Update app.py

app.py

@@ -14,12 +14,12 @@ import tempfile
 import platform
 from sympy import symbols, solve, I, re, im, Poly, simplify, N
 import mpmath
-import scipy 
+import scipy
 
 # Set page config with wider layout
 st.set_page_config(
     page_title="Matrix Analysis Dashboard",
-    page_icon="📊",
+    page_icon="📊",
     layout="wide",
     initial_sidebar_state="expanded"
 )
@@ -390,7 +390,7 @@ CubicRoots solveCubic(double a, double b, double c, double d) {
         }
         
         if (std::abs(delta0) < zero_threshold) {
-            // Delta0 ≈ 0: One double root and one simple root
+            // Delta0 ≈ 0: One double root and one simple root
             double simple = std::cbrt(-delta1);
             double doubleRoot = -simple/2 - shift;
             double simpleRoot = simple - shift;
@@ -718,21 +718,21 @@ bool eigenvalueAnalysis(int n, int p, double a, double y, int fineness,
               << ", theory_tolerance = " << theory_tolerance << std::endl;
     std::cout << "Output will be saved to: " << output_file << std::endl;
     
-    // ─── Beta range parameters ────────────────────────────────────────
+    // ─── 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 ────────────────────────────────────────
+    // ─── 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 ────────────────────────────────
+        // ─── Random‐Gaussian X and S_n ────────────────────────────────
         std::random_device rd;
         std::mt19937_64 rng{rd()};
         std::normal_distribution<double> norm(0.0, 1.0);
@@ -742,7 +742,7 @@ bool eigenvalueAnalysis(int n, int p, double a, double y, int fineness,
             for(int j = 0; j < n; ++j)
                 X.at<double>(i,j) = norm(rng);
         
-        // ─── Process each beta value ─────────────────────────────────
+        // ─── Process each beta value ─────────────────────────────────
         for (int beta_idx = 0; beta_idx < num_beta_points; ++beta_idx) {
             double beta = beta_values[beta_idx];
             
@@ -750,7 +750,7 @@ bool eigenvalueAnalysis(int n, int p, double a, double y, int fineness,
             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 ──────────────────────────────────
+            // ─── 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);
@@ -761,10 +761,10 @@ bool eigenvalueAnalysis(int n, int p, double a, double y, int fineness,
                 T_n.at<double>(i,i) = diags[i];
             }
             
-            // ─── Form B_n = (1/n) * X * T_n * X^T ────────────
+            // ─── 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 ────────────────────────────
+            // ─── Compute eigenvalues of B ────────────────────────────
             cv::Mat eigVals;
             cv::eigen(B, eigVals);
             std::vector<double> eigs(n);  
@@ -822,7 +822,7 @@ int main(int argc, char* argv[]) {
     
     try {
         if (mode == "eigenvalues") {
-            // ─── Eigenvalue analysis mode ───────────────────────────────────────────
+            // ─── 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;
@@ -859,7 +859,7 @@ int main(int argc, char* argv[]) {
 
 # 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("🔄 Recompile C++ Code")
+need_compile = not os.path.exists(executable) or st.sidebar.button("🔄 Recompile C++ Code")
 
 if need_compile:
     with st.sidebar:
@@ -893,11 +893,11 @@ if need_compile:
                 
                 if success:
                     compiled = True
-                    st.success(f"✅ Successfully compiled with: {cmd}")
+                    st.success(f"✅ Successfully compiled with: {cmd}")
                     break
             
             if not compiled:
-                st.error("❌ All compilation attempts failed.")
+                st.error("❌ All compilation attempts failed.")
                 with st.expander("Compilation Details"):
                     st.code(compile_output)
                 st.stop()
@@ -906,7 +906,7 @@ if need_compile:
             if platform.system() != "Windows":
                 os.chmod(executable, 0o755)
             
-            st.success("✅ C++ code compiled successfully!")
+            st.success("✅ C++ code compiled successfully!")
 
 # Set higher precision for mpmath
 mpmath.mp.dps = 100  # 100 digits of precision
@@ -1044,7 +1044,7 @@ def compute_ImS_vs_Z(a, y, beta, num_points, z_min, z_max, progress_callback=Non
             progress_callback(i / num_points)
             
         # Coefficients for the cubic equation:
-        # zas³ + [z(a+1)+a(1-y)]s² + [z+(a+1)-y-yβ(a-1)]s + 1 = 0
+        # zas³ + [z(a+1)+a(1-y)]s² + [z+(a+1)-y-yβ(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)
@@ -1118,8 +1118,8 @@ def create_dash_style_visualization(result, cubic_a, cubic_y, cubic_beta):
         rows=2, 
         cols=1,
         subplot_titles=(
-            f"Imaginary Parts of Roots: a={cubic_a}, y={cubic_y}, β={cubic_beta}",
-            f"Real Parts of Roots: a={cubic_a}, y={cubic_y}, β={cubic_beta}"
+            f"Imaginary Parts of Roots: a={cubic_a}, y={cubic_y}, β={cubic_beta}",
+            f"Real Parts of Roots: a={cubic_a}, y={cubic_y}, β={cubic_beta}"
         ),
         vertical_spacing=0.15,
         specs=[[{"type": "scatter"}], [{"type": "scatter"}]]
@@ -1131,9 +1131,9 @@ def create_dash_style_visualization(result, cubic_a, cubic_y, cubic_beta):
             x=z_values, 
             y=ims_values1,
             mode='lines',
-            name='Im(s₁)',
+            name='Im(s₁)',
             line=dict(color='rgb(239, 85, 59)', width=2.5),
-            hovertemplate='z: %{x:.4f}<br>Im(s₁): %{y:.6f}<extra>Root 1</extra>'
+            hovertemplate='z: %{x:.4f}<br>Im(s₁): %{y:.6f}<extra>Root 1</extra>'
         ),
         row=1, col=1
     )
@@ -1143,9 +1143,9 @@ def create_dash_style_visualization(result, cubic_a, cubic_y, cubic_beta):
             x=z_values, 
             y=ims_values2,
             mode='lines',
-            name='Im(s₂)',
+            name='Im(s₂)',
             line=dict(color='rgb(0, 129, 201)', width=2.5),
-            hovertemplate='z: %{x:.4f}<br>Im(s₂): %{y:.6f}<extra>Root 2</extra>'
+            hovertemplate='z: %{x:.4f}<br>Im(s₂): %{y:.6f}<extra>Root 2</extra>'
         ),
         row=1, col=1
     )
@@ -1155,9 +1155,9 @@ def create_dash_style_visualization(result, cubic_a, cubic_y, cubic_beta):
             x=z_values, 
             y=ims_values3,
             mode='lines',
-            name='Im(s₃)',
+            name='Im(s₃)',
             line=dict(color='rgb(0, 176, 80)', width=2.5),
-            hovertemplate='z: %{x:.4f}<br>Im(s₃): %{y:.6f}<extra>Root 3</extra>'
+            hovertemplate='z: %{x:.4f}<br>Im(s₃): %{y:.6f}<extra>Root 3</extra>'
         ),
         row=1, col=1
     )
@@ -1168,9 +1168,9 @@ def create_dash_style_visualization(result, cubic_a, cubic_y, cubic_beta):
             x=z_values, 
             y=real_values1,
             mode='lines',
-            name='Re(s₁)',
+            name='Re(s₁)',
             line=dict(color='rgb(239, 85, 59)', width=2.5),
-            hovertemplate='z: %{x:.4f}<br>Re(s₁): %{y:.6f}<extra>Root 1</extra>'
+            hovertemplate='z: %{x:.4f}<br>Re(s₁): %{y:.6f}<extra>Root 1</extra>'
         ),
         row=2, col=1
     )
@@ -1180,9 +1180,9 @@ def create_dash_style_visualization(result, cubic_a, cubic_y, cubic_beta):
             x=z_values, 
             y=real_values2,
             mode='lines',
-            name='Re(s₂)',
+            name='Re(s₂)',
             line=dict(color='rgb(0, 129, 201)', width=2.5),
-            hovertemplate='z: %{x:.4f}<br>Re(s₂): %{y:.6f}<extra>Root 2</extra>'
+            hovertemplate='z: %{x:.4f}<br>Re(s₂): %{y:.6f}<extra>Root 2</extra>'
         ),
         row=2, col=1
     )
@@ -1192,9 +1192,9 @@ def create_dash_style_visualization(result, cubic_a, cubic_y, cubic_beta):
             x=z_values, 
             y=real_values3,
             mode='lines',
-            name='Re(s₃)',
+            name='Re(s₃)',
             line=dict(color='rgb(0, 176, 80)', width=2.5),
-            hovertemplate='z: %{x:.4f}<br>Re(s₃): %{y:.6f}<extra>Root 3</extra>'
+            hovertemplate='z: %{x:.4f}<br>Re(s₃): %{y:.6f}<extra>Root 3</extra>'
         ),
         row=2, col=1
     )
@@ -1484,7 +1484,7 @@ def create_complex_plane_visualization(result, z_idx):
             symbol='circle',
             line=dict(width=1, color='black')
         ),
-        text=['s₁', 's₂', 's₃'],
+        text=['s₁', 's₂', 's₃'],
         textposition="top center",
         name='Roots'
     ))
@@ -1616,7 +1616,7 @@ with st.sidebar.expander("Theme & Appearance"):
         color_theory_min = 'rgb(180, 30, 180)'
 
 # Create tabs for different analyses
-tab1, tab2 = st.tabs(["📊 Eigenvalue Analysis (C++)", "📈 Im(s) vs z Analysis (SymPy)"])
+tab1, tab2 = st.tabs(["📊 Eigenvalue Analysis (C++)", "📈 Im(s) vs z Analysis (SymPy)"])
 
 # Tab 1: Eigenvalue Analysis (KEEP UNCHANGED from original)
 with tab1:
@@ -1650,7 +1650,7 @@ with tab1:
             max_value=500, 
             value=100, 
             step=10,
-            help="Number of points to calculate along the β axis (0 to 1)",
+            help="Number of points to calculate along the β axis (0 to 1)",
             key="eig_fineness"
         )
         st.markdown('</div>', unsafe_allow_html=True)
@@ -1833,7 +1833,7 @@ with tab1:
                                     color=color_max,
                                     line=dict(color='white', width=1)
                                 ),
-                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Max</extra>'
+                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Max</extra>'
                             ))
                             
                             fig.add_trace(go.Scatter(
@@ -1848,7 +1848,7 @@ with tab1:
                                     color=color_min,
                                     line=dict(color='white', width=1)
                                 ),
-                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Min</extra>'
+                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Min</extra>'
                             ))
                             
                             fig.add_trace(go.Scatter(
@@ -1863,7 +1863,7 @@ with tab1:
                                     color=color_theory_max,
                                     line=dict(color='white', width=1)
                                 ),
-                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Max</extra>'
+                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Max</extra>'
                             ))
                             
                             fig.add_trace(go.Scatter(
@@ -1878,7 +1878,7 @@ with tab1:
                                     color=color_theory_min,
                                     line=dict(color='white', width=1)
                                 ),
-                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Min</extra>'
+                                hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Min</extra>'
                             ))
                             
                             # Configure layout for better appearance
@@ -1892,7 +1892,7 @@ with tab1:
                                     'yanchor': 'top'
                                 },
                                 xaxis={
-                                    'title': {'text': 'β Parameter', 'font': {'size': 18, 'color': '#424242'}},
+                                    'title': {'text': 'β Parameter', 'font': {'size': 18, 'color': '#424242'}},
                                     'tickfont': {'size': 14},
                                     'gridcolor': 'rgba(220, 220, 220, 0.5)',
                                     'showgrid': True
@@ -1988,7 +1988,7 @@ with tab1:
                             color=color_max,
                             line=dict(color='white', width=1)
                         ),
-                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Max</extra>'
+                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Max</extra>'
                     ))
                     
                     fig.add_trace(go.Scatter(
@@ -2003,7 +2003,7 @@ with tab1:
                             color=color_min,
                             line=dict(color='white', width=1)
                         ),
-                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Min</extra>'
+                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Empirical Min</extra>'
                     ))
                     
                     fig.add_trace(go.Scatter(
@@ -2018,7 +2018,7 @@ with tab1:
                             color=color_theory_max,
                             line=dict(color='white', width=1)
                         ),
-                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Max</extra>'
+                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Max</extra>'
                     ))
                     
                     fig.add_trace(go.Scatter(
@@ -2033,7 +2033,7 @@ with tab1:
                             color=color_theory_min,
                             line=dict(color='white', width=1)
                         ),
-                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Min</extra>'
+                        hovertemplate='β: %{x:.3f}<br>Value: %{y:.6f}<extra>Theoretical Min</extra>'
                     ))
                     
                     # Configure layout for better appearance
@@ -2047,7 +2047,7 @@ with tab1:
                             'yanchor': 'top'
                         },
                         xaxis={
-                            'title': {'text': 'β Parameter', 'font': {'size': 18, 'color': '#424242'}},
+                            'title': {'text': 'β Parameter', 'font': {'size': 18, 'color': '#424242'}},
                             'tickfont': {'size': 14},
                             'gridcolor': 'rgba(220, 220, 220, 0.5)',
                             'showgrid': True
@@ -2076,10 +2076,10 @@ with tab1:
                     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.")
+                    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.info("👈 Set parameters and click 'Generate Eigenvalue Analysis' to create a visualization.")
         
         st.markdown('</div>', unsafe_allow_html=True)
 
@@ -2099,7 +2099,7 @@ with tab2:
                                 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,
+        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)
         
@@ -2304,16 +2304,17 @@ with tab2:
                             help="Select a specific z value to visualize its roots in the complex plane"
                         )
                         
-                        # Create complex plane visualization
+                
+        # Create complex plane visualization
                         complex_fig = create_complex_plane_visualization(result, z_idx)
                         st.plotly_chart(complex_fig, use_container_width=True)
                     
                 except Exception as e:
-                    st.info("👈 Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.")
+                    st.info("Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.")
                     st.error(f"Error loading previous data: {str(e)}")
             else:
                 # Show placeholder
-                st.info("👈 Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.")
+                st.info(" Set parameters and click 'Generate Im(s) vs z Analysis' to create a visualization.")
         
         st.markdown('</div>', unsafe_allow_html=True)