Add back python code in new dir

rand_distr/plots/py/main.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+OUT = "target"
+EXT = "png"
+
+
+def standard_normal():
+    from scipy.stats import norm
+    # Possible values for the distribution
+    x = np.linspace(-3, 3, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for the standard normal distribution
+    ax.plot(x, norm.pdf(x), label='Standard normal')
+
+    # Adding title and labels
+    ax.set_title('Standard normal distribution')
+    ax.set_xlabel('Z-score (standard deviations from the mean)')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/standard_normal.{EXT}")
+    plt.close()
+
+
+def normal():
+    # Defining the normal distribution PDF
+    def y(mu, sigma, x):
+        from scipy.stats import norm
+        return norm.pdf(x, loc=mu, scale=sigma)
+
+    inputs = [(0, 0.5), (0, 1), (0, 2), (-2, 1)]
+    # Possible values for the distribution
+    x = np.linspace(-5, 5, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of mu and sigma
+    for mu, sigma in inputs:
+        ax.plot(x, y(mu, sigma, x), label=f'μ = {mu}, σ = {sigma}')
+
+    # Adding title and labels
+    ax.set_title('Normal distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/normal.{EXT}")
+    plt.close()
+
+
+def chi_squared():
+    def y(x, df):
+        from scipy.stats import chi2
+        y = chi2.pdf(x, df)
+        y[y > 1.0] = np.nan
+        return y
+    # Degrees of freedom for the distribution
+    df_values = [1, 2, 3, 5, 9]
+    # Possible values for the distribution
+    x = np.linspace(0, 10, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of the degrees of freedom
+    for df in df_values:
+        ax.plot(x, y(x, df), label=f'k = {df}')
+
+    # Adding title and labels
+    ax.set_title('Chi-squared distribution')
+    ax.set_xlabel('Chi-squared statistic')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/chi_squared.{EXT}")
+    plt.close()
+
+
+def binomial():
+    # Defining the Binomial distribution PMF
+    def y(n, p, k):
+        from scipy.stats import binom
+        return binom.pmf(k, n, p)
+
+    inputs = [(10, 0.2), (10, 0.6)]
+    # Possible outcomes for a Binomial distributed variable
+    outcomes = np.arange(0, 11)
+    width = 0.5
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PMF for each value of n and p
+    for i, (n, p) in enumerate(inputs):
+        ax.bar(outcomes + i * width - width / 2, y(n, p, outcomes), width=width, label=f'n = {n}, p = {p}')
+
+    # Adding title and labels
+    ax.set_title('Binomial distribution')
+    ax.set_xlabel('k (number of successes)')
+    ax.set_ylabel('Probability')
+    ax.set_xticks(outcomes)  # set the ticks to be the outcome values
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/binomial.{EXT}")
+    plt.close()
+
+
+def cauchy():
+    # Possible values for the distribution
+    x = np.linspace(-7, 7, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    inputs = [(0, 0.5), (0, 1), (0, 2), (-2, 1)]
+
+    # Plotting the PDF for the Cauchy distribution
+    for x0, gamma in inputs:
+        ax.plot(x, 1 / (np.pi * gamma * (1 + ((x - x0) / gamma)**2)), label=f'x₀ = {x0}, γ = {gamma}')
+
+    # Adding title and labels
+    ax.set_title('Cauchy distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('P(x)')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/cauchy.{EXT}")
+    plt.close()
+
+
+def dirichlet():
+    def plot_dirichlet(alpha, ax):
+        """
+        Plots a Dirichlet distribution given alpha parameters and axis.
+        """
+        # Create a 2D meshgrid of points
+        resolution = 200  # Resolution of the visualization
+        x = np.linspace(0, 1, resolution)
+        y = np.linspace(0, 1, resolution)
+        X, Y = np.meshgrid(x, y)
+        # Flatten the grid to pass to the distribution
+        XY = np.vstack((X.flatten(), Y.flatten()))
+
+        # Calculate remaining coordinate for the 3-simplex (3D Dirichlet is defined on a triangle in 2D)
+        Z = 1 - X - Y
+        # Filter out points outside the triangle
+        valid = (Z >= 0)
+        # Prepare the probability density function (PDF) array
+        PDF = np.zeros(X.shape).flatten()
+
+        # Calculate PDF only for valid points
+        if np.any(valid):
+            from scipy.stats import dirichlet
+            # The 3rd coordinate for the Dirichlet distribution
+            Z_valid = Z.flatten()[valid]
+            # Stack the coordinates for the distribution input
+            XYZ_valid = np.vstack((XY[:, valid], Z_valid))
+            # Calculate the Dirichlet PDF
+            PDF[valid] = dirichlet.pdf(XYZ_valid.T, alpha)
+
+        # Reshape PDF back into the 2D shape of the grid
+        PDF = PDF.reshape(X.shape)
+
+        # Create a contour plot on the provided axis
+        contour = ax.contourf(X, Y, PDF, levels=15, cmap='Blues')
+        # Add a colorbar
+        plt.colorbar(contour, ax=ax, pad=0.05, aspect=10)
+        # Set limits and labels
+        ax.set_xlim(0, 1)
+        ax.set_ylim(0, 1)
+        ax.set_xticks([])
+        ax.set_yticks([])
+        ax.set_xlabel(r'$x_1$', fontsize=12)
+        ax.set_ylabel(r'$x_2$', fontsize=12)
+        # Set title for the subplot
+        ax.set_title(r'$\alpha = {}$'.format(alpha), fontsize=14)
+
+    # Define alpha parameters for the Dirichlet distributions to be plotted
+    alpha_params = [
+        (1.5, 1.5, 1.5),
+        (5.0, 5.0, 5.0),
+        (1.0, 2.0, 2.0),
+        (2.0, 4.0, 8.0)
+    ]
+
+    # Create a figure with subplots
+    fig, axes = plt.subplots(2, 2, figsize=(10, 8))
+
+    # Loop through the list of alpha parameters
+    for alpha, ax in zip(alpha_params, axes.flatten()):
+        plot_dirichlet(alpha, ax)
+
+    plt.savefig(f"{OUT}/dirichlet.{EXT}")
+    plt.close()
+
+
+def exponential():
+    # Defining the Exponential distribution PDF
+    def y(lmbda, x):
+        from scipy.stats import expon
+        return expon.pdf(x, scale=1 / lmbda)
+
+    # Possible values of lambda for the distribution
+    lambda_values = [0.5, 1, 2]
+    # Possible values for the distribution
+    x = np.linspace(0, 5, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of lambda
+    for lmbda in lambda_values:
+        ax.plot(x, y(lmbda, x), label=f'λ = {lmbda}')
+
+    # Adding title and labels
+    ax.set_title('Exponential distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/exponential.{EXT}")
+    plt.close()
+
+
+def gamma():
+    # Defining the Gamma distribution PDF
+    def y(k, theta, x):
+        from scipy.stats import gamma
+        return gamma.pdf(x, k, scale=theta)
+
+    inputs = [(1, 1), (2, 1), (3, 1), (1, 2), (2, 2), (3, 2)]
+    # Possible values for the distribution
+    x = np.linspace(0, 7, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of alpha and beta
+    for k, theta in inputs:
+        ax.plot(x, y(k, theta, x), label=f'k = {k}, θ = {theta}')
+
+    # Adding title and labels
+    ax.set_title('Gamma distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/gamma.{EXT}")
+    plt.close()
+
+
+def poisson():
+    # Defining the Poisson distribution PMF
+    def y(lmbda, k):
+        from scipy.stats import poisson
+        return poisson.pmf(k, lmbda)
+
+    # Possible values of lambda for the distribution
+    lambda_values = [0.5, 1, 2, 4, 10]
+    # Possible outcomes for a Poisson distributed variable
+    outcomes = np.arange(0, 15)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PMF for each value of lambda
+    for i, lmbda in enumerate(lambda_values):
+        ax.plot(outcomes, y(lmbda, outcomes), 'o-', label=f'λ = {lmbda}')
+
+    # Adding title and labels
+    ax.set_title('Poisson distribution')
+    ax.set_xlabel('Outcome')
+    ax.set_ylabel('Probability')
+    ax.set_xticks(outcomes)  # set the ticks to be the outcome values
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/poisson.{EXT}")
+    plt.close()
+
+
+def weibull():
+    # Defining the Weibull distribution PDF
+    def y(alpha, x):
+        from scipy.stats import weibull_min
+        return weibull_min.pdf(x, alpha)
+
+    # Possible values of alpha for the distribution
+    alpha_values = [0.5, 1, 2]
+    # Possible values for the distribution
+    x = np.linspace(0, 5, 1000)
+
+    # Creating the figure and the axis
+    fig, ax = plt.subplots()
+
+    # Plotting the PDF for each value of alpha
+    for alpha in alpha_values:
+        ax.plot(x, y(alpha, x), label=f'α = {alpha}')
+
+    # Adding title and labels
+    ax.set_title('Weibull distribution')
+    ax.set_xlabel('x')
+    ax.set_ylabel('Probability density')
+
+    # Adding a legend
+    ax.legend()
+
+    plt.savefig(f"{OUT}/weibull.{EXT}")
+    plt.close()
+
+
+if __name__ == "__main__":
+    # standard_normal()
+    normal()
+    # chi_squared()
+    # binomial()
+    # cauchy()
+    # dirichlet()
+    # exponential()
+    # gamma()
+    # poisson()
+    # weibull()

rand_distr/plots/py/requirements.txt

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+numpy==1.26.4
+matplotlib==3.8.4
+scipy==1.13.0