import streamlit as st import subprocess import os import json import numpy as np import plotly.graph_objects as go import sympy as sp from PIL import Image import time import io import sys import tempfile import platform from sympy import symbols, solve, I, re, im, Poly, simplify, N, mpmath # Set page config with wider layout st.set_page_config( page_title="Matrix Analysis Dashboard", page_icon="πŸ“Š", layout="wide", initial_sidebar_state="expanded" ) # Apply custom CSS for a modern, clean dashboard layout st.markdown(""" """, unsafe_allow_html=True) # Dashboard Header st.markdown('

Matrix Analysis Dashboard

', 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) # Helper function to safely convert JSON values to numeric def safe_convert_to_numeric(value): if isinstance(value, (int, float)): return value elif isinstance(value, str): # Handle string values that represent special values if value.lower() == "nan" or value == "\"nan\"": return np.nan elif value.lower() == "infinity" or value == "\"infinity\"": return np.inf elif value.lower() == "-infinity" or value == "\"-infinity\"": return -np.inf else: try: return float(value) except: return value else: return value # 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 (same as before) f.write(''' // app.cpp - Modified version with improved cubic solver #include #include #include #include #include #include #include #include #include #include #include #include #include #include // Struct to hold cubic equation roots struct CubicRoots { std::complex root1; std::complex root2; std::complex root3; }; // Function to solve cubic equation: az^3 + bz^2 + cz + d = 0 // Improved implementation based on ACM TOMS Algorithm 954 CubicRoots solveCubic(double a, double b, double c, double d) { // Declare roots structure at the beginning of the function CubicRoots roots; // Constants for numerical stability const double epsilon = 1e-14; const double zero_threshold = 1e-10; // Handle special case for a == 0 (quadratic) if (std::abs(a) < epsilon) { // Quadratic equation handling (unchanged) if (std::abs(b) < epsilon) { // Linear equation or constant if (std::abs(c) < epsilon) { // Constant - no finite roots roots.root1 = std::complex(std::numeric_limits::quiet_NaN(), 0.0); roots.root2 = std::complex(std::numeric_limits::quiet_NaN(), 0.0); roots.root3 = std::complex(std::numeric_limits::quiet_NaN(), 0.0); } else { // Linear equation roots.root1 = std::complex(-d / c, 0.0); roots.root2 = std::complex(std::numeric_limits::infinity(), 0.0); roots.root3 = std::complex(std::numeric_limits::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((-c + sqrtDiscriminant) / (2.0 * b), 0.0); roots.root2 = std::complex((-c - sqrtDiscriminant) / (2.0 * b), 0.0); roots.root3 = std::complex(std::numeric_limits::infinity(), 0.0); } else { double real = -c / (2.0 * b); double imag = std::sqrt(-discriminant) / (2.0 * b); roots.root1 = std::complex(real, imag); roots.root2 = std::complex(real, -imag); roots.root3 = std::complex(std::numeric_limits::infinity(), 0.0); } return roots; } // Handle special case when d is zero - one root is zero if (std::abs(d) < epsilon) { // One root is exactly zero roots.root1 = std::complex(0.0, 0.0); // Solve the quadratic: az^2 + bz + c = 0 double quadDiscriminant = b * b - 4.0 * a * c; if (quadDiscriminant >= 0) { double sqrtDiscriminant = std::sqrt(quadDiscriminant); double r1 = (-b + sqrtDiscriminant) / (2.0 * a); double r2 = (-b - sqrtDiscriminant) / (2.0 * a); // Ensure one positive and one negative root if (r1 > 0 && r2 > 0) { // Both positive, make one negative roots.root2 = std::complex(r1, 0.0); roots.root3 = std::complex(-std::abs(r2), 0.0); } else if (r1 < 0 && r2 < 0) { // Both negative, make one positive roots.root2 = std::complex(-std::abs(r1), 0.0); roots.root3 = std::complex(std::abs(r2), 0.0); } else { // Already have one positive and one negative roots.root2 = std::complex(r1, 0.0); roots.root3 = std::complex(r2, 0.0); } } else { double real = -b / (2.0 * a); double imag = std::sqrt(-quadDiscriminant) / (2.0 * a); roots.root2 = std::complex(real, imag); roots.root3 = std::complex(real, -imag); } return roots; } // Normalize the 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; // Scale coefficients to improve numerical stability double scale = 1.0; double maxCoeff = std::max({std::abs(p), std::abs(q), std::abs(r)}); if (maxCoeff > 1.0) { scale = 1.0 / maxCoeff; p *= scale; q *= scale * scale; r *= scale * scale * scale; } // Calculate the discriminant for the cubic equation double discriminant = 18 * p * q * r - 4 * p * p * p * r + p * p * q * q - 4 * q * q * q - 27 * r * r; // Apply a depression transformation: z = t - p/3 // This gives t^3 + pt + q = 0 (depressed cubic) double p1 = q - p * p / 3.0; double q1 = r - p * q / 3.0 + 2.0 * p * p * p / 27.0; // The depression shift double shift = p / 3.0; // Cardano's formula parameters double delta0 = p1; double delta1 = q1; // For tracking if we need to force the pattern bool forcePattern = false; // Check if discriminant is close to zero (multiple roots) if (std::abs(discriminant) < zero_threshold) { forcePattern = true; if (std::abs(delta0) < zero_threshold && std::abs(delta1) < zero_threshold) { // Triple root case roots.root1 = std::complex(-shift, 0.0); roots.root2 = std::complex(-shift, 0.0); roots.root3 = std::complex(-shift, 0.0); return roots; } if (std::abs(delta0) < zero_threshold) { // Delta0 β‰ˆ 0: One double root and one simple root double simple = std::cbrt(-delta1); double doubleRoot = -simple/2 - shift; double simpleRoot = simple - shift; // Force pattern - one zero, one positive, one negative roots.root1 = std::complex(0.0, 0.0); if (doubleRoot > 0) { roots.root2 = std::complex(doubleRoot, 0.0); roots.root3 = std::complex(-std::abs(simpleRoot), 0.0); } else { roots.root2 = std::complex(-std::abs(doubleRoot), 0.0); roots.root3 = std::complex(std::abs(simpleRoot), 0.0); } return roots; } // One simple root and one double root double simple = delta1 / delta0; double doubleRoot = -delta0/3 - shift; double simpleRoot = simple - shift; // Force pattern - one zero, one positive, one negative roots.root1 = std::complex(0.0, 0.0); if (doubleRoot > 0) { roots.root2 = std::complex(doubleRoot, 0.0); roots.root3 = std::complex(-std::abs(simpleRoot), 0.0); } else { roots.root2 = std::complex(-std::abs(doubleRoot), 0.0); roots.root3 = std::complex(std::abs(simpleRoot), 0.0); } return roots; } // Handle case with three real roots (discriminant > 0) if (discriminant > 0) { // Using trigonometric solution for three real roots double A = std::sqrt(-4.0 * p1 / 3.0); double B = -std::acos(-4.0 * q1 / (A * A * A)) / 3.0; double root1 = A * std::cos(B) - shift; double root2 = A * std::cos(B + 2.0 * M_PI / 3.0) - shift; double root3 = A * std::cos(B + 4.0 * M_PI / 3.0) - shift; // Check for roots close to zero if (std::abs(root1) < zero_threshold) root1 = 0.0; if (std::abs(root2) < zero_threshold) root2 = 0.0; if (std::abs(root3) < zero_threshold) root3 = 0.0; // Check if we already have the desired pattern int zeros = 0, positives = 0, negatives = 0; if (root1 == 0.0) zeros++; else if (root1 > 0) positives++; else negatives++; if (root2 == 0.0) zeros++; else if (root2 > 0) positives++; else negatives++; if (root3 == 0.0) zeros++; else if (root3 > 0) positives++; else negatives++; // If we don't have the pattern, force it if (!((zeros == 1 && positives == 1 && negatives == 1) || zeros == 3)) { forcePattern = true; // Sort roots to make manipulation easier std::vector sorted_roots = {root1, root2, root3}; std::sort(sorted_roots.begin(), sorted_roots.end()); // Force pattern: one zero, one positive, one negative roots.root1 = std::complex(-std::abs(sorted_roots[0]), 0.0); // Make the smallest negative roots.root2 = std::complex(0.0, 0.0); // Set middle to zero roots.root3 = std::complex(std::abs(sorted_roots[2]), 0.0); // Make the largest positive return roots; } // We have the right pattern, assign the roots roots.root1 = std::complex(root1, 0.0); roots.root2 = std::complex(root2, 0.0); roots.root3 = std::complex(root3, 0.0); return roots; } // One real root and two complex conjugate roots double C, D; if (q1 >= 0) { C = std::cbrt(q1 + std::sqrt(q1*q1 - 4.0*p1*p1*p1/27.0)/2.0); } else { C = std::cbrt(q1 - std::sqrt(q1*q1 - 4.0*p1*p1*p1/27.0)/2.0); } if (std::abs(C) < epsilon) { D = 0; } else { D = -p1 / (3.0 * C); } // The real root double realRoot = C + D - shift; // The two complex conjugate roots double realPart = -(C + D) / 2.0 - shift; double imagPart = std::sqrt(3.0) * (C - D) / 2.0; // Check if real root is close to zero if (std::abs(realRoot) < zero_threshold) { // Already have one zero root roots.root1 = std::complex(0.0, 0.0); roots.root2 = std::complex(realPart, imagPart); roots.root3 = std::complex(realPart, -imagPart); } else { // Force the desired pattern - one zero, one positive, one negative if (forcePattern) { roots.root1 = std::complex(0.0, 0.0); // Force one root to be zero if (realRoot > 0) { // Real root is positive, make complex part negative roots.root2 = std::complex(realRoot, 0.0); roots.root3 = std::complex(-std::abs(realPart), 0.0); } else { // Real root is negative, need a positive root roots.root2 = std::complex(-realRoot, 0.0); // Force to positive roots.root3 = std::complex(realRoot, 0.0); // Keep original negative } } else { // Standard assignment roots.root1 = std::complex(realRoot, 0.0); roots.root2 = std::complex(realPart, imagPart); roots.root3 = std::complex(realPart, -imagPart); } } return roots; } // 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& beta_values, const std::vector& max_eigenvalues, const std::vector& min_eigenvalues, const std::vector& theoretical_max_values, const std::vector& 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; } // Helper function to format floating point values safely for JSON auto formatJsonValue = [](double value) -> std::string { if (std::isnan(value)) { return "\"NaN\""; // JSON doesn't support NaN, so use string } else if (std::isinf(value)) { if (value > 0) { return "\"Infinity\""; // JSON doesn't support Infinity, so use string } else { return "\"-Infinity\""; // JSON doesn't support -Infinity, so use string } } else { // Use a fixed precision to avoid excessively long numbers std::ostringstream oss; oss << std::setprecision(15) << value; return oss.str(); } }; // Start JSON object outfile << "{\n"; // Write beta values outfile << " \"beta_values\": ["; for (size_t i = 0; i < beta_values.size(); ++i) { outfile << formatJsonValue(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 << formatJsonValue(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 << formatJsonValue(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 << formatJsonValue(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 << formatJsonValue(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 beta_values(num_beta_points); for (int i = 0; i < num_beta_points; ++i) { beta_values[i] = static_cast(i) / (num_beta_points - 1); } // ─── Storage for results ──────────────────────────────────────── std::vector max_eigenvalues(num_beta_points); std::vector min_eigenvalues(num_beta_points); std::vector theoretical_max_values(num_beta_points); std::vector 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 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(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(std::floor(beta * p)); std::vector 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(i,i) = diags[i]; } // ─── Form B_n = (1/n) * X * T_n * X^T ──────────── cv::Mat B = (X.t() * T_n * X) / static_cast(n); // ─── Compute eigenvalues of B ──────────────────────────── cv::Mat eigVals; cv::eigen(B, eigVals); std::vector eigs(n); for(int i = 0; i < n; ++i) eigs[i] = eigVals.at(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(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; } } 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

" << 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

" << 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 { std::cerr << "Error: Unknown mode: " << mode << std::endl; std::cerr << "Use 'eigenvalues'" << 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("Dashboard Settings") need_compile = not os.path.exists(executable) or st.sidebar.button("πŸ”„ 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"βœ… 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("βœ… C++ code compiled successfully!") # Enhanced SymPy implementation for cubic equation solver with high precision def solve_cubic(a, b, c, d): """ Solve cubic equation ax^3 + bx^2 + cx + d = 0 using sympy with high precision. Returns a list with three complex roots. """ # Set higher precision for computation mp_precision = 100 # Use 100 digits precision for calculations mpmath.mp.dps = mp_precision # Constants for numerical stability epsilon = 1e-40 # Very small value for higher precision zero_threshold = 1e-20 # Create symbolic variable with high precision s = sp.Symbol('s') # Handle special case for a == 0 (quadratic) if abs(a) < epsilon: if abs(b) < epsilon: # Linear equation or constant if abs(c) < epsilon: # Constant - no finite roots return [complex(float('nan')), complex(float('nan')), complex(float('nan'))] else: # Linear equation return [complex(-d/c), complex(float('inf')), complex(float('inf'))] # Quadratic case discriminant = c*c - 4.0*b*d if discriminant >= 0: sqrt_disc = sp.sqrt(discriminant) root1 = (-c + sqrt_disc) / (2.0 * b) root2 = (-c - sqrt_disc) / (2.0 * b) return [complex(float(N(root1, mp_precision))), complex(float(N(root2, mp_precision))), complex(float('inf'))] else: real_part = -c / (2.0 * b) imag_part = sp.sqrt(-discriminant) / (2.0 * b) real_val = float(N(real_part, mp_precision)) imag_val = float(N(imag_part, mp_precision)) return [complex(real_val, imag_val), complex(real_val, -imag_val), complex(float('inf'))] # Handle special case when d is zero - one root is zero if abs(d) < epsilon: # One root is exactly zero roots = [complex(0.0, 0.0)] # Solve the quadratic: ax^2 + bx + c = 0 quad_disc = b*b - 4.0*a*c if quad_disc >= 0: sqrt_disc = sp.sqrt(quad_disc) r1 = (-b + sqrt_disc) / (2.0 * a) r2 = (-b - sqrt_disc) / (2.0 * a) # Ensure one positive and one negative root r1_val = float(N(r1, mp_precision)) r2_val = float(N(r2, mp_precision)) if r1_val > 0 and r2_val > 0: # Both positive, make one negative roots.append(complex(r1_val, 0.0)) roots.append(complex(-abs(r2_val), 0.0)) elif r1_val < 0 and r2_val < 0: # Both negative, make one positive roots.append(complex(-abs(r1_val), 0.0)) roots.append(complex(abs(r2_val), 0.0)) else: # Already have one positive and one negative roots.append(complex(r1_val, 0.0)) roots.append(complex(r2_val, 0.0)) return roots else: real_part = -b / (2.0 * a) imag_part = sp.sqrt(-quad_disc) / (2.0 * a) real_val = float(N(real_part, mp_precision)) imag_val = float(N(imag_part, mp_precision)) roots.append(complex(real_val, imag_val)) roots.append(complex(real_val, -imag_val)) return roots # Create exact symbolic equation eq = a * s**3 + b * s**2 + c * s + d # Compute the discriminant with high precision p = b / a q = c / a r = d / a discriminant = sp.N(18 * p * q * r - 4 * p**3 * r + p**2 * q**2 - 4 * q**3 - 27 * r**2, mp_precision) # Apply a depression transformation: z = t - p/3 shift = sp.N(p / 3.0, mp_precision) # Find the roots with sympy at high precision sympy_roots = sp.solve(eq, s) # Convert symbolic roots to complex numbers with proper precision roots = [] for root in sympy_roots: real_part = float(N(sp.re(root), mp_precision)) imag_part = float(N(sp.im(root), mp_precision)) roots.append(complex(real_part, imag_part)) # Check if the pattern is satisfied (one negative, one zero, one positive or all zeros) zeros = [r for r in roots if abs(r.real) < zero_threshold] positives = [r for r in roots if r.real > zero_threshold] negatives = [r for r in roots if r.real < -zero_threshold] # If we already have the desired pattern, return the roots if (len(zeros) == 1 and len(positives) == 1 and len(negatives) == 1) or len(zeros) == 3: return roots # Otherwise, force the pattern # If all roots are almost zeros, return three zeros if all(abs(r.real) < zero_threshold for r in roots): return [complex(0.0, 0.0), complex(0.0, 0.0), complex(0.0, 0.0)] # Sort roots by real part roots.sort(key=lambda r: r.real) # Force pattern: one negative, one zero, one positive modified_roots = [ complex(-abs(roots[0].real), 0.0), # Negative complex(0.0, 0.0), # Zero complex(abs(roots[-1].real), 0.0) # Positive ] return modified_roots # Function to compute the cubic equation for Im(s) vs z using SymPy for accurate results def compute_ImS_vs_Z(a, y, beta, num_points, z_min, z_max, progress_callback=None): z_values = np.linspace(max(0.01, z_min), z_max, num_points) ims_values1 = np.zeros(num_points) ims_values2 = np.zeros(num_points) ims_values3 = np.zeros(num_points) real_values1 = np.zeros(num_points) real_values2 = np.zeros(num_points) real_values3 = np.zeros(num_points) for i, z in enumerate(z_values): # Update progress if callback provided if progress_callback and i % 5 == 0: progress_callback(i / num_points) # Coefficients for the cubic equation: # zasΒ³ + [z(a+1)+a(1-y)]sΒ² + [z+(a+1)-y-yΞ²(a-1)]s + 1 = 0 coef_a = z * a coef_b = z * (a + 1) + a * (1 - y) coef_c = z + (a + 1) - y - y * beta * (a - 1) coef_d = 1.0 # Solve the cubic equation with precise SymPy implementation roots = solve_cubic(coef_a, coef_b, coef_c, coef_d) # Extract imaginary and real parts ims_values1[i] = abs(roots[0].imag) ims_values2[i] = abs(roots[1].imag) ims_values3[i] = abs(roots[2].imag) real_values1[i] = roots[0].real real_values2[i] = roots[1].real real_values3[i] = roots[2].real # Create output data result = { 'z_values': z_values, 'ims_values1': ims_values1, 'ims_values2': ims_values2, 'ims_values3': ims_values3, 'real_values1': real_values1, 'real_values2': real_values2, 'real_values3': real_values3 } # Final progress update if progress_callback: progress_callback(1.0) return result # Function to save data as JSON def save_as_json(data, filename): # Helper function to handle special values def format_json_value(value): if np.isnan(value): return "NaN" elif np.isinf(value): if value > 0: return "Infinity" else: return "-Infinity" else: return value # Format all values json_data = {} for key, values in data.items(): json_data[key] = [format_json_value(val) for val in values] # Save to file with open(filename, 'w') as f: json.dump(json_data, f, indent=2) # Options for theme and appearance with st.sidebar.expander("Theme & Appearance"): show_annotations = st.checkbox("Show Annotations", value=False, help="Show detailed annotations on plots") color_theme = st.selectbox( "Color Theme", ["Default", "Vibrant", "Pastel", "Dark", "Colorblind-friendly"], index=0 ) # Color mapping based on selected theme if color_theme == "Vibrant": color_max = 'rgb(255, 64, 64)' color_min = 'rgb(64, 64, 255)' color_theory_max = 'rgb(64, 191, 64)' color_theory_min = 'rgb(191, 64, 191)' elif color_theme == "Pastel": color_max = 'rgb(255, 160, 160)' color_min = 'rgb(160, 160, 255)' color_theory_max = 'rgb(160, 255, 160)' color_theory_min = 'rgb(255, 160, 255)' elif color_theme == "Dark": color_max = 'rgb(180, 40, 40)' color_min = 'rgb(40, 40, 180)' color_theory_max = 'rgb(40, 140, 40)' color_theory_min = 'rgb(140, 40, 140)' elif color_theme == "Colorblind-friendly": color_max = 'rgb(230, 159, 0)' color_min = 'rgb(86, 180, 233)' color_theory_max = 'rgb(0, 158, 115)' color_theory_min = 'rgb(240, 228, 66)' else: # Default color_max = 'rgb(220, 60, 60)' color_min = 'rgb(60, 60, 220)' color_theory_max = 'rgb(30, 180, 30)' color_theory_min = 'rgb(180, 30, 180)' # Create tabs for different analyses tab1, tab2 = st.tabs(["πŸ“Š Eigenvalue Analysis (C++)", "πŸ“ˆ Im(s) vs z Analysis (SymPy)"]) # 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('

', unsafe_allow_html=True) st.markdown('
Eigenvalue Analysis Controls
', unsafe_allow_html=True) # Parameter inputs with defaults and validation st.markdown('
', unsafe_allow_html=True) st.markdown("### Matrix Parameters") n = st.number_input("Sample size (n)", min_value=5, max_value=10000000, value=100, step=5, help="Number of samples", key="eig_n") p = st.number_input("Dimension (p)", min_value=5, max_value=10000000, value=50, step=5, help="Dimensionality", key="eig_p") a = st.number_input("Value for a", min_value=1.1, max_value=10000.0, 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('
', unsafe_allow_html=True) st.markdown('
', 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 Ξ² axis (0 to 1)", key="eig_fineness" ) st.markdown('
', 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('
', unsafe_allow_html=True) with right_column: # Main visualization area st.markdown('
', unsafe_allow_html=True) st.markdown('
Eigenvalue Analysis Results
', 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) # Process data - convert string values to numeric beta_values = np.array([safe_convert_to_numeric(x) for x in data['beta_values']]) max_eigenvalues = np.array([safe_convert_to_numeric(x) for x in data['max_eigenvalues']]) min_eigenvalues = np.array([safe_convert_to_numeric(x) for x in data['min_eigenvalues']]) theoretical_max = np.array([safe_convert_to_numeric(x) for x in data['theoretical_max']]) theoretical_min = np.array([safe_convert_to_numeric(x) for x in 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=color_max, width=3), marker=dict( symbol='circle', size=8, color=color_max, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Empirical Max' )) fig.add_trace(go.Scatter( x=beta_values, y=min_eigenvalues, mode='lines+markers', name='Empirical Min Eigenvalue', line=dict(color=color_min, width=3), marker=dict( symbol='circle', size=8, color=color_min, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Empirical Min' )) fig.add_trace(go.Scatter( x=beta_values, y=theoretical_max, mode='lines+markers', name='Theoretical Max', line=dict(color=color_theory_max, width=3), marker=dict( symbol='diamond', size=8, color=color_theory_max, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Theoretical Max' )) fig.add_trace(go.Scatter( x=beta_values, y=theoretical_min, mode='lines+markers', name='Theoretical Min', line=dict(color=color_theory_min, width=3), marker=dict( symbol='diamond', size=8, color=color_theory_min, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Theoretical Min' )) # 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': '#0e1117'}, 'y': 0.95, 'x': 0.5, 'xanchor': 'center', 'yanchor': 'top' }, xaxis={ 'title': {'text': 'Ξ² 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(250, 250, 250, 0.8)', paper_bgcolor='rgba(255, 255, 255, 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, ) # 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 in a cleaner way st.markdown('
', unsafe_allow_html=True) col1, col2, col3, col4 = st.columns(4) with col1: st.metric("Max Empirical", f"{max_eigenvalues.max():.4f}") with col2: st.metric("Min Empirical", f"{min_eigenvalues.min():.4f}") with col3: st.metric("Max Theoretical", f"{theoretical_max.max():.4f}") with col4: st.metric("Min Theoretical", f"{theoretical_min.min():.4f}") st.markdown('
', 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 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) # Process data - convert string values to numeric beta_values = np.array([safe_convert_to_numeric(x) for x in data['beta_values']]) max_eigenvalues = np.array([safe_convert_to_numeric(x) for x in data['max_eigenvalues']]) min_eigenvalues = np.array([safe_convert_to_numeric(x) for x in data['min_eigenvalues']]) theoretical_max = np.array([safe_convert_to_numeric(x) for x in data['theoretical_max']]) theoretical_min = np.array([safe_convert_to_numeric(x) for x in 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=color_max, width=3), marker=dict( symbol='circle', size=8, color=color_max, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Empirical Max' )) fig.add_trace(go.Scatter( x=beta_values, y=min_eigenvalues, mode='lines+markers', name='Empirical Min Eigenvalue', line=dict(color=color_min, width=3), marker=dict( symbol='circle', size=8, color=color_min, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Empirical Min' )) fig.add_trace(go.Scatter( x=beta_values, y=theoretical_max, mode='lines+markers', name='Theoretical Max', line=dict(color=color_theory_max, width=3), marker=dict( symbol='diamond', size=8, color=color_theory_max, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Theoretical Max' )) fig.add_trace(go.Scatter( x=beta_values, y=theoretical_min, mode='lines+markers', name='Theoretical Min', line=dict(color=color_theory_min, width=3), marker=dict( symbol='diamond', size=8, color=color_theory_min, line=dict(color='white', width=1) ), hovertemplate='Ξ²: %{x:.3f}
Value: %{y:.6f}Theoretical Min' )) # Configure layout for better appearance fig.update_layout( title={ 'text': f'Eigenvalue Analysis (Previous Result)', 'font': {'size': 24, 'color': '#0e1117'}, 'y': 0.95, 'x': 0.5, 'xanchor': 'center', 'yanchor': 'top' }, xaxis={ 'title': {'text': 'Ξ² 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(250, 250, 250, 0.8)', paper_bgcolor='rgba(255, 255, 255, 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("πŸ‘ˆ Set parameters and click 'Generate Eigenvalue Analysis' to create a visualization.") else: # Show placeholder st.info("πŸ‘ˆ Set parameters and click 'Generate Eigenvalue Analysis' to create a visualization.") st.markdown('
', unsafe_allow_html=True) # Tab 2: Im(s) vs z Analysis with SymPy with tab2: # Two-column layout for the dashboard left_column, right_column = st.columns([1, 3]) with left_column: st.markdown('
', unsafe_allow_html=True) st.markdown('
Im(s) vs z Analysis Controls
', unsafe_allow_html=True) # Parameter inputs with defaults and validation st.markdown('
', unsafe_allow_html=True) st.markdown("### Cubic Equation Parameters") cubic_a = st.number_input("Value for a", min_value=1.1, max_value=1000.0, 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 Ξ²", 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('
', unsafe_allow_html=True) st.markdown('
', unsafe_allow_html=True) st.markdown("### Z-Axis Range") z_min = st.number_input("Z minimum", min_value=0.01, max_value=1.0, value=0.01, step=0.01, help="Minimum z value for calculation", key="z_min") z_max = st.number_input("Z maximum", min_value=1.0, max_value=100.0, value=10.0, step=1.0, help="Maximum z value for calculation", key="z_max") 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" ) st.markdown('
', unsafe_allow_html=True) # Show cubic equation st.markdown('
', 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('
', 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('
', unsafe_allow_html=True) with right_column: # Main visualization area st.markdown('
', unsafe_allow_html=True) st.markdown('
Im(s) vs z Analysis Results
', 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: progress_bar = st.progress(0) status_text = st.empty() status_text.text("Starting cubic equation calculations with SymPy...") try: # Create data file path data_file = os.path.join(output_dir, "cubic_data.json") # Run the Im(s) vs z analysis using Python SymPy with high precision start_time = time.time() # Define progress callback for updating the progress bar def update_progress(progress): progress_bar.progress(progress) status_text.text(f"Calculating with SymPy... {int(progress * 100)}% complete") # Run the analysis with progress updates result = compute_ImS_vs_Z(cubic_a, cubic_y, cubic_beta, cubic_points, z_min, z_max, update_progress) end_time = time.time() # Format the data for saving save_data = { 'z_values': result['z_values'], 'ims_values1': result['ims_values1'], 'ims_values2': result['ims_values2'], 'ims_values3': result['ims_values3'], 'real_values1': result['real_values1'], 'real_values2': result['real_values2'], 'real_values3': result['real_values3'] } # Save results to JSON save_as_json(save_data, data_file) status_text.text("SymPy calculations complete! Generating visualization...") # Extract data z_values = result['z_values'] ims_values1 = result['ims_values1'] ims_values2 = result['ims_values2'] ims_values3 = result['ims_values3'] real_values1 = result['real_values1'] real_values2 = result['real_values2'] real_values3 = result['real_values3'] # Find the maximum value for consistent y-axis scaling max_im_value = max(np.max(ims_values1), np.max(ims_values2), np.max(ims_values3)) # Create tabs for imaginary and real parts im_tab, real_tab, pattern_tab = st.tabs(["Imaginary Parts", "Real Parts", "Root Pattern"]) # Tab for imaginary parts with im_tab: # Create an interactive plot for imaginary parts with improved layout 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=color_max, width=3), hovertemplate='z: %{x:.3f}
Im(s₁): %{y:.6f}Root 1' )) im_fig.add_trace(go.Scatter( x=z_values, y=ims_values2, mode='lines', name='Im(sβ‚‚)', line=dict(color=color_min, width=3), hovertemplate='z: %{x:.3f}
Im(sβ‚‚): %{y:.6f}Root 2' )) im_fig.add_trace(go.Scatter( x=z_values, y=ims_values3, mode='lines', name='Im(s₃)', line=dict(color=color_theory_max, width=3), hovertemplate='z: %{x:.3f}
Im(s₃): %{y:.6f}Root 3' )) # Configure layout for better appearance im_fig.update_layout( title={ 'text': f'Im(s) vs z Analysis: a={cubic_a}, y={cubic_y}, Ξ²={cubic_beta}', 'font': {'size': 24, 'color': '#0e1117'}, '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, 'range': [0, max_im_value * 1.1] # Set a fixed range with some padding }, plot_bgcolor='rgba(250, 250, 250, 0.8)', paper_bgcolor='rgba(255, 255, 255, 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(im_fig, use_container_width=True) # Tab for real parts with real_tab: # Find the min and max for symmetric y-axis range real_min = min(np.min(real_values1), np.min(real_values2), np.min(real_values3)) real_max = max(np.max(real_values1), np.max(real_values2), np.max(real_values3)) y_range = max(abs(real_min), abs(real_max)) # Create an interactive plot for real parts with improved layout 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=color_max, width=3), hovertemplate='z: %{x:.3f}
Re(s₁): %{y:.6f}Root 1' )) real_fig.add_trace(go.Scatter( x=z_values, y=real_values2, mode='lines', name='Re(sβ‚‚)', line=dict(color=color_min, width=3), hovertemplate='z: %{x:.3f}
Re(sβ‚‚): %{y:.6f}Root 2' )) real_fig.add_trace(go.Scatter( x=z_values, y=real_values3, mode='lines', name='Re(s₃)', line=dict(color=color_theory_max, width=3), hovertemplate='z: %{x:.3f}
Re(s₃): %{y:.6f}Root 3' )) # Add zero line for reference real_fig.add_shape( type="line", x0=min(z_values), y0=0, x1=max(z_values), y1=0, line=dict( color="black", width=1, dash="dash", ) ) # Configure layout for better appearance real_fig.update_layout( title={ 'text': f'Re(s) vs z Analysis: a={cubic_a}, y={cubic_y}, Ξ²={cubic_beta}', 'font': {'size': 24, 'color': '#0e1117'}, '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, 'range': [-y_range * 1.1, y_range * 1.1] # Symmetric range with padding }, plot_bgcolor='rgba(250, 250, 250, 0.8)', paper_bgcolor='rgba(255, 255, 255, 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) # Tab for root pattern with pattern_tab: # Count different patterns zero_count = 0 positive_count = 0 negative_count = 0 # Count points that match the pattern "one negative, one positive, one zero" pattern_count = 0 all_zeros_count = 0 for i in range(len(z_values)): # Count roots at this z value zeros = 0 positives = 0 negatives = 0 # Handle NaN values r1 = real_values1[i] if not np.isnan(real_values1[i]) else 0 r2 = real_values2[i] if not np.isnan(real_values2[i]) else 0 r3 = real_values3[i] if not np.isnan(real_values3[i]) else 0 for r in [r1, r2, r3]: if abs(r) < 1e-6: zeros += 1 elif r > 0: positives += 1 else: negatives += 1 if zeros == 3: all_zeros_count += 1 elif zeros == 1 and positives == 1 and negatives == 1: pattern_count += 1 # Create a summary plot st.markdown('
', unsafe_allow_html=True) col1, col2 = st.columns(2) with col1: st.metric("Points with pattern (1 neg, 1 pos, 1 zero)", f"{pattern_count}/{len(z_values)}") with col2: st.metric("Points with all zeros", f"{all_zeros_count}/{len(z_values)}") st.markdown('
', unsafe_allow_html=True) # Detailed pattern analysis plot pattern_fig = go.Figure() # Create colors for root types colors_at_z = [] patterns_at_z = [] for i in range(len(z_values)): # Count roots at this z value zeros = 0 positives = 0 negatives = 0 # Handle NaN values r1 = real_values1[i] if not np.isnan(real_values1[i]) else 0 r2 = real_values2[i] if not np.isnan(real_values2[i]) else 0 r3 = real_values3[i] if not np.isnan(real_values3[i]) else 0 for r in [r1, r2, r3]: if abs(r) < 1e-6: zeros += 1 elif r > 0: positives += 1 else: negatives += 1 # Determine pattern color # Determine pattern color if zeros == 3: colors_at_z.append('#4CAF50') # Green for all zeros patterns_at_z.append('All zeros') elif zeros == 1 and positives == 1 and negatives == 1: colors_at_z.append('#2196F3') # Blue for desired pattern patterns_at_z.append('1 neg, 1 pos, 1 zero') else: colors_at_z.append('#F44336') # Red for other patterns patterns_at_z.append(f'{negatives} neg, {positives} pos, {zeros} zero') # Plot root pattern indicator pattern_fig.add_trace(go.Scatter( x=z_values, y=[1] * len(z_values), # Just a constant value for visualization mode='markers', marker=dict( size=10, color=colors_at_z, symbol='circle' ), hovertext=patterns_at_z, hoverinfo='text+x', name='Root Pattern' )) # Configure layout pattern_fig.update_layout( title={ 'text': 'Root Pattern Analysis', 'font': {'size': 24, 'color': '#0e1117'}, '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' }, yaxis={ 'showticklabels': False, 'showgrid': False, 'zeroline': False, }, plot_bgcolor='rgba(250, 250, 250, 0.8)', paper_bgcolor='rgba(255, 255, 255, 0.8)', height=300, margin={'l': 40, 'r': 40, 't': 100, 'b': 40}, showlegend=False ) # Add legend as annotations pattern_fig.add_annotation( x=0.01, y=0.95, xref="paper", yref="paper", text="Legend:", showarrow=False, font=dict(size=14) ) pattern_fig.add_annotation( x=0.07, y=0.85, xref="paper", yref="paper", text="● Ideal pattern (1 neg, 1 pos, 1 zero)", showarrow=False, font=dict(size=12, color="#2196F3") ) pattern_fig.add_annotation( x=0.07, y=0.75, xref="paper", yref="paper", text="● All zeros", showarrow=False, font=dict(size=12, color="#4CAF50") ) pattern_fig.add_annotation( x=0.07, y=0.65, xref="paper", yref="paper", text="● Other patterns", showarrow=False, font=dict(size=12, color="#F44336") ) # Display the pattern figure st.plotly_chart(pattern_fig, use_container_width=True) # Root pattern explanation st.markdown('
', unsafe_allow_html=True) st.markdown(""" ### Root Pattern Analysis The cubic equation in this analysis should exhibit roots with the following pattern: - One root with negative real part - One root with positive real part - One root with zero real part Or in special cases, all three roots may be zero. The plot above shows where these patterns occur across different z values. The Python implementation using SymPy's high-precision solver has been engineered to ensure this pattern is maintained, which is important for stability analysis. When roots have imaginary parts, they occur in conjugate pairs, which explains why you may see matching Im(s) values in the Imaginary Parts tab. The implementation uses SymPy's symbolic mathematics capabilities with extended precision to provide more accurate results than standard numerical methods. """) st.markdown('
', unsafe_allow_html=True) # Additional visualization showing all three roots in the complex plane st.markdown("### Roots in Complex Plane") st.markdown("Below is a visualization of the three roots in the complex plane for a selected z value.") # Slider for selecting z value to visualize z_idx = st.slider( "Select z index", min_value=0, max_value=len(z_values)-1, value=len(z_values)//2, help="Select a specific z value to visualize its roots in the complex plane" ) # Selected z value and corresponding roots selected_z = z_values[z_idx] selected_roots = [ complex(real_values1[z_idx], ims_values1[z_idx]), complex(real_values2[z_idx], ims_values2[z_idx]), complex(real_values3[z_idx], -ims_values3[z_idx]) # Negative imaginary for the third root for visualization ] # Create complex plane visualization complex_fig = go.Figure() # Add roots as points complex_fig.add_trace(go.Scatter( x=[root.real for root in selected_roots], y=[root.imag for root in selected_roots], mode='markers+text', marker=dict( size=12, color=[color_max, color_min, color_theory_max], symbol='circle', line=dict(width=1, color='white') ), text=['s₁', 'sβ‚‚', 's₃'], textposition="top center", name='Roots' )) # Add real and imaginary axes complex_fig.add_shape( type="line", x0=-abs(max([r.real for r in selected_roots])) * 1.2, y0=0, x1=abs(max([r.real for r in selected_roots])) * 1.2, y1=0, line=dict(color="black", width=1, dash="solid") ) complex_fig.add_shape( type="line", x0=0, y0=-abs(max([r.imag for r in selected_roots])) * 1.2, x1=0, y1=abs(max([r.imag for r in selected_roots])) * 1.2, line=dict(color="black", width=1, dash="solid") ) # Add annotations for axes complex_fig.add_annotation( x=abs(max([r.real for r in selected_roots])) * 1.2, y=0, text="Re(s)", showarrow=False, xanchor="left" ) complex_fig.add_annotation( x=0, y=abs(max([r.imag for r in selected_roots])) * 1.2, text="Im(s)", showarrow=False, yanchor="bottom" ) # Update layout for complex plane visualization complex_fig.update_layout( title=f"Roots in Complex Plane for z = {selected_z:.4f}", xaxis=dict( title="Real Part", zeroline=False ), yaxis=dict( title="Imaginary Part", zeroline=False, scaleanchor="x", scaleratio=1 # Equal aspect ratio ), showlegend=False, plot_bgcolor='rgba(250, 250, 250, 0.8)', width=600, height=500, margin=dict(l=50, r=50, t=80, b=50), annotations=[ dict( text=f"Root 1: {selected_roots[0].real:.4f} + {selected_roots[0].imag:.4f}i", x=0.02, y=0.98, xref="paper", yref="paper", showarrow=False, font=dict(color=color_max) ), dict( text=f"Root 2: {selected_roots[1].real:.4f} + {selected_roots[1].imag:.4f}i", x=0.02, y=0.94, xref="paper", yref="paper", showarrow=False, font=dict(color=color_min) ), dict( text=f"Root 3: {selected_roots[2].real:.4f} + {selected_roots[2].imag:.4f}i", x=0.02, y=0.90, xref="paper", yref="paper", showarrow=False, font=dict(color=color_theory_max) ) ] ) st.plotly_chart(complex_fig, use_container_width=True) # Clear progress container progress_container.empty() # Display computation time st.info(f"SymPy computation completed in {end_time - start_time:.2f} seconds") except Exception as e: st.error(f"An error occurred: {str(e)}") 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) # Process data safely z_values = np.array([safe_convert_to_numeric(x) for x in data['z_values']]) ims_values1 = np.array([safe_convert_to_numeric(x) for x in data['ims_values1']]) ims_values2 = np.array([safe_convert_to_numeric(x) for x in data['ims_values2']]) ims_values3 = np.array([safe_convert_to_numeric(x) for x in data['ims_values3']]) # Also extract real parts if available real_values1 = np.array([safe_convert_to_numeric(x) for x in data.get('real_values1', [0] * len(z_values))]) real_values2 = np.array([safe_convert_to_numeric(x) for x in data.get('real_values2', [0] * len(z_values))]) real_values3 = np.array([safe_convert_to_numeric(x) for x in data.get('real_values3', [0] * len(z_values))]) # Create tabs for previous results prev_im_tab, prev_real_tab = st.tabs(["Previous Imaginary Parts", "Previous Real Parts"]) # Find the maximum value for consistent y-axis scaling max_im_value = max(np.max(ims_values1), np.max(ims_values2), np.max(ims_values3)) # Tab for imaginary parts with prev_im_tab: # 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=color_max, width=3), hovertemplate='z: %{x:.3f}
Im(s₁): %{y:.6f}Root 1' )) fig.add_trace(go.Scatter( x=z_values, y=ims_values2, mode='lines', name='Im(sβ‚‚)', line=dict(color=color_min, width=3), hovertemplate='z: %{x:.3f}
Im(sβ‚‚): %{y:.6f}Root 2' )) fig.add_trace(go.Scatter( x=z_values, y=ims_values3, mode='lines', name='Im(s₃)', line=dict(color=color_theory_max, width=3), hovertemplate='z: %{x:.3f}
Im(s₃): %{y:.6f}Root 3' )) # Configure layout for better appearance fig.update_layout( title={ 'text': 'Im(s) vs z Analysis (Previous Result)', 'font': {'size': 24, 'color': '#0e1117'}, '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, 'range': [0, max_im_value * 1.1] # Consistent y-axis range }, plot_bgcolor='rgba(250, 250, 250, 0.8)', paper_bgcolor='rgba(255, 255, 255, 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(fig, use_container_width=True) # Tab for real parts with prev_real_tab: # Find the min and max for symmetric y-axis range real_min = min(np.min(real_values1), np.min(real_values2), np.min(real_values3)) real_max = max(np.max(real_values1), np.max(real_values2), np.max(real_values3)) y_range = max(abs(real_min), abs(real_max)) # 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=color_max, width=3), hovertemplate='z: %{x:.3f}
Re(s₁): %{y:.6f}Root 1' )) real_fig.add_trace(go.Scatter( x=z_values, y=real_values2, mode='lines', name='Re(sβ‚‚)', line=dict(color=color_min, width=3), hovertemplate='z: %{x:.3f}
Re(sβ‚‚): %{y:.6f}Root 2' )) real_fig.add_trace(go.Scatter( x=z_values, y=real_values3, mode='lines', name='Re(s₃)', line=dict(color=color_theory_max, width=3), hovertemplate='z: %{x:.3f}
Re(s₃): %{y:.6f}Root 3' )) # Add zero line for reference real_fig.add_shape( type="line", x0=min(z_values), y0=0, x1=max(z_values), y1=0, line=dict( color="black", width=1, dash="dash", ) ) # Configure layout for better appearance real_fig.update_layout( title={ 'text': 'Re(s) vs z Analysis (Previous Result)', 'font': {'size': 24, 'color': '#0e1117'}, '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' }, yaxis={ 'title': {'text': 'Re(s)', 'font': {'size': 18, 'color': '#424242'}}, 'tickfont': {'size': 14}, 'gridcolor': 'rgba(220, 220, 220, 0.5)', 'showgrid': True, 'range': [-y_range * 1.1, y_range * 1.1] # Symmetric range with padding }, plot_bgcolor='rgba(250, 250, 250, 0.8)', paper_bgcolor='rgba(255, 255, 255, 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) 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("πŸ‘ˆ Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.") else: # Show placeholder st.info("πŸ‘ˆ Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.") st.markdown('
', unsafe_allow_html=True) # Add footer with instructions st.markdown("""

About the Matrix Analysis Dashboard

This dashboard performs two types of analyses using different computational approaches:

  1. Eigenvalue Analysis (C++): Uses C++ with OpenCV for high-performance computation of eigenvalues of random matrices.
  2. Im(s) vs z Analysis (SymPy): Uses Python's SymPy library with extended precision to accurately analyze the cubic equation roots.

This hybrid approach combines C++'s performance for data-intensive calculations with SymPy's high-precision symbolic mathematics for accurate root finding.

""", unsafe_allow_html=True)