added different versions

Final/Home.py

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+import streamlit as st
+import torch 
+import plotly.graph_objects as go
+
+st.set_page_config(page_title="PyTorch Distributions")
+st.title('PyTorch Distributions')
+
+st.markdown("This is a Streamlit app that demonstrates the probability density functions of various PyTorch distributions. "
+            "Use the sidebar to select between continuous and discrete distributions, and set the parameters of the selected distribution.")
+
+st.markdown("---")

Final/config/config_continuous.py

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+import streamlit as st
+import torch
+
+CONTINUOUS_DISTRIBUTIONS = {
+    "Uniform": {
+        "params": lambda: {
+            "a": st.sidebar.slider("Lower Bound (a)", -10.0, 10.0, -5.0),
+            "b": st.sidebar.slider("Upper Bound (b)", -10.0, 10.0, 5.0),
+        },
+        "dist": lambda p: torch.distributions.Uniform(p["a"], p["b"]),
+        "support": lambda p: (p["a"], p["b"]),
+    },
+    "Normal": {
+        "params": lambda: {
+            "mu": st.sidebar.slider("Mean (μ)", -10.0, 10.0, 0.0),
+            "sigma": st.sidebar.slider("Standard Deviation (σ)", 0.1, 10.0, 1.0),
+        },
+        "dist": lambda p: torch.distributions.Normal(p["mu"], p["sigma"]),
+        "support": None,
+    },
+    "LogNormal": {
+        "params": lambda: {
+            "mu": st.sidebar.slider("Log Mean (μ)", -5.0, 5.0, 0.0),
+            "sigma": st.sidebar.slider("Log Std Dev (σ)", 0.1, 3.0, 1.0),
+        },
+        "dist": lambda p: torch.distributions.LogNormal(p["mu"], p["sigma"]),
+        "support": lambda p: (0, None),
+    }
+}

Final/config/config_discrete.py

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+import streamlit as st
+import torch
+
+DISCRETE_DISTRIBUTIONS = {
+    "Binomial": {
+        "params": lambda: {
+            "n": st.sidebar.slider("Total Count (n)", 1, 20, 10),
+            "p": st.sidebar.slider("Success Probability (p)", 0.0, 1.0, 0.5),
+        },
+        "dist": lambda p: torch.distributions.Binomial(p["n"], p["p"]),
+        "support": lambda p: (0, p["n"]),
+    },
+    "Poisson": {
+        "params": lambda: {
+            "lambda": st.sidebar.slider("Rate (λ)", 0.1, 10.0, 3.0),
+        },
+        "dist": lambda p: torch.distributions.Poisson(p["lambda"]),
+        "support": lambda p: (0, None),
+    }
+}

Final/pages/Continuous.py

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+import streamlit as st
+import torch
+import plotly.graph_objects as go
+from config.config_continuous import CONTINUOUS_DISTRIBUTIONS
+from utils import compute_pdf
+
+st.title("Continuous Distributions")
+
+selected_dist = st.sidebar.selectbox("Choose a Distribution", list(CONTINUOUS_DISTRIBUTIONS.keys()))
+params = CONTINUOUS_DISTRIBUTIONS[selected_dist]["params"]()
+dist = CONTINUOUS_DISTRIBUTIONS[selected_dist]["dist"](params)
+support = CONTINUOUS_DISTRIBUTIONS[selected_dist].get("support")
+support = support(params) if callable(support) else None
+
+x_range = torch.linspace(-10, 10, 1000)
+pdf = compute_pdf(dist, x_range, support)
+
+fig = go.Figure()
+fig.add_trace(go.Scatter(x=x_range.numpy(), y=pdf.numpy(), mode="lines", name=selected_dist))
+st.plotly_chart(fig)

Final/pages/Discrete.py

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+import streamlit as st
+import torch
+import plotly.graph_objects as go
+from config.config_discrete import DISCRETE_DISTRIBUTIONS
+
+st.title("Discrete Distributions")
+
+selected_dist = st.sidebar.selectbox("Choose a Distribution", list(DISCRETE_DISTRIBUTIONS.keys()))
+params = DISCRETE_DISTRIBUTIONS[selected_dist]["params"]()
+dist = DISCRETE_DISTRIBUTIONS[selected_dist]["dist"](params)
+support = DISCRETE_DISTRIBUTIONS[selected_dist].get("support")
+support = support(params) if callable(support) else None
+
+if support:
+    min_val, max_val = support
+    x_range = torch.arange(min_val, max_val + 1 if max_val is not None else 20)
+else:
+    x_range = torch.arange(0, 20)
+
+pmf = dist.log_prob(x_range).exp()
+
+fig = go.Figure()
+fig.add_trace(go.Bar(x=x_range.numpy(), y=pmf.numpy(), name=selected_dist))
+st.plotly_chart(fig)

Final/utils.py

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+import torch
+
+def compute_pdf(dist, x_range, support):
+    pdf = torch.zeros_like(x_range, dtype=torch.float)
+
+    if support:
+        min_val, max_val = support
+        mask = (x_range >= min_val) if min_val is not None else torch.ones_like(x_range, dtype=torch.bool)
+        if max_val is not None:
+            mask &= (x_range <= max_val)
+    else:
+        mask = torch.ones_like(x_range, dtype=torch.bool)
+
+    pdf[mask] = dist.log_prob(x_range[mask]).exp()
+    return pdf

app-v1.py

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+import streamlit as st
+import torch 
+import matplotlib.pyplot as plt
+
+st.title('PyTorch Distributions')
+
+mu = st.slider('Mean', -10.0, 10.0, 0.0)
+sigma = st.slider('Standard Deviation', 0.1, 10.0, 1.0)
+
+normal_dist = torch.distributions.Normal(mu, sigma)
+
+x_range = torch.linspace(-10, 10, 1000)
+pdf = normal_dist.log_prob(x_range).exp()
+
+plt.plot(x_range.numpy(), pdf.numpy())
+plt.xlabel('x')
+plt.ylabel('Probability Density')
+st.pyplot(plt)
+
+

app-v2.py

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+"""
+v2: In this version, beyond v1, we will add some LaTeX and Markdown to the app.
+"""
+
+import streamlit as st
+import torch 
+import matplotlib.pyplot as plt
+
+st.title('PyTorch Distributions')
+
+mu = st.slider('Mean', -10.0, 10.0, 0.0)
+sigma = st.slider('Standard Deviation', 0.1, 10.0, 1.0)
+
+normal_dist = torch.distributions.Normal(mu, sigma)
+
+x_range = torch.linspace(-10, 10, 1000)
+pdf = normal_dist.log_prob(x_range).exp()
+
+st.markdown('The **probability density function** of a normal distribution is given by:')
+st.latex(r'f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)')
+
+
+plt.plot(x_range.numpy(), pdf.numpy())
+plt.xlabel('x')
+plt.ylabel('Probability Density')
+st.pyplot(plt)
+
+

app-v3.py

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+"""
+v3: In this version, beyond v2, we will add a table to mention some properties of the normal distribution. 
+We wcan do this via the st.table() function.
+"""
+
+import streamlit as st
+import torch 
+import matplotlib.pyplot as plt
+import pandas as pd
+
+
+st.title('PyTorch Distributions')
+
+mu = st.slider('Mean', -10.0, 10.0, 0.0)
+sigma = st.slider('Standard Deviation', 0.1, 10.0, 1.0)
+
+normal_dist = torch.distributions.Normal(mu, sigma)
+
+x_range = torch.linspace(-10, 10, 1000)
+pdf = normal_dist.log_prob(x_range).exp()
+
+st.markdown('The **probability density function** of a normal distribution is given by:')
+st.latex(r'f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)')
+
+
+data = {
+    'Property': ['Mean', 'Standard Deviation', 'Variance', 'Entropy'],
+    'Value': [mu, sigma, sigma**2, normal_dist.entropy().item()]
+}
+
+df = pd.DataFrame(data)
+st.table(df)
+
+
+plt.plot(x_range.numpy(), pdf.numpy())
+plt.xlabel('x')
+plt.ylabel('Probability Density')
+st.pyplot(plt)
+
+

app-v4.py

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+"""
+v4: In this version, beyond v3, we will make the graph interactive using st.LineChart and plotly.
+"""
+
+import streamlit as st
+import torch 
+import matplotlib.pyplot as plt
+import pandas as pd
+import plotly.graph_objects as go
+
+
+
+st.title('PyTorch Distributions')
+
+mu = st.slider('Mean', -10.0, 10.0, 0.0)
+sigma = st.slider('Standard Deviation', 0.1, 10.0, 1.0)
+
+normal_dist = torch.distributions.Normal(mu, sigma)
+
+x_range = torch.linspace(-10, 10, 1000)
+pdf = normal_dist.log_prob(x_range).exp()
+
+st.markdown('The **probability density function** of a normal distribution is given by:')
+st.latex(r'f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)')
+
+
+data = {
+    'Property': ['Mean', 'Standard Deviation', 'Variance', 'Entropy'],
+    'Value': [mu, sigma, sigma**2, normal_dist.entropy().item()]
+}
+
+df = pd.DataFrame(data)
+st.table(df)
+
+chart_data = pd.DataFrame({"x": x_range, "pdf": pdf})
+st.markdown('#### Probability Density Function (made using `st.line_chart`)')
+st.line_chart(chart_data, x='x', y='pdf', x_label='x', y_label='f(x)', use_container_width=True)
+
+st.markdown('#### Probability Density Function (made using `plotly`)')
+fig = go.Figure()
+fig.add_trace(go.Scatter(x=x_range, y=pdf, mode='lines', name='',
+                         hovertemplate='x: %{x:.2f}<br>f(x): %{y:.2f}'))
+fig.update_layout(xaxis_title='x', yaxis_title='f(x)')
+
+st.plotly_chart(fig)
+
+
+
+

app-v5.py

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+"""
+v5: In this version, beyond v4, we will:
+- only be using plotly
+- add a sidebar for capturing user input and right side for displaying the plot
+"""
+
+import streamlit as st
+import torch 
+import pandas as pd
+import plotly.graph_objects as go
+
+st.title('PyTorch Distributions')
+
+# Sidebar for user input
+st.sidebar.header("Distribution Parameters")
+mu = st.sidebar.slider('Mean (\u03BC)', -10.0, 10.0, 0.0)
+sigma = st.sidebar.slider('Standard Deviation (\u03C3)', 0.1, 10.0, 1.0)
+
+normal_dist = torch.distributions.Normal(mu, sigma)
+
+x_range = torch.linspace(-10, 10, 1000)
+pdf = normal_dist.log_prob(x_range).exp()
+
+st.sidebar.markdown("### Selected Parameters")
+st.sidebar.write(f"**Mean (\u03BC):** {mu:.2f}")
+st.sidebar.write(f"**Standard Deviation (\u03C3):** {sigma:.2f}")
+st.sidebar.write(f"**Variance:** {sigma**2:.4f}")
+st.sidebar.write(f"**Entropy:** {normal_dist.entropy().item():.4f}")
+
+# Main plot area
+st.markdown('#### Probability Density Function')
+fig = go.Figure()
+fig.add_trace(go.Scatter(x=x_range, y=pdf, mode='lines',
+                         name='', hovertemplate='x: %{x:.4f}<br>f(x): %{y:.4f}'))
+fig.update_layout(xaxis_title='x', yaxis_title='f(x)', showlegend=False)
+
+st.plotly_chart(fig)

app-v6.py

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+"""
+v6: In this version, beyond v5, we will:
+- use a selectbox to choose the distribution type amongst: Normal and Uniform
+- use a slider to set the parameters of the selected distribution
+- display the selected parameters in the sidebar
+"""
+
+import streamlit as st
+import torch 
+import pandas as pd
+import plotly.graph_objects as go
+
+st.title('PyTorch Distributions')
+
+# Sidebar for user input
+st.sidebar.header("Distribution Parameters")
+
+dist_type = st.sidebar.selectbox("Select Distribution", ["Normal", "Uniform"])
+x_range = torch.linspace(-10, 10, 1000)
+
+if dist_type == "Normal":
+    mu = st.sidebar.slider('Mean (μ)', -10.0, 10.0, 0.0)
+    sigma = st.sidebar.slider('Standard Deviation (σ)', 0.1, 10.0, 1.0)
+    dist = torch.distributions.Normal(mu, sigma)
+    pdf = dist.log_prob(x_range).exp()
+    st.sidebar.markdown("### Selected Parameters")
+    st.sidebar.write(f"**Mean (μ):** {mu:.2f}")
+    st.sidebar.write(f"**Standard Deviation (σ):** {sigma:.2f}")
+    st.sidebar.write(f"**Entropy:** {dist.entropy().item():.2f}")
+
+elif dist_type == "Uniform":
+    a = st.sidebar.slider('Lower Bound (a)', -10.0, 10.0, -5.0)
+    b = st.sidebar.slider('Upper Bound (b)', -10.0, 10.0, 5.0)
+    if a >= b:
+        st.sidebar.error("Lower bound must be less than upper bound")
+    else:
+        dist = torch.distributions.Uniform(a, b)
+        x_mask = (x_range >= a) & (x_range <= b)
+        pdf = torch.zeros_like(x_range)
+        pdf[x_mask] = torch.distributions.Uniform(a, b).log_prob(x_range[x_mask]).exp()
+        
+        st.sidebar.markdown("### Selected Parameters")
+        st.sidebar.write(f"**Lower Bound (a):** {a:.2f}")
+        st.sidebar.write(f"**Upper Bound (b):** {b:.2f}")
+        st.sidebar.write(f"**Entropy:** {dist.entropy().item():.2f}")
+
+# Main plot area
+st.markdown(f'#### Probability Density Function for {dist_type} Distribution')
+fig = go.Figure()
+fig.add_trace(go.Scatter(x=x_range, y=pdf, mode='lines',
+                         name='', hovertemplate='x: %{x:.2f}<br>f(x): %{y:.2f}'))
+fig.update_layout(xaxis_title='x', yaxis_title='f(x)', showlegend=False)
+
+st.plotly_chart(fig)

multipage-v1/Home.py

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+import streamlit as st
+import torch 
+import plotly.graph_objects as go
+
+st.set_page_config(page_title="PyTorch Distributions")
+st.title('PyTorch Distributions')
+
+st.markdown("This is a Streamlit app that demonstrates the probability density functions of various PyTorch distributions. "
+            "Use the sidebar to select between continuous and discrete distributions, and set the parameters of the selected distribution.")
+
+st.markdown("---")

multipage-v1/pages/Continuous.py

@@ -0,0 +1,49 @@
+import streamlit as st
+import torch
+import plotly.graph_objects as go
+
+st.title("Continuous Distributions")
+
+# Sidebar selection
+dist_type = st.sidebar.radio("Select Distribution", ["Normal", "Uniform"])
+
+# Common x range
+x_range = torch.linspace(-10, 10, 1000)
+pdf = torch.zeros_like(x_range)
+
+if dist_type == "Normal":
+    st.sidebar.header("Normal Distribution Parameters")
+    mu = st.sidebar.slider("Mean (μ)", -10.0, 10.0, 0.0)
+    sigma = st.sidebar.slider("Standard Deviation (σ)", 0.1, 10.0, 1.0)
+    
+    dist = torch.distributions.Normal(mu, sigma)
+    pdf = dist.log_prob(x_range).exp()
+
+    st.sidebar.markdown("### Selected Parameters")
+    st.sidebar.write(f"**Mean (μ):** {mu:.2f}")
+    st.sidebar.write(f"**Standard Deviation (σ):** {sigma:.2f}")
+    st.sidebar.write(f"**Entropy:** {dist.entropy().item():.2f}")
+
+elif dist_type == "Uniform":
+    st.sidebar.header("Uniform Distribution Parameters")
+    a = st.sidebar.slider("Lower Bound (a)", -10.0, 10.0, -5.0)
+    b = st.sidebar.slider("Upper Bound (b)", -10.0, 10.0, 5.0)
+    
+    if a >= b:
+        st.sidebar.error("Lower bound must be less than upper bound")
+    else:
+        dist = torch.distributions.Uniform(a, b)
+        mask = (x_range >= a) & (x_range <= b)
+        pdf[mask] = dist.log_prob(x_range[mask]).exp()
+
+        st.sidebar.markdown("### Selected Parameters")
+        st.sidebar.write(f"**Lower Bound (a):** {a:.2f}")
+        st.sidebar.write(f"**Upper Bound (b):** {b:.2f}")
+        st.sidebar.write(f"**Entropy:** {dist.entropy().item():.2f}")
+
+# Plot
+st.markdown(f'#### Probability Density Function for {dist_type} Distribution')
+fig = go.Figure()
+fig.add_trace(go.Scatter(x=x_range, y=pdf, mode='lines'))
+fig.update_layout(xaxis_title='x', yaxis_title='f(x)', showlegend=False)
+st.plotly_chart(fig)

multipage-v1/pages/Discrete.py

@@ -0,0 +1,48 @@
+import streamlit as st
+import torch
+import plotly.graph_objects as go
+
+st.title("Discrete Distributions")
+
+# Sidebar selection
+dist_type = st.sidebar.radio("Select Distribution", ["Poisson", "Binomial"])
+
+# Common x range for discrete distributions
+x_range = torch.arange(0, 20, 1)
+pmf = torch.zeros_like(x_range, dtype=torch.float)
+
+if dist_type == "Poisson":
+    st.sidebar.header("Poisson Distribution Parameters")
+    lambda_ = st.sidebar.slider("Rate (λ)", 0.1, 10.0, 3.0)
+    
+    dist = torch.distributions.Poisson(lambda_)
+    pmf = torch.exp(dist.log_prob(x_range))
+
+    st.sidebar.markdown("### Selected Parameters")
+    st.sidebar.write(f"**Rate (λ):** {lambda_:.2f}")
+    st.sidebar.write(f"**Mean:** {dist.mean.item():.2f}")
+    st.sidebar.write(f"**Variance:** {dist.variance.item():.2f}")
+
+elif dist_type == "Binomial":
+    st.sidebar.header("Binomial Distribution Parameters")
+    n = st.sidebar.slider("Number of Trials (n)", 1, 20, 10)
+    p = st.sidebar.slider("Success Probability (p)", 0.01, 1.0, 0.5)
+    
+    dist = torch.distributions.Binomial(n, torch.tensor(p))
+    
+    # Adjust x_range to be within [0, n]
+    x_range = torch.arange(0, n + 1)  
+    pmf = torch.exp(dist.log_prob(x_range))
+
+    st.sidebar.markdown("### Selected Parameters")
+    st.sidebar.write(f"**Trials (n):** {n}")
+    st.sidebar.write(f"**Probability (p):** {p:.2f}")
+    st.sidebar.write(f"**Mean:** {dist.mean.item():.2f}")
+    st.sidebar.write(f"**Variance:** {dist.variance.item():.2f}")
+
+# Plot
+st.markdown(f'#### Probability Mass Function for {dist_type} Distribution')
+fig = go.Figure()
+fig.add_trace(go.Bar(x=x_range.tolist(), y=pmf.tolist()))
+fig.update_layout(xaxis_title='x', yaxis_title='P(x)', showlegend=False)
+st.plotly_chart(fig)