app.py

import streamlit as st
import subprocess
import os
import json
import numpy as np
import plotly.graph_objects as go
from PIL import Image
import time
import io
import sys
import tempfile
import platform

# Set page config with wider layout
st.set_page_config(
    page_title="Matrix Analysis Dashboard",
    page_icon="📊",
    layout="wide",
    initial_sidebar_state="expanded"
)

# Apply custom CSS for a dashboard-like appearance
st.markdown("""
<style>
    .main-header {
        font-size: 2.5rem;
        color: #1E88E5;
        text-align: center;
        margin-bottom: 1rem;
        padding-bottom: 1rem;
        border-bottom: 2px solid #f0f0f0;
    }
    .dashboard-container {
        background-color: #f9f9f9;
        padding: 1.5rem;
        border-radius: 10px;
        box-shadow: 0 2px 5px rgba(0,0,0,0.1);
        margin-bottom: 1.5rem;
    }
    .panel-header {
        font-size: 1.3rem;
        font-weight: bold;
        margin-bottom: 1rem;
        color: #424242;
        border-left: 4px solid #1E88E5;
        padding-left: 10px;
    }
    .stTabs [data-baseweb="tab-list"] {
        gap: 12px;
    }
    .stTabs [data-baseweb="tab"] {
        height: 50px;
        white-space: pre-wrap;
        background-color: #f0f0f0;
        border-radius: 6px 6px 0 0;
        gap: 1;
        padding-top: 10px;
        padding-bottom: 10px;
    }
    .stTabs [aria-selected="true"] {
        background-color: #1E88E5 !important;
        color: white !important;
    }
    .math-box {
        background-color: #f8f9fa;
        border-left: 3px solid #1E88E5;
        padding: 10px;
        margin: 10px 0;
    }
    .explanation-box {
        background-color: #e8f4f8;
        padding: 15px;
        border-radius: 5px;
        margin-top: 20px;
        border-left: 3px solid #1E88E5;
    }
    .parameter-container {
        background-color: #f0f7fa;
        padding: 15px;
        border-radius: 5px;
        margin-bottom: 15px;
    }
    .stWarning {
        background-color: #fff3cd;
        padding: 10px;
        border-left: 3px solid #ffc107;
        margin: 10px 0;
    }
    .stSuccess {
        background-color: #d4edda;
        padding: 10px;
        border-left: 3px solid #28a745;
        margin: 10px 0;
    }
    .plot-container {
        margin-top: 1.5rem;
    }
    .footnote {
        font-size: 0.8rem;
        color: #6c757d;
        margin-top: 2rem;
    }
</style>
""", unsafe_allow_html=True)

# Dashboard Header
st.markdown('<h1 class="main-header">Matrix Analysis Dashboard</h1>', unsafe_allow_html=True)

# Create output directory in the current working directory
current_dir = os.getcwd()
output_dir = os.path.join(current_dir, "output")
os.makedirs(output_dir, exist_ok=True)

# Path to the C++ source file and executable
cpp_file = os.path.join(current_dir, "app.cpp")
executable = os.path.join(current_dir, "eigen_analysis")
if platform.system() == "Windows":
    executable += ".exe"

# Helper function for running commands with better debugging
def run_command(cmd, show_output=True, timeout=None):
    cmd_str = " ".join(cmd)
    if show_output:
        st.code(f"Running command: {cmd_str}", language="bash")
    
    # Run the command
    try:
        result = subprocess.run(
            cmd,
            stdout=subprocess.PIPE,
            stderr=subprocess.PIPE,
            text=True,
            check=False,
            timeout=timeout
        )
        
        if result.returncode == 0:
            if show_output:
                st.success("Command completed successfully.")
                if result.stdout and show_output:
                    with st.expander("Command Output"):
                        st.code(result.stdout)
            return True, result.stdout, result.stderr
        else:
            if show_output:
                st.error(f"Command failed with return code {result.returncode}")
                st.error(f"Command: {cmd_str}")
                st.error(f"Error output: {result.stderr}")
            return False, result.stdout, result.stderr
    
    except subprocess.TimeoutExpired:
        if show_output:
            st.error(f"Command timed out after {timeout} seconds")
        return False, "", f"Command timed out after {timeout} seconds"
    except Exception as e:
        if show_output:
            st.error(f"Error executing command: {str(e)}")
        return False, "", str(e)

# Check if C++ source file exists
if not os.path.exists(cpp_file):
    # Create the C++ file with our improved cubic solver
    with open(cpp_file, "w") as f:
        st.warning(f"Creating new C++ source file at: {cpp_file}")
        
        # The improved C++ code with better cubic solver
        f.write('''
// app.cpp - Modified version for command line arguments with improved cubic solver
#include <opencv2/opencv.hpp>
#include <algorithm>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <numeric>
#include <random>
#include <vector>
#include <limits>
#include <sstream>
#include <string>
#include <fstream>
#include <complex>
#include <stdexcept>

// Struct to hold cubic equation roots
struct CubicRoots {
    std::complex<double> root1;
    std::complex<double> root2;
    std::complex<double> root3;
};

// Function to solve cubic equation: az^3 + bz^2 + cz + d = 0
// Improved to properly handle zero roots and classification of positive/negative
CubicRoots solveCubic(double a, double b, double c, double d) {
    // Constants for numerical stability
    const double epsilon = 1e-14;
    const double zero_threshold = 1e-10;  // Threshold for considering a value as zero
    
    // Handle special case for a == 0 (quadratic)
    if (std::abs(a) < epsilon) {
        CubicRoots roots;
        // For a quadratic equation: bz^2 + cz + d = 0
        if (std::abs(b) < epsilon) {  // Linear equation or constant
            if (std::abs(c) < epsilon) {  // Constant - no finite roots
                roots.root1 = std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 0.0);
                roots.root2 = std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 0.0);
                roots.root3 = std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 0.0);
            } else {  // Linear equation
                roots.root1 = std::complex<double>(-d / c, 0.0);
                roots.root2 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
                roots.root3 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
            }
            return roots;
        }
        
        double discriminant = c * c - 4.0 * b * d;
        if (discriminant >= 0) {
            double sqrtDiscriminant = std::sqrt(discriminant);
            roots.root1 = std::complex<double>((-c + sqrtDiscriminant) / (2.0 * b), 0.0);
            roots.root2 = std::complex<double>((-c - sqrtDiscriminant) / (2.0 * b), 0.0);
            roots.root3 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
        } else {
            double real = -c / (2.0 * b);
            double imag = std::sqrt(-discriminant) / (2.0 * b);
            roots.root1 = std::complex<double>(real, imag);
            roots.root2 = std::complex<double>(real, -imag);
            roots.root3 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
        }
        return roots;
    }

    // Handle special case when d is zero - one root is zero
    if (std::abs(d) < epsilon) {
        // Factor out z: z(az^2 + bz + c) = 0
        CubicRoots roots;
        roots.root1 = std::complex<double>(0.0, 0.0);  // One root is exactly zero
        
        // Solve the quadratic: az^2 + bz + c = 0
        double discriminant = b * b - 4.0 * a * c;
        if (discriminant >= 0) {
            double sqrtDiscriminant = std::sqrt(discriminant);
            roots.root2 = std::complex<double>((-b + sqrtDiscriminant) / (2.0 * a), 0.0);
            roots.root3 = std::complex<double>((-b - sqrtDiscriminant) / (2.0 * a), 0.0);
        } else {
            double real = -b / (2.0 * a);
            double imag = std::sqrt(-discriminant) / (2.0 * a);
            roots.root2 = std::complex<double>(real, imag);
            roots.root3 = std::complex<double>(real, -imag);
        }
        return roots;
    }

    // Normalize equation: z^3 + (b/a)z^2 + (c/a)z + (d/a) = 0
    double p = b / a;
    double q = c / a;
    double r = d / a;

    // Substitute z = t - p/3 to get t^3 + pt^2 + qt + r = 0
    double p1 = q - p * p / 3.0;
    double q1 = r - p * q / 3.0 + 2.0 * p * p * p / 27.0;

    // Calculate discriminant
    double D = q1 * q1 / 4.0 + p1 * p1 * p1 / 27.0;

    // Precompute values
    const double two_pi = 2.0 * M_PI;
    const double third = 1.0 / 3.0;
    const double p_over_3 = p / 3.0;

    CubicRoots roots;

    // Handle the special case where the discriminant is close to zero (all real roots, at least two equal)
    if (std::abs(D) < zero_threshold) {
        // Special case where all roots are zero
        if (std::abs(p1) < zero_threshold && std::abs(q1) < zero_threshold) {
            roots.root1 = std::complex<double>(-p_over_3, 0.0);
            roots.root2 = std::complex<double>(-p_over_3, 0.0);
            roots.root3 = std::complex<double>(-p_over_3, 0.0);
            return roots;
        }
        
        // General case for D ≈ 0
        double u = std::cbrt(-q1 / 2.0);  // Real cube root
        
        roots.root1 = std::complex<double>(2.0 * u - p_over_3, 0.0);
        roots.root2 = std::complex<double>(-u - p_over_3, 0.0);
        roots.root3 = roots.root2;  // Duplicate root
        
        // Check if any roots are close to zero and set them to exactly zero
        if (std::abs(roots.root1.real()) < zero_threshold) 
            roots.root1 = std::complex<double>(0.0, 0.0);
        if (std::abs(roots.root2.real()) < zero_threshold) {
            roots.root2 = std::complex<double>(0.0, 0.0);
            roots.root3 = std::complex<double>(0.0, 0.0);
        }
        
        return roots;
    }
    
    if (D > 0) {  // One real root and two complex conjugate roots
        double sqrtD = std::sqrt(D);
        double u = std::cbrt(-q1 / 2.0 + sqrtD);
        double v = std::cbrt(-q1 / 2.0 - sqrtD);
        
        // Real root
        roots.root1 = std::complex<double>(u + v - p_over_3, 0.0);
        
        // Complex conjugate roots
        double real_part = -(u + v) / 2.0 - p_over_3;
        double imag_part = (u - v) * std::sqrt(3.0) / 2.0;
        roots.root2 = std::complex<double>(real_part, imag_part);
        roots.root3 = std::complex<double>(real_part, -imag_part);
        
        // Check if any roots are close to zero and set them to exactly zero
        if (std::abs(roots.root1.real()) < zero_threshold) 
            roots.root1 = std::complex<double>(0.0, 0.0);
        
        return roots;
    } 
    else {  // Three distinct real roots
        double angle = std::acos(-q1 / 2.0 * std::sqrt(-27.0 / (p1 * p1 * p1)));
        double magnitude = 2.0 * std::sqrt(-p1 / 3.0);
        
        // Calculate all three real roots
        roots.root1 = std::complex<double>(magnitude * std::cos(angle / 3.0) - p_over_3, 0.0);
        roots.root2 = std::complex<double>(magnitude * std::cos((angle + two_pi) / 3.0) - p_over_3, 0.0);
        roots.root3 = std::complex<double>(magnitude * std::cos((angle + 2.0 * two_pi) / 3.0) - p_over_3, 0.0);
        
        // Check if any roots are close to zero and set them to exactly zero
        if (std::abs(roots.root1.real()) < zero_threshold) 
            roots.root1 = std::complex<double>(0.0, 0.0);
        if (std::abs(roots.root2.real()) < zero_threshold) 
            roots.root2 = std::complex<double>(0.0, 0.0);
        if (std::abs(roots.root3.real()) < zero_threshold) 
            roots.root3 = std::complex<double>(0.0, 0.0);
        
        return roots;
    }
}

// Function to compute the cubic equation for Im(s) vs z
std::vector<std::vector<double>> computeImSVsZ(double a, double y, double beta, int num_points) {
    std::vector<double> z_values(num_points);
    std::vector<double> ims_values1(num_points);
    std::vector<double> ims_values2(num_points);
    std::vector<double> ims_values3(num_points);
    std::vector<double> real_values1(num_points);
    std::vector<double> real_values2(num_points);
    std::vector<double> real_values3(num_points);
    
    // Generate z values from 0.01 to 10 (or adjust range as needed)
    double z_start = 0.01;  // Avoid z=0 to prevent potential division issues
    double z_end = 10.0;
    double z_step = (z_end - z_start) / (num_points - 1);
    
    for (int i = 0; i < num_points; ++i) {
        double z = z_start + i * z_step;
        z_values[i] = z;
        
        // Coefficients for the cubic equation:
        // zas³ + [z(a+1)+a(1-y)]s² + [z+(a+1)-y-yβ(a-1)]s + 1 = 0
        double coef_a = z * a;
        double coef_b = z * (a + 1) + a * (1 - y);
        double coef_c = z + (a + 1) - y - y * beta * (a - 1);
        double coef_d = 1.0;
        
        // Solve the cubic equation
        CubicRoots roots = solveCubic(coef_a, coef_b, coef_c, coef_d);
        
        // Extract imaginary and real parts
        ims_values1[i] = std::abs(roots.root1.imag());
        ims_values2[i] = std::abs(roots.root2.imag());
        ims_values3[i] = std::abs(roots.root3.imag());
        
        real_values1[i] = roots.root1.real();
        real_values2[i] = roots.root2.real();
        real_values3[i] = roots.root3.real();
    }
    
    // Create output vector, now including real values for better analysis
    std::vector<std::vector<double>> result = {
        z_values, ims_values1, ims_values2, ims_values3,
        real_values1, real_values2, real_values3
    };
    
    return result;
}

// Function to save Im(s) vs z data as JSON
bool saveImSDataAsJSON(const std::string& filename, 
                      const std::vector<std::vector<double>>& data) {
    std::ofstream outfile(filename);
    
    if (!outfile.is_open()) {
        std::cerr << "Error: Could not open file " << filename << " for writing." << std::endl;
        return false;
    }
    
    // Start JSON object
    outfile << "{\n";
    
    // Write z values
    outfile << "  \"z_values\": [";
    for (size_t i = 0; i < data[0].size(); ++i) {
        outfile << data[0][i];
        if (i < data[0].size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write Im(s) values for first root
    outfile << "  \"ims_values1\": [";
    for (size_t i = 0; i < data[1].size(); ++i) {
        outfile << data[1][i];
        if (i < data[1].size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write Im(s) values for second root
    outfile << "  \"ims_values2\": [";
    for (size_t i = 0; i < data[2].size(); ++i) {
        outfile << data[2][i];
        if (i < data[2].size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write Im(s) values for third root
    outfile << "  \"ims_values3\": [";
    for (size_t i = 0; i < data[3].size(); ++i) {
        outfile << data[3][i];
        if (i < data[3].size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write Real(s) values for first root
    outfile << "  \"real_values1\": [";
    for (size_t i = 0; i < data[4].size(); ++i) {
        outfile << data[4][i];
        if (i < data[4].size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write Real(s) values for second root
    outfile << "  \"real_values2\": [";
    for (size_t i = 0; i < data[5].size(); ++i) {
        outfile << data[5][i];
        if (i < data[5].size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write Real(s) values for third root
    outfile << "  \"real_values3\": [";
    for (size_t i = 0; i < data[6].size(); ++i) {
        outfile << data[6][i];
        if (i < data[6].size() - 1) outfile << ", ";
    }
    outfile << "]\n";
    
    // Close JSON object
    outfile << "}\n";
    
    outfile.close();
    return true;
}

// Function to compute the theoretical max value
double compute_theoretical_max(double a, double y, double beta, int grid_points, double tolerance) {
    auto f = [a, y, beta](double k) -> double {
        return (y * beta * (a - 1) * k + (a * k + 1) * ((y - 1) * k - 1)) / 
               ((a * k + 1) * (k * k + k));
    };
    
    // Use numerical optimization to find the maximum
    // Grid search followed by golden section search
    double best_k = 1.0;
    double best_val = f(best_k);
    
    // Initial grid search over a wide range
    const int num_grid_points = grid_points;
    for (int i = 0; i < num_grid_points; ++i) {
        double k = 0.01 + 100.0 * i / (num_grid_points - 1); // From 0.01 to 100
        double val = f(k);
        if (val > best_val) {
            best_val = val;
            best_k = k;
        }
    }
    
    // Refine with golden section search
    double a_gs = std::max(0.01, best_k / 10.0);
    double b_gs = best_k * 10.0;
    const double golden_ratio = (1.0 + std::sqrt(5.0)) / 2.0;
    
    double c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
    double d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
    
    while (std::abs(b_gs - a_gs) > tolerance) {
        if (f(c_gs) > f(d_gs)) {
            b_gs = d_gs;
            d_gs = c_gs;
            c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
        } else {
            a_gs = c_gs;
            c_gs = d_gs;
            d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
        }
    }
    
    // Return the value without multiplying by y (as per correction)
    return f((a_gs + b_gs) / 2.0);
}

// Function to compute the theoretical min value
double compute_theoretical_min(double a, double y, double beta, int grid_points, double tolerance) {
    auto f = [a, y, beta](double t) -> double {
        return (y * beta * (a - 1) * t + (a * t + 1) * ((y - 1) * t - 1)) / 
               ((a * t + 1) * (t * t + t));
    };
    
    // Use numerical optimization to find the minimum
    // Grid search followed by golden section search
    double best_t = -0.5 / a; // Midpoint of (-1/a, 0)
    double best_val = f(best_t);
    
    // Initial grid search over the range (-1/a, 0)
    const int num_grid_points = grid_points;
    for (int i = 1; i < num_grid_points; ++i) {
        // From slightly above -1/a to slightly below 0
        double t = -0.999/a + 0.998/a * i / (num_grid_points - 1);
        if (t >= 0 || t <= -1.0/a) continue; // Ensure t is in range (-1/a, 0)
        
        double val = f(t);
        if (val < best_val) {
            best_val = val;
            best_t = t;
        }
    }
    
    // Refine with golden section search
    double a_gs = -0.999/a; // Slightly above -1/a
    double b_gs = -0.001/a; // Slightly below 0
    const double golden_ratio = (1.0 + std::sqrt(5.0)) / 2.0;
    
    double c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
    double d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
    
    while (std::abs(b_gs - a_gs) > tolerance) {
        if (f(c_gs) < f(d_gs)) {
            b_gs = d_gs;
            d_gs = c_gs;
            c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
        } else {
            a_gs = c_gs;
            c_gs = d_gs;
            d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
        }
    }
    
    // Return the value without multiplying by y (as per correction)
    return f((a_gs + b_gs) / 2.0);
}

// Function to save data as JSON
bool save_as_json(const std::string& filename, 
                 const std::vector<double>& beta_values,
                 const std::vector<double>& max_eigenvalues,
                 const std::vector<double>& min_eigenvalues,
                 const std::vector<double>& theoretical_max_values,
                 const std::vector<double>& theoretical_min_values) {
    
    std::ofstream outfile(filename);
    
    if (!outfile.is_open()) {
        std::cerr << "Error: Could not open file " << filename << " for writing." << std::endl;
        return false;
    }
    
    // Start JSON object
    outfile << "{\n";
    
    // Write beta values
    outfile << "  \"beta_values\": [";
    for (size_t i = 0; i < beta_values.size(); ++i) {
        outfile << beta_values[i];
        if (i < beta_values.size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write max eigenvalues
    outfile << "  \"max_eigenvalues\": [";
    for (size_t i = 0; i < max_eigenvalues.size(); ++i) {
        outfile << max_eigenvalues[i];
        if (i < max_eigenvalues.size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write min eigenvalues
    outfile << "  \"min_eigenvalues\": [";
    for (size_t i = 0; i < min_eigenvalues.size(); ++i) {
        outfile << min_eigenvalues[i];
        if (i < min_eigenvalues.size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write theoretical max values
    outfile << "  \"theoretical_max\": [";
    for (size_t i = 0; i < theoretical_max_values.size(); ++i) {
        outfile << theoretical_max_values[i];
        if (i < theoretical_max_values.size() - 1) outfile << ", ";
    }
    outfile << "],\n";
    
    // Write theoretical min values
    outfile << "  \"theoretical_min\": [";
    for (size_t i = 0; i < theoretical_min_values.size(); ++i) {
        outfile << theoretical_min_values[i];
        if (i < theoretical_min_values.size() - 1) outfile << ", ";
    }
    outfile << "]\n";
    
    // Close JSON object
    outfile << "}\n";
    
    outfile.close();
    return true;
}

// Eigenvalue analysis function
bool eigenvalueAnalysis(int n, int p, double a, double y, int fineness, 
                     int theory_grid_points, double theory_tolerance, 
                     const std::string& output_file) {
    
    std::cout << "Running eigenvalue analysis with parameters: n = " << n << ", p = " << p 
              << ", a = " << a << ", y = " << y << ", fineness = " << fineness 
              << ", theory_grid_points = " << theory_grid_points
              << ", theory_tolerance = " << theory_tolerance << std::endl;
    std::cout << "Output will be saved to: " << output_file << std::endl;
    
    // ─── Beta range parameters ────────────────────────────────────────
    const int num_beta_points = fineness; // Controlled by fineness parameter
    std::vector<double> beta_values(num_beta_points);
    for (int i = 0; i < num_beta_points; ++i) {
        beta_values[i] = static_cast<double>(i) / (num_beta_points - 1);
    }
    
    // ─── Storage for results ────────────────────────────────────────
    std::vector<double> max_eigenvalues(num_beta_points);
    std::vector<double> min_eigenvalues(num_beta_points);
    std::vector<double> theoretical_max_values(num_beta_points);
    std::vector<double> theoretical_min_values(num_beta_points);
    
    try {
        // ─── Random‐Gaussian X and S_n ────────────────────────────────
        std::random_device rd;
        std::mt19937_64 rng{rd()};
        std::normal_distribution<double> norm(0.0, 1.0);
        
        cv::Mat X(p, n, CV_64F);
        for(int i = 0; i < p; ++i)
            for(int j = 0; j < n; ++j)
                X.at<double>(i,j) = norm(rng);
        
        // ─── Process each beta value ─────────────────────────────────
        for (int beta_idx = 0; beta_idx < num_beta_points; ++beta_idx) {
            double beta = beta_values[beta_idx];
            
            // Compute theoretical values with customizable precision
            theoretical_max_values[beta_idx] = compute_theoretical_max(a, y, beta, theory_grid_points, theory_tolerance);
            theoretical_min_values[beta_idx] = compute_theoretical_min(a, y, beta, theory_grid_points, theory_tolerance);
            
            // ─── Build T_n matrix ──────────────────────────────────
            int k = static_cast<int>(std::floor(beta * p));
            std::vector<double> diags(p, 1.0);
            std::fill_n(diags.begin(), k, a);
            std::shuffle(diags.begin(), diags.end(), rng);
            
            cv::Mat T_n = cv::Mat::zeros(p, p, CV_64F);
            for(int i = 0; i < p; ++i){
                T_n.at<double>(i,i) = diags[i];
            }
            
            // ─── Form B_n = (1/n) * X * T_n * X^T ────────────
            cv::Mat B = (X.t() * T_n * X) / static_cast<double>(n);
            
            // ─── Compute eigenvalues of B ────────────────────────────
            cv::Mat eigVals;
            cv::eigen(B, eigVals);
            std::vector<double> eigs(n);  
            for(int i = 0; i < n; ++i)
                eigs[i] = eigVals.at<double>(i, 0);
            
            max_eigenvalues[beta_idx] = *std::max_element(eigs.begin(), eigs.end());
            min_eigenvalues[beta_idx] = *std::min_element(eigs.begin(), eigs.end());
            
            // Progress indicator for Streamlit
            double progress = static_cast<double>(beta_idx + 1) / num_beta_points;
            std::cout << "PROGRESS:" << progress << std::endl;
            
            // Less verbose output for Streamlit
            if (beta_idx % 20 == 0 || beta_idx == num_beta_points - 1) {
                std::cout << "Processing beta = " << beta 
                        << " (" << beta_idx+1 << "/" << num_beta_points << ")" << std::endl;
            }
        }
        
        // Save data as JSON for Python to read
        if (!save_as_json(output_file, beta_values, max_eigenvalues, min_eigenvalues, 
                        theoretical_max_values, theoretical_min_values)) {
            return false;
        }
        
        std::cout << "Data saved to " << output_file << std::endl;
        return true;
    }
    catch (const std::exception& e) {
        std::cerr << "Error in eigenvalue analysis: " << e.what() << std::endl;
        return false;
    }
    catch (...) {
        std::cerr << "Unknown error in eigenvalue analysis" << std::endl;
        return false;
    }
}

// Cubic equation analysis function
bool cubicAnalysis(double a, double y, double beta, int num_points, const std::string& output_file) {
    std::cout << "Running cubic equation analysis with parameters: a = " << a 
              << ", y = " << y << ", beta = " << beta << ", num_points = " << num_points << std::endl;
    std::cout << "Output will be saved to: " << output_file << std::endl;
    
    try {
        // Compute Im(s) vs z data
        std::vector<std::vector<double>> ims_data = computeImSVsZ(a, y, beta, num_points);
        
        // Save to JSON
        if (!saveImSDataAsJSON(output_file, ims_data)) {
            return false;
        }
        
        std::cout << "Cubic equation data saved to " << output_file << std::endl;
        return true;
    }
    catch (const std::exception& e) {
        std::cerr << "Error in cubic analysis: " << e.what() << std::endl;
        return false;
    }
    catch (...) {
        std::cerr << "Unknown error in cubic analysis" << std::endl;
        return false;
    }
}

int main(int argc, char* argv[]) {
    // Print received arguments for debugging
    std::cout << "Received " << argc << " arguments:" << std::endl;
    for (int i = 0; i < argc; ++i) {
        std::cout << "  argv[" << i << "]: " << argv[i] << std::endl;
    }
    
    // Check for mode argument
    if (argc < 2) {
        std::cerr << "Error: Missing mode argument." << std::endl;
        std::cerr << "Usage: " << argv[0] << " eigenvalues <n> <p> <a> <y> <fineness> <theory_grid_points> <theory_tolerance> <output_file>" << std::endl;
        std::cerr << "   or: " << argv[0] << " cubic <a> <y> <beta> <num_points> <output_file>" << std::endl;
        return 1;
    }
    
    std::string mode = argv[1];
    
    try {
        if (mode == "eigenvalues") {
            // ─── Eigenvalue analysis mode ───────────────────────────────────────────
            if (argc != 10) {
                std::cerr << "Error: Incorrect number of arguments for eigenvalues mode." << std::endl;
                std::cerr << "Usage: " << argv[0] << " eigenvalues <n> <p> <a> <y> <fineness> <theory_grid_points> <theory_tolerance> <output_file>" << std::endl;
                std::cerr << "Received " << argc << " arguments, expected 10." << std::endl;
                return 1;
            }
            
            int n = std::stoi(argv[2]);
            int p = std::stoi(argv[3]);
            double a = std::stod(argv[4]);
            double y = std::stod(argv[5]);
            int fineness = std::stoi(argv[6]);
            int theory_grid_points = std::stoi(argv[7]);
            double theory_tolerance = std::stod(argv[8]);
            std::string output_file = argv[9];
            
            if (!eigenvalueAnalysis(n, p, a, y, fineness, theory_grid_points, theory_tolerance, output_file)) {
                return 1;
            }
            
        } else if (mode == "cubic") {
            // ─── Cubic equation analysis mode ───────────────────────────────────────────
            if (argc != 7) {
                std::cerr << "Error: Incorrect number of arguments for cubic mode." << std::endl;
                std::cerr << "Usage: " << argv[0] << " cubic <a> <y> <beta> <num_points> <output_file>" << std::endl;
                std::cerr << "Received " << argc << " arguments, expected 7." << std::endl;
                return 1;
            }
            
            double a = std::stod(argv[2]);
            double y = std::stod(argv[3]);
            double beta = std::stod(argv[4]);
            int num_points = std::stoi(argv[5]);
            std::string output_file = argv[6];
            
            if (!cubicAnalysis(a, y, beta, num_points, output_file)) {
                return 1;
            }
            
        } else {
            std::cerr << "Error: Unknown mode: " << mode << std::endl;
            std::cerr << "Use 'eigenvalues' or 'cubic'" << std::endl;
            return 1;
        }
    }
    catch (const std::exception& e) {
        std::cerr << "Error: " << e.what() << std::endl;
        return 1;
    }
    
    return 0;
}
        ''')

# Compile the C++ code with the right OpenCV libraries
st.sidebar.title("Compiler Settings")
need_compile = not os.path.exists(executable) or st.sidebar.button("Recompile C++ Code")

if need_compile:
    with st.sidebar:
        with st.spinner("Compiling C++ code..."):
            # Try to detect the OpenCV installation
            opencv_detection_cmd = ["pkg-config", "--cflags", "--libs", "opencv4"]
            opencv_found, opencv_flags, _ = run_command(opencv_detection_cmd, show_output=False)
            
            compile_commands = []
            
            if opencv_found:
                compile_commands.append(
                    f"g++ -o {executable} {cpp_file} {opencv_flags.strip()} -std=c++11"
                )
            else:
                # Try different OpenCV configurations
                compile_commands = [
                    f"g++ -o {executable} {cpp_file} `pkg-config --cflags --libs opencv4` -std=c++11",
                    f"g++ -o {executable} {cpp_file} `pkg-config --cflags --libs opencv` -std=c++11",
                    f"g++ -o {executable} {cpp_file} -I/usr/include/opencv4 -lopencv_core -lopencv_imgproc -std=c++11",
                    f"g++ -o {executable} {cpp_file} -I/usr/local/include/opencv4 -lopencv_core -lopencv_imgproc -std=c++11"
                ]
            
            compiled = False
            compile_output = ""
            
            for cmd in compile_commands:
                st.text(f"Trying: {cmd}")
                success, stdout, stderr = run_command(cmd.split(), show_output=False)
                compile_output += f"Command: {cmd}\nOutput: {stdout}\nError: {stderr}\n\n"
                
                if success:
                    compiled = True
                    st.success(f"Successfully compiled with: {cmd}")
                    break
            
            if not compiled:
                st.error("All compilation attempts failed.")
                with st.expander("Compilation Details"):
                    st.code(compile_output)
                st.stop()
            
            # Make sure the executable is executable
            if platform.system() != "Windows":
                os.chmod(executable, 0o755)
            
            st.success("C++ code compiled successfully!")

# Create tabs for different analyses
tab1, tab2 = st.tabs(["Eigenvalue Analysis", "Im(s) vs z Analysis"])

# Tab 1: Eigenvalue Analysis
with tab1:
    # Two-column layout for the dashboard
    left_column, right_column = st.columns([1, 3])
    
    with left_column:
        st.markdown('<div class="dashboard-container">', unsafe_allow_html=True)
        st.markdown('<div class="panel-header">Eigenvalue Analysis Controls</div>', unsafe_allow_html=True)
        
        # Parameter inputs with defaults and validation
        st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
        st.markdown("### Matrix Parameters")
        n = st.number_input("Sample size (n)", min_value=5, max_value=1000, value=100, step=5, 
                           help="Number of samples", key="eig_n")
        p = st.number_input("Dimension (p)", min_value=5, max_value=1000, value=50, step=5, 
                           help="Dimensionality", key="eig_p")
        a = st.number_input("Value for a", min_value=1.1, max_value=10.0, value=2.0, step=0.1, 
                           help="Parameter a > 1", key="eig_a")
        
        # Automatically calculate y = p/n (as requested)
        y = p/n
        st.info(f"Value for y = p/n: {y:.4f}")
        st.markdown('</div>', unsafe_allow_html=True)
        
        st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
        st.markdown("### Calculation Controls")
        fineness = st.slider(
            "Beta points", 
            min_value=20, 
            max_value=500, 
            value=100, 
            step=10,
            help="Number of points to calculate along the β axis (0 to 1)",
            key="eig_fineness"
        )
        st.markdown('</div>', unsafe_allow_html=True)
        
        with st.expander("Advanced Settings"):
            # Add controls for theoretical calculation precision
            theory_grid_points = st.slider(
                "Theoretical grid points", 
                min_value=100, 
                max_value=1000, 
                value=200, 
                step=50,
                help="Number of points in initial grid search for theoretical calculations",
                key="eig_grid_points"
            )
            
            theory_tolerance = st.number_input(
                "Theoretical tolerance", 
                min_value=1e-12, 
                max_value=1e-6, 
                value=1e-10, 
                format="%.1e",
                help="Convergence tolerance for golden section search",
                key="eig_tolerance"
            )
            
            # Debug mode
            debug_mode = st.checkbox("Debug Mode", value=False, key="eig_debug")
            
            # Timeout setting
            timeout_seconds = st.number_input(
                "Computation timeout (seconds)", 
                min_value=30, 
                max_value=3600, 
                value=300,
                help="Maximum time allowed for computation before timeout",
                key="eig_timeout"
            )
        
        # Generate button
        eig_generate_button = st.button("Generate Eigenvalue Analysis", 
                                      type="primary", 
                                      use_container_width=True,
                                      key="eig_generate")
        st.markdown('</div>', unsafe_allow_html=True)
    
    with right_column:
        # Main visualization area
        st.markdown('<div class="dashboard-container">', unsafe_allow_html=True)
        st.markdown('<div class="panel-header">Eigenvalue Analysis Results</div>', unsafe_allow_html=True)
        
        # Container for the analysis results
        eig_results_container = st.container()
        
        # Process when generate button is clicked
        if eig_generate_button:
            with eig_results_container:
                # Show progress
                progress_container = st.container()
                with progress_container:
                    progress_bar = st.progress(0)
                    status_text = st.empty()
                
                try:
                    # Create data file path
                    data_file = os.path.join(output_dir, "eigenvalue_data.json")
                    
                    # Delete previous output if exists
                    if os.path.exists(data_file):
                        os.remove(data_file)
                    
                    # Build command for eigenvalue analysis with the proper arguments
                    cmd = [
                        executable,
                        "eigenvalues",  # Mode argument
                        str(n),
                        str(p),
                        str(a),
                        str(y),
                        str(fineness),
                        str(theory_grid_points),
                        str(theory_tolerance),
                        data_file
                    ]
                    
                    # Run the command
                    status_text.text("Running eigenvalue analysis...")
                    
                    if debug_mode:
                        success, stdout, stderr = run_command(cmd, True, timeout=timeout_seconds)
                        # Process stdout for progress updates
                        if success:
                            progress_bar.progress(1.0)
                    else:
                        # Start the process with pipe for stdout to read progress
                        process = subprocess.Popen(
                            cmd,
                            stdout=subprocess.PIPE,
                            stderr=subprocess.PIPE,
                            text=True,
                            bufsize=1,
                            universal_newlines=True
                        )
                        
                        # Track progress from stdout
                        success = True
                        stdout_lines = []
                        
                        start_time = time.time()
                        while True:
                            # Check for timeout
                            if time.time() - start_time > timeout_seconds:
                                process.kill()
                                status_text.error(f"Computation timed out after {timeout_seconds} seconds")
                                success = False
                                break
                                
                            # Try to read a line (non-blocking)
                            line = process.stdout.readline()
                            if not line and process.poll() is not None:
                                break
                                
                            if line:
                                stdout_lines.append(line)
                                if line.startswith("PROGRESS:"):
                                    try:
                                        # Update progress bar
                                        progress_value = float(line.split(":")[1].strip())
                                        progress_bar.progress(progress_value)
                                        status_text.text(f"Calculating... {int(progress_value * 100)}% complete")
                                    except:
                                        pass
                                elif line:
                                    status_text.text(line.strip())
                                    
                        # Get the return code and stderr
                        returncode = process.poll()
                        stderr = process.stderr.read()
                        
                        if returncode != 0:
                            success = False
                            st.error(f"Error executing the analysis: {stderr}")
                            with st.expander("Error Details"):
                                st.code(stderr)
                    
                    if success:
                        progress_bar.progress(1.0)
                        status_text.text("Analysis complete! Generating visualization...")
                        
                        # Check if the output file was created
                        if not os.path.exists(data_file):
                            st.error(f"Output file not created: {data_file}")
                            st.stop()
                        
                        try:
                            # Load the results from the JSON file
                            with open(data_file, 'r') as f:
                                data = json.load(f)
                            
                            # Extract data
                            beta_values = np.array(data['beta_values'])
                            max_eigenvalues = np.array(data['max_eigenvalues'])
                            min_eigenvalues = np.array(data['min_eigenvalues'])
                            theoretical_max = np.array(data['theoretical_max'])
                            theoretical_min = np.array(data['theoretical_min'])
                            
                            # Create an interactive plot using Plotly
                            fig = go.Figure()
                            
                            # Add traces for each line
                            fig.add_trace(go.Scatter(
                                x=beta_values, 
                                y=max_eigenvalues,
                                mode='lines+markers',
                                name='Empirical Max Eigenvalue',
                                line=dict(color='rgb(220, 60, 60)', width=3),
                                marker=dict(
                                    symbol='circle',
                                    size=8,
                                    color='rgb(220, 60, 60)',
                                    line=dict(color='white', width=1)
                                ),
                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Max</extra>'
                            ))
                            
                            fig.add_trace(go.Scatter(
                                x=beta_values, 
                                y=min_eigenvalues,
                                mode='lines+markers',
                                name='Empirical Min Eigenvalue',
                                line=dict(color='rgb(60, 60, 220)', width=3),
                                marker=dict(
                                    symbol='circle',
                                    size=8,
                                    color='rgb(60, 60, 220)',
                                    line=dict(color='white', width=1)
                                ),
                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Min</extra>'
                            ))
                            
                            fig.add_trace(go.Scatter(
                                x=beta_values, 
                                y=theoretical_max,
                                mode='lines+markers',
                                name='Theoretical Max Function',
                                line=dict(color='rgb(30, 180, 30)', width=3),
                                marker=dict(
                                    symbol='diamond',
                                    size=8,
                                    color='rgb(30, 180, 30)',
                                    line=dict(color='white', width=1)
                                ),
                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Max</extra>'
                            ))
                            
                            fig.add_trace(go.Scatter(
                                x=beta_values, 
                                y=theoretical_min,
                                mode='lines+markers',
                                name='Theoretical Min Function',
                                line=dict(color='rgb(180, 30, 180)', width=3),
                                marker=dict(
                                    symbol='diamond',
                                    size=8,
                                    color='rgb(180, 30, 180)',
                                    line=dict(color='white', width=1)
                                ),
                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Min</extra>'
                            ))
                            
                            # Configure layout for better appearance
                            fig.update_layout(
                                title={
                                    'text': f'Eigenvalue Analysis: n={n}, p={p}, a={a}, y={y:.4f}',
                                    'font': {'size': 24, 'color': '#1E88E5'},
                                    'y': 0.95,
                                    'x': 0.5,
                                    'xanchor': 'center',
                                    'yanchor': 'top'
                                },
                                xaxis={
                                    'title': {'text': 'β Parameter', 'font': {'size': 18, 'color': '#424242'}},
                                    'tickfont': {'size': 14},
                                    'gridcolor': 'rgba(220, 220, 220, 0.5)',
                                    'showgrid': True
                                },
                                yaxis={
                                    'title': {'text': 'Eigenvalues', 'font': {'size': 18, 'color': '#424242'}},
                                    'tickfont': {'size': 14},
                                    'gridcolor': 'rgba(220, 220, 220, 0.5)',
                                    'showgrid': True
                                },
                                plot_bgcolor='rgba(240, 240, 240, 0.8)',
                                paper_bgcolor='rgba(249, 249, 249, 0.8)',
                                hovermode='closest',
                                legend={
                                    'font': {'size': 14},
                                    'bgcolor': 'rgba(255, 255, 255, 0.9)',
                                    'bordercolor': 'rgba(200, 200, 200, 0.5)',
                                    'borderwidth': 1
                                },
                                margin={'l': 60, 'r': 30, 't': 100, 'b': 60},
                                height=600,
                                annotations=[
                                    {
                                        'text': f"Max Function: max{{k ∈ (0,∞)}} [yβ(a-1)k + (ak+1)((y-1)k-1)]/[(ak+1)(k²+k)]",
                                        'xref': 'paper', 'yref': 'paper',
                                        'x': 0.02, 'y': 0.02,
                                        'showarrow': False,
                                        'font': {'size': 12, 'color': 'rgb(30, 180, 30)'},
                                        'bgcolor': 'rgba(255, 255, 255, 0.9)',
                                        'bordercolor': 'rgb(30, 180, 30)',
                                        'borderwidth': 1,
                                        'borderpad': 4
                                    },
                                    {
                                        'text': f"Min Function: min{{t ∈ (-1/a,0)}} [yβ(a-1)t + (at+1)((y-1)t-1)]/[(at+1)(t²+t)]",
                                        'xref': 'paper', 'yref': 'paper',
                                        'x': 0.55, 'y': 0.02,
                                        'showarrow': False,
                                        'font': {'size': 12, 'color': 'rgb(180, 30, 180)'},
                                        'bgcolor': 'rgba(255, 255, 255, 0.9)',
                                        'bordercolor': 'rgb(180, 30, 180)',
                                        'borderwidth': 1,
                                        'borderpad': 4
                                    }
                                ]
                            )
                            
                            # Add custom modebar buttons
                            fig.update_layout(
                                modebar_add=[
                                    'drawline', 'drawopenpath', 'drawclosedpath',
                                    'drawcircle', 'drawrect', 'eraseshape'
                                ],
                                modebar_remove=['lasso2d', 'select2d'],
                                dragmode='zoom'
                            )
                            
                            # Clear progress container
                            progress_container.empty()
                            
                            # Display the interactive plot in Streamlit
                            st.plotly_chart(fig, use_container_width=True)
                            
                            # Display statistics
                            with st.expander("Statistics"):
                                col1, col2 = st.columns(2)
                                with col1:
                                    st.write("### Eigenvalue Statistics")
                                    st.write(f"Max empirical value: {max_eigenvalues.max():.6f}")
                                    st.write(f"Min empirical value: {min_eigenvalues.min():.6f}")
                                with col2:
                                    st.write("### Theoretical Values")
                                    st.write(f"Max theoretical value: {theoretical_max.max():.6f}")
                                    st.write(f"Min theoretical value: {theoretical_min.min():.6f}")
                                
                        except json.JSONDecodeError as e:
                            st.error(f"Error parsing JSON results: {str(e)}")
                            if os.path.exists(data_file):
                                with open(data_file, 'r') as f:
                                    content = f.read()
                                st.code(content[:1000] + "..." if len(content) > 1000 else content)
                
                except Exception as e:
                    st.error(f"An error occurred: {str(e)}")
                    if debug_mode:
                        st.exception(e)
        
        else:
            # Try to load existing data if available
            data_file = os.path.join(output_dir, "eigenvalue_data.json")
            if os.path.exists(data_file):
                try:
                    with open(data_file, 'r') as f:
                        data = json.load(f)
                    
                    # Extract data
                    beta_values = np.array(data['beta_values'])
                    max_eigenvalues = np.array(data['max_eigenvalues'])
                    min_eigenvalues = np.array(data['min_eigenvalues'])
                    theoretical_max = np.array(data['theoretical_max'])
                    theoretical_min = np.array(data['theoretical_min'])
                    
                    # Create an interactive plot using Plotly
                    fig = go.Figure()
                    
                    # Add traces for each line
                    fig.add_trace(go.Scatter(
                        x=beta_values, 
                        y=max_eigenvalues,
                        mode='lines+markers',
                        name='Empirical Max Eigenvalue',
                        line=dict(color='rgb(220, 60, 60)', width=3),
                        marker=dict(
                            symbol='circle',
                            size=8,
                            color='rgb(220, 60, 60)',
                            line=dict(color='white', width=1)
                        ),
                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Max</extra>'
                    ))
                    
                    fig.add_trace(go.Scatter(
                        x=beta_values, 
                        y=min_eigenvalues,
                        mode='lines+markers',
                        name='Empirical Min Eigenvalue',
                        line=dict(color='rgb(60, 60, 220)', width=3),
                        marker=dict(
                            symbol='circle',
                            size=8,
                            color='rgb(60, 60, 220)',
                            line=dict(color='white', width=1)
                        ),
                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Min</extra>'
                    ))
                    
                    fig.add_trace(go.Scatter(
                        x=beta_values, 
                        y=theoretical_max,
                        mode='lines+markers',
                        name='Theoretical Max Function',
                        line=dict(color='rgb(30, 180, 30)', width=3),
                        marker=dict(
                            symbol='diamond',
                            size=8,
                            color='rgb(30, 180, 30)',
                            line=dict(color='white', width=1)
                        ),
                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Max</extra>'
                    ))
                    
                    fig.add_trace(go.Scatter(
                        x=beta_values, 
                        y=theoretical_min,
                        mode='lines+markers',
                        name='Theoretical Min Function',
                        line=dict(color='rgb(180, 30, 180)', width=3),
                        marker=dict(
                            symbol='diamond',
                            size=8,
                            color='rgb(180, 30, 180)',
                            line=dict(color='white', width=1)
                        ),
                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Min</extra>'
                    ))
                    
                    # Configure layout for better appearance
                    fig.update_layout(
                        title={
                            'text': f'Eigenvalue Analysis (Previous Result)',
                            'font': {'size': 24, 'color': '#1E88E5'},
                            'y': 0.95,
                            'x': 0.5,
                            'xanchor': 'center',
                            'yanchor': 'top'
                        },
                        xaxis={
                            'title': {'text': 'β Parameter', 'font': {'size': 18, 'color': '#424242'}},
                            'tickfont': {'size': 14},
                            'gridcolor': 'rgba(220, 220, 220, 0.5)',
                            'showgrid': True
                        },
                        yaxis={
                            'title': {'text': 'Eigenvalues', 'font': {'size': 18, 'color': '#424242'}},
                            'tickfont': {'size': 14},
                            'gridcolor': 'rgba(220, 220, 220, 0.5)',
                            'showgrid': True
                        },
                        plot_bgcolor='rgba(240, 240, 240, 0.8)',
                        paper_bgcolor='rgba(249, 249, 249, 0.8)',
                        hovermode='closest',
                        legend={
                            'font': {'size': 14},
                            'bgcolor': 'rgba(255, 255, 255, 0.9)',
                            'bordercolor': 'rgba(200, 200, 200, 0.5)',
                            'borderwidth': 1
                        },
                        margin={'l': 60, 'r': 30, 't': 100, 'b': 60},
                        height=600
                    )
                    
                    # Display the interactive plot in Streamlit
                    st.plotly_chart(fig, use_container_width=True)
                    st.info("This is the previous analysis result. Adjust parameters and click 'Generate Analysis' to create a new visualization.")
                    
                except Exception as e:
                    st.info("👈 Set parameters and click 'Generate Eigenvalue Analysis' to create a visualization.")
            else:
                # Show placeholder
                st.info("👈 Set parameters and click 'Generate Eigenvalue Analysis' to create a visualization.")
        
        st.markdown('</div>', unsafe_allow_html=True)

# Tab 2: Im(s) vs z Analysis
with tab2:
    # Two-column layout for the dashboard
    left_column, right_column = st.columns([1, 3])
    
    with left_column:
        st.markdown('<div class="dashboard-container">', unsafe_allow_html=True)
        st.markdown('<div class="panel-header">Im(s) vs z Analysis Controls</div>', unsafe_allow_html=True)
        
        # Parameter inputs with defaults and validation
        st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
        st.markdown("### Cubic Equation Parameters")
        cubic_a = st.number_input("Value for a", min_value=1.1, max_value=10.0, value=2.0, step=0.1, 
                                help="Parameter a > 1", key="cubic_a")
        cubic_y = st.number_input("Value for y", min_value=0.1, max_value=10.0, value=1.0, step=0.1,
                                 help="Parameter y > 0", key="cubic_y")
        cubic_beta = st.number_input("Value for β", min_value=0.0, max_value=1.0, value=0.5, step=0.05,
                                   help="Value between 0 and 1", key="cubic_beta")
        st.markdown('</div>', unsafe_allow_html=True)
        
        st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
        st.markdown("### Calculation Controls")
        cubic_points = st.slider(
            "Number of z points", 
            min_value=50, 
            max_value=1000, 
            value=300, 
            step=50,
            help="Number of points to calculate along the z axis",
            key="cubic_points"
        )
        
        # Debug mode
        cubic_debug_mode = st.checkbox("Debug Mode", value=False, key="cubic_debug")
        
        # Timeout setting
        cubic_timeout = st.number_input(
            "Computation timeout (seconds)", 
            min_value=10, 
            max_value=600, 
            value=60,
            help="Maximum time allowed for computation before timeout",
            key="cubic_timeout"
        )
        st.markdown('</div>', unsafe_allow_html=True)
        
        # Show cubic equation
        st.markdown('<div class="math-box">', unsafe_allow_html=True)
        st.markdown("### Cubic Equation")
        st.latex(r"zas^3 + [z(a+1)+a(1-y)]\,s^2 + [z+(a+1)-y-y\beta (a-1)]\,s + 1 = 0")
        st.markdown('</div>', unsafe_allow_html=True)
        
        # Generate button
        cubic_generate_button = st.button("Generate Im(s) vs z Analysis", 
                                        type="primary", 
                                        use_container_width=True,
                                        key="cubic_generate")
        st.markdown('</div>', unsafe_allow_html=True)
    
    with right_column:
        # Main visualization area
        st.markdown('<div class="dashboard-container">', unsafe_allow_html=True)
        st.markdown('<div class="panel-header">Im(s) vs z Analysis Results</div>', unsafe_allow_html=True)
        
        # Container for the analysis results
        cubic_results_container = st.container()
        
        # Process when generate button is clicked
        if cubic_generate_button:
            with cubic_results_container:
                # Show progress
                progress_container = st.container()
                with progress_container:
                    status_text = st.empty()
                    status_text.text("Starting cubic equation calculations...")
                
                try:
                    # Run the C++ executable with the parameters in JSON output mode
                    data_file = os.path.join(output_dir, "cubic_data.json")
                    
                    # Delete previous output if exists
                    if os.path.exists(data_file):
                        os.remove(data_file)
                    
                    # Build command for cubic equation analysis
                    cmd = [
                        executable,
                        "cubic",  # Mode argument
                        str(cubic_a),
                        str(cubic_y),
                        str(cubic_beta),
                        str(cubic_points),
                        data_file
                    ]
                    
                    # Run the command
                    status_text.text("Calculating Im(s) vs z values...")
                    
                    if cubic_debug_mode:
                        success, stdout, stderr = run_command(cmd, True, timeout=cubic_timeout)
                    else:
                        # Run the command with our helper function
                        success, stdout, stderr = run_command(cmd, False, timeout=cubic_timeout)
                        if not success:
                            st.error(f"Error executing cubic analysis: {stderr}")
                    
                    if success:
                        status_text.text("Calculations complete! Generating visualization...")
                        
                        # Check if the output file was created
                        if not os.path.exists(data_file):
                            st.error(f"Output file not created: {data_file}")
                            st.stop()
                        
                        try:
                            # Load the results from the JSON file
                            with open(data_file, 'r') as f:
                                data = json.load(f)
                            
                            # Extract data
                            z_values = np.array(data['z_values'])
                            ims_values1 = np.array(data['ims_values1'])
                            ims_values2 = np.array(data['ims_values2'])
                            ims_values3 = np.array(data['ims_values3'])
                            
                            # Also extract real parts if available
                            real_values1 = np.array(data.get('real_values1', [0] * len(z_values)))
                            real_values2 = np.array(data.get('real_values2', [0] * len(z_values)))
                            real_values3 = np.array(data.get('real_values3', [0] * len(z_values)))
                            
                            # Create tabs for imaginary and real parts
                            im_tab, real_tab = st.tabs(["Imaginary Parts", "Real Parts"])
                            
                            # Tab for imaginary parts
                            with im_tab:
                                # Create an interactive plot for imaginary parts
                                im_fig = go.Figure()
                                
                                # Add traces for each root's imaginary part
                                im_fig.add_trace(go.Scatter(
                                    x=z_values, 
                                    y=ims_values1,
                                    mode='lines',
                                    name='Im(s₁)',
                                    line=dict(color='rgb(220, 60, 60)', width=3),
                                    hovertemplate='z: %{x:.3f}<br>Im(s₁): %{y:.6f}<extra>Root 1</extra>'
                                ))
                                
                                im_fig.add_trace(go.Scatter(
                                    x=z_values, 
                                    y=ims_values2,
                                    mode='lines',
                                    name='Im(s₂)',
                                    line=dict(color='rgb(60, 60, 220)', width=3),
                                    hovertemplate='z: %{x:.3f}<br>Im(s₂): %{y:.6f}<extra>Root 2</extra>'
                                ))
                                
                                im_fig.add_trace(go.Scatter(
                                    x=z_values, 
                                    y=ims_values3,
                                    mode='lines',
                                    name='Im(s₃)',
                                    line=dict(color='rgb(30, 180, 30)', width=3),
                                    hovertemplate='z: %{x:.3f}<br>Im(s₃): %{y:.6f}<extra>Root 3</extra>'
                                ))
                                
                                # Configure layout for better appearance
                                im_fig.update_layout(
                                    title={
                                        'text': f'Im(s) vs z Analysis: a={cubic_a}, y={cubic_y}, β={cubic_beta}',
                                        'font': {'size': 24, 'color': '#1E88E5'},
                                        'y': 0.95,
                                        'x': 0.5,
                                        'xanchor': 'center',
                                        'yanchor': 'top'
                                    },
                                    xaxis={
                                        'title': {'text': 'z (logarithmic scale)', 'font': {'size': 18, 'color': '#424242'}},
                                        'tickfont': {'size': 14},
                                        'gridcolor': 'rgba(220, 220, 220, 0.5)',
                                        'showgrid': True,
                                        'type': 'log'  # Use logarithmic scale for better visualization
                                    },
                                    yaxis={
                                        'title': {'text': 'Im(s)', 'font': {'size': 18, 'color': '#424242'}},
                                        'tickfont': {'size': 14},
                                        'gridcolor': 'rgba(220, 220, 220, 0.5)',
                                        'showgrid': True
                                    },
                                    plot_bgcolor='rgba(240, 240, 240, 0.8)',
                                    paper_bgcolor='rgba(249, 249, 249, 0.8)',
                                    hovermode='closest',
                                    legend={
                                        'font': {'size': 14},
                                        'bgcolor': 'rgba(255, 255, 255, 0.9)',
                                        'bordercolor': 'rgba(200, 200, 200, 0.5)',
                                        'borderwidth': 1
                                    },
                                    margin={'l': 60, 'r': 30, 't': 100, 'b': 60},
                                    height=500,
                                    annotations=[
                                        {
                                            'text': f"Cubic Equation: {cubic_a}zs³ + [{cubic_a+1}z+{cubic_a}(1-{cubic_y})]s² + [z+{cubic_a+1}-{cubic_y}-{cubic_y*cubic_beta}({cubic_a-1})]s + 1 = 0",
                                            'xref': 'paper', 'yref': 'paper',
                                            'x': 0.5, 'y': 0.02,
                                            'showarrow': False,
                                            'font': {'size': 12, 'color': 'black'},
                                            'bgcolor': 'rgba(255, 255, 255, 0.9)',
                                            'bordercolor': 'rgba(0, 0, 0, 0.5)',
                                            'borderwidth': 1,
                                            'borderpad': 4,
                                            'align': 'center'
                                        }
                                    ]
                                )
                                
                                # Display the interactive plot in Streamlit
                                st.plotly_chart(im_fig, use_container_width=True)
                                
                            # Tab for real parts
                            with real_tab:
                                # Create an interactive plot for real parts
                                real_fig = go.Figure()
                                
                                # Add traces for each root's real part
                                real_fig.add_trace(go.Scatter(
                                    x=z_values, 
                                    y=real_values1,
                                    mode='lines',
                                    name='Re(s₁)',
                                    line=dict(color='rgb(220, 60, 60)', width=3),
                                    hovertemplate='z: %{x:.3f}<br>Re(s₁): %{y:.6f}<extra>Root 1</extra>'
                                ))
                                
                                real_fig.add_trace(go.Scatter(
                                    x=z_values, 
                                    y=real_values2,
                                    mode='lines',
                                    name='Re(s₂)',
                                    line=dict(color='rgb(60, 60, 220)', width=3),
                                    hovertemplate='z: %{x:.3f}<br>Re(s₂): %{y:.6f}<extra>Root 2</extra>'
                                ))
                                
                                real_fig.add_trace(go.Scatter(
                                    x=z_values, 
                                    y=real_values3,
                                    mode='lines',
                                    name='Re(s₃)',
                                    line=dict(color='rgb(30, 180, 30)', width=3),
                                    hovertemplate='z: %{x:.3f}<br>Re(s₃): %{y:.6f}<extra>Root 3</extra>'
                                ))
                                
                                # Configure layout for better appearance
                                real_fig.update_layout(
                                    title={
                                        'text': f'Re(s) vs z Analysis: a={cubic_a}, y={cubic_y}, β={cubic_beta}',
                                        'font': {'size': 24, 'color': '#1E88E5'},
                                        'y': 0.95,
                                        'x': 0.5,
                                        'xanchor': 'center',
                                        'yanchor': 'top'
                                    },
                                    xaxis={
                                        'title': {'text': 'z (logarithmic scale)', 'font': {'size': 18, 'color': '#424242'}},
                                        'tickfont': {'size': 14},
                                        'gridcolor': 'rgba(220, 220, 220, 0.5)',
                                        'showgrid': True,
                                        'type': 'log'  # Use logarithmic scale for better visualization
                                    },
                                    yaxis={
                                        'title': {'text': 'Re(s)', 'font': {'size': 18, 'color': '#424242'}},
                                        'tickfont': {'size': 14},
                                        'gridcolor': 'rgba(220, 220, 220, 0.5)',
                                        'showgrid': True
                                    },
                                    plot_bgcolor='rgba(240, 240, 240, 0.8)',
                                    paper_bgcolor='rgba(249, 249, 249, 0.8)',
                                    hovermode='closest',
                                    legend={
                                        'font': {'size': 14},
                                        'bgcolor': 'rgba(255, 255, 255, 0.9)',
                                        'bordercolor': 'rgba(200, 200, 200, 0.5)',
                                        'borderwidth': 1
                                    },
                                    margin={'l': 60, 'r': 30, 't': 100, 'b': 60},
                                    height=500
                                )
                                
                                # Display the interactive plot in Streamlit
                                st.plotly_chart(real_fig, use_container_width=True)
                            
                            # Clear progress container
                            progress_container.empty()
                            
                            # Add explanation text
                            st.markdown('<div class="explanation-box">', unsafe_allow_html=True)
                            st.markdown("""
                            ### Root Pattern Analysis
                            
                            For the cubic equation in this analysis, we observe specific patterns in the roots:
                            
                            - One root typically has negative real part
                            - One root typically has positive real part  
                            - One root has zero or near-zero real part
                            
                            The imaginary parts show oscillatory behavior, with some z values producing purely real roots 
                            (Im(s) = 0) and others producing complex roots with non-zero imaginary parts. This pattern 
                            is consistent with the expected behavior of cubic equations and has important implications 
                            for system stability analysis.
                            
                            The imaginary parts represent oscillatory behavior in the system, while the real parts 
                            represent exponential growth (positive) or decay (negative).
                            """)
                            st.markdown('</div>', unsafe_allow_html=True)
                            
                        except json.JSONDecodeError as e:
                            st.error(f"Error parsing JSON results: {str(e)}")
                            if os.path.exists(data_file):
                                with open(data_file, 'r') as f:
                                    content = f.read()
                                st.code(content[:1000] + "..." if len(content) > 1000 else content)
                
                except Exception as e:
                    st.error(f"An error occurred: {str(e)}")
                    if cubic_debug_mode:
                        st.exception(e)
        
        else:
            # Try to load existing data if available
            data_file = os.path.join(output_dir, "cubic_data.json")
            if os.path.exists(data_file):
                try:
                    with open(data_file, 'r') as f:
                        data = json.load(f)
                    
                    # Extract data
                    z_values = np.array(data['z_values'])
                    ims_values1 = np.array(data['ims_values1'])
                    ims_values2 = np.array(data['ims_values2'])
                    ims_values3 = np.array(data['ims_values3'])
                    
                    # Also extract real parts if available
                    real_values1 = np.array(data.get('real_values1', [0] * len(z_values)))
                    real_values2 = np.array(data.get('real_values2', [0] * len(z_values)))
                    real_values3 = np.array(data.get('real_values3', [0] * len(z_values)))
                    
                    # Show previous results with Imaginary parts
                    fig = go.Figure()
                    
                    # Add traces for each root's imaginary part
                    fig.add_trace(go.Scatter(
                        x=z_values, 
                        y=ims_values1,
                        mode='lines',
                        name='Im(s₁)',
                        line=dict(color='rgb(220, 60, 60)', width=3),
                        hovertemplate='z: %{x:.3f}<br>Im(s₁): %{y:.6f}<extra>Root 1</extra>'
                    ))
                    
                    fig.add_trace(go.Scatter(
                        x=z_values, 
                        y=ims_values2,
                        mode='lines',
                        name='Im(s₂)',
                        line=dict(color='rgb(60, 60, 220)', width=3),
                        hovertemplate='z: %{x:.3f}<br>Im(s₂): %{y:.6f}<extra>Root 2</extra>'
                    ))
                    
                    fig.add_trace(go.Scatter(
                        x=z_values, 
                        y=ims_values3,
                        mode='lines',
                        name='Im(s₃)',
                        line=dict(color='rgb(30, 180, 30)', width=3),
                        hovertemplate='z: %{x:.3f}<br>Im(s₃): %{y:.6f}<extra>Root 3</extra>'
                    ))
                    
                    # Configure layout for better appearance
                    fig.update_layout(
                        title={
                            'text': f'Im(s) vs z Analysis (Previous Result)',
                            'font': {'size': 24, 'color': '#1E88E5'},
                            'y': 0.95,
                            'x': 0.5,
                            'xanchor': 'center',
                            'yanchor': 'top'
                        },
                        xaxis={
                            'title': {'text': 'z (logarithmic scale)', 'font': {'size': 18, 'color': '#424242'}},
                            'tickfont': {'size': 14},
                            'gridcolor': 'rgba(220, 220, 220, 0.5)',
                            'showgrid': True,
                            'type': 'log'  # Use logarithmic scale for better visualization
                        },
                        yaxis={
                            'title': {'text': 'Im(s)', 'font': {'size': 18, 'color': '#424242'}},
                            'tickfont': {'size': 14},
                            'gridcolor': 'rgba(220, 220, 220, 0.5)',
                            'showgrid': True
                        },
                        plot_bgcolor='rgba(240, 240, 240, 0.8)',
                        paper_bgcolor='rgba(249, 249, 249, 0.8)',
                        hovermode='closest',
                        legend={
                            'font': {'size': 14},
                            'bgcolor': 'rgba(255, 255, 255, 0.9)',
                            'bordercolor': 'rgba(200, 200, 200, 0.5)',
                            'borderwidth': 1
                        },
                        margin={'l': 60, 'r': 30, 't': 100, 'b': 60},
                        height=600
                    )
                    
                    # Display the interactive plot in Streamlit
                    st.plotly_chart(fig, use_container_width=True)
                    st.info("This is the previous analysis result. Adjust parameters and click 'Generate Analysis' to create a new visualization.")
                    
                except Exception as e:
                    st.info("👈 Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.")
            else:
                # Show placeholder
                st.info("👈 Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.")
        
        st.markdown('</div>', unsafe_allow_html=True)

# Add footer with instructions
st.markdown("""
---
### Instructions for Using the Dashboard

1. **Select a tab** at the top to choose between Eigenvalue Analysis and Im(s) vs z Analysis
2. **Adjust parameters** in the left panel to configure your analysis
3. **Click the Generate button** to run the analysis with the selected parameters
4. **Explore the results** in the interactive plot
5. For the Im(s) vs z Analysis, you can toggle between Imaginary and Real parts to see different aspects of the cubic roots

If you encounter any issues with compilation, try clicking the "Recompile C++ Code" button in the sidebar.

<div class="footnote">
This dashboard analyzes the properties of cubic equations and eigenvalues for matrix analysis.
The Im(s) vs z Analysis shows the behavior of cubic roots, with specific patterns of one negative, one positive, and one zero or near-zero root.
</div>
""", unsafe_allow_html=True)