diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..d7f19c8 --- /dev/null +++ b/.gitignore @@ -0,0 +1,4 @@ +# L'inzio di questo file è specifico per ogniuno di noi +Funzioni\ matlab.txt +prova* +test* \ No newline at end of file diff --git a/funzioni.ipynb b/funzioni.ipynb index e7e9e42..313d3c3 100644 --- a/funzioni.ipynb +++ b/funzioni.ipynb @@ -15,12 +15,12 @@ "metadata": {}, "outputs": [], "source": [ - "pip install matplotlib numpy pandas scipy" + "# pip install matplotlib numpy pandas scipy" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "e31f5b72", "metadata": {}, "outputs": [], @@ -79,10 +79,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "id": "3d561eb0", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.5 3. ]\n", + "a 0.50000\n", + "b 0.57735\n", + "dtype: float64\n" + ] + } + ], "source": [ "def media(x, dim = 0):\n", " uA = np.nanstd(x, axis=dim, ddof=1)\n", @@ -250,18 +261,19 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "id": "78c30380", "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "A = 1.9900 +- 0.0892\n", - "B = 0.0500 +- 0.2959\n", - "cov_AB = -0.023880\n", - "p-value chi² = 0.7187\n" + "ename": "NameError", + "evalue": "name 'pd' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mNameError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[1]\u001b[39m\u001b[32m, line 49\u001b[39m\n\u001b[32m 45\u001b[39m chi = sc.stats.chi2.cdf(x2, dof) \u001b[38;5;66;03m# P(X² > x2)\u001b[39;00m\n\u001b[32m 47\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m A, B, sigma_A, sigma_B, cov_AB, chi\n\u001b[32m---> \u001b[39m\u001b[32m49\u001b[39m df = \u001b[43mpd\u001b[49m.DataFrame({\n\u001b[32m 50\u001b[39m \u001b[33m\"\u001b[39m\u001b[33mx\u001b[39m\u001b[33m\"\u001b[39m:[\u001b[32m1.0\u001b[39m, \u001b[32m2.0\u001b[39m, \u001b[32m3.0\u001b[39m, \u001b[32m4.0\u001b[39m, \u001b[32m5.0\u001b[39m],\n\u001b[32m 51\u001b[39m \u001b[33m\"\u001b[39m\u001b[33my\u001b[39m\u001b[33m\"\u001b[39m:[\u001b[32m2.1\u001b[39m, \u001b[32m3.9\u001b[39m, \u001b[32m6.2\u001b[39m, \u001b[32m7.8\u001b[39m, \u001b[32m10.1\u001b[39m],\n\u001b[32m 52\u001b[39m \u001b[33m\"\u001b[39m\u001b[33mux\u001b[39m\u001b[33m\"\u001b[39m:[\u001b[32m0.1\u001b[39m, \u001b[32m0.1\u001b[39m, \u001b[32m0.1\u001b[39m, \u001b[32m0.1\u001b[39m, \u001b[32m0.1\u001b[39m],\n\u001b[32m 53\u001b[39m \u001b[33m\"\u001b[39m\u001b[33muy\u001b[39m\u001b[33m\"\u001b[39m:[\u001b[32m0.2\u001b[39m, \u001b[32m0.2\u001b[39m, \u001b[32m0.2\u001b[39m, \u001b[32m0.2\u001b[39m, \u001b[32m0.2\u001b[39m]\n\u001b[32m 54\u001b[39m })\n\u001b[32m 56\u001b[39m A, B, sA, sB, covAB, chi = reg_lin(df[\u001b[33m\"\u001b[39m\u001b[33mx\u001b[39m\u001b[33m\"\u001b[39m], df[\u001b[33m\"\u001b[39m\u001b[33my\u001b[39m\u001b[33m\"\u001b[39m], df[\u001b[33m\"\u001b[39m\u001b[33mux\u001b[39m\u001b[33m\"\u001b[39m], df[\u001b[33m\"\u001b[39m\u001b[33muy\u001b[39m\u001b[33m\"\u001b[39m])\n\u001b[32m 57\u001b[39m \u001b[38;5;28mprint\u001b[39m(\u001b[33m\"\u001b[39m\u001b[33mAx + B : \u001b[39m\u001b[33m\"\u001b[39m)\n", + "\u001b[31mNameError\u001b[39m: name 'pd' is not defined" ] } ], @@ -310,7 +322,7 @@ " # 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.sf(x2, dof) # P(X² > x2)\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", @@ -322,6 +334,7 @@ " })\n", "\n", "A, B, sA, sB, covAB, chi = reg_lin(df[\"x\"], df[\"y\"], df[\"ux\"], df[\"uy\"])\n", + "print(\"Ax + B : \")\n", "print(f\"A = {A:.4f} +- {sA:.4f}\")\n", "print(f\"B = {B:.4f} +- {sB:.4f}\")\n", "print(f\"cov_AB = {covAB:.6f}\")\n", diff --git a/molla/mollaStatica.ipynb b/molla/mollaStatica.ipynb new file mode 100644 index 0000000..b8ca40c --- /dev/null +++ b/molla/mollaStatica.ipynb @@ -0,0 +1,835 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "4b8ea041", + "metadata": {}, + "source": [ + "# Statistica della molla statica\n", + "Passo passo logica dello studio di una molla in condizione statica" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "6bf32773", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Requirement already satisfied: matplotlib in ./.venv/lib/python3.13/site-packages (3.10.8)\n", + "Requirement already satisfied: numpy in ./.venv/lib/python3.13/site-packages (2.4.3)\n", + "Requirement already satisfied: pandas in ./.venv/lib/python3.13/site-packages (3.0.1)\n", + "Requirement already satisfied: scipy in ./.venv/lib/python3.13/site-packages (1.17.1)\n", + "Requirement already satisfied: seaborn in ./.venv/lib/python3.13/site-packages (0.13.2)\n", + "Requirement already satisfied: contourpy>=1.0.1 in ./.venv/lib/python3.13/site-packages (from matplotlib) (1.3.3)\n", + "Requirement already satisfied: cycler>=0.10 in ./.venv/lib/python3.13/site-packages (from matplotlib) (0.12.1)\n", + "Requirement already satisfied: fonttools>=4.22.0 in ./.venv/lib/python3.13/site-packages (from matplotlib) (4.62.0)\n", + "Requirement already satisfied: kiwisolver>=1.3.1 in ./.venv/lib/python3.13/site-packages (from matplotlib) (1.5.0)\n", + "Requirement already satisfied: packaging>=20.0 in ./.venv/lib/python3.13/site-packages (from matplotlib) (26.0)\n", + "Requirement already satisfied: pillow>=8 in ./.venv/lib/python3.13/site-packages (from matplotlib) (12.1.1)\n", + "Requirement already satisfied: pyparsing>=3 in ./.venv/lib/python3.13/site-packages (from matplotlib) (3.3.2)\n", + "Requirement already satisfied: python-dateutil>=2.7 in ./.venv/lib/python3.13/site-packages (from matplotlib) (2.9.0.post0)\n", + "Requirement already satisfied: six>=1.5 in ./.venv/lib/python3.13/site-packages (from python-dateutil>=2.7->matplotlib) (1.17.0)\n", + "Note: you may need to restart the kernel to use updated packages.\n" + ] + } + ], + "source": [ + "pip install matplotlib numpy pandas scipy seaborn" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "2e1b4f68", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import scipy as sc\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "\n", + "g = 9.805\n", + "ug = 0.001\n" + ] + }, + { + "cell_type": "markdown", + "id": "9986ac20", + "metadata": {}, + "source": [ + "## Sezione inutile all'ultilizzo in lab: creazione di dati pseudo random" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "a5b574c7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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40.1500.1583290.1435220.1532350.1251210.0703990.0635780.0776590.0727950.0676910.0664850.074349
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60.2000.2026720.1840250.2018950.2299970.0901620.0981330.0961540.1007080.0979340.0943790.102352
70.2250.2288830.2605490.2267840.2016360.1045270.1113350.1052120.1137550.1080670.1080220.107109
80.2500.2512240.2429920.2386270.2662120.1290120.1186450.1244430.1181030.1230030.1216080.124631
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110.3250.3240900.3309650.3349000.3575830.1605490.1587220.1603880.1563240.1575410.1622960.161074
120.3500.3472890.3557420.3631320.3472370.1803100.1688080.1678610.1681990.1669440.1729480.166314
130.3750.3750100.4122610.3586740.3665820.1788740.1820600.1851820.1827080.1785800.1882490.183653
140.4000.3865010.3961720.4132980.4093230.2025180.1921070.1996460.1911320.1972800.2052520.192378
150.4250.4172140.3940870.4181900.3962040.2135740.2084890.2092440.2010620.2169480.2052090.215061
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\n", + "
" + ], + "text/plain": [ + " m1 m2 m3 m4 m5 Dx1 Dx2 \\\n", + "0 0.050 0.052432 0.038498 0.041740 0.066845 0.018047 0.025734 \n", + "1 0.075 0.072613 0.062558 0.077425 0.015478 0.042429 0.040160 \n", + "2 0.100 0.103347 0.101605 0.099361 0.093900 0.052411 0.046097 \n", + "3 0.125 0.118064 0.150049 0.124056 0.153998 0.059645 0.056738 \n", + "4 0.150 0.158329 0.143522 0.153235 0.125121 0.070399 0.063578 \n", + "5 0.175 0.174045 0.152967 0.181660 0.176064 0.087671 0.090652 \n", + "6 0.200 0.202672 0.184025 0.201895 0.229997 0.090162 0.098133 \n", + "7 0.225 0.228883 0.260549 0.226784 0.201636 0.104527 0.111335 \n", + "8 0.250 0.251224 0.242992 0.238627 0.266212 0.129012 0.118645 \n", + "9 0.275 0.275899 0.251327 0.280781 0.312978 0.136631 0.140951 \n", + "10 0.300 0.293292 0.293954 0.296745 0.308939 0.153415 0.151791 \n", + "11 0.325 0.324090 0.330965 0.334900 0.357583 0.160549 0.158722 \n", + "12 0.350 0.347289 0.355742 0.363132 0.347237 0.180310 0.168808 \n", + "13 0.375 0.375010 0.412261 0.358674 0.366582 0.178874 0.182060 \n", + "14 0.400 0.386501 0.396172 0.413298 0.409323 0.202518 0.192107 \n", + "15 0.425 0.417214 0.394087 0.418190 0.396204 0.213574 0.208489 \n", + "16 0.450 0.448536 0.480177 0.439624 0.472196 0.226967 0.217532 \n", + "17 0.475 0.476295 0.480740 0.472676 0.475891 0.241500 0.235796 \n", + "\n", + " Dx3 Dx4 Dx5 Dx6 Dx7 \n", + "0 0.031742 0.022223 0.021998 0.021180 0.022974 \n", + "1 0.037280 0.033654 0.042858 0.037256 0.043517 \n", + "2 0.050659 0.049701 0.047669 0.039527 0.049989 \n", + "3 0.066964 0.065501 0.064932 0.051581 0.068314 \n", + "4 0.077659 0.072795 0.067691 0.066485 0.074349 \n", + "5 0.088689 0.087106 0.078646 0.081791 0.080701 \n", + "6 0.096154 0.100708 0.097934 0.094379 0.102352 \n", + "7 0.105212 0.113755 0.108067 0.108022 0.107109 \n", + "8 0.124443 0.118103 0.123003 0.121608 0.124631 \n", + "9 0.132259 0.137163 0.137445 0.130444 0.140669 \n", + "10 0.151211 0.146986 0.148656 0.147098 0.150745 \n", + "11 0.160388 0.156324 0.157541 0.162296 0.161074 \n", + "12 0.167861 0.168199 0.166944 0.172948 0.166314 \n", + "13 0.185182 0.182708 0.178580 0.188249 0.183653 \n", + "14 0.199646 0.191132 0.197280 0.205252 0.192378 \n", + "15 0.209244 0.201062 0.216948 0.205209 0.215061 \n", + "16 0.216700 0.220931 0.220583 0.228625 0.223440 \n", + "17 0.234180 0.236741 0.226907 0.227570 0.237174 " + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rng = np.random.default_rng(42)\n", + "\n", + "m1 = np.arange(0.05, 0.5, 0.025)\n", + "rng = np.random.default_rng(50)\n", + "m2 = m1 + rng.normal(0, 0.0050, size=m1.size)\n", + "rng = np.random.default_rng(51)\n", + "m3 = m1 + rng.normal(0, 0.020, size=m1.size)\n", + "rng = np.random.default_rng(52)\n", + "m4 = m1 + rng.normal(0, 0.010, size=m1.size)\n", + "rng = np.random.default_rng(55)\n", + "m5 = m1 + rng.normal(0, 0.020, size=m1.size)\n", + "\n", + "\n", + "K_vera = 20.0\n", + "\n", + "Dx_vero = (m1 * g) / K_vera\n", + "Dx_errore1 = Dx_vero + rng.normal(0, 0.0050, size=Dx_vero.size)\n", + "rng = np.random.default_rng(43)\n", + "Dx_errore2 = Dx_vero + rng.normal(0, 0.0050, size=Dx_vero.size)\n", + "rng = np.random.default_rng(44)\n", + "Dx_errore3 = Dx_vero + rng.normal(0, 0.0050, size=Dx_vero.size)\n", + "rng = np.random.default_rng(45)\n", + "Dx_errore4 = Dx_vero + rng.normal(0, 0.0050, size=Dx_vero.size)\n", + "rng = np.random.default_rng(46)\n", + "Dx_errore5 = Dx_vero + rng.normal(0, 0.0050, size=Dx_vero.size)\n", + "rng = np.random.default_rng(47)\n", + "Dx_errore6 = Dx_vero + rng.normal(0, 0.0050, size=Dx_vero.size)\n", + "rng = np.random.default_rng(48)\n", + "Dx_errore7 = Dx_vero + rng.normal(0, 0.0050, size=Dx_vero.size)\n", + "\n", + "df = pd.DataFrame({\n", + " 'm1': m1,\n", + " 'm2': m2,\n", + " 'm3': m3,\n", + " 'm4': m4,\n", + " 'm5': m5,\n", + " 'Dx1': Dx_errore1,\n", + " 'Dx2': Dx_errore2,\n", + " 'Dx3': Dx_errore3,\n", + " 'Dx4': Dx_errore4,\n", + " 'Dx5': Dx_errore5,\n", + " 'Dx6': Dx_errore6,\n", + " 'Dx7': Dx_errore7,\n", + "})\n", + "\n", + "df" + ] + }, + { + "cell_type": "markdown", + "id": "e90c3495", + "metadata": {}, + "source": [ + "## Realmente vorremmo prendere i dati da un csv\n", + "```python\n", + "df = pd.read_csv(r'molla.csv')\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "f3b7dfe0", + "metadata": {}, + "source": [ + "# Inzio dello studio statistico della molla" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d98f6172", + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "Cannot perform reduction 'mean' with string dtype", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mTypeError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 61\u001b[39m\n\u001b[32m 57\u001b[39m sigma = np.sqrt(\u001b[32m1.0\u001b[39m / den)\n\u001b[32m 59\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m media, sigma\n\u001b[32m---> \u001b[39m\u001b[32m61\u001b[39m df = \u001b[43mcalcola_Dx_stats\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdf\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43merr_arbitrario_DX\u001b[49m\u001b[43m=\u001b[49m\u001b[32;43m0.01\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[32m 62\u001b[39m df = calcola_m_stats(df, err_arbitrario_m=\u001b[32m0.01\u001b[39m)\n\u001b[32m 64\u001b[39m df[\u001b[33m\"\u001b[39m\u001b[33mK\u001b[39m\u001b[33m\"\u001b[39m] = df.m * g / df.Dx\n", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 19\u001b[39m, in \u001b[36mcalcola_Dx_stats\u001b[39m\u001b[34m(df, err_arbitrario_DX)\u001b[39m\n\u001b[32m 16\u001b[39m sigma = valori.std(ddof=\u001b[32m1\u001b[39m) \u001b[38;5;66;03m# sigma sperimentale S\u001b[39;00m\n\u001b[32m 17\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m pd.Series({\u001b[33m'\u001b[39m\u001b[33mDx\u001b[39m\u001b[33m'\u001b[39m: media, \u001b[33m'\u001b[39m\u001b[33muDx\u001b[39m\u001b[33m'\u001b[39m: sigma})\n\u001b[32m---> \u001b[39m\u001b[32m19\u001b[39m stats = \u001b[43mdf\u001b[49m\u001b[43m.\u001b[49m\u001b[43mapply\u001b[49m\u001b[43m(\u001b[49m\u001b[43mriga_stats\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m=\u001b[49m\u001b[32;43m1\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[32m 20\u001b[39m df[\u001b[33m'\u001b[39m\u001b[33mDx\u001b[39m\u001b[33m'\u001b[39m] = stats[\u001b[33m'\u001b[39m\u001b[33mDx\u001b[39m\u001b[33m'\u001b[39m]\n\u001b[32m 21\u001b[39m df[\u001b[33m'\u001b[39m\u001b[33muDx\u001b[39m\u001b[33m'\u001b[39m] = stats[\u001b[33m'\u001b[39m\u001b[33muDx\u001b[39m\u001b[33m'\u001b[39m]\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/frame.py:12419\u001b[39m, in \u001b[36mDataFrame.apply\u001b[39m\u001b[34m(self, func, axis, raw, result_type, args, by_row, engine, engine_kwargs, **kwargs)\u001b[39m\n\u001b[32m 12405\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mUnknown engine \u001b[39m\u001b[33m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mengine\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m'\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m 12407\u001b[39m op = frame_apply(\n\u001b[32m 12408\u001b[39m \u001b[38;5;28mself\u001b[39m,\n\u001b[32m 12409\u001b[39m func=func,\n\u001b[32m (...)\u001b[39m\u001b[32m 12417\u001b[39m kwargs=kwargs,\n\u001b[32m 12418\u001b[39m )\n\u001b[32m> \u001b[39m\u001b[32m12419\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mop\u001b[49m\u001b[43m.\u001b[49m\u001b[43mapply\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m.__finalize__(\u001b[38;5;28mself\u001b[39m, method=\u001b[33m\"\u001b[39m\u001b[33mapply\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m 12420\u001b[39m \u001b[38;5;28;01melif\u001b[39;00m \u001b[38;5;28mhasattr\u001b[39m(engine, \u001b[33m\"\u001b[39m\u001b[33m__pandas_udf__\u001b[39m\u001b[33m\"\u001b[39m):\n\u001b[32m 12421\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m result_type \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/apply.py:1015\u001b[39m, in \u001b[36mFrameApply.apply\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m 1012\u001b[39m \u001b[38;5;28;01melif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.raw:\n\u001b[32m 1013\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m.apply_raw(engine=\u001b[38;5;28mself\u001b[39m.engine, engine_kwargs=\u001b[38;5;28mself\u001b[39m.engine_kwargs)\n\u001b[32m-> \u001b[39m\u001b[32m1015\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mapply_standard\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/apply.py:1167\u001b[39m, in \u001b[36mFrameApply.apply_standard\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m 1165\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mapply_standard\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[32m 1166\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m.engine == \u001b[33m\"\u001b[39m\u001b[33mpython\u001b[39m\u001b[33m\"\u001b[39m:\n\u001b[32m-> \u001b[39m\u001b[32m1167\u001b[39m results, res_index = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mapply_series_generator\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 1168\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[32m 1169\u001b[39m results, res_index = \u001b[38;5;28mself\u001b[39m.apply_series_numba()\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/apply.py:1183\u001b[39m, in \u001b[36mFrameApply.apply_series_generator\u001b[39m\u001b[34m(self)\u001b[39m\n\u001b[32m 1180\u001b[39m results = {}\n\u001b[32m 1182\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m i, v \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(series_gen):\n\u001b[32m-> \u001b[39m\u001b[32m1183\u001b[39m results[i] = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 1184\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(results[i], ABCSeries):\n\u001b[32m 1185\u001b[39m \u001b[38;5;66;03m# If we have a view on v, we need to make a copy because\u001b[39;00m\n\u001b[32m 1186\u001b[39m \u001b[38;5;66;03m# series_generator will swap out the underlying data\u001b[39;00m\n\u001b[32m 1187\u001b[39m results[i] = results[i].copy(deep=\u001b[38;5;28;01mFalse\u001b[39;00m)\n", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 15\u001b[39m, in \u001b[36mcalcola_Dx_stats..riga_stats\u001b[39m\u001b[34m(row)\u001b[39m\n\u001b[32m 13\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m pd.Series({\u001b[33m'\u001b[39m\u001b[33mDx\u001b[39m\u001b[33m'\u001b[39m: valori.iloc[\u001b[32m0\u001b[39m], \u001b[33m'\u001b[39m\u001b[33muDx\u001b[39m\u001b[33m'\u001b[39m: err_arbitrario_DX})\n\u001b[32m 14\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[32m---> \u001b[39m\u001b[32m15\u001b[39m media = \u001b[43mvalori\u001b[49m\u001b[43m.\u001b[49m\u001b[43mmean\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 16\u001b[39m sigma = valori.std(ddof=\u001b[32m1\u001b[39m) \u001b[38;5;66;03m# sigma sperimentale S\u001b[39;00m\n\u001b[32m 17\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m pd.Series({\u001b[33m'\u001b[39m\u001b[33mDx\u001b[39m\u001b[33m'\u001b[39m: media, \u001b[33m'\u001b[39m\u001b[33muDx\u001b[39m\u001b[33m'\u001b[39m: sigma})\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/util/_decorators.py:336\u001b[39m, in \u001b[36mdeprecate_nonkeyword_arguments..decorate..wrapper\u001b[39m\u001b[34m(*args, **kwargs)\u001b[39m\n\u001b[32m 330\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(args) > num_allow_args:\n\u001b[32m 331\u001b[39m warnings.warn(\n\u001b[32m 332\u001b[39m msg.format(arguments=_format_argument_list(allow_args)),\n\u001b[32m 333\u001b[39m klass,\n\u001b[32m 334\u001b[39m stacklevel=find_stack_level(),\n\u001b[32m 335\u001b[39m )\n\u001b[32m--> \u001b[39m\u001b[32m336\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/series.py:8113\u001b[39m, in \u001b[36mSeries.mean\u001b[39m\u001b[34m(self, axis, skipna, numeric_only, **kwargs)\u001b[39m\n\u001b[32m 8063\u001b[39m \u001b[38;5;129m@deprecate_nonkeyword_arguments\u001b[39m(Pandas4Warning, allowed_args=[\u001b[33m\"\u001b[39m\u001b[33mself\u001b[39m\u001b[33m\"\u001b[39m], name=\u001b[33m\"\u001b[39m\u001b[33mmean\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m 8064\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mmean\u001b[39m(\n\u001b[32m 8065\u001b[39m \u001b[38;5;28mself\u001b[39m,\n\u001b[32m (...)\u001b[39m\u001b[32m 8069\u001b[39m **kwargs,\n\u001b[32m 8070\u001b[39m ) -> Any:\n\u001b[32m 8071\u001b[39m \u001b[38;5;250m \u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m 8072\u001b[39m \u001b[33;03m Return the mean of the values over the requested axis.\u001b[39;00m\n\u001b[32m 8073\u001b[39m \n\u001b[32m (...)\u001b[39m\u001b[32m 8111\u001b[39m \u001b[33;03m 2.0\u001b[39;00m\n\u001b[32m 8112\u001b[39m \u001b[33;03m \"\"\"\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m8113\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mNDFrame\u001b[49m\u001b[43m.\u001b[49m\u001b[43mmean\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m 8114\u001b[39m \u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m=\u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mskipna\u001b[49m\u001b[43m=\u001b[49m\u001b[43mskipna\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnumeric_only\u001b[49m\u001b[43m=\u001b[49m\u001b[43mnumeric_only\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\n\u001b[32m 8115\u001b[39m \u001b[43m \u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/generic.py:11831\u001b[39m, in \u001b[36mNDFrame.mean\u001b[39m\u001b[34m(self, axis, skipna, numeric_only, **kwargs)\u001b[39m\n\u001b[32m 11823\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mmean\u001b[39m(\n\u001b[32m 11824\u001b[39m \u001b[38;5;28mself\u001b[39m,\n\u001b[32m 11825\u001b[39m *,\n\u001b[32m (...)\u001b[39m\u001b[32m 11829\u001b[39m **kwargs,\n\u001b[32m 11830\u001b[39m ) -> Series | \u001b[38;5;28mfloat\u001b[39m:\n\u001b[32m> \u001b[39m\u001b[32m11831\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_stat_function\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m 11832\u001b[39m \u001b[43m \u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mmean\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnanops\u001b[49m\u001b[43m.\u001b[49m\u001b[43mnanmean\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mskipna\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnumeric_only\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\n\u001b[32m 11833\u001b[39m \u001b[43m \u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/generic.py:11785\u001b[39m, in \u001b[36mNDFrame._stat_function\u001b[39m\u001b[34m(self, name, func, axis, skipna, numeric_only, **kwargs)\u001b[39m\n\u001b[32m 11781\u001b[39m nv.validate_func(name, (), kwargs)\n\u001b[32m 11783\u001b[39m validate_bool_kwarg(skipna, \u001b[33m\"\u001b[39m\u001b[33mskipna\u001b[39m\u001b[33m\"\u001b[39m, none_allowed=\u001b[38;5;28;01mFalse\u001b[39;00m)\n\u001b[32m> \u001b[39m\u001b[32m11785\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_reduce\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m 11786\u001b[39m \u001b[43m \u001b[49m\u001b[43mfunc\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mname\u001b[49m\u001b[43m=\u001b[49m\u001b[43mname\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m=\u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mskipna\u001b[49m\u001b[43m=\u001b[49m\u001b[43mskipna\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnumeric_only\u001b[49m\u001b[43m=\u001b[49m\u001b[43mnumeric_only\u001b[49m\n\u001b[32m 11787\u001b[39m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/series.py:7480\u001b[39m, in \u001b[36mSeries._reduce\u001b[39m\u001b[34m(self, op, name, axis, skipna, numeric_only, filter_type, **kwds)\u001b[39m\n\u001b[32m 7476\u001b[39m \u001b[38;5;28mself\u001b[39m._get_axis_number(axis)\n\u001b[32m 7478\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(delegate, ExtensionArray):\n\u001b[32m 7479\u001b[39m \u001b[38;5;66;03m# dispatch to ExtensionArray interface\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m7480\u001b[39m result = \u001b[43mdelegate\u001b[49m\u001b[43m.\u001b[49m\u001b[43m_reduce\u001b[49m\u001b[43m(\u001b[49m\u001b[43mname\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mskipna\u001b[49m\u001b[43m=\u001b[49m\u001b[43mskipna\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwds\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 7482\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[32m 7483\u001b[39m \u001b[38;5;66;03m# dispatch to numpy arrays\u001b[39;00m\n\u001b[32m 7484\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m numeric_only \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mself\u001b[39m.dtype.kind \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;129;01min\u001b[39;00m \u001b[33m\"\u001b[39m\u001b[33miufcb\u001b[39m\u001b[33m\"\u001b[39m:\n\u001b[32m 7485\u001b[39m \u001b[38;5;66;03m# i.e. not is_numeric_dtype(self.dtype)\u001b[39;00m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/uni/lab/.venv/lib/python3.13/site-packages/pandas/core/arrays/string_.py:967\u001b[39m, in \u001b[36mStringArray._reduce\u001b[39m\u001b[34m(self, name, skipna, keepdims, axis, **kwargs)\u001b[39m\n\u001b[32m 964\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m._from_sequence([result], dtype=\u001b[38;5;28mself\u001b[39m.dtype)\n\u001b[32m 965\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m result\n\u001b[32m--> \u001b[39m\u001b[32m967\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mCannot perform reduction \u001b[39m\u001b[33m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mname\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m'\u001b[39m\u001b[33m with string dtype\u001b[39m\u001b[33m\"\u001b[39m)\n", + "\u001b[31mTypeError\u001b[39m: Cannot perform reduction 'mean' with string dtype" + ] + } + ], + "source": [ + "df = pd.read_csv(r'statica1.csv')\n", + "\n", + "def calcola_Dx_stats(df, err_arbitrario_DX):\n", + " dx_cols = [col for col in df.columns if col.startswith('Dx')]\n", + " \n", + " def riga_stats(row):\n", + " valori = row[dx_cols].dropna()\n", + " n = len(valori)\n", + " \n", + " if n == 0:\n", + " return pd.Series({'Dx': np.nan, 'uDx': np.nan})\n", + " elif n == 1:\n", + " return pd.Series({'Dx': valori.iloc[0], 'uDx': err_arbitrario_DX})\n", + " else:\n", + " media = valori.mean()\n", + " sigma = valori.std(ddof=1) # sigma sperimentale S\n", + " return pd.Series({'Dx': media, 'uDx': sigma})\n", + " \n", + " stats = df.apply(riga_stats, axis=1)\n", + " df['Dx'] = stats['Dx']\n", + " df['uDx'] = stats['uDx']\n", + " \n", + " return df\n", + "\n", + "def calcola_m_stats(df, err_arbitrario_m):\n", + " m_cols = [col for col in df.columns if col.startswith('m')]\n", + " \n", + " def riga_stats(row):\n", + " valori = row[m_cols].dropna()\n", + " n = len(valori)\n", + " \n", + " if n == 0:\n", + " return pd.Series({'m': np.nan, 'um': np.nan})\n", + " elif n == 1:\n", + " return pd.Series({'m': valori.iloc[0], 'um': err_arbitrario_m})\n", + " else:\n", + " media = valori.mean()\n", + " sigma = valori.std(ddof=1) # sigma sperimentale S\n", + " return pd.Series({'m': media, 'um': sigma})\n", + " \n", + " stats = df.apply(riga_stats, axis=1)\n", + " df['m'] = stats['m']\n", + " df['um'] = stats['um']\n", + " \n", + " return df\n", + "\n", + "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", + "df = calcola_Dx_stats(df, err_arbitrario_DX=0.01)\n", + "df = calcola_m_stats(df, err_arbitrario_m=0.01)\n", + "\n", + "df[\"K\"] = df.m * g / df.Dx\n", + "df[\"uK\"] = np.sqrt( (df.m * g / df.Dx**2)**2 * df.uDx**2 + (g/df.Dx)**2 * df.um**2 + (df.m / df.Dx)**2 * ug**2)\n", + "\n", + "df[\"F\"] = df.m * g\n", + "df[\"uF\"] = np.sqrt( df.m**2 * ug**2 + g**2 * df.um**2)\n", + "media_K, sigma_K = mediaPesata(df[\"K\"], df[\"uK\"])\n", + "\n", + "#chi 2\n", + "chi2_val = np.sum((df[\"K\"] - media_K)**2 / df[\"uK\"]**2) # formula corretta\n", + "dof = len(df[\"K\"]) - 1 # -1 perché stimi solo la media\n", + "chi2_rid = chi2_val / dof\n", + "p_value = 1 - sc.stats.chi2.cdf(chi2_val, dof)\n", + "\n", + "print(\"#\"*60)\n", + "print(\"Valori di K\")\n", + "print(\"media pesata K:\", media_K)\n", + "print(\"sigma K:\", sigma_K)\n", + "print(f\"Chi2 : {chi2_val:.4f}\")\n", + "print(f\"DOF : {dof}\")\n", + "print(f\"Chi2 ridotto : {chi2_rid:.4f} (ideale ~ 1)\")\n", + "print(f\"p-value : {p_value:.4f}\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "215645fe", + "metadata": {}, + "source": [ + "## Fit lineare di K\n", + "Funzione fatta come quella spiegata dalla Carpi." + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "6b8e71d0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "############################################################\n", + "Calcolo della regressione lineare\n", + "A = 19.8275 +- 0.4716\n", + "B = 0.0194 +- 0.0685\n", + "cov_AB = -0.029082\n", + "p-value chi² = 0.0016\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", + "A, B, sA, sB, covAB, chi = reg_lin(df[\"Dx\"], df[\"F\"], df[\"uDx\"], df[\"uF\"])\n", + "print(\"#\"*60)\n", + "print(\"Calcolo della regressione lineare\")\n", + "print(f\"A = {A:.4f} +- {sA:.4f}\")\n", + "print(f\"B = {B:.4f} +- {sB:.4f}\")\n", + "print(f\"cov_AB = {covAB:.6f}\")\n", + "print(f\"p-value chi² = {chi:.4f}\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "bfbc49bf", + "metadata": {}, + "source": [ + "## Grafico potente dei dati" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3d1f0dc8", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "<>:25: SyntaxWarning: invalid escape sequence '\\p'\n", + "<>:25: SyntaxWarning: invalid escape sequence '\\p'\n", + "/tmp/ipykernel_2965/2212367346.py:25: SyntaxWarning: invalid escape sequence '\\p'\n", + " label=r\"Incertezza fit $\\pm\\,\\sigma$\")\n" + ] + }, + { + "data": { + "text/plain": [ + "Text(0.04, 0.95, '$k = A = (19.8 \\\\pm 0.5)\\\\ \\\\mathrm{N/m}$\\n$B = (0.020 \\\\pm 0.075)\\\\ \\\\mathrm{N}$')" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Colori e grafica in generale generati da LLM\n", + "\n", + "mpl.rcParams.update({\n", + " \"font.family\": \"serif\",\n", + " \"font.serif\": [\"Times New Roman\", \"DejaVu Serif\"],\n", + " \"mathtext.fontset\": \"stix\",\n", + " \"axes.labelsize\": 13,\n", + " \"xtick.labelsize\": 11,\n", + " \"ytick.labelsize\": 11,\n", + " \"legend.fontsize\": 11,\n", + " \"figure.dpi\": 150,\n", + "})\n", + "\n", + "fig, ax = plt.subplots(figsize=(7, 5))\n", + "\n", + "x_fit = np.linspace(-0.05, df[\"Dx\"].max() * 1.10, 100)\n", + "y_fit = A * x_fit + B\n", + "sigma_fit = np.sqrt((x_fit * sA)**2 + sB**2)\n", + "\n", + "'''\n", + "ax.fill_between(x_fit,\n", + " y_fit - sigma_fit,\n", + " y_fit + sigma_fit,\n", + " alpha=0.20, color=\"#C0392B\",\n", + " label=r\"Incertezza fit $\\pm\\,\\sigma$\")\n", + "'''\n", + "ax.plot(x_fit, y_fit,\n", + " color=\"#C0392B\", linewidth=1, zorder=3,\n", + " label=rf\"Fit: $F = ({A:.2f} \\pm {sA:.2f})\\,\\Delta x + ({B:.3f} \\pm {sB:.3f})$ N\")\n", + "\n", + "ax.errorbar(\n", + " df[\"Dx\"], df[\"F\"],\n", + " xerr=df[\"uDx\"], # barre orizzontali (errore su Δx)\n", + " yerr=df[\"uF\"], # barre verticali (errore su F)\n", + " fmt=\"none\", # simbolo cerchio per il punto\n", + " color=\"#1A5276\",\n", + " ecolor=\"#1A5276\",\n", + " elinewidth=1.0, # spessore delle barre\n", + " capsize=4, # cappelletto alle estremità\n", + " capthick=1.0,\n", + " markersize=5,\n", + " zorder=5,\n", + " label=\"Dati sperimentali\",\n", + ")\n", + "\n", + "ax.set_xlabel(r\"$\\Delta x\\ \\mathrm{[m]}$\")\n", + "ax.set_ylabel(r\"$F\\ \\mathrm{[N]}$\")\n", + "ax.set_title(\"Forza / Estensione — Legge di Hooke\", pad=10)\n", + " \n", + "ax.legend(framealpha=0.9, edgecolor=\"0.7\")\n", + "ax.grid(True, linestyle=\"--\", linewidth=0.5, alpha=0.5)\n", + "ax.set_xlim(left=0)\n", + " \n", + "# Testo con i parametri del fit (opzionale)\n", + "textstr = (rf\"$k = A = ({A:.1f} \\pm {sA:.1f})\\ \\mathrm{{N/m}}$\" \"\\n\"\n", + " rf\"$B = ({B:.3f} \\pm {sB:.3f})\\ \\mathrm{{N}}$\")\n", + "ax.text(0.04, 0.95, textstr,\n", + " transform=ax.transAxes,\n", + " verticalalignment=\"top\",\n", + " bbox=dict(boxstyle=\"round,pad=0.4\", facecolor=\"white\", alpha=0.8, edgecolor=\"0.7\"),\n", + " fontsize=10)\n" + ] + } + ], + "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 +} diff --git a/molla/mollaStatica1.ipynb b/molla/mollaStatica1.ipynb new file mode 100644 index 0000000..6fb0734 --- /dev/null +++ b/molla/mollaStatica1.ipynb @@ -0,0 +1,931 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 145, + "id": "f34c5b88", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import scipy as sc\n", + "from scipy.stats import chi2\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "import statsmodels.api as sm\n", + "\n", + "\n", + "g = 9.806\n", + "ug = 0.001" + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "id": "08efb2be", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'\\ndf[\"K\"] = df.m * g / df.Dx\\ndf[\"uK\"] = np.sqrt( (df.m * g / df.Dx**2)**2 * df.uDx**2 + (g/df.Dx)**2 * df.um**2 + (df.m / df.Dx)**2 * ug**2)\\n\\ndf[\"F\"] = df.m * g\\ndf[\"uF\"] = np.sqrt( df.m**2 * ug**2 + g**2 * df.um**2)\\nmedia_K, sigma_K = mediaPesata(df[\"K\"], df[\"uK\"])\\n\\n\\n#chi 2\\nchi2_val = np.sum((df[\"K\"] - media_K)**2 / df[\"uK\"]**2) # formula corretta\\ndof = len(df[\"K\"]) - 1 # -1 perché stimi solo la media\\nchi2_rid = chi2_val / dof\\np_value = 1 - sc.stats.chi2.cdf(chi2_val, dof)\\n\\nprint(\"#\"*60)\\nprint(\"Valori di K\")\\nprint(\"media pesata K:\", media_K)\\nprint(\"sigma K:\", sigma_K)\\nprint(f\"Chi2 : {chi2_val:.4f}\")\\nprint(f\"DOF : {dof}\")\\nprint(f\"Chi2 ridotto : {chi2_rid:.4f} (ideale ~ 1)\")\\nprint(f\"p-value : {p_value:.4f}\")\\n'" + ] + }, + "execution_count": 146, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_csv(r'statica1.csv')\n", + "\n", + "def calcola_Dx_stats(df, err_arbitrario_DX):\n", + " dx_cols = [col for col in df.columns if col.startswith('Dx')]\n", + " \n", + " def riga_stats(row):\n", + " valori = row[dx_cols].dropna()\n", + " n = len(valori)\n", + " \n", + " if n == 0:\n", + " return pd.Series({'Dx': np.nan, 'uDx': np.nan})\n", + " elif n == 1:\n", + " return pd.Series({'Dx': valori.iloc[0], 'uDx': err_arbitrario_DX})\n", + " else:\n", + " media = valori.mean()\n", + " sigma = valori.std(ddof=1) # sigma sperimentale S\n", + " return pd.Series({'Dx': media, 'uDx': sigma})\n", + " \n", + " stats = df.apply(riga_stats, axis=1)\n", + " df['Dx'] = stats['Dx']\n", + " df['uDx'] = stats['uDx']\n", + " \n", + " return df\n", + "\n", + "def calcola_m_stats(df, err_arbitrario_m):\n", + " m_cols = [col for col in df.columns if col.startswith('m')]\n", + " \n", + " def riga_stats(row):\n", + " valori = row[m_cols].dropna()\n", + " n = len(valori)\n", + " \n", + " if n == 0:\n", + " return pd.Series({'m': np.nan, 'um': np.nan})\n", + " elif n == 1:\n", + " return pd.Series({'m': valori.iloc[0], 'um': err_arbitrario_m})\n", + " else:\n", + " media = valori.mean()\n", + " sigma = valori.std(ddof=1) # sigma sperimentale S\n", + " return pd.Series({'m': media, 'um': sigma})\n", + " \n", + " stats = df.apply(riga_stats, axis=1)\n", + " df['m'] = stats['m']\n", + " df['um'] = stats['um']\n", + " \n", + " return df\n", + "\n", + "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", + "df = calcola_Dx_stats(df, err_arbitrario_DX=0.01)\n", + "df = calcola_m_stats(df, err_arbitrario_m=0.0028867513)\n", + "\n", + "\n", + "\n", + "'''\n", + "df[\"K\"] = df.m * g / df.Dx\n", + "df[\"uK\"] = np.sqrt( (df.m * g / df.Dx**2)**2 * df.uDx**2 + (g/df.Dx)**2 * df.um**2 + (df.m / df.Dx)**2 * ug**2)\n", + "\n", + "df[\"F\"] = df.m * g\n", + "df[\"uF\"] = np.sqrt( df.m**2 * ug**2 + g**2 * df.um**2)\n", + "media_K, sigma_K = mediaPesata(df[\"K\"], df[\"uK\"])\n", + "\n", + "\n", + "#chi 2\n", + "chi2_val = np.sum((df[\"K\"] - media_K)**2 / df[\"uK\"]**2) # formula corretta\n", + "dof = len(df[\"K\"]) - 1 # -1 perché stimi solo la media\n", + "chi2_rid = chi2_val / dof\n", + "p_value = 1 - sc.stats.chi2.cdf(chi2_val, dof)\n", + "\n", + "print(\"#\"*60)\n", + "print(\"Valori di K\")\n", + "print(\"media pesata K:\", media_K)\n", + "print(\"sigma K:\", sigma_K)\n", + "print(f\"Chi2 : {chi2_val:.4f}\")\n", + "print(f\"DOF : {dof}\")\n", + "print(f\"Chi2 ridotto : {chi2_rid:.4f} (ideale ~ 1)\")\n", + "print(f\"p-value : {p_value:.4f}\")\n", + "'''" + ] + }, + { + "cell_type": "code", + "execution_count": 147, + "id": "5494409f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " m1 Dx1 Dx2 Dx3 Dx4 Dx5 Dx6 Dx uDx \\\n", + "0 88.97 77.26 77.28 77.26 77.28 77.24 77.42 77.290000 0.065422 \n", + "1 108.61 68.92 68.94 69.00 68.98 68.90 69.02 68.960000 0.047329 \n", + "2 128.64 60.88 61.00 60.82 60.94 61.08 60.94 60.943333 0.090701 \n", + "3 148.38 52.96 52.96 52.78 52.88 52.88 53.00 52.910000 0.079750 \n", + "4 168.53 44.42 44.68 44.48 44.80 44.92 44.52 44.636667 0.196943 \n", + "\n", + " m um \n", + "0 88.97 0.002887 \n", + "1 108.61 0.002887 \n", + "2 128.64 0.002887 \n", + "3 148.38 0.002887 \n", + "4 168.53 0.002887 " + ] + }, + "execution_count": 147, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df" + ] + }, + { + "cell_type": "code", + "execution_count": 148, + "id": "976d5531", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]\n", + "############################################################\n", + "[ 8.33 16.34666667 24.38 32.65333333 8.01666667 16.05\n", + " 24.32333333 8.03333333 16.30666667 8.27333333]\n", + "[0.08074652 0.11183321 0.10315038 0.2075251 0.10230673 0.09273618\n", + " 0.20255041 0.12077527 0.21682558 0.21247745]\n", + "############################################################\n", + "[-19.64 -39.67 -59.41 -79.56 -20.03 -39.77 -59.92 -19.74 -39.89 -20.15]\n", + "[0.00408248 0.00408248 0.00408248 0.00408248 0.00408248 0.00408248\n", + " 0.00408248 0.00408248 0.00408248 0.00408248]\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.Dx[x] - df.Dx[j] for x,j in perm])\n", + "ueste = np.array([np.sqrt(df.uDx[x]**2 + df.uDx[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", + "\n", + "print(\"#\"* 60)\n", + "print(este)\n", + "print(ueste)\n", + "\n", + "print(\"#\"* 60)\n", + "print(masse)\n", + "print(umasse)" + ] + }, + { + "cell_type": "code", + "execution_count": 149, + "id": "2ad19283", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[23.12002881 23.79714641 23.89558901 23.89236505 24.50072931 24.29810717\n", + " 24.15686666 24.09590539 23.98781725 23.88286463]\n", + "[0.22417698 0.16284102 0.10114355 0.15187011 0.31272214 0.1404374\n", + " 0.20118598 0.36230687 0.31897871 0.61338857]\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": 150, + "id": "5f59d6c9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K-medio: 23.948686783351924\n", + "sigmaC: 0.05731089207006433\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": 151, + "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: 2.238e+04\n", + "Date: Wed, 01 Apr 2026 Prob (F-statistic): 4.46e-15\n", + "Time: 11:03:56 Log-Likelihood: -27.237\n", + "No. Observations: 10 AIC: 58.47\n", + "Df Residuals: 8 BIC: 59.08\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0999 2.914 0.034 0.973 -6.621 6.821\n", + "este 23.9663 0.160 149.602 0.000 23.597 24.336\n", + "==============================================================================\n", + "Omnibus: 0.134 Durbin-Watson: 0.595\n", + "Prob(Omnibus): 0.935 Jarque-Bera (JB): 0.285\n", + "Skew: -0.202 Prob(JB): 0.867\n", + "Kurtosis: 2.277 Cond. No. 40.8\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) = 23.96627 ± 0.16020\n", + "intercetta = 0.09992 ± 2.91442\n", + "R² = 0.99964\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}\")\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 152, + "id": "1d42b009", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "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": 153, + "id": "986ff4a6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Chi^2 = 25.02317\n", + "Gradi di libertà = 8\n", + "Chi^2 ridotto = 3.12790\n", + "Probabilità P(0 → chi^2) = 0.99846\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": 154, + "id": "ef0817f4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0 13.640283\n", + "1 1.141735\n", + "2 0.543390\n", + "3 0.255239\n", + "4 2.911852\n", + "5 5.525530\n", + "6 0.872958\n", + "7 0.105774\n", + "8 0.002341\n", + "9 0.024062\n", + "dtype: float64" + ] + }, + "execution_count": 154, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "((data[\"F\"] - F_fit) / sigma)**2" + ] + }, + { + "cell_type": "code", + "execution_count": 155, + "id": "cebe6742", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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esteuesteFuF
08.3300000.080747192.589840.044591
116.3466670.111833389.004020.056359
224.3800000.103150582.574460.071639
332.6533330.207525780.165360.089064
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816.3066670.216826391.161340.056514
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\n", + "
" + ], + "text/plain": [ + " este ueste F uF\n", + "0 8.330000 0.080747 192.58984 0.044591\n", + "1 16.346667 0.111833 389.00402 0.056359\n", + "2 24.380000 0.103150 582.57446 0.071639\n", + "3 32.653333 0.207525 780.16536 0.089064\n", + "4 8.016667 0.102307 196.41418 0.044764\n", + "5 16.050000 0.092736 389.98462 0.056429\n", + "6 24.323333 0.202550 587.57552 0.072063\n", + "7 8.033333 0.120775 193.57044 0.044635\n", + "8 16.306667 0.216826 391.16134 0.056514\n", + "9 8.273333 0.212477 197.59090 0.044818" + ] + }, + "execution_count": 155, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 160, + "id": "2d4b7144", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ax + B : \n", + "A = 24.04493 +- 0.13159\n", + "B = -1.56967 +- 2.08087\n", + "cov_AB = -0.246320\n", + "p-value chi² = 0.9978741\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": 157, + "id": "32e9948f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Chi^2 = 24.13715\n", + "Gradi di libertà = 8\n", + "Chi^2 ridotto = 3.01714\n", + "Probabilità P(0 → chi^2) = 0.99783\n" + ] + } + ], + "source": [ + "F_fit = B + A * data[\"este\"]\n", + "sigma = 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": 158, + "id": "e2407a04", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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" + ] + } + ], + "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 +} diff --git a/molla/mollaStatica2.ipynb b/molla/mollaStatica2.ipynb new file mode 100644 index 0000000..9b704af --- /dev/null +++ b/molla/mollaStatica2.ipynb @@ -0,0 +1,884 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 29, + "id": "f34c5b88", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import scipy as sc\n", + "from scipy.stats import chi2\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "import statsmodels.api as sm\n", + "\n", + "\n", + "g = 9.806\n", + "ug = 0.001" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "08efb2be", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'\\ndf[\"K\"] = df.m * g / df.Dx\\ndf[\"uK\"] = np.sqrt( (df.m * g / df.Dx**2)**2 * df.uDx**2 + (g/df.Dx)**2 * df.um**2 + (df.m / df.Dx)**2 * ug**2)\\n\\ndf[\"F\"] = df.m * g\\ndf[\"uF\"] = np.sqrt( df.m**2 * ug**2 + g**2 * df.um**2)\\nmedia_K, sigma_K = mediaPesata(df[\"K\"], df[\"uK\"])\\n\\n\\n#chi 2\\nchi2_val = np.sum((df[\"K\"] - media_K)**2 / df[\"uK\"]**2) # formula corretta\\ndof = len(df[\"K\"]) - 1 # -1 perché stimi solo la media\\nchi2_rid = chi2_val / dof\\np_value = 1 - sc.stats.chi2.cdf(chi2_val, dof)\\n\\nprint(\"#\"*60)\\nprint(\"Valori di K\")\\nprint(\"media pesata K:\", media_K)\\nprint(\"sigma K:\", sigma_K)\\nprint(f\"Chi2 : {chi2_val:.4f}\")\\nprint(f\"DOF : {dof}\")\\nprint(f\"Chi2 ridotto : {chi2_rid:.4f} (ideale ~ 1)\")\\nprint(f\"p-value : {p_value:.4f}\")\\n'" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_csv(r'statica2.csv')\n", + "\n", + "def calcola_Dx_stats(df, err_arbitrario_DX):\n", + " dx_cols = [col for col in df.columns if col.startswith('Dx')]\n", + " \n", + " def riga_stats(row):\n", + " valori = row[dx_cols].dropna()\n", + " n = len(valori)\n", + " \n", + " if n == 0:\n", + " return pd.Series({'Dx': np.nan, 'uDx': np.nan})\n", + " elif n == 1:\n", + " return pd.Series({'Dx': valori.iloc[0], 'uDx': err_arbitrario_DX})\n", + " else:\n", + " media = valori.mean()\n", + " sigma = valori.std(ddof=1) # sigma sperimentale S\n", + " return pd.Series({'Dx': media, 'uDx': sigma})\n", + " \n", + " stats = df.apply(riga_stats, axis=1)\n", + " df['Dx'] = stats['Dx']\n", + " df['uDx'] = stats['uDx']\n", + " \n", + " return df\n", + "\n", + "def calcola_m_stats(df, err_arbitrario_m):\n", + " m_cols = [col for col in df.columns if col.startswith('m')]\n", + " \n", + " def riga_stats(row):\n", + " valori = row[m_cols].dropna()\n", + " n = len(valori)\n", + " \n", + " if n == 0:\n", + " return pd.Series({'m': np.nan, 'um': np.nan})\n", + " elif n == 1:\n", + " return pd.Series({'m': valori.iloc[0], 'um': err_arbitrario_m})\n", + " else:\n", + " media = valori.mean()\n", + " sigma = valori.std(ddof=1) # sigma sperimentale S\n", + " return pd.Series({'m': media, 'um': sigma})\n", + " \n", + " stats = df.apply(riga_stats, axis=1)\n", + " df['m'] = stats['m']\n", + " df['um'] = stats['um']\n", + " \n", + " return df\n", + "\n", + "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", + "df = calcola_Dx_stats(df, err_arbitrario_DX=0.01)\n", + "df = calcola_m_stats(df, err_arbitrario_m=0.0028867513)\n", + "\n", + "\n", + "\n", + "'''\n", + "df[\"K\"] = df.m * g / df.Dx\n", + "df[\"uK\"] = np.sqrt( (df.m * g / df.Dx**2)**2 * df.uDx**2 + (g/df.Dx)**2 * df.um**2 + (df.m / df.Dx)**2 * ug**2)\n", + "\n", + "df[\"F\"] = df.m * g\n", + "df[\"uF\"] = np.sqrt( df.m**2 * ug**2 + g**2 * df.um**2)\n", + "media_K, sigma_K = mediaPesata(df[\"K\"], df[\"uK\"])\n", + "\n", + "\n", + "#chi 2\n", + "chi2_val = np.sum((df[\"K\"] - media_K)**2 / df[\"uK\"]**2) # formula corretta\n", + "dof = len(df[\"K\"]) - 1 # -1 perché stimi solo la media\n", + "chi2_rid = chi2_val / dof\n", + "p_value = 1 - sc.stats.chi2.cdf(chi2_val, dof)\n", + "\n", + "print(\"#\"*60)\n", + "print(\"Valori di K\")\n", + "print(\"media pesata K:\", media_K)\n", + "print(\"sigma K:\", sigma_K)\n", + "print(f\"Chi2 : {chi2_val:.4f}\")\n", + "print(f\"DOF : {dof}\")\n", + "print(f\"Chi2 ridotto : {chi2_rid:.4f} (ideale ~ 1)\")\n", + "print(f\"p-value : {p_value:.4f}\")\n", + "'''" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "5494409f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " m1 Dx1 Dx2 Dx3 Dx4 Dx5 Dx6 Dx \\\n", + "0 49.246667 212.10 211.64 212.00 212.18 212.52 212.04 212.080000 \n", + "1 69.276667 150.92 150.26 150.02 150.16 150.40 150.18 150.323333 \n", + "2 88.966667 90.34 90.34 90.38 90.52 90.26 90.28 90.353333 \n", + "3 108.610000 29.82 30.18 30.10 30.20 30.10 30.40 30.133333 \n", + "\n", + " uDx m um \n", + "0 0.284816 49.246667 0.002887 \n", + "1 0.317847 69.276667 0.002887 \n", + "2 0.092664 88.966667 0.002887 \n", + "3 0.188750 108.610000 0.002887 " + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "976d5531", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]\n", + "############################################################\n", + "[ 61.75666667 121.72666667 181.94666667 59.97 120.19\n", + " 60.22 ]\n", + "[0.42678644 0.29951071 0.34168211 0.33107904 0.36966652 0.21026967]\n", + "############################################################\n", + "[-20.03 -39.72 -59.36333333 -19.69 -39.33333333\n", + " -19.64333333]\n", + "[0.00408248 0.00408248 0.00408248 0.00408248 0.00408248 0.00408248]\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.Dx[x] - df.Dx[j] for x,j in perm])\n", + "ueste = np.array([np.sqrt(df.uDx[x]**2 + df.uDx[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", + "\n", + "print(\"#\"* 60)\n", + "print(este)\n", + "print(ueste)\n", + "\n", + "print(\"#\"* 60)\n", + "print(masse)\n", + "print(umasse)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "2ad19283", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[3.18045307 3.19974522 3.19938176 3.21961214 3.2091078 3.19864707]\n", + "[0.02199135 0.00788665 0.00602107 0.01779022 0.00988124 0.01119321]\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": 34, + "id": "5f59d6c9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "K-medio: 3.201234977342435\n", + "sigmaC: 0.003860115909468001\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": 35, + "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: 1.277e+05\n", + "Date: Wed, 01 Apr 2026 Prob (F-statistic): 3.68e-10\n", + "Time: 11:24:04 Log-Likelihood: -7.2416\n", + "No. Observations: 6 AIC: 18.48\n", + "Df Residuals: 4 BIC: 18.07\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0265 0.991 0.027 0.980 -2.724 2.777\n", + "este 3.2011 0.009 357.408 0.000 3.176 3.226\n", + "==============================================================================\n", + "Omnibus: nan Durbin-Watson: 1.155\n", + "Prob(Omnibus): nan Jarque-Bera (JB): 0.275\n", + "Skew: -0.058 Prob(JB): 0.871\n", + "Kurtosis: 1.957 Cond. No. 271.\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) = 3.20112 ± 0.00896\n", + "intercetta = 0.02655 ± 0.99066\n", + "R² = 0.99997\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; 6 samples were given.\n", + " warn(\"omni_normtest is not valid with less than 8 observations; %i \"\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}\")\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "1d42b009", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "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": 37, + "id": "986ff4a6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Chi^2 = 2.77690\n", + "Gradi di libertà = 4\n", + "Chi^2 ridotto = 0.69422\n", + "Probabilità P(0 → chi^2) = 0.40417\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": 38, + "id": "ef0817f4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0 0.908593\n", + "1 0.040832\n", + "2 0.097969\n", + "3 1.041093\n", + "4 0.620683\n", + "5 0.067728\n", + "dtype: float64" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "((data[\"F\"] - F_fit) / sigma)**2" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "cebe6742", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " este ueste F uF\n", + "0 61.756667 0.426786 196.414180 0.044764\n", + "1 121.726667 0.299511 389.494320 0.056394\n", + "2 181.946667 0.341682 582.116847 0.071601\n", + "3 59.970000 0.331079 193.080140 0.044613\n", + "4 120.190000 0.369667 385.702667 0.056123\n", + "5 60.220000 0.210270 192.622527 0.044592" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "2d4b7144", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ax + B : \n", + "A = 3.2002 +- 0.0092\n", + "B = 0.1195 +- 0.9523\n", + "cov_AB = -0.007941\n", + "p-value chi² = 0.4020\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:.4f} +- {sA:.4f}\")\n", + "print(f\"B = {B:.4f} +- {sB:.4f}\")\n", + "print(f\"cov_AB = {covAB:.6f}\")\n", + "print(f\"p-value chi² = {chi:.4f}\")\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "32e9948f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Chi^2 = 2.76835\n", + "Gradi di libertà = 4\n", + "Chi^2 ridotto = 0.69209\n", + "Probabilità P(0 → chi^2) = 0.40269\n" + ] + } + ], + "source": [ + "F_fit = B + A * data[\"este\"]\n", + "sigma = 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": 42, + "id": "e2407a04", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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" + ] + } + ], + "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 +} diff --git a/molla/statica1.csv b/molla/statica1.csv new file mode 100644 index 0000000..aebbd50 --- /dev/null +++ b/molla/statica1.csv @@ -0,0 +1,6 @@ +m1,Dx1,Dx2,Dx3,Dx4,Dx5,Dx6 +88.970,77.26,77.28,77.26,77.28,77.24,77.42 +108.61,68.92,68.94,69.00,68.98,68.90,69.02 +128.64,60.88,61.00,60.82,60.94,61.08,60.94 +148.38,52.96,52.96,52.78,52.88,52.88,53.00 +168.53,44.42,44.68,44.48,44.80,44.92,44.52 \ No newline at end of file diff --git a/molla/statica2.csv b/molla/statica2.csv new file mode 100644 index 0000000..8f38853 --- /dev/null +++ b/molla/statica2.csv @@ -0,0 +1,5 @@ +m1,Dx1,Dx2,Dx3,Dx4,Dx5,Dx6 +49.2466666666667,212.10,211.64,212.00,212.18,212.52,212.04 +69.2766666666667,150.92,150.26,150.02,150.16,150.40,150.18 +88.9666666666667,90.34,90.34,90.38,90.52,90.26,90.28 +108.61,29.82,30.18,30.10,30.20,30.10,30.40