import streamlit as st
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import random

# Configuring the page
st.set_page_config(page_title="Historical Statistics Calculator")

# Streamlit app layout
st.header("Calculate Statistics from Historical Data")

with st.expander("Data Generation Settings"):
    N = st.number_input("Define the number of elements for each data list:", min_value=10, max_value=1000, step=1, value=100)

    # Button to generate the numbers
    generate_button = st.button("Generate Data")

if generate_button:
    # Generate two lists of N random numbers each within a defined range
    x = [random.randint(0, 20) for _ in range(N)]
    y = [random.randint(0, 20) for _ in range(N)]

    st.session_state['x'] = x
    st.session_state['y'] = y

# Check if data is available in the session state
if 'x' in st.session_state and 'y' in st.session_state:
    x = st.session_state['x']
    y = st.session_state['y']

    # Calculate statistics
    x_bar = np.mean(x)
    y_bar = np.mean(y)

    st.subheader("Summary Statistics")
    col1, col2 = st.columns(2)
    with col1:
        st.metric("E(x)", f"{x_bar:.2f}")
        st.metric("var(x)", f"{np.var(x):.2f}")
    with col2:
        st.metric("E(y)", f"{y_bar:.2f}")
        st.metric("var(y)", f"{np.var(y):.2f}")

    # Correlation
    cov_xy = np.corrcoef(x, y)[0, 1]
    st.metric("Correlation (x, y)", f"{cov_xy:.2f}")

    # Plots
    fig, ax = plt.subplots()
    ax.scatter(x, y)
    ax.set_title("Scatter Plot of x vs y")
    ax.set_xlabel("x values")
    ax.set_ylabel("y values")
    st.pyplot(fig)

    # Plot of returns
    fig2, ax2 = plt.subplots()
    ax2.plot(np.arange(len(x)), x, label='x')
    ax2.plot(np.arange(len(y)), y, label='y')
    ax2.set_ylim(-10, 40)
    ax2.set_title("Time Series of Returns")
    ax2.set_xlabel("Time")
    ax2.set_ylabel("Returns")
    ax2.legend()
    st.pyplot(fig2)

    # Portfolio weights and returns calculation
    w_x = (x_bar - y_bar + np.var(y) - cov_xy * np.sqrt(np.var(x) * np.var(y))) / (
        np.var(x) + np.var(y) - 2 * cov_xy * np.sqrt(np.var(x) * np.var(y))
    )
    w_y = 1 - w_x

    var_r = (w_x**2)*np.var(x) + (w_y**2)*np.var(y) + 2*w_x*w_y*cov_xy*np.sqrt(np.var(x) * np.var(y))

    st.subheader("Portfolio Metrics")
    st.write("Assuming x and y represent portfolio returns:")
    st.write(f"Weight of x (w_x): {w_x:.2f}")
    st.write(f"Weight of y (w_y): {w_y:.2f}")
    st.write(f"Expected Portfolio Return (E(r)): {w_x*x_bar + w_y*y_bar:.2f}")
    st.write(f"Portfolio Variance (var(r)): {var_r:.2f}")

else:
    st.warning("Please generate data to display results.")