feat: probability-explorer prototype

Author: peplxx

.gitignore

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+# Python-generated files
+__pycache__/
+*.py[oc]
+build/
+dist/
+wheels/
+*.egg-info
+
+# Virtual environments
+.venv

README.md

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+import streamlit as st
+import numpy as np
+import matplotlib.pyplot as plt
+import scipy.special
+import math
+from scipy.stats import multivariate_normal
+st.title("Probability Explorer")
+
+# Create two columns for layout
+left_col, right_col = st.columns([1, 2])
+
+with left_col:
+    # Add interactive elements for probability exploration
+    # Select distribution type
+    dist_type = st.selectbox(
+        'Select probability distribution',
+        ['Multivariate Normal', 'Binomial', 'Normal', 'Poisson', 'Uniform']
+    )
+    st.write(f'Selected distribution: {dist_type}')
+
+    # Parameters based on distribution type
+    if dist_type == 'Multivariate Normal':
+        st.write('Mean Vector:')
+        mean1 = st.slider('μ₁', -5.0, 5.0, 0.0, 0.1)
+        mean2 = st.slider('μ₂', -5.0, 5.0, 0.0, 0.1)
+        
+        st.write('Covariance Matrix:')
+        var1 = st.slider('σ₁²', 0.1, 5.0, 1.0, 0.1)
+        var2 = st.slider('σ₂²', 0.1, 5.0, 1.0, 0.1)
+        corr = st.slider('Correlation ρ', -1.0, 1.0, 0.0, 0.1)
+        
+        # Calculate covariance from correlation
+        cov12 = corr * np.sqrt(var1 * var2)
+        
+        # Display covariance matrix
+        cov_matrix = np.array([[var1, cov12], [cov12, var2]])
+        st.write("Covariance Matrix:")
+        st.write(cov_matrix)
+        
+    elif dist_type == 'Normal':
+        mean = st.slider('Mean', -10.0, 10.0, 0.0, 0.1)
+        std = st.slider('Standard deviation', 0.1, 5.0, 1.0, 0.1)
+        st.write(f'Mean: {mean}, Standard deviation: {std}')
+    elif dist_type == 'Uniform':
+        a = st.slider('Lower bound (a)', -10.0, 10.0, 0.0, 0.1)
+        b = st.slider('Upper bound (b)', -10.0, 10.0, 1.0, 0.1)
+        if b <= a:
+            st.error('Upper bound must be greater than lower bound')
+            b = a + 0.1
+    else:
+        # Slider for probability value
+        probability = st.slider('Select a probability value', 0.0, 1.0, 0.5, 0.1)
+        st.write(f'Selected probability: {probability}')
+
+        # Number of trials input
+        trials = st.number_input('Number of trials', min_value=1, value=100)
+        st.write(f'Number of trials: {trials}')
+
+    # Add auto-update toggle
+    auto_update = st.checkbox('Auto-update plot', value=True)
+
+    # Set confidence level
+    confidence = 0.95
+
+def calculate_and_plot():
+    # Add these lines at the start of the function to access the variables
+    global mean, std, probability, trials, a, b, mean1, mean2, var1, var2, cov12
+    
+    with right_col:
+        st.write('Calculating probability distribution...')
+        
+        # Display formula based on distribution type
+        if dist_type == 'Multivariate Normal':
+            st.latex(r'f(x) = \frac{1}{2\pi|\Sigma|^{1/2}} \exp\left(-\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu)\right)')
+        elif dist_type == 'Normal':
+            st.latex(r'f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}')
+        elif dist_type == 'Binomial':
+            st.latex(r'P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}')
+        elif dist_type == 'Poisson':
+            st.latex(r'P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}')
+        elif dist_type == 'Uniform':
+            st.latex(r'f(x) = \frac{1}{b-a} \text{ for } a \leq x \leq b')
+        
+        # Create figure
+        fig, ax = plt.subplots()
+        
+        # Generate data based on selected distribution
+        if dist_type == 'Multivariate Normal':
+            # Create grid of points
+            x, y = np.mgrid[-5:5:.01, -5:5:.01]
+            pos = np.dstack((x, y))
+            
+            # Define distribution parameters
+            mean = [mean1, mean2]
+            cov = [[var1, cov12], [cov12, var2]]
+            
+            # Create multivariate normal distribution
+            rv = multivariate_normal(mean, cov)
+            
+            # Calculate pdf
+            z = rv.pdf(pos)
+            
+            # Create contour plot
+            plt.contourf(x, y, z, levels=20, cmap='viridis')
+            plt.colorbar(label='Probability Density')
+            
+            ax.set_xlabel('X₁')
+            ax.set_ylabel('X₂')
+            
+        elif dist_type == 'Normal':
+            x = np.linspace(mean - 4*std, mean + 4*std, 100)
+            y = np.exp(-((x - mean)**2)/(2*std**2))/(std*np.sqrt(2*np.pi))
+            ax.plot(x, y)
+        elif dist_type == 'Binomial':
+            x = np.arange(0, trials + 1)
+            y = [scipy.special.comb(trials, k) * (probability**k) * ((1-probability)**(trials-k)) for k in x]
+            ax.plot(x, y)
+        elif dist_type == 'Poisson':
+            x = np.arange(0, trials + 1)
+            y = [(probability**k * np.exp(-probability))/math.factorial(k) for k in x]
+            ax.plot(x, y)
+        elif dist_type == 'Uniform':
+            x = np.linspace(a - 0.5, b + 0.5, 100)
+            y = np.where((x >= a) & (x <= b), 1/(b-a), 0)
+            ax.plot(x, y)
+
+        ax.set_title(f'{dist_type} Distribution')
+        ax.grid(True)
+        
+        # Display plot in Streamlit
+        st.pyplot(fig)
+        st.success(icon="🔥", body="Distribution calculated!")
+
+# Calculate either on button press or automatically based on toggle
+if auto_update:
+    calculate_and_plot()
+else:
+    with left_col:
+        if st.button('Calculate Distribution'):
+            calculate_and_plot()

hello.py

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+[project]
+name = "probabilty-explorer"
+version = "0.1.0"
+description = "Add your description here"
+readme = "README.md"
+requires-python = ">=3.10"
+dependencies = [
+    "matplotlib>=3.9.2",
+    "scipy>=1.14.1",
+    "streamlit>=1.40.1",
+]