{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4557c12a",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bf8113f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9017764272564dc6a06a4b5963a2d871",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HBox(children=(Text(value='a * x + b', description='f(x) =', layout=Layout(width='420px')), But…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_12072/1355624997.py:333: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
      "  plt.tight_layout()\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bf9f49f0dda84eeea2349a7eaadd5ab4",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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width=1200.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "25a3fc7b5bf24dcca81672a20bbd7687",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bfe2b9ab3d534e048055dbf644ad0aeb",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=900.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as patches\n",
    "from matplotlib.widgets import RectangleSelector\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display\n",
    "from scipy.optimize import curve_fit\n",
    "import ast\n",
    "import re\n",
    "import scipy\n",
    "import ipysheet\n",
    "\n",
    "# Dati di esempio\n",
    "import pandas as pd\n",
    "# df = pd.read_csv(\"dati.csv\")\n",
    "# x_data = df[\"nome_colonna_x\"].values\n",
    "# y_data = df[\"nome_colonna_y\"].values\n",
    "\n",
    "np.random.seed(42)\n",
    "x_data = np.linspace(0, 100, 101)\n",
    "y_data = 2.5 * x_data**2 + 1.2 * x_data + 1 + np.random.normal(0, 100, 101)\n",
    "\n",
    "\n",
    "\n",
    "# Stato\n",
    "selected_mask = np.ones(len(x_data), dtype=bool)\n",
    "fit_history   = []\n",
    "\n",
    "# Figura matplotlib\n",
    "fig, ax = plt.subplots(figsize=(9, 5))\n",
    "plt.subplots_adjust(bottom=0.12)\n",
    "\n",
    "sc_all    = ax.scatter(x_data, y_data, c='steelblue', s=25, alpha=0.5, zorder=2, label='tutti i punti')\n",
    "sc_sel    = ax.scatter([], [], c='tomato', s=45, alpha=0.9, zorder=3, label='selezionati')\n",
    "line_fit, = ax.plot([], [], color='darkorange', lw=2.5, zorder=4, label='fit')\n",
    "fit_text  = ax.text(0.02, 0.97, '', transform=ax.transAxes, fontsize=10, color='darkorange',\n",
    "                    va='top', ha='left', bbox=dict(boxstyle='round,pad=0.3', facecolor='white', alpha=0.7))\n",
    "box_patch = patches.Rectangle((0, 0), 0, 0, linewidth=1.5, edgecolor='tomato',\n",
    "                               facecolor='tomato', alpha=0.08, linestyle='--', zorder=1)\n",
    "ax.add_patch(box_patch)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.legend(loc='upper right', fontsize=9)\n",
    "ax.grid(True, alpha=0.3)\n",
    "\n",
    "# UI\n",
    "func_input     = widgets.Text(value='a * x + b', description='f(x) =', layout=widgets.Layout(width='420px'))\n",
    "fit_btn        = widgets.Button(description='Esegui fit',      button_style='primary')\n",
    "clear_btn      = widgets.Button(description='Reset selezione', button_style='warning')\n",
    "clear_hist_btn = widgets.Button(description='Reset storia fit', button_style='danger')\n",
    "sel_label      = widgets.Label(value=f'Selezionati: {len(x_data)} / {len(x_data)}')\n",
    "out_log        = widgets.Output(layout=widgets.Layout(border='1px solid #ddd', padding='8px', min_height='80px'))\n",
    "\n",
    "# RectangleSelector\n",
    "def on_select(eclick, erelease):\n",
    "    global selected_mask\n",
    "    if eclick.xdata is None or erelease.xdata is None:\n",
    "        return\n",
    "\n",
    "    x0, x1 = sorted([eclick.xdata, erelease.xdata])\n",
    "    y0, y1 = sorted([eclick.ydata,  erelease.ydata])\n",
    "\n",
    "    selected_mask = ((x_data >= x0) & (x_data <= x1) &\n",
    "                     (y_data >= y0) & (y_data <= y1))\n",
    "\n",
    "    pts = np.column_stack([x_data[selected_mask], y_data[selected_mask]])\n",
    "    sc_sel.set_offsets(pts if pts.size > 0 else np.empty((0, 2)))\n",
    "\n",
    "    box_patch.set_xy((x0, y0))\n",
    "    box_patch.set_width(x1 - x0)\n",
    "    box_patch.set_height(y1 - y0)\n",
    "    box_patch.set_visible(True)\n",
    "    sel_label.value = f'Selezionati: {int(selected_mask.sum())} / {len(x_data)}'\n",
    "    fig.canvas.draw_idle()\n",
    "\n",
    "rect_selector = RectangleSelector(ax, on_select, useblit=True, button=[1], minspanx=0, minspany=0, spancoords='data', interactive=False)\n",
    "\n",
    "# Parsing\n",
    "def extract_params(expr):\n",
    "    expr = re.sub(r'^[a-zA-Z_]\\s*=\\s*', '', expr.strip())\n",
    "    try:\n",
    "        tree  = ast.parse(expr, mode='eval')\n",
    "        names = {node.id for node in ast.walk(tree) if isinstance(node, ast.Name)}\n",
    "        exclude = {'x', 'np', 'numpy', 'math', 'pi', 'e', 'inf', 'True', 'False', 'None',\n",
    "                   'exp', 'log', 'sin', 'cos', 'sqrt', 'tan', 'tanh', 'sinh', 'cosh', 'abs', 'min', 'max'}\n",
    "        return sorted(names - exclude)\n",
    "    except SyntaxError:\n",
    "        return []\n",
    "\n",
    "# Costruttore funzione\n",
    "def build_func(expr, params):\n",
    "    ns = {'np': np, 'exp': np.exp, 'log': np.log, 'sin': np.sin, 'cos': np.cos,\n",
    "          'sqrt': np.sqrt, 'tan': np.tan, 'sinh': np.sinh, 'cosh': np.cosh,\n",
    "          'pi': np.pi, 'e': np.e, 'inf': np.inf}\n",
    "    exec(f\"def _f(x, {', '.join(params)}):\\n    return {expr}\", ns)\n",
    "    return ns['_f']\n",
    "\n",
    "# Fit\n",
    "def run_fit(_):\n",
    "    out_log.clear_output(wait=True)\n",
    "    with out_log:\n",
    "        try:\n",
    "            expr   = func_input.value.strip()\n",
    "            params = extract_params(expr)\n",
    "\n",
    "            if not params:\n",
    "                print(\"Nessun parametro trovato. Usa lettere (es. a, b, k).\")\n",
    "                return\n",
    "\n",
    "            xs = x_data[selected_mask]\n",
    "            ys = y_data[selected_mask]\n",
    "\n",
    "            n  = len(xs)\n",
    "            k  = len(params)\n",
    "\n",
    "            if n < k + 1:\n",
    "                print(f\"Troppo pochi punti ({n}) per {k} parametri.\")\n",
    "                return\n",
    "\n",
    "            fn         = build_func(expr, params)\n",
    "            p0         = np.ones(k) * 0.5\n",
    "            popt, pcov = curve_fit(fn, xs, ys, p0=p0, maxfev=20_000)\n",
    "            perr       = np.sqrt(np.diag(pcov))\n",
    "\n",
    "            # curva nel grafico\n",
    "            x_fit = np.linspace(x_data.min(), x_data.max(), 500)\n",
    "            y_fit = fn(x_fit, *popt)\n",
    "            line_fit.set_data(x_fit, y_fit)\n",
    "\n",
    "            # Label\n",
    "            label_expr = expr\n",
    "            for p, v in zip(params, popt):\n",
    "                label_expr = re.sub(rf'\\b{p}\\b', f'{v:.3g}', label_expr)\n",
    "            fit_text.set_text(f'y = {label_expr}')\n",
    "            fig.canvas.draw_idle()\n",
    "\n",
    "            # statistiche Uso nomi mega chiari\n",
    "            valori_predetti        = fn(xs, *popt)\n",
    "            somma_quadri_residuali = np.sum((ys - valori_predetti) ** 2)\n",
    "            somma_quadri_totali    = np.sum((ys - ys.mean()) ** 2)\n",
    "            r2      = 1 - somma_quadri_residuali / somma_quadri_totali\n",
    "            rmse    = np.sqrt(somma_quadri_residuali / n)\n",
    "            GdL     = max(n - k, 1)\n",
    "            varianza_residuali = somma_quadri_residuali / GdL\n",
    "            p_value = scipy.stats.chi2.sf(somma_quadri_residuali, df=GdL)\n",
    "\n",
    "            # log-verosimiglianza gaussiana con σ² = somma_quadri_residuali/n (stima ML)\n",
    "            # Stavo facendo mettere apposto la parte grafica a Cloude e se ne è saltato fuori con questa aggiunta\n",
    "            # Se vero quello che mi ha spiegato è molto figa e utile\n",
    "            # In ogni caso basta ignorarne i risultati se fa paura e/o perdere tempo\n",
    "            log_lik = -n / 2 * (np.log(2 * np.pi * somma_quadri_residuali / n) + 1)\n",
    "\n",
    "            AIC  = 2 * k - 2 * log_lik\n",
    "            BIC  = k * np.log(n) - 2 * log_lik\n",
    "            AICc = AIC + (2 * k * (k + 1)) / max(n - k - 1, 1)\n",
    "\n",
    "            # salva in storia\n",
    "            fit_history.append({\n",
    "                'expr'   : expr,\n",
    "                'k'      : k,\n",
    "                'n'      : n,\n",
    "                'R2'     : r2,\n",
    "                'RMSE'   : rmse,\n",
    "                'varianza_residuali': varianza_residuali,\n",
    "                'AIC'    : AIC,\n",
    "                'AICc'   : AICc,\n",
    "                'BIC'    : BIC,\n",
    "            })\n",
    "\n",
    "            # stampa fit corrente\n",
    "            print(f\"Modello #{len(fit_history)}  —  fit su {n} punti\\n\")\n",
    "            print(f\"{'Parametro':<12} {'Valore':>14} {'± Errore Std':>14}\")\n",
    "            print(\"─\" * 42)\n",
    "            for p, v, e in zip(params, popt, perr):\n",
    "                print(f\"{p:<12} {v:>14.6g} {e:>14.6g}\")\n",
    "            print(f\"\\nR²          = {r2:.6f}\")\n",
    "            print(f\"RMSE        = {rmse:.6g}\")\n",
    "            print(f\"χ² rid(σ²=1)= {varianza_residuali:.6g}   (varianza residua)\")\n",
    "            print(f\"p-value     = {p_value:.4g}   (prob. χ² ≥ osservato, GdL={GdL})\")\n",
    "            print(f\"log L       = {log_lik:.4f}\")\n",
    "            print(f\"AIC         = {AIC:.4f}\")\n",
    "            print(f\"AICc        = {AICc:.4f}   ← usa questo se n/k < 40\")\n",
    "            print(f\"BIC         = {BIC:.4f}\")\n",
    "            print(f\"Punti usati = {n} / {len(x_data)}   |   k={k}   |   GdL={GdL}\")\n",
    "\n",
    "            #Questo pezzo di codice è puro frutto dell'AI, è molto divertente anche come logica\n",
    "            # ── confronto modelli (solo se ce ne sono almeno 2) ───────────────\n",
    "            if len(fit_history) > 1:\n",
    "                best_AICc = min(h['AICc'] for h in fit_history)\n",
    "                best_BIC  = min(h['BIC']  for h in fit_history)\n",
    "                delta     = np.array([h['AICc'] - best_AICc for h in fit_history])\n",
    "                pesi      = np.exp(-delta / 2)\n",
    "                pesi     /= pesi.sum()\n",
    "\n",
    "                W = 72\n",
    "                print(f\"\\n{'═'*W}\")\n",
    "                print(f\"  CONFRONTO TRA MODELLI FITTATI\")\n",
    "                print(f\"  Quante volte hai premuto 'Esegui fit': {len(fit_history)}\")\n",
    "                print(f\"{'═'*W}\")\n",
    "\n",
    "                # ── tabella principale ────────────────────────────────────────────────────\n",
    "                print(f\"\\n  {'#':<3} {'Funzione':<26} {'param':>5} {'punti':>6} \"\n",
    "                    f\"{'R²':>7} {'RMSE':>9} {'AICc':>9} {'ΔAICc':>7}\")\n",
    "                print(f\"  {'─'*3} {'─'*26} {'─'*5} {'─'*6} \"\n",
    "                    f\"{'─'*7} {'─'*9} {'─'*9} {'─'*7}\")\n",
    "\n",
    "                for i, (h, w) in enumerate(zip(fit_history, pesi)):\n",
    "                    is_best_AICc = abs(h['AICc'] - best_AICc) < 1e-6\n",
    "                    is_best_BIC  = abs(h['BIC']  - best_BIC)  < 1e-6\n",
    "                    marker = ' ◀' if is_best_AICc else '  '\n",
    "                    print(f\"  {i+1:<3} {h['expr']:<26} {h['k']:>5} {h['n']:>6} \"\n",
    "                        f\"{h['R2']:>7.4f} {h['RMSE']:>9.4g} \"\n",
    "                        f\"{h['AICc']:>9.2f} {delta[i]:>7.2f}{marker}\")\n",
    "\n",
    "                print(f\"\\n  ◀ = modello preferito secondo AICc\")\n",
    "                print(f\"\\n  R²   : quanto il modello spiega i dati (1.000 = perfetto)\")\n",
    "                print(f\"  RMSE : errore tipico in unità di y (più basso = meglio)\")\n",
    "                print(f\"  AICc : criterio di selezione del modello (più basso = meglio)\")\n",
    "                print(f\"  ΔAICc: distanza dal modello migliore (0 = sei il migliore)\")\n",
    "\n",
    "                # ── interpretazione ΔAICc ────────────────────────────────────────────────\n",
    "                print(f\"\\n{'─'*W}\")\n",
    "                print(f\"  INTERPRETAZIONE ΔAICc\")\n",
    "                print(f\"{'─'*W}\")\n",
    "                soglie = [(2, \"equivalente al migliore — entrambi plausibili\"),\n",
    "                        (7, \"supporto minore — il migliore è preferibile\"),\n",
    "                        (10, \"supporto debole — usare solo se motivato teoricamente\"),\n",
    "                        (float('inf'), \"da scartare — i dati non supportano questo modello\")]\n",
    "                for i, (h, w) in enumerate(zip(fit_history, pesi)):\n",
    "                    d = delta[i]\n",
    "                    for soglia, giudizio in soglie:\n",
    "                        if d < soglia:\n",
    "                            break\n",
    "                    best_tag = \" (migliore)\" if d < 1e-6 else \"\"\n",
    "                    print(f\"\\n  Modello #{i+1}  →  y = {h['expr']}{best_tag}\")\n",
    "                    print(f\"    ΔAICc = {d:.2f}  →  {giudizio}\")\n",
    "\n",
    "                # ── pesi di Akaike ────────────────────────────────────────────────────────\n",
    "                print(f\"\\n{'─'*W}\")\n",
    "                print(f\"  PROBABILITÀ RELATIVA DI CIASCUN MODELLO  (pesi di Akaike)\")\n",
    "                print(f\"  Interpretazione: dato il set di dati, quanto è probabile\")\n",
    "                print(f\"  che questo sia il modello migliore tra quelli confrontati?\")\n",
    "                print(f\"{'─'*W}\")\n",
    "                for i, (h, w) in enumerate(zip(fit_history, pesi)):\n",
    "                    bar    = '█' * max(1, int(w * 40))\n",
    "                    empty  = '░' * (40 - max(1, int(w * 40)))\n",
    "                    perc   = w * 100\n",
    "                    print(f\"\\n  #{i+1}  y = {h['expr']}\")\n",
    "                    print(f\"       probabilità = {perc:5.1f}%  {bar}{empty}\")\n",
    "\n",
    "                # ── verdetto finale ───────────────────────────────────────────────────────\n",
    "                best_idx = int(np.argmin(delta))\n",
    "                best_h   = fit_history[best_idx]\n",
    "                print(f\"\\n{'═'*W}\")\n",
    "                print(f\"  VERDETTO\")\n",
    "                print(f\"{'═'*W}\")\n",
    "                print(f\"  Il modello preferito dai dati è il #{best_idx+1}:\")\n",
    "                print(f\"    y = {best_h['expr']}\")\n",
    "                print(f\"    con {best_h['k']} parametri su {best_h['n']} punti\")\n",
    "                print(f\"    R² = {best_h['R2']:.4f}  |  RMSE = {best_h['RMSE']:.4g}  |  AICc = {best_h['AICc']:.2f}\")\n",
    "                if pesi[best_idx] > 0.9:\n",
    "                    print(f\"\\n  ✓ Scelta netta: peso {pesi[best_idx]*100:.1f}% — gli altri modelli hanno\")\n",
    "                    print(f\"    scarso supporto dai dati.\")\n",
    "                elif pesi[best_idx] > 0.6:\n",
    "                    print(f\"\\n  ~ Scelta abbastanza chiara (peso {pesi[best_idx]*100:.1f}%),\")\n",
    "                    print(f\"    ma considera anche il modello con ΔAICc minore.\")\n",
    "                else:\n",
    "                    print(f\"\\n  ! Scelta incerta (peso {pesi[best_idx]*100:.1f}%): i modelli sono\")\n",
    "                    print(f\"    statisticamente equivalenti — scegli quello più semplice\")\n",
    "                    print(f\"    o quello più motivato dalla teoria.\")\n",
    "                print(f\"{'═'*W}\\n\")\n",
    "\n",
    "        except Exception as e:\n",
    "            print(f\"Errore: {e}\")\n",
    "\n",
    "# Reset\n",
    "def reset(_):\n",
    "    global selected_mask\n",
    "    selected_mask = np.ones(len(x_data), dtype=bool)\n",
    "    sc_sel.set_offsets(np.empty((0, 2)))\n",
    "    box_patch.set_visible(False)\n",
    "    line_fit.set_data([], [])\n",
    "    fit_text.set_text('')\n",
    "    sel_label.value = f'Selezionati: {len(x_data)} / {len(x_data)}'\n",
    "    fig.canvas.draw_idle()\n",
    "    out_log.clear_output()\n",
    "\n",
    "# Reset storia fit (aggiunta da Cloude)\n",
    "def reset_history(_):\n",
    "    fit_history.clear()\n",
    "    out_log.clear_output()\n",
    "    with out_log:\n",
    "        print(\"Storia dei fit azzerata.\")\n",
    "\n",
    "clear_btn.on_click(reset)\n",
    "clear_hist_btn.on_click(reset_history)\n",
    "\n",
    "# Layout\n",
    "display(widgets.VBox([\n",
    "    widgets.HBox([func_input, fit_btn, clear_btn, clear_hist_btn]),\n",
    "    sel_label,\n",
    "    fig.canvas,\n",
    "    out_log\n",
    "]))\n",
    "\n",
    "# AGGIUNTA — Grafici dei residui Completamente separata\n",
    "# Caratteri strani per la copia:      ŷ         σ         ±\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "# Figura separata per i residui (viene creata vuota all'avvio,\n",
    "# poi popolata ogni volta che si preme \"Esegui fit\")\n",
    "fig_res, axes_res = plt.subplots(\n",
    "    1, 2,\n",
    "    figsize=(12, 4),\n",
    "    gridspec_kw={'wspace': 0.35}\n",
    ")\n",
    "fig_res.suptitle('Analisi dei residui  —  ultimo fit', fontsize=12, fontweight='bold', y=1.02)\n",
    "\n",
    "ax_res1, ax_res2 = axes_res\n",
    "\n",
    "for ax in axes_res:\n",
    "    ax.axhline(0, color='#444', lw=1, linestyle='--', zorder=1)\n",
    "    ax.grid(True, alpha=0.25)\n",
    "\n",
    "ax_res1.set_xlabel('x')\n",
    "ax_res1.set_ylabel('residuo  (y - ŷ)')\n",
    "ax_res1.set_title('Grafico 1 — Residui vs x\\n(bande ±1σ evidenziate)')\n",
    "\n",
    "ax_res2.set_xlabel('ŷ  (valore predetto)')\n",
    "ax_res2.set_ylabel('residuo  (y - ŷ)')\n",
    "ax_res2.set_title('Grafico 2 — Residui vs ŷ\\n(plot classico)')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# funzione che aggiorna i grafici dei residui\n",
    "def update_residual_plots(xs, ys, y_pred):\n",
    "    residuals = ys - y_pred\n",
    "    sigma     = residuals.std(ddof=1)          # deviazione standard campionaria\n",
    "\n",
    "    # pulizia assi\n",
    "    for ax in axes_res:\n",
    "        ax.cla()\n",
    "        ax.axhline(0, color='#444', lw=1, linestyle='--', zorder=1)\n",
    "        ax.grid(True, alpha=0.25)\n",
    "\n",
    "    # GRAFICO 1\n",
    "    ax_res1.set_xlabel('x')\n",
    "    ax_res1.set_ylabel('residuo  (y - ŷ)')\n",
    "    ax_res1.set_title('Grafico 1 — Residui vs x\\n(bande ±1σ evidenziate)')\n",
    "\n",
    "    # bande\n",
    "    x_min, x_max = xs.min(), xs.max()\n",
    "    ax_res1.axhspan(-sigma,  sigma,\n",
    "                    color='steelblue', alpha=0.12, zorder=0, label='±1σ')\n",
    "    ax_res1.axhline( sigma, color='steelblue', lw=1.2, linestyle=':', zorder=2)\n",
    "    ax_res1.axhline(-sigma, color='steelblue', lw=1.2, linestyle=':', zorder=2)\n",
    "\n",
    "    # colore punti: dentro/fuori banda\n",
    "    inside  = np.abs(residuals) <= sigma\n",
    "    outside = ~inside\n",
    "\n",
    "    ax_res1.scatter(xs[inside],  residuals[inside],\n",
    "                    c='steelblue', s=30, alpha=0.75, zorder=3,\n",
    "                    label=f'entro ±1σ  ({inside.sum()})')\n",
    "    if outside.any():\n",
    "        ax_res1.scatter(xs[outside], residuals[outside],\n",
    "                        c='tomato', s=40, alpha=0.9, zorder=4, marker='D',\n",
    "                        label=f'fuori ±1σ  ({outside.sum()})')\n",
    "\n",
    "    # annotazione percentuale Carina\n",
    "    pct = inside.mean() * 100\n",
    "    ax_res1.text(0.98, 0.97,\n",
    "                 f'{pct:.1f}% entro ±1σ\\nσ = {sigma:.4g}',\n",
    "                 transform=ax_res1.transAxes,\n",
    "                 ha='right', va='top', fontsize=9,\n",
    "                 bbox=dict(boxstyle='round,pad=0.3', facecolor='white', alpha=0.75))\n",
    "\n",
    "    ax_res1.legend(fontsize=8, loc='lower right')\n",
    "\n",
    "    # GRAFICO 2 : residui Classici\n",
    "    ax_res2.set_xlabel('ŷ  (valore predetto)')\n",
    "    ax_res2.set_ylabel('residuo  (y - ŷ)')\n",
    "    ax_res2.set_title('Grafico 2 — Residui vs ŷ\\n(plot classico)')\n",
    "\n",
    "    ax_res2.scatter(y_pred, residuals,\n",
    "                    c='darkorange', s=30, alpha=0.75, edgecolors='none', zorder=3)\n",
    "\n",
    "    # uso solo una regressione lineare sui residui (utile per capire se residui lineari)\n",
    "    # Serve per il debugging della funzione di fit e mostra se usi una retta per dati su una parabola\n",
    "    if len(y_pred) > 2:\n",
    "        idx_sort  = np.argsort(y_pred)\n",
    "        xp        = y_pred[idx_sort]\n",
    "        yp        = residuals[idx_sort]\n",
    "        coeff     = np.polyfit(xp, yp, 1)\n",
    "        trend     = np.polyval(coeff, xp)\n",
    "        ax_res2.plot(xp, trend, color='gray', lw=1.5, linestyle='--',\n",
    "                     alpha=0.7, label=f'tendenza lineare\\n(slope={coeff[0]:.3g})')\n",
    "        ax_res2.legend(fontsize=8, loc='best')\n",
    "\n",
    "    # titolo figura\n",
    "    last_expr = fit_history[-1]['expr'] if fit_history else '?'\n",
    "    fig_res.suptitle(f'Analisi dei residui  —  ultimo fit:  y = {last_expr}',\n",
    "                     fontsize=11, fontweight='bold', y=1.02)\n",
    "\n",
    "    fig_res.canvas.draw_idle()\n",
    "\n",
    "\n",
    "# Salviamo il run_fit originale\n",
    "_run_fit_original = run_fit\n",
    "\n",
    "def run_fit_with_residuals(btn):\n",
    "    _run_fit_original(btn)\n",
    "\n",
    "    try:\n",
    "        expr   = func_input.value.strip()\n",
    "        params = extract_params(expr)\n",
    "        fn     = build_func(expr, params)\n",
    "\n",
    "        xs = x_data[selected_mask]\n",
    "        ys = y_data[selected_mask]\n",
    "\n",
    "        # ri-esegui curve_fit solo per prendere popt\n",
    "        p0         = np.ones(len(params)) * 0.5\n",
    "        popt, _    = curve_fit(fn, xs, ys, p0=p0, maxfev=20_000)\n",
    "        y_pred     = fn(xs, *popt)\n",
    "\n",
    "        update_residual_plots(xs, ys, y_pred)\n",
    "    except Exception:\n",
    "        pass\n",
    "fit_btn.on_click(run_fit_with_residuals)   #Non fa i residui fit_btn.on_click(run_fit)\n",
    "\n",
    "# Widget di output per i grafici dei residui\n",
    "residuals_out = widgets.Output()\n",
    "with residuals_out:\n",
    "    display(fig_res.canvas)\n",
    "\n",
    "display(residuals_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fc48565a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8e0f68f82e6447a4992ceabd871c4208",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Sheet(cells=(Cell(column_end=0, column_start=0, row_end=11, row_start=0, squeeze_row=False, type='text', value…"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_str = [f'{v:.17g}' for v in x_data[selected_mask]]\n",
    "y_str = [f'{v:.17g}' for v in y_data[selected_mask]]\n",
    "\n",
    "sheet = ipysheet.sheet(rows=len(x_data[selected_mask]), columns=2)\n",
    "ipysheet.column(0, x_str, label='Colonna 1')\n",
    "ipysheet.column(1, y_str, label='Colonna 2')\n",
    "\n",
    "sheet"
   ]
  }
 ],
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