1621 lines
223 KiB
Plaintext
1621 lines
223 KiB
Plaintext
{
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"cells": [
|
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{
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||
"cell_type": "code",
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"execution_count": 26,
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"id": "f34c5b88",
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"metadata": {},
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||
"outputs": [],
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"source": [
|
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"import numpy as np\n",
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"import pandas as pd\n",
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"import scipy as sc\n",
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"from scipy.stats import chi2\n",
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"from scipy.odr import ODR, Model, RealData\n",
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"import seaborn as sns\n",
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"import matplotlib.pyplot as plt\n",
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"import matplotlib as mpl\n",
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"import statsmodels.api as sm\n",
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"\n",
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"\n",
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"g = 9.806\n",
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"ug = 0.001\n",
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"\n",
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"m_mol = 15.43\n",
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"um_mol = 0.01"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"id": "08efb2be",
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"metadata": {},
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"outputs": [],
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"source": [
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"df = pd.read_csv(r'dinamica2.csv')\n",
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"\n",
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"def calcola_stats(df, prefix, err_arbitrario):\n",
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" cols = [col for col in df.columns if col.startswith(prefix)]\n",
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"\n",
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" def riga_stats(row):\n",
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" valori = row[cols].dropna()\n",
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" n = len(valori)\n",
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"\n",
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" if n == 0:\n",
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" return pd.Series({prefix: np.nan, f\"u{prefix}\": np.nan})\n",
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" elif n == 1:\n",
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" return pd.Series({prefix: valori.iloc[0], f\"u{prefix}\": err_arbitrario})\n",
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" else:\n",
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" media = valori.mean()\n",
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" sigma = valori.std(ddof=1)\n",
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" sigma = sigma * np.sqrt(24) if prefix == \"w\" else sigma # Line cursed per non duplicare il codice\n",
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" return pd.Series({prefix: media, f\"u{prefix}\": sigma})\n",
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"\n",
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" stats = df.apply(riga_stats, axis=1)\n",
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" df[prefix] = stats[prefix]\n",
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" df[f\"u{prefix}\"] = stats[f\"u{prefix}\"]\n",
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"\n",
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" return df\n",
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"\n",
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"\n",
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"df = calcola_stats(df, \"w\", err_arbitrario=0.0002)\n",
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"df = calcola_stats(df, \"m\", err_arbitrario=0.01)\n",
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"df = calcola_stats(df, \"c\", err_arbitrario=0.01)\n",
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"df = calcola_stats(df, \"a\", err_arbitrario=0.01)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"id": "5494409f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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" <th>ua2</th>\n",
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" <th>w2</th>\n",
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" <th>t3</th>\n",
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" <th>a4</th>\n",
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" <th>ua4</th>\n",
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" <th>w4</th>\n",
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||
" <th>uw4</th>\n",
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||
" <th>c4</th>\n",
|
||
" <th>uc4</th>\n",
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||
" <th>t4</th>\n",
|
||
" <th>w</th>\n",
|
||
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||
" <th>m</th>\n",
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||
" <th>um</th>\n",
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||
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|
||
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|
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||
" </tr>\n",
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" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0</th>\n",
|
||
" <td>49.25</td>\n",
|
||
" <td>9.7171</td>\n",
|
||
" <td>0.016</td>\n",
|
||
" <td>7.65650</td>\n",
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||
" <td>0.00040</td>\n",
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||
" <td>484.4550</td>\n",
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||
" <td>0.011</td>\n",
|
||
" <td>15.62</td>\n",
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||
" <td>8.9110</td>\n",
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||
" <td>0.015</td>\n",
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||
" <td>7.65690</td>\n",
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||
" <td>0.00040</td>\n",
|
||
" <td>484.516</td>\n",
|
||
" <td>0.011</td>\n",
|
||
" <td>15.58</td>\n",
|
||
" <td>10.446</td>\n",
|
||
" <td>0.027</td>\n",
|
||
" <td>7.66030</td>\n",
|
||
" <td>0.00050</td>\n",
|
||
" <td>485.082</td>\n",
|
||
" <td>0.019</td>\n",
|
||
" <td>15.76</td>\n",
|
||
" <td>8.377</td>\n",
|
||
" <td>0.016</td>\n",
|
||
" <td>7.65820</td>\n",
|
||
" <td>0.00040</td>\n",
|
||
" <td>484.752</td>\n",
|
||
" <td>0.011</td>\n",
|
||
" <td>15.87</td>\n",
|
||
" <td>7.657975</td>\n",
|
||
" <td>0.008385</td>\n",
|
||
" <td>49.25</td>\n",
|
||
" <td>0.01</td>\n",
|
||
" <td>484.70125</td>\n",
|
||
" <td>0.284314</td>\n",
|
||
" <td>9.362775</td>\n",
|
||
" <td>0.908254</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>69.28</td>\n",
|
||
" <td>9.8600</td>\n",
|
||
" <td>0.016</td>\n",
|
||
" <td>6.55968</td>\n",
|
||
" <td>0.00029</td>\n",
|
||
" <td>423.3520</td>\n",
|
||
" <td>0.011</td>\n",
|
||
" <td>18.31</td>\n",
|
||
" <td>10.3900</td>\n",
|
||
" <td>0.012</td>\n",
|
||
" <td>6.55891</td>\n",
|
||
" <td>0.00022</td>\n",
|
||
" <td>423.154</td>\n",
|
||
" <td>0.009</td>\n",
|
||
" <td>18.27</td>\n",
|
||
" <td>10.491</td>\n",
|
||
" <td>0.013</td>\n",
|
||
" <td>6.56002</td>\n",
|
||
" <td>0.00024</td>\n",
|
||
" <td>423.697</td>\n",
|
||
" <td>0.010</td>\n",
|
||
" <td>18.34</td>\n",
|
||
" <td>10.968</td>\n",
|
||
" <td>0.019</td>\n",
|
||
" <td>6.56000</td>\n",
|
||
" <td>0.00030</td>\n",
|
||
" <td>423.465</td>\n",
|
||
" <td>0.014</td>\n",
|
||
" <td>18.16</td>\n",
|
||
" <td>6.559652</td>\n",
|
||
" <td>0.002542</td>\n",
|
||
" <td>69.28</td>\n",
|
||
" <td>0.01</td>\n",
|
||
" <td>423.41700</td>\n",
|
||
" <td>0.226641</td>\n",
|
||
" <td>10.427250</td>\n",
|
||
" <td>0.454472</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>88.97</td>\n",
|
||
" <td>11.5840</td>\n",
|
||
" <td>0.014</td>\n",
|
||
" <td>5.84417</td>\n",
|
||
" <td>0.00020</td>\n",
|
||
" <td>363.2290</td>\n",
|
||
" <td>0.010</td>\n",
|
||
" <td>20.27</td>\n",
|
||
" <td>10.1763</td>\n",
|
||
" <td>0.017</td>\n",
|
||
" <td>5.84585</td>\n",
|
||
" <td>0.00028</td>\n",
|
||
" <td>363.354</td>\n",
|
||
" <td>0.012</td>\n",
|
||
" <td>20.44</td>\n",
|
||
" <td>12.044</td>\n",
|
||
" <td>0.018</td>\n",
|
||
" <td>5.84500</td>\n",
|
||
" <td>0.00026</td>\n",
|
||
" <td>363.183</td>\n",
|
||
" <td>0.013</td>\n",
|
||
" <td>20.54</td>\n",
|
||
" <td>11.224</td>\n",
|
||
" <td>0.016</td>\n",
|
||
" <td>5.84513</td>\n",
|
||
" <td>0.00025</td>\n",
|
||
" <td>363.233</td>\n",
|
||
" <td>0.011</td>\n",
|
||
" <td>20.49</td>\n",
|
||
" <td>5.845038</td>\n",
|
||
" <td>0.003374</td>\n",
|
||
" <td>88.97</td>\n",
|
||
" <td>0.01</td>\n",
|
||
" <td>363.24975</td>\n",
|
||
" <td>0.073109</td>\n",
|
||
" <td>11.257075</td>\n",
|
||
" <td>0.794837</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>108.61</td>\n",
|
||
" <td>11.5420</td>\n",
|
||
" <td>0.026</td>\n",
|
||
" <td>5.32780</td>\n",
|
||
" <td>0.00030</td>\n",
|
||
" <td>303.5502</td>\n",
|
||
" <td>0.019</td>\n",
|
||
" <td>22.49</td>\n",
|
||
" <td>8.4240</td>\n",
|
||
" <td>0.017</td>\n",
|
||
" <td>5.32820</td>\n",
|
||
" <td>0.00030</td>\n",
|
||
" <td>303.581</td>\n",
|
||
" <td>0.012</td>\n",
|
||
" <td>22.27</td>\n",
|
||
" <td>10.501</td>\n",
|
||
" <td>0.022</td>\n",
|
||
" <td>5.32960</td>\n",
|
||
" <td>0.00030</td>\n",
|
||
" <td>303.842</td>\n",
|
||
" <td>0.016</td>\n",
|
||
" <td>22.55</td>\n",
|
||
" <td>9.959</td>\n",
|
||
" <td>0.014</td>\n",
|
||
" <td>5.32822</td>\n",
|
||
" <td>0.00020</td>\n",
|
||
" <td>303.445</td>\n",
|
||
" <td>0.010</td>\n",
|
||
" <td>22.15</td>\n",
|
||
" <td>5.328455</td>\n",
|
||
" <td>0.003858</td>\n",
|
||
" <td>108.61</td>\n",
|
||
" <td>0.01</td>\n",
|
||
" <td>303.60455</td>\n",
|
||
" <td>0.168669</td>\n",
|
||
" <td>10.106500</td>\n",
|
||
" <td>1.299853</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>128.64</td>\n",
|
||
" <td>11.5740</td>\n",
|
||
" <td>0.020</td>\n",
|
||
" <td>4.92663</td>\n",
|
||
" <td>0.00023</td>\n",
|
||
" <td>242.9620</td>\n",
|
||
" <td>0.014</td>\n",
|
||
" <td>24.33</td>\n",
|
||
" <td>11.5920</td>\n",
|
||
" <td>0.023</td>\n",
|
||
" <td>4.92537</td>\n",
|
||
" <td>0.00029</td>\n",
|
||
" <td>242.876</td>\n",
|
||
" <td>0.017</td>\n",
|
||
" <td>24.38</td>\n",
|
||
" <td>10.264</td>\n",
|
||
" <td>0.023</td>\n",
|
||
" <td>4.92430</td>\n",
|
||
" <td>0.00030</td>\n",
|
||
" <td>242.789</td>\n",
|
||
" <td>0.017</td>\n",
|
||
" <td>25.09</td>\n",
|
||
" <td>9.118</td>\n",
|
||
" <td>0.021</td>\n",
|
||
" <td>4.92610</td>\n",
|
||
" <td>0.00030</td>\n",
|
||
" <td>243.115</td>\n",
|
||
" <td>0.015</td>\n",
|
||
" <td>24.26</td>\n",
|
||
" <td>4.925600</td>\n",
|
||
" <td>0.004943</td>\n",
|
||
" <td>128.64</td>\n",
|
||
" <td>0.01</td>\n",
|
||
" <td>242.93550</td>\n",
|
||
" <td>0.138954</td>\n",
|
||
" <td>10.637000</td>\n",
|
||
" <td>1.188344</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" m1 a1 ua1 w1 uw1 c1 uc1 t1 a2 \\\n",
|
||
"0 49.25 9.7171 0.016 7.65650 0.00040 484.4550 0.011 15.62 8.9110 \n",
|
||
"1 69.28 9.8600 0.016 6.55968 0.00029 423.3520 0.011 18.31 10.3900 \n",
|
||
"2 88.97 11.5840 0.014 5.84417 0.00020 363.2290 0.010 20.27 10.1763 \n",
|
||
"3 108.61 11.5420 0.026 5.32780 0.00030 303.5502 0.019 22.49 8.4240 \n",
|
||
"4 128.64 11.5740 0.020 4.92663 0.00023 242.9620 0.014 24.33 11.5920 \n",
|
||
"\n",
|
||
" ua2 w2 uw2 c2 uc2 t2 a3 ua3 w3 \\\n",
|
||
"0 0.015 7.65690 0.00040 484.516 0.011 15.58 10.446 0.027 7.66030 \n",
|
||
"1 0.012 6.55891 0.00022 423.154 0.009 18.27 10.491 0.013 6.56002 \n",
|
||
"2 0.017 5.84585 0.00028 363.354 0.012 20.44 12.044 0.018 5.84500 \n",
|
||
"3 0.017 5.32820 0.00030 303.581 0.012 22.27 10.501 0.022 5.32960 \n",
|
||
"4 0.023 4.92537 0.00029 242.876 0.017 24.38 10.264 0.023 4.92430 \n",
|
||
"\n",
|
||
" uw3 c3 uc3 t3 a4 ua4 w4 uw4 c4 \\\n",
|
||
"0 0.00050 485.082 0.019 15.76 8.377 0.016 7.65820 0.00040 484.752 \n",
|
||
"1 0.00024 423.697 0.010 18.34 10.968 0.019 6.56000 0.00030 423.465 \n",
|
||
"2 0.00026 363.183 0.013 20.54 11.224 0.016 5.84513 0.00025 363.233 \n",
|
||
"3 0.00030 303.842 0.016 22.55 9.959 0.014 5.32822 0.00020 303.445 \n",
|
||
"4 0.00030 242.789 0.017 25.09 9.118 0.021 4.92610 0.00030 243.115 \n",
|
||
"\n",
|
||
" uc4 t4 w uw m um c uc \\\n",
|
||
"0 0.011 15.87 7.657975 0.008385 49.25 0.01 484.70125 0.284314 \n",
|
||
"1 0.014 18.16 6.559652 0.002542 69.28 0.01 423.41700 0.226641 \n",
|
||
"2 0.011 20.49 5.845038 0.003374 88.97 0.01 363.24975 0.073109 \n",
|
||
"3 0.010 22.15 5.328455 0.003858 108.61 0.01 303.60455 0.168669 \n",
|
||
"4 0.015 24.26 4.925600 0.004943 128.64 0.01 242.93550 0.138954 \n",
|
||
"\n",
|
||
" a ua \n",
|
||
"0 9.362775 0.908254 \n",
|
||
"1 10.427250 0.454472 \n",
|
||
"2 11.257075 0.794837 \n",
|
||
"3 10.106500 1.299853 \n",
|
||
"4 10.637000 1.188344 "
|
||
]
|
||
},
|
||
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|
||
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|
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|
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|
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|
||
"source": [
|
||
"pd.set_option('display.max_columns', None)\n",
|
||
"pd.set_option('display.width', None)\n",
|
||
"\n",
|
||
"df"
|
||
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||
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"cell_type": "code",
|
||
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"id": "976d5531",
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{
|
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"[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]\n",
|
||
"10\n",
|
||
"############################################################\n",
|
||
"[ 61.28425 121.4515 181.0967 241.76575 60.16725 119.81245 180.4815\n",
|
||
" 59.6452 120.31425 60.66905]\n",
|
||
"[0.36359352 0.29356288 0.33058029 0.31645313 0.23814054 0.28251562\n",
|
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" 0.26584645 0.18383143 0.15701353 0.21853469]\n",
|
||
"############################################################\n",
|
||
"[-20.03 -39.72 -59.36 -79.39 -19.69 -39.33 -59.36 -19.64 -39.67 -20.03]\n",
|
||
"[0.01414214 0.01414214 0.01414214 0.01414214 0.01414214 0.01414214\n",
|
||
" 0.01414214 0.01414214 0.01414214 0.01414214]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"perm = [(x,i) for x in range(0,len(df)) for i in range(x+1,len(df))]\n",
|
||
"\n",
|
||
"este = np.array([df.c[x] - df.c[j] for x,j in perm])\n",
|
||
"ueste = np.array([np.sqrt(df.uc[x]**2 + df.uc[j]**2) for x,j in perm])\n",
|
||
"\n",
|
||
"masse = np.array([df.m[x] - df.m[j] for x,j in perm])\n",
|
||
"umasse = np.array([np.sqrt(df.um[x]**2 + df.um[j]**2) for x,j in perm])\n",
|
||
"\n",
|
||
"\n",
|
||
"print(perm)\n",
|
||
"print(len(perm))\n",
|
||
"\n",
|
||
"print(\"#\"* 60)\n",
|
||
"print(este)\n",
|
||
"print(ueste)\n",
|
||
"\n",
|
||
"print(\"#\"* 60)\n",
|
||
"print(masse)\n",
|
||
"print(umasse)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"id": "2ad19283",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[3.20496996 3.20699473 3.21421738 3.22005222 3.20905709 3.21894745\n",
|
||
" 3.22517355 3.22892437 3.23323314 3.23746919]\n",
|
||
"[0.01915174 0.00784216 0.00592618 0.00426631 0.01291295 0.00768498\n",
|
||
" 0.00482359 0.01022511 0.00438647 0.01188811]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"F = masse * g\n",
|
||
"uF = np.sqrt((g * umasse)**2 + (masse * ug)**2)\n",
|
||
"\n",
|
||
"K = - F / este\n",
|
||
"uK = np.sqrt((1/este)**2 * uF**2 + (F / este**2)**2 * ueste**2 )\n",
|
||
"\n",
|
||
"\n",
|
||
"print(K)\n",
|
||
"print(uK)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"id": "5f59d6c9",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"K-medio: 3.222622761146456\n",
|
||
"sigmaC: 0.002054455999024885\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"def mediaPesata(x, ux, dim = 0):\n",
|
||
" x_arr = x.to_numpy() if isinstance(x, (pd.Series, pd.DataFrame)) else np.asarray(x)\n",
|
||
" sigma_arr = ux.to_numpy() if isinstance(ux, (pd.Series, pd.DataFrame)) else np.asarray(ux)\n",
|
||
"\n",
|
||
" w = 1.0 / (sigma_arr ** 2)\n",
|
||
"\n",
|
||
" num = np.nansum(w * x_arr, axis=dim)\n",
|
||
" den = np.nansum(w, axis=dim)\n",
|
||
"\n",
|
||
" media = num / den\n",
|
||
" sigma = np.sqrt(1.0 / den)\n",
|
||
"\n",
|
||
" return media, sigma\n",
|
||
"\n",
|
||
"media, uA = mediaPesata(K, uK)\n",
|
||
"print(\"K-medio:\", media)\n",
|
||
"print(\"sigmaC: \", uA)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"id": "aefe7756",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" OLS Regression Results \n",
|
||
"==============================================================================\n",
|
||
"Dep. Variable: F R-squared: 1.000\n",
|
||
"Model: OLS Adj. R-squared: 1.000\n",
|
||
"Method: Least Squares F-statistic: 3.114e+05\n",
|
||
"Date: Fri, 03 Apr 2026 Prob (F-statistic): 1.19e-19\n",
|
||
"Time: 11:31:18 Log-Likelihood: -14.035\n",
|
||
"No. Observations: 10 AIC: 32.07\n",
|
||
"Df Residuals: 8 BIC: 32.68\n",
|
||
"Df Model: 1 \n",
|
||
"Covariance Type: nonrobust \n",
|
||
"==============================================================================\n",
|
||
" coef std err t P>|t| [0.025 0.975]\n",
|
||
"------------------------------------------------------------------------------\n",
|
||
"const 0.0101 0.778 0.013 0.990 -1.785 1.805\n",
|
||
"este 3.2197 0.006 558.014 0.000 3.206 3.233\n",
|
||
"==============================================================================\n",
|
||
"Omnibus: 0.921 Durbin-Watson: 0.565\n",
|
||
"Prob(Omnibus): 0.631 Jarque-Bera (JB): 0.614\n",
|
||
"Skew: 0.062 Prob(JB): 0.736\n",
|
||
"Kurtosis: 1.792 Cond. No. 302.\n",
|
||
"==============================================================================\n",
|
||
"\n",
|
||
"Notes:\n",
|
||
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
|
||
"\n",
|
||
"RISULTATI REGRESSIONE:\n",
|
||
"k (pendenza) = 3.21975 ± 0.00577\n",
|
||
"intercetta = 0.01011 ± 0.77845\n",
|
||
"R² = 0.99997\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"data = pd.DataFrame({\n",
|
||
" \"este\": este,\n",
|
||
" \"ueste\": ueste,\n",
|
||
" \"F\": - F,\n",
|
||
" \"uF\": uF\n",
|
||
"})\n",
|
||
"\n",
|
||
"\n",
|
||
"X = sm.add_constant(data[\"este\"])\n",
|
||
"model = sm.OLS(data[\"F\"], X).fit()\n",
|
||
"\n",
|
||
"print(model.summary())\n",
|
||
"\n",
|
||
"# Estrazione parametri\n",
|
||
"intercetta = model.params[\"const\"]\n",
|
||
"pente = model.params[\"este\"]\n",
|
||
"u_intercetta = model.bse[\"const\"]\n",
|
||
"u_pente = model.bse[\"este\"]\n",
|
||
"R2 = model.rsquared\n",
|
||
"\n",
|
||
"print(\"\\nRISULTATI REGRESSIONE:\")\n",
|
||
"print(f\"k (pendenza) = {pente:.5f} ± {u_pente:.5f}\")\n",
|
||
"print(f\"intercetta = {intercetta:.5f} ± {u_intercetta:.5f}\")\n",
|
||
"print(f\"R² = {R2:.5f}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 33,
|
||
"id": "8d795186",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Chi^2 = 18.49884\n",
|
||
"Gradi di libertà = 8\n",
|
||
"Chi^2 ridotto = 2.31235\n",
|
||
"Probabilità P(0 → chi^2) = 0.98222\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"## X^2 sui dai fatti così\n",
|
||
"F_fit = intercetta + pente * data[\"este\"]\n",
|
||
"sigma = np.sqrt(data[\"uF\"]**2 + (pente * data[\"ueste\"])**2)\n",
|
||
"\n",
|
||
"\n",
|
||
"chi2_val = np.sum( ((data[\"F\"] - F_fit) / sigma)**2 )\n",
|
||
"\n",
|
||
"N = len(data)\n",
|
||
"nu = N - 2\n",
|
||
"\n",
|
||
"chi2_red = chi2_val / nu\n",
|
||
"P = chi2.cdf(chi2_val, df=nu)\n",
|
||
"\n",
|
||
"\n",
|
||
"print(f\"Chi^2 = {chi2_val:.5f}\")\n",
|
||
"print(f\"Gradi di libertà = {nu}\")\n",
|
||
"print(f\"Chi^2 ridotto = {chi2_red:.5f}\")\n",
|
||
"print(f\"Probabilità P(0 → chi^2) = {P:.5f}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 34,
|
||
"id": "1d42b009",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"\n",
|
||
"sns.set_theme(style=\"whitegrid\")\n",
|
||
"\n",
|
||
"plt.figure(figsize=(10,6))\n",
|
||
"\n",
|
||
"# Seaborn scatter\n",
|
||
"sns.scatterplot(\n",
|
||
" data=data,\n",
|
||
" x=\"este\",\n",
|
||
" y=\"F\",\n",
|
||
" s=7\n",
|
||
")\n",
|
||
"\n",
|
||
"# Barre d’errore\n",
|
||
"plt.errorbar(\n",
|
||
" data[\"este\"],\n",
|
||
" data[\"F\"],\n",
|
||
" xerr=data[\"ueste\"],\n",
|
||
" yerr=data[\"uF\"],\n",
|
||
" fmt=\"none\",\n",
|
||
" ecolor=\"gray\",\n",
|
||
" elinewidth=1,\n",
|
||
" capsize=3,\n",
|
||
" alpha=0.7\n",
|
||
")\n",
|
||
"\n",
|
||
"# Linea di regressione\n",
|
||
"xfit = np.linspace(0, data[\"este\"].max(), 200)\n",
|
||
"yfit = intercetta + pente * xfit\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.plot(\n",
|
||
" xfit,\n",
|
||
" yfit,\n",
|
||
" color=\"crimson\",\n",
|
||
" linewidth=1,\n",
|
||
" zorder=10,\n",
|
||
" label=\"Fit lineare\"\n",
|
||
")\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.xlim(left=0)\n",
|
||
"plt.ylim(bottom=0)\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.xlabel(\"Δx (mm)\")\n",
|
||
"plt.ylabel(\"Forza F (mN)\")\n",
|
||
"plt.title(\"Legge di Hooke — punti permutati con errorbar\")\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True, linestyle=\"--\", alpha=0.1)\n",
|
||
"\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 35,
|
||
"id": "986ff4a6",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Chi^2 = 18.49884\n",
|
||
"Gradi di libertà = 8\n",
|
||
"Chi^2 ridotto = 2.31235\n",
|
||
"Probabilità P(0 → chi^2) = 0.98222\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"F_fit = intercetta + pente * data[\"este\"]\n",
|
||
"sigma = np.sqrt(data[\"uF\"]**2 + (pente * data[\"ueste\"])**2)\n",
|
||
"\n",
|
||
"chi2_val = np.sum( ((data[\"F\"] - F_fit) / sigma)**2 )\n",
|
||
"\n",
|
||
"N = len(data)\n",
|
||
"nu = N - 2\n",
|
||
"\n",
|
||
"chi2_red = chi2_val / nu\n",
|
||
"P = chi2.cdf(chi2_val, df=nu)\n",
|
||
"\n",
|
||
"\n",
|
||
"print(f\"Chi^2 = {chi2_val:.5f}\")\n",
|
||
"print(f\"Gradi di libertà = {nu}\")\n",
|
||
"print(f\"Chi^2 ridotto = {chi2_red:.5f}\")\n",
|
||
"print(f\"Probabilità P(0 → chi^2) = {P:.5f}\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 36,
|
||
"id": "ef0817f4",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0 0.603364\n",
|
||
"1 2.659042\n",
|
||
"2 0.885979\n",
|
||
"3 0.003753\n",
|
||
"4 0.702764\n",
|
||
"5 0.013285\n",
|
||
"6 1.242733\n",
|
||
"7 0.779930\n",
|
||
"8 9.404606\n",
|
||
"9 2.203380\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 36,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"((data[\"F\"] - F_fit) / sigma)**2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 37,
|
||
"id": "cebe6742",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>este</th>\n",
|
||
" <th>ueste</th>\n",
|
||
" <th>F</th>\n",
|
||
" <th>uF</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0</th>\n",
|
||
" <td>61.28425</td>\n",
|
||
" <td>0.363594</td>\n",
|
||
" <td>196.41418</td>\n",
|
||
" <td>0.140117</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>121.45150</td>\n",
|
||
" <td>0.293563</td>\n",
|
||
" <td>389.49432</td>\n",
|
||
" <td>0.144254</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>181.09670</td>\n",
|
||
" <td>0.330580</td>\n",
|
||
" <td>582.08416</td>\n",
|
||
" <td>0.150848</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>241.76575</td>\n",
|
||
" <td>0.316453</td>\n",
|
||
" <td>778.49834</td>\n",
|
||
" <td>0.159795</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>60.16725</td>\n",
|
||
" <td>0.238141</td>\n",
|
||
" <td>193.08014</td>\n",
|
||
" <td>0.140069</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>5</th>\n",
|
||
" <td>119.81245</td>\n",
|
||
" <td>0.282516</td>\n",
|
||
" <td>385.66998</td>\n",
|
||
" <td>0.144147</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>6</th>\n",
|
||
" <td>180.48150</td>\n",
|
||
" <td>0.265846</td>\n",
|
||
" <td>582.08416</td>\n",
|
||
" <td>0.150848</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>7</th>\n",
|
||
" <td>59.64520</td>\n",
|
||
" <td>0.183831</td>\n",
|
||
" <td>192.58984</td>\n",
|
||
" <td>0.140062</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>8</th>\n",
|
||
" <td>120.31425</td>\n",
|
||
" <td>0.157014</td>\n",
|
||
" <td>389.00402</td>\n",
|
||
" <td>0.144240</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>9</th>\n",
|
||
" <td>60.66905</td>\n",
|
||
" <td>0.218535</td>\n",
|
||
" <td>196.41418</td>\n",
|
||
" <td>0.140117</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" este ueste F uF\n",
|
||
"0 61.28425 0.363594 196.41418 0.140117\n",
|
||
"1 121.45150 0.293563 389.49432 0.144254\n",
|
||
"2 181.09670 0.330580 582.08416 0.150848\n",
|
||
"3 241.76575 0.316453 778.49834 0.159795\n",
|
||
"4 60.16725 0.238141 193.08014 0.140069\n",
|
||
"5 119.81245 0.282516 385.66998 0.144147\n",
|
||
"6 180.48150 0.265846 582.08416 0.150848\n",
|
||
"7 59.64520 0.183831 192.58984 0.140062\n",
|
||
"8 120.31425 0.157014 389.00402 0.144240\n",
|
||
"9 60.66905 0.218535 196.41418 0.140117"
|
||
]
|
||
},
|
||
"execution_count": 37,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"data"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 38,
|
||
"id": "2d4b7144",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Ax + B : \n",
|
||
"A = 3.21951 +- 0.00470\n",
|
||
"B = 0.42600 +- 0.57172\n",
|
||
"cov_AB = -0.002417\n",
|
||
"p-value chi² = 0.9584088\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"def sigma_y_equiv(x, y, sigma_x, sigma_y):\n",
|
||
" # Stima iniziale di A con sola sigma_y\n",
|
||
" sy2 = sigma_y**2\n",
|
||
" Sw = np.sum(1 / sy2)\n",
|
||
" Sx = np.sum(x / sy2)\n",
|
||
" Sxx = np.sum(x**2 / sy2)\n",
|
||
" Sy = np.sum(y / sy2)\n",
|
||
" Sxy = np.sum(x * y / sy2)\n",
|
||
" delta = Sxx * Sw - Sx**2\n",
|
||
" A_est = (Sxy * Sw - Sx * Sy) / delta\n",
|
||
"\n",
|
||
" # Propagazione\n",
|
||
" sigma_eq = np.sqrt(sigma_y**2 + A_est**2 * sigma_x**2)\n",
|
||
" return sigma_eq\n",
|
||
"\n",
|
||
"\n",
|
||
"def reg_lin(x, y, sigma_x, sigma_y):\n",
|
||
" x = np.asarray(x, dtype=float)\n",
|
||
" y = np.asarray(y, dtype=float)\n",
|
||
" sigma_x = np.asarray(sigma_x, dtype=float)\n",
|
||
" sigma_y = np.asarray(sigma_y, dtype=float)\n",
|
||
"\n",
|
||
" # Propagazione errore x → y\n",
|
||
" sigma_y_eq = sigma_y_equiv(x, y, sigma_x, sigma_y)\n",
|
||
"\n",
|
||
" # Somme pesate\n",
|
||
" w = 1.0 / sigma_y_eq**2\n",
|
||
" Sw = np.sum(w)\n",
|
||
" Sx = np.sum(w * x)\n",
|
||
" Sxx = np.sum(w * x**2)\n",
|
||
" Sy = np.sum(w * y)\n",
|
||
" Sxy = np.sum(w * x * y)\n",
|
||
" delta = Sxx * Sw - Sx**2\n",
|
||
"\n",
|
||
" # Parametri\n",
|
||
" A = (Sxy * Sw - Sx * Sy) / delta\n",
|
||
" B = (Sxx * Sy - Sxy * Sx) / delta\n",
|
||
" sigma_A = np.sqrt(Sw / delta)\n",
|
||
" sigma_B = np.sqrt(Sxx / delta)\n",
|
||
" cov_AB = -Sx / delta\n",
|
||
"\n",
|
||
" # Chi quadro\n",
|
||
" x2 = np.sum((y - A * x - B)**2 / sigma_y_eq**2)\n",
|
||
" dof = len(x) - 2\n",
|
||
" chi = sc.stats.chi2.cdf(x2, dof) # P(X² > x2)\n",
|
||
"\n",
|
||
" return A, B, sigma_A, sigma_B, cov_AB, chi\n",
|
||
"\n",
|
||
"\n",
|
||
"A, B, sA, sB, covAB, chi = reg_lin(data[\"este\"], data[\"F\"], data[\"ueste\"], data[\"uF\"])\n",
|
||
"print(\"Ax + B : \")\n",
|
||
"print(f\"A = {A:.5f} +- {sA:.5f}\")\n",
|
||
"print(f\"B = {B:.5f} +- {sB:.5f}\")\n",
|
||
"print(f\"cov_AB = {covAB:.6f}\")\n",
|
||
"print(f\"p-value chi² = {chi:.7f}\")\n",
|
||
"\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 39,
|
||
"id": "32e9948f",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Chi^2 = 16.05746\n",
|
||
"Gradi di libertà = 8\n",
|
||
"Chi^2 ridotto = 2.00718\n",
|
||
"Probabilità P(0 → chi^2) = 0.95843\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"F_fit = B + A * data[\"este\"]\n",
|
||
"sigma = np.sqrt(data[\"uF\"]**2 + (A * data[\"ueste\"])**2)\n",
|
||
"\n",
|
||
"\n",
|
||
"chi2_val = np.sum( ((data[\"F\"] - F_fit) / sigma)**2 )\n",
|
||
"\n",
|
||
"N = len(data)\n",
|
||
"nu = N - 2\n",
|
||
"\n",
|
||
"chi2_red = chi2_val / nu\n",
|
||
"P = chi2.cdf(chi2_val, df=nu)\n",
|
||
"\n",
|
||
"\n",
|
||
"print(f\"Chi^2 = {chi2_val:.5f}\")\n",
|
||
"print(f\"Gradi di libertà = {nu}\")\n",
|
||
"print(f\"Chi^2 ridotto = {chi2_red:.5f}\")\n",
|
||
"print(f\"Probabilità P(0 → chi^2) = {P:.5f}\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 40,
|
||
"id": "e2407a04",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"\n",
|
||
"sns.set_theme(style=\"whitegrid\")\n",
|
||
"\n",
|
||
"plt.figure(figsize=(10,6))\n",
|
||
"\n",
|
||
"# Seaborn scatter\n",
|
||
"sns.scatterplot(\n",
|
||
" data=data,\n",
|
||
" x=\"este\",\n",
|
||
" y=\"F\",\n",
|
||
" s=7\n",
|
||
")\n",
|
||
"\n",
|
||
"# Barre d’errore\n",
|
||
"plt.errorbar(\n",
|
||
" data[\"este\"],\n",
|
||
" data[\"F\"],\n",
|
||
" xerr=data[\"ueste\"],\n",
|
||
" yerr=data[\"uF\"],\n",
|
||
" fmt=\"none\",\n",
|
||
" ecolor=\"gray\",\n",
|
||
" elinewidth=1,\n",
|
||
" capsize=3,\n",
|
||
" alpha=0.7\n",
|
||
")\n",
|
||
"\n",
|
||
"# Linea di regressione\n",
|
||
"xfit = np.linspace(0, data[\"este\"].max(), 200)\n",
|
||
"yfit = B + A * xfit\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.plot(\n",
|
||
" xfit,\n",
|
||
" yfit,\n",
|
||
" color=\"crimson\",\n",
|
||
" linewidth=1,\n",
|
||
" zorder=10,\n",
|
||
" label=\"Fit lineare\"\n",
|
||
")\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.xlim(left=0)\n",
|
||
"plt.ylim(bottom=0)\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.xlabel(\"Δx (mm)\")\n",
|
||
"plt.ylabel(\"Forza F (mN)\")\n",
|
||
"plt.title(\"Legge di Hooke — punti permutati con errorbar\")\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True, linestyle=\"--\", alpha=0.1)\n",
|
||
"\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 41,
|
||
"id": "95dde99f",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"0 0.673181\n",
|
||
"1 0.917483\n",
|
||
"2 1.155540\n",
|
||
"3 1.390456\n",
|
||
"4 1.627202\n",
|
||
"Name: w, dtype: float64\n",
|
||
"0 0.001474\n",
|
||
"1 0.000711\n",
|
||
"2 0.001334\n",
|
||
"3 0.002013\n",
|
||
"4 0.003266\n",
|
||
"dtype: float64\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"## Dinamica davvero\n",
|
||
"\n",
|
||
"Meq = df.m + ( m_mol / 3 )\n",
|
||
"uMeq = np.sqrt( df.um**2 + um_mol**2 / 9 )\n",
|
||
"\n",
|
||
"T2 = ( 2 * np.pi / df.w )**2\n",
|
||
"uT2 = np.sqrt( (8*np.pi**2 / df.w**3)**2 * df.uw**2 ) \n",
|
||
"print(T2)\n",
|
||
"print(uT2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 42,
|
||
"id": "1bb433f0",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" OLS Regression Results \n",
|
||
"==============================================================================\n",
|
||
"Dep. Variable: tmp2 R-squared: 1.000\n",
|
||
"Model: OLS Adj. R-squared: 1.000\n",
|
||
"Method: Least Squares F-statistic: 7.624e+04\n",
|
||
"Date: Fri, 03 Apr 2026 Prob (F-statistic): 1.05e-07\n",
|
||
"Time: 11:31:19 Log-Likelihood: 23.705\n",
|
||
"No. Observations: 5 AIC: -43.41\n",
|
||
"Df Residuals: 3 BIC: -44.19\n",
|
||
"Df Model: 1 \n",
|
||
"Covariance Type: nonrobust \n",
|
||
"==============================================================================\n",
|
||
" coef std err t P>|t| [0.025 0.975]\n",
|
||
"------------------------------------------------------------------------------\n",
|
||
"const 0.0219 0.004 5.124 0.014 0.008 0.035\n",
|
||
"masse 0.0120 4.35e-05 276.124 0.000 0.012 0.012\n",
|
||
"==============================================================================\n",
|
||
"Omnibus: nan Durbin-Watson: 1.430\n",
|
||
"Prob(Omnibus): nan Jarque-Bera (JB): 0.670\n",
|
||
"Skew: -0.251 Prob(JB): 0.716\n",
|
||
"Kurtosis: 1.279 Cond. No. 344.\n",
|
||
"==============================================================================\n",
|
||
"\n",
|
||
"Notes:\n",
|
||
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
|
||
"\n",
|
||
"RISULTATI REGRESSIONE:\n",
|
||
"B) = 0.0120187 ± 0.0000435\n",
|
||
"intercetta = 0.02190 ± 0.00427\n",
|
||
"R² = 0.99996\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/home/jack/uni/lab/.venv/lib/python3.13/site-packages/statsmodels/stats/stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 5 samples were given.\n",
|
||
" warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"dfDin = pd.DataFrame({\n",
|
||
" \"masse\": Meq,\n",
|
||
" \"umasse\": uMeq,\n",
|
||
" \"tmp2\": T2,\n",
|
||
" \"utmp2\": uT2\n",
|
||
"})\n",
|
||
"\n",
|
||
"\n",
|
||
"X = sm.add_constant(dfDin[\"masse\"])\n",
|
||
"model = sm.OLS(dfDin[\"tmp2\"], X).fit()\n",
|
||
"\n",
|
||
"print(model.summary())\n",
|
||
"\n",
|
||
"# Estrazione parametri\n",
|
||
"intercetta = model.params[\"const\"]\n",
|
||
"pente = model.params[\"masse\"]\n",
|
||
"u_intercetta = model.bse[\"const\"]\n",
|
||
"u_pente = model.bse[\"masse\"]\n",
|
||
"R2 = model.rsquared\n",
|
||
"\n",
|
||
"print(\"\\nRISULTATI REGRESSIONE:\")\n",
|
||
"print(f\"B) = {pente:.7f} ± {u_pente:.7f}\")\n",
|
||
"print(f\"intercetta = {intercetta:.5f} ± {u_intercetta:.5f}\")\n",
|
||
"print(f\"R² = {R2:.5f}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 43,
|
||
"id": "67d16b84",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"K : 3.284762657868823\n",
|
||
"uK : 3.786606732225535e-06\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"\n",
|
||
"K = (2*np.pi)**2 / pente / 1000\n",
|
||
"uK = np.sqrt( (4*np.pi / pente**2)**2 * u_pente**2 ) / 1e6\n",
|
||
"\n",
|
||
"print(\"K : \", K)\n",
|
||
"print(\"uK :\", uK)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 44,
|
||
"id": "a0ba5c8d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"sns.set_theme(style=\"whitegrid\")\n",
|
||
"\n",
|
||
"plt.figure(figsize=(10,6))\n",
|
||
"\n",
|
||
"# Seaborn scatter\n",
|
||
"sns.scatterplot(\n",
|
||
" data=dfDin,\n",
|
||
" x=\"masse\",\n",
|
||
" y=\"tmp2\",\n",
|
||
" s=7\n",
|
||
")\n",
|
||
"\n",
|
||
"# Barre d’errore\n",
|
||
"plt.errorbar(\n",
|
||
" dfDin[\"masse\"],\n",
|
||
" dfDin[\"tmp2\"],\n",
|
||
" xerr=dfDin[\"umasse\"],\n",
|
||
" yerr=dfDin[\"utmp2\"],\n",
|
||
" fmt=\"none\",\n",
|
||
" ecolor=\"gray\",\n",
|
||
" elinewidth=1,\n",
|
||
" capsize=3,\n",
|
||
" alpha=0.7\n",
|
||
")\n",
|
||
"\n",
|
||
"# Linea di regressione\n",
|
||
"xfit = np.linspace(0, dfDin[\"masse\"].max(), 200)\n",
|
||
"yfit = intercetta + pente * xfit\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.plot(\n",
|
||
" xfit,\n",
|
||
" yfit,\n",
|
||
" color=\"crimson\",\n",
|
||
" linewidth=1,\n",
|
||
" zorder=10,\n",
|
||
" label=\"Fit lineare\"\n",
|
||
")\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.xlim(left=0)\n",
|
||
"plt.ylim(bottom=0)\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.xlabel(\"Meq (g)\")\n",
|
||
"plt.ylabel(\"T^2 (s^2)\")\n",
|
||
"plt.title(\"Legge di Stocazzo — punti permutati con errorbar\")\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True, linestyle=\"--\", alpha=0.1)\n",
|
||
"\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 45,
|
||
"id": "859f2337",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Ax + B : \n",
|
||
"A = 0.0120540 +- 0.0000313\n",
|
||
"B = 0.0198573 +- 0.0025536\n",
|
||
"cov_AB = -0.000000\n",
|
||
"p-value chi² = 0.9131\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"def sigma_y_equiv(x, y, sigma_x, sigma_y):\n",
|
||
" # Stima iniziale di A con sola sigma_y\n",
|
||
" sy2 = sigma_y**2\n",
|
||
" Sw = np.sum(1 / sy2)\n",
|
||
" Sx = np.sum(x / sy2)\n",
|
||
" Sxx = np.sum(x**2 / sy2)\n",
|
||
" Sy = np.sum(y / sy2)\n",
|
||
" Sxy = np.sum(x * y / sy2)\n",
|
||
" delta = Sxx * Sw - Sx**2\n",
|
||
" A_est = (Sxy * Sw - Sx * Sy) / delta\n",
|
||
"\n",
|
||
" # Propagazione\n",
|
||
" sigma_eq = np.sqrt(sigma_y**2 + A_est**2 * sigma_x**2)\n",
|
||
" return sigma_eq\n",
|
||
"\n",
|
||
"\n",
|
||
"def reg_lin(x, y, sigma_x, sigma_y):\n",
|
||
" x = np.asarray(x, dtype=float)\n",
|
||
" y = np.asarray(y, dtype=float)\n",
|
||
" sigma_x = np.asarray(sigma_x, dtype=float)\n",
|
||
" sigma_y = np.asarray(sigma_y, dtype=float)\n",
|
||
"\n",
|
||
" # Propagazione errore x → y\n",
|
||
" sigma_y_eq = sigma_y_equiv(x, y, sigma_x, sigma_y)\n",
|
||
"\n",
|
||
" # Somme pesate\n",
|
||
" w = 1.0 / sigma_y_eq**2\n",
|
||
" Sw = np.sum(w)\n",
|
||
" Sx = np.sum(w * x)\n",
|
||
" Sxx = np.sum(w * x**2)\n",
|
||
" Sy = np.sum(w * y)\n",
|
||
" Sxy = np.sum(w * x * y)\n",
|
||
" delta = Sxx * Sw - Sx**2\n",
|
||
"\n",
|
||
" # Parametri\n",
|
||
" A = (Sxy * Sw - Sx * Sy) / delta\n",
|
||
" B = (Sxx * Sy - Sxy * Sx) / delta\n",
|
||
" sigma_A = np.sqrt(Sw / delta)\n",
|
||
" sigma_B = np.sqrt(Sxx / delta)\n",
|
||
" cov_AB = -Sx / delta\n",
|
||
"\n",
|
||
" # Chi quadro\n",
|
||
" x2 = np.sum((y - A * x - B)**2 / sigma_y_eq**2)\n",
|
||
" dof = len(x) - 2\n",
|
||
" chi = sc.stats.chi2.cdf(x2, dof) # P(X² > x2)\n",
|
||
"\n",
|
||
" return A, B, sigma_A, sigma_B, cov_AB, chi\n",
|
||
"\n",
|
||
"\n",
|
||
"A, B, sA, sB, covAB, chi = reg_lin(dfDin[\"masse\"], dfDin[\"tmp2\"], dfDin[\"umasse\"], dfDin[\"utmp2\"])\n",
|
||
"print(\"Ax + B : \")\n",
|
||
"print(f\"A = {A:.7f} +- {sA:.7f}\")\n",
|
||
"print(f\"B = {B:.7f} +- {sB:.7f}\")\n",
|
||
"print(f\"cov_AB = {covAB:.6f}\")\n",
|
||
"print(f\"p-value chi² = {chi:.4f}\")\n",
|
||
"\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 46,
|
||
"id": "fef04a85",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"K nostro: 3.275133343668113\n",
|
||
"uK nostro: 0.0001776827257612153\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"K = (2*np.pi)**2 / A / 1000\n",
|
||
"uK = np.sqrt( (4*np.pi / A**2)**2 * uA**2 ) / 1e6\n",
|
||
"\n",
|
||
"print(\"K nostro: \", K)\n",
|
||
"print(\"uK nostro:\", uK)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 47,
|
||
"id": "5b191469",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Chi^2 = 6.57093\n",
|
||
"Gradi di libertà = 3\n",
|
||
"Chi^2 ridotto = 2.19031\n",
|
||
"Probabilità P(0 → chi^2) = 0.91309\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"F_fit = B + A * dfDin[\"masse\"]\n",
|
||
"sigma = np.sqrt(dfDin[\"utmp2\"]**2 + (A * dfDin[\"umasse\"])**2)\n",
|
||
"\n",
|
||
"\n",
|
||
"chi2_val = np.sum( ((dfDin[\"tmp2\"] - F_fit) / sigma)**2 )\n",
|
||
"\n",
|
||
"N = len(dfDin)\n",
|
||
"nu = N - 2\n",
|
||
"\n",
|
||
"chi2_red = chi2_val / nu\n",
|
||
"P = chi2.cdf(chi2_val, df=nu)\n",
|
||
"\n",
|
||
"\n",
|
||
"print(f\"Chi^2 = {chi2_val:.5f}\")\n",
|
||
"print(f\"Gradi di libertà = {nu}\")\n",
|
||
"print(f\"Chi^2 ridotto = {chi2_red:.5f}\")\n",
|
||
"print(f\"Probabilità P(0 → chi^2) = {P:.5f}\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 48,
|
||
"id": "ee9d9744",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0 2.486198\n",
|
||
"1 0.533770\n",
|
||
"2 0.859257\n",
|
||
"3 0.083522\n",
|
||
"4 2.608185\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 48,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"((dfDin[\"tmp2\"] - F_fit) / sigma)**2\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 49,
|
||
"id": "59281ecb",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"=== REGRESSIONE T^2 vs Meq (ODR/York) ===\n",
|
||
"A = 0.0120540 ± 0.0000463\n",
|
||
"B = 0.0198570 ± 0.0037792\n",
|
||
"cov(A,B) = -7.804236195803344e-08\n",
|
||
"chi² = 6.57093\n",
|
||
"chi² ridotto = 2.19031\n",
|
||
"\n",
|
||
"=== COSTANTE ELASTICA DINAMICA DA ODR ===\n",
|
||
"k = 3.275132 ± 0.012588 N/m\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"\n",
|
||
"# --- DATI DELLA TUA ANALISI ---\n",
|
||
"x = Meq.to_numpy() # masse equivalenti\n",
|
||
"sx = uMeq.to_numpy() # errori masse equivalenti\n",
|
||
"y = T2.to_numpy() # T^2\n",
|
||
"sy = uT2.to_numpy() # errori di T^2\n",
|
||
"\n",
|
||
"# --- MODELLO LINEARE ---\n",
|
||
"def f(B, x):\n",
|
||
" return B[0] * x + B[1] # A*x + B\n",
|
||
"\n",
|
||
"# Pacchetto \"RealData\" con errori anche su x\n",
|
||
"dati = RealData(x, y, sx=sx, sy=sy)\n",
|
||
"\n",
|
||
"# Modello lineare\n",
|
||
"modello = Model(f)\n",
|
||
"\n",
|
||
"# Esecuzione ODR (metodo di York)\n",
|
||
"odr = ODR(dati, modello, beta0=[0.01, 0]) # stima iniziale: A≈0.01, B≈0\n",
|
||
"out = odr.run()\n",
|
||
"\n",
|
||
"A, B = out.beta\n",
|
||
"sA, sB = out.sd_beta\n",
|
||
"cov_AB = out.cov_beta[0, 1]\n",
|
||
"chi2 = out.sum_square\n",
|
||
"chi2_red = out.res_var\n",
|
||
"\n",
|
||
"print(\"=== REGRESSIONE T^2 vs Meq (ODR/York) ===\")\n",
|
||
"print(f\"A = {A:.7f} ± {sA:.7f}\")\n",
|
||
"print(f\"B = {B:.7f} ± {sB:.7f}\")\n",
|
||
"print(f\"cov(A,B) = {cov_AB}\")\n",
|
||
"print(f\"chi² = {chi2:.5f}\")\n",
|
||
"print(f\"chi² ridotto = {chi2_red:.5f}\")\n",
|
||
"\n",
|
||
"# --- COSTANTE ELASTICA ---\n",
|
||
"K = (2*np.pi)**2 / A / 1000 # k in N/m → convertito a N/mm?\n",
|
||
"uK = (2*np.pi)**2 / (A**2) * sA / 1000\n",
|
||
"\n",
|
||
"print(\"\\n=== COSTANTE ELASTICA DINAMICA DA ODR ===\")\n",
|
||
"print(f\"k = {K:.6f} ± {uK:.6f} N/m\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 50,
|
||
"id": "a53e863f",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"=== REGRESSIONE T^2 vs Meq (Metodo di Y0RK 2004) ===\n",
|
||
"A = 0.0120540 ± 0.0000313\n",
|
||
"B = 0.0198570 ± 0.0025536\n",
|
||
"cov(A,B) = -7.804416866416002e-08\n",
|
||
"chi² = 6.57093\n",
|
||
"chi² ridotto = 2.19031\n",
|
||
"\n",
|
||
"=== COSTANTE ELASTICA DINAMICA (York 2004) ===\n",
|
||
"k = 3.275132 ± 0.008506 N/m\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# --- DATI ---\n",
|
||
"x = Meq.to_numpy().astype(float)\n",
|
||
"sx = uMeq.to_numpy().astype(float)\n",
|
||
"y = T2.to_numpy().astype(float)\n",
|
||
"sy = uT2.to_numpy().astype(float)\n",
|
||
"\n",
|
||
"# --- METODO DI YORK 2004 ---\n",
|
||
"def york_fit(x, y, sx, sy, max_iter=50, tol=1e-15):\n",
|
||
" # Pesi iniziali\n",
|
||
" wx = 1 / sx**2\n",
|
||
" wy = 1 / sy**2\n",
|
||
"\n",
|
||
" # Stima iniziale della pendenza (OLS y|x)\n",
|
||
" A = np.cov(x, y, aweights=wy)[0,1] / np.cov(x, x, aweights=wy)[0,1]\n",
|
||
"\n",
|
||
" for _ in range(max_iter):\n",
|
||
" A_old = A\n",
|
||
"\n",
|
||
" # 1) Pesi combinati (eq. 9)\n",
|
||
" Wi = (wx * wy) / (A**2 * wy + wx)\n",
|
||
"\n",
|
||
" # 2) x̄ e ȳ pesati (eq. 10)\n",
|
||
" X_bar = np.sum(Wi * x) / np.sum(Wi)\n",
|
||
" Y_bar = np.sum(Wi * y) / np.sum(Wi)\n",
|
||
"\n",
|
||
" # 3) Variabili centrate\n",
|
||
" Ui = x - X_bar\n",
|
||
" Vi = y - Y_bar\n",
|
||
"\n",
|
||
" # 4) β (eq. 11)\n",
|
||
" beta_i = Wi * (Ui / wy + A * Vi / wx)\n",
|
||
"\n",
|
||
" # 5) Aggiornamento pendenza (eq. 12)\n",
|
||
" A = np.sum(Wi * beta_i * Vi) / np.sum(Wi * beta_i * Ui)\n",
|
||
"\n",
|
||
" # Convergenza\n",
|
||
" if abs(A - A_old) < tol:\n",
|
||
" break\n",
|
||
"\n",
|
||
" # 6) Intercetta (eq. 13)\n",
|
||
" B = Y_bar - A * X_bar\n",
|
||
"\n",
|
||
" # --- ERRORI (eq. 14–16) ---\n",
|
||
" # S = Σ Wi (xi - x̄)²\n",
|
||
" S = np.sum(Wi * Ui**2)\n",
|
||
"\n",
|
||
" sA = np.sqrt(1 / S)\n",
|
||
" sB = np.sqrt(1 / np.sum(Wi) + X_bar**2 * sA**2)\n",
|
||
"\n",
|
||
" # cov(A,B)\n",
|
||
" cov_AB = -X_bar * sA**2\n",
|
||
"\n",
|
||
" # CHI QUADRATO (eq. 17)\n",
|
||
" chi2 = np.sum(Wi * (Vi - A * Ui)**2)\n",
|
||
" dof = len(x) - 2\n",
|
||
" chi2_red = chi2 / dof\n",
|
||
"\n",
|
||
" return A, B, sA, sB, cov_AB, chi2, chi2_red\n",
|
||
"\n",
|
||
"A, B, sA, sB, cov_AB, chi2, chi2_red = york_fit(x, y, sx, sy)\n",
|
||
"\n",
|
||
"print(\"=== REGRESSIONE T^2 vs Meq (Metodo di Y0RK 2004) ===\")\n",
|
||
"print(f\"A = {A:.7f} ± {sA:.7f}\")\n",
|
||
"print(f\"B = {B:.7f} ± {sB:.7f}\")\n",
|
||
"print(f\"cov(A,B) = {cov_AB}\")\n",
|
||
"print(f\"chi² = {chi2:.5f}\")\n",
|
||
"print(f\"chi² ridotto = {chi2_red:.5f}\")\n",
|
||
"K = (2*np.pi)**2 / A / 1000\n",
|
||
"uK = (2*np.pi)**2 / (A**2) * sA / 1000\n",
|
||
"\n",
|
||
"print(\"\\n=== COSTANTE ELASTICA DINAMICA (York 2004) ===\")\n",
|
||
"print(f\"k = {K:.6f} ± {uK:.6f} N/m\")"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": ".venv",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.13.5"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|