# Import necessary libraries
import streamlit as st
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
import plotly.graph_objects as go

# Define the functions from your code
def Phi(z):
    return norm.cdf(z)

def phi(z):
    return norm.pdf(z)

# Define the BCNOLLN CDF based on the provided formula
def F_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd):
    # Convert y1, y2 to z-scores
    z1 = (y1 - mu1) / sigma1
    z2 = (y2 - mu2) / sigma2
    
    # Compute H functions
    H1_z1 = Phi(z1)**alpha1 + (1 - Phi(z1))**beta1
    H2_z2 = Phi(z2)**alpha2 + (1 - Phi(z2))**beta2
    
    # Compute the BCNOLLN CDF
    term1 = (Phi(z1)*alpha1 / H1_z1)**(-lambd)
    term2 = (Phi(z2)*alpha2 / H2_z2)**(-lambd)
    term = term1 + term2 - 1
    cdf = term**(-1/lambd)
    
    return cdf

def f_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd):
    z1 = (y1 - mu1) / sigma1
    z2 = (y2 - mu2) / sigma2
    
    H1_z1 = Phi(z1)**alpha1 + (1 - Phi(z1))**beta1
    H2_z2 = Phi(z2)**alpha2 + (1 - Phi(z2))**beta2
    
    term1 = (Phi(z1)**alpha1 / H1_z1)**(-lambd)
    term2 = (Phi(z2)**alpha2 / H2_z2)**(-lambd)
    common_term = (term1 + term2 - 1)**(-(2*lambd + 1)/lambd)
    
    factor1 = (phi(z1) * Phi(z1)**(alpha1 - 1) * (1 - Phi(z1))**(beta1 - 1) *
               (alpha1 + (beta1 - alpha1) * Phi(z1))) / (sigma1 * H1_z1**2)
    
    factor2 = (phi(z2) * Phi(z2)**(alpha2 - 1) * (1 - Phi(z2))**(beta2 - 1) *
               (alpha2 + (beta2 - alpha2) * Phi(z2))) / (sigma2 * H2_z2**2)
    
    pdf = (lambd + 1) * common_term * (factor1 * factor2)
    
    return pdf

# Streamlit app
st.title('BCNOLLN Distribution Visualizer')

# Input fields for parameters
mu1 = st.sidebar.number_input('Mean μ1', value=0.0)
sigma1 = st.sidebar.number_input('Standard deviation σ1', value=1.0, min_value=0.1)
alpha1 = st.sidebar.number_input('Alpha1 α1', value=0.2, min_value=0.0, max_value=1.0)
beta1 = st.sidebar.number_input('Beta1 β1', value=0.2, min_value=0.0, max_value=1.0)

mu2 = st.sidebar.number_input('Mean μ2', value=0.0)
sigma2 = st.sidebar.number_input('Standard deviation σ2', value=1.0, min_value=0.1)
alpha2 = st.sidebar.number_input('Alpha2 α2', value=0.9, min_value=0.0, max_value=1.0)
beta2 = st.sidebar.number_input('Beta2 β2', value=0.3, min_value=0.0, max_value=1.0)

lambd = st.sidebar.number_input('Lambda λ', value=-0.5)

# Generate y1 and y2 values
y1, y2 = np.meshgrid(np.linspace(-3, 3, 100), np.linspace(-3, 3, 100))

# Calculate PDF values
pdf_values = f_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd)

# Calculate CDF values
cdf_values = F_BCNOLLN(y1, y2, mu1, sigma1, alpha1, beta1, mu2, sigma2, alpha2, beta2, lambd)


# Plotting
#fig, ax = plt.subplots()
#cp = ax.contourf(y1, y2, pdf_values, cmap='viridis')
#fig.colorbar(cp)
#ax.set_title('BCNOLLN PDF Contour Plot')
#ax.set_xlabel('y1')
#ax.set_ylabel('y2')


# Create a 3D contour plot with Plotly
fig = go.Figure(data=[go.Surface(z=pdf_values, x=y1, y=y2, colorscale='Viridis')])
fig.update_layout(title='BCNOLLN PDF 3D Contour Plot', autosize=True,
                  scene=dict(
                      xaxis_title='y1',
                      yaxis_title='y2',
                      zaxis_title='PDF'
                  ))

# Display the plot in Streamlit
st.plotly_chart(fig)

# Create a 3D contour plot with Plotly
fig = go.Figure(data=[go.Surface(z=cdf_values, x=y1, y=y2, colorscale='Viridis')])
fig.update_layout(title='BCNOLLN CDF 3D Contour Plot', autosize=True,
                  scene=dict(
                      xaxis_title='y1',
                      yaxis_title='y2',
                      zaxis_title='PDF'
                  ))

# Display the plot in Streamlit
st.plotly_chart(fig)

#st.pyplot(fig)