107 lines
2.5 KiB
Python
107 lines
2.5 KiB
Python
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from numpy import fmax
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from plot import *
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def get_fig():
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fig, ax = plt.subplots(figsize=size_half_half)
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ax.grid()
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ax.set_xlabel(f"$x$")
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ax.set_ylabel("PDF")
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return fig, ax
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# GAUSS / NORMAL
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def fgauss(x, mu, sigma_sqr):
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return 1 / (np.sqrt(2 * np.pi * sigma_sqr)) * np.exp(-(x - mu)**2 / (2 * sigma_sqr))
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def gauss():
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fig, ax = get_fig()
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x = np.linspace(-5, 5, 300)
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for mu, sigma_sqr in [(0, 1), (0, 0.2), (0, 5), (-2, 2)]:
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y = fgauss(x, mu, sigma_sqr)
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label = texvar("mu", mu) + ", " + texvar("sigma^2", sigma_sqr)
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ax.plot(x, y, label=label)
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ax.legend()
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return fig
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export(gauss(), "distribution_gauss")
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# CAUCHY / LORENTZ
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def fcauchy(x, x_0, gamma):
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return 1 / (np.pi * gamma * (1 + ((x - x_0)/gamma)**2))
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def cauchy():
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fig, ax = get_fig()
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x = np.linspace(-5, 5, 300)
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for x_0, gamma in [(0, 1), (0, 0.5), (0, 2), (-2, 1)]:
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y = fcauchy(x, x_0, gamma)
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label = f"$x_0 = {x_0}$ , {texvar('gamma', gamma)}"
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ax.plot(x, y, label=label)
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ax.legend()
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return fig
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export(cauchy(), "distribution_cauchy")
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# MAXWELL-BOLTZMANN
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def fmaxwell(x, a):
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return np.sqrt(2/np.pi) * x**2 / a**3 * np.exp(-x**2 /(2*a**2))
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def maxwell():
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fig, ax = get_fig()
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x = np.linspace(0, 20, 300)
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for a in [1, 2, 5]:
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y = fmaxwell(x, a)
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label = f"$a = {a}$"
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ax.plot(x, y, label=label)
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ax.legend()
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return fig
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export(maxwell(), "distribution_maxwell-boltzmann")
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# POISSON
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def fpoisson(k, l):
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return l**k * np.exp(-l) / scp.special.factorial(k)
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def poisson():
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fig, ax = get_fig()
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k = np.arange(0, 21, dtype=int)
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for l in [1, 4, 10]:
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y = fpoisson(k, l)
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label = texvar("lambda", l)
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ax.plot(k, y, color="#555")
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ax.scatter(k, y, label=label)
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ax.set_xlabel(f"$k$")
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ax.set_ylabel(f"PMF")
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ax.legend()
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return fig
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export(poisson(), "distribution_poisson")
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# BINOMIAL
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def binom(n, k):
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return scp.special.factorial(n) / (
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scp.special.factorial(k) *
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scp.special.factorial((n-k))
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)
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def fbinomial(k, n, p):
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return binom(n, k) * p**k * (1-p)**(n-k)
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def binomial():
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fig, ax = get_fig()
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n = 20
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k = np.arange(0, n+1, dtype=int)
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for p in [0.3, 0.5, 0.7]:
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y = fbinomial(k, n, p)
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label = f"$n={n}$, $p={p}$"
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ax.plot(k, y, color="#555")
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ax.scatter(k, y, label=label)
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ax.set_xlabel(f"$k$")
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ax.set_ylabel(f"PMF")
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ax.legend()
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return fig
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export(binomial(), "distribution_binomial")
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# FERMI-DIRAC
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# BOSE-EINSTEIN
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