np.std(rand) / np.sqrt(N) * 100, '%')
print('Elapsed time: %.4f ms' % (tf - t0, ))
x = np.linspace(x0, xf, N)
plt.figure(figsize=(9, 6))
plt.hist(numpy_cauchy,
bins=50,
density=True,
color=(0, 0, 1, 0.8),
label='NumPy sample')
plt.hist(rand,
bins=50,
density=True,
color=(0, 1, 0, 0.5),
label='MCRand sample')
plt.plot(x,
cauchy(x, x0_cauchy, gamma),
color='r',
label=r'Cauchy PDF $γ=%.2f$, $x_0=%.2f$' % (gamma, x0_cauchy))
plt.text(-10,
0.34,
r'PDF(x)=$\frac{1}{\pi\gamma[1+(\frac{x-x_0}{\gamma})^2]}$',
size=15)
plt.title('Cauchy distribution test')
plt.xlabel('Sample number')
plt.ylabel('Probability')
plt.xlim(-11, 11)
plt.ylim(0, 0.38)
plt.legend(loc='upper right')
plt.show()