{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9c25e271",
   "metadata": {},
   "outputs": [],
   "source": [
    "import importlib\n",
    "from statlib import *\n",
    "\n",
    "g  = 9.806\n",
    "ug = 0.004"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "233e717f",
   "metadata": {},
   "source": [
    "# Calcolo w0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e1efad4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# k e m varie configurazioni\n",
    "\n",
    "# k [N/m]\n",
    "k1  = 23.631\n",
    "uk1 = 0.017\n",
    "\n",
    "k2  = 3.2053\n",
    "uk2 = 0.0013\n",
    "\n",
    "# m [g]\n",
    "m_CD   = [63.13, 83.04, 103.02, 122.83, 142.77, 162.44, 182.33]\n",
    "m_rete = [58.96, 78.86,  98.85, 118.66, 138.61, 158.26, 178.16]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81d935ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creazione Data\n",
    "\n",
    "df = pd.DataFrame()\n",
    "df[\"m_CD\"]    = m_CD\n",
    "df[\"um_CD\"]   = 0.01/np.sqrt(12)\n",
    "df[\"m_rete\"]  = m_rete\n",
    "df[\"um_rete\"] = 0.01/np.sqrt(12)\n",
    "df[\"k1\"]      = k1\n",
    "df[\"uk1\"]     = uk1\n",
    "df[\"k2\"]      = k2\n",
    "df[\"uk2\"]     = uk2\n",
    "\n",
    "param_sistema = Data(df)\n",
    "param_sistema.analisi_stat = df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7b2c2af7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a5b577c48b9e41549f4804af6032b481",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Sheet(cells=(Cell(column_end=0, column_start=0, row_end=6, row_start=0, squeeze_row=False, type='numeric', val…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calcolo w0 varie cnfigurazioni\n",
    "\n",
    "m_CD, m_rete, k1, k2 = sp.symbols('m_CD, m_rete, k1, k2', positive=True)\n",
    "\n",
    "w0_1_CD   = sp.sqrt(k1/(m_CD/1000))\n",
    "w0_1_rete = sp.sqrt(k1/(m_rete/1000))\n",
    "w0_2_CD   = sp.sqrt(k2/(m_CD/1000))\n",
    "w0_2_rete = sp.sqrt(k2/(m_rete/1000))\n",
    "\n",
    "param_sistema = param_sistema.calc_var(w0_1_CD, \"w0_1_CD\")\n",
    "param_sistema = param_sistema.calc_var(w0_1_rete, \"w0_1_rete\")\n",
    "param_sistema = param_sistema.calc_var(w0_2_CD, \"w0_2_CD\")\n",
    "param_sistema = param_sistema.calc_var(w0_2_rete, \"w0_2_rete\")\n",
    "\n",
    "sheet = ipysheet.from_dataframe(param_sistema.analisi_stat)\n",
    "display(sheet)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecf23a81",
   "metadata": {},
   "source": [
    "# Creazione classi dati\n",
    "\n",
    "Selezione picchi delle oscillazioni"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c040f35e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# config = [molla1_leggera_rete_inizio, molla1_leggera_rete_fine, molla1_leggera_rete_mid,\n",
    "#           molla1_pesante_rete_inizio, molla1_pesante_rete_fine, molla1_pesante_rete_mid,\n",
    "#           molla1_leggera_CD_inizio,   molla1_leggera_CD_fine,   molla1_leggera_CD_mid,\n",
    "#           molla1_pesante_CD_inizio,   molla1_pesante_CD_fine,   molla1_pesante_CD_mid,\n",
    "#           molla2_leggera_rete_inizio, molla2_leggera_rete_fine, molla2_leggera_rete_mid,\n",
    "#           molla2_pesante_rete_inizio, molla2_pesante_rete_fine, molla2_pesante_rete_mid,\n",
    "#           molla2_leggera_CD_inizio,   molla2_leggera_CD_fine,   molla2_leggera_CD_mid,\n",
    "#           molla2_pesante_CD_inizio,   molla2_pesante_CD_fine,   molla2_pesante_CD_mid]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c9611e53",
   "metadata": {},
   "outputs": [],
   "source": [
    "h = [0.51415, 0.4983, 0.485, 0.4735]\n",
    "df = pd.DataFrame()\n",
    "df[\"h\"] = h\n",
    "molla2_leggera_rete_inizio = Data(df)\n",
    "molla2_leggera_rete_inizio.analisi_stat = df\n",
    "\n",
    "h = [0.5121, 0.498, 0.4856, 0.47389]\n",
    "df = pd.DataFrame()\n",
    "df[\"h\"] = h\n",
    "molla2_leggera_CD_inizio = Data(df)\n",
    "molla2_leggera_CD_inizio.analisi_stat = df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3014c983",
   "metadata": {},
   "outputs": [],
   "source": [
    "config = [molla2_leggera_rete_inizio,\n",
    "          molla2_leggera_CD_inizio]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28734bca",
   "metadata": {},
   "source": [
    "# Calcolo A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "00b5d09c",
   "metadata": {},
   "outputs": [],
   "source": [
    "molla2_leggera_CD_inizio.analisi_stat[\"h1\"] = molla2_leggera_CD_inizio.analisi_stat[\"h\"][1]\n",
    "molla2_leggera_CD_inizio.analisi_stat[\"h2\"] = molla2_leggera_CD_inizio.analisi_stat[\"h\"][2]\n",
    "\n",
    "molla2_leggera_rete_inizio.analisi_stat[\"h1\"] = molla2_leggera_rete_inizio.analisi_stat[\"h\"][1]\n",
    "molla2_leggera_rete_inizio.analisi_stat[\"h2\"] = molla2_leggera_rete_inizio.analisi_stat[\"h\"][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2e3e28c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo numerico x e y\n",
    "\n",
    "for data in config:\n",
    "    data.analisi_stat[\"h1\"] = data.analisi_stat[\"h\"][1]\n",
    "    data.analisi_stat[\"h2\"] = data.analisi_stat[\"h\"][2]\n",
    "    data.analisi_stat[\"uh1\"] = 0.001\n",
    "    data.analisi_stat[\"uh2\"] = 0.001\n",
    "    data.analisi_stat[\"uh\"] = 0.001\n",
    "    data.analisi_stat[\"n\"] = [1, 2, 3, 4]\n",
    "    data.analisi_stat[\"un\"] = 0.000000001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "857214ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "h, h1, h2 = sp.symbols('h h1 h2')\n",
    "h0 = (h*h2-h1**2) / (2*h1 + h + h2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4c030372",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b83544b403c04d0493ef734f9dc039ab",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Sheet(cells=(Cell(column_end=0, column_start=0, row_start=0, squeeze_row=False, type='numeric', value=[0.51415…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ab432f011593444aa2d42ae9fe4f3601",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Sheet(cells=(Cell(column_end=0, column_start=0, row_start=0, squeeze_row=False, type='numeric', value=[0.5121,…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calcolo numerico x e y\n",
    "\n",
    "for data in config:\n",
    "    data = data.calc_var(h0, \"h0\")\n",
    "    sheet = ipysheet.from_dataframe(data.analisi_stat)\n",
    "    display(sheet)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b522bfe",
   "metadata": {},
   "source": [
    "# Rgressione lineare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30f903b5",
   "metadata": {},
   "source": [
    "## Attrito proporzionale a v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "64e483e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo simbolico x e y\n",
    "\n",
    "# x = n-1\n",
    "n = sp.Symbol('n', positive=True)\n",
    "x = n-1\n",
    "\n",
    "# y = ln(h1/hn)\n",
    "h1, hn = sp.symbols('h1 hn', positive=True)\n",
    "y = sp.ln(h1/hn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b0df03fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo numerico x e y\n",
    "\n",
    "for data in config:\n",
    "    data = data.calc_var(x, \"x\")\n",
    "    data = data.calc_var(y, \"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "497ed583",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regressione\n",
    "\n",
    "for data in config:\n",
    "    data = data.reg_lin(stampa_param=True, plot_regressione=True, calc_residui=True,\n",
    "                            x_label=\"\", y_label=\"\", r_label=\"\",\n",
    "                            titolo_reg=\"\", titolo_residui=\"\",\n",
    "                            cd_A=4, cd_B=4, scala_barre=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "453d5b53",
   "metadata": {},
   "source": [
    "## Attrito proporzionale a v^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cdb8d336",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo simbolico x e y\n",
    "\n",
    "# x = n-1\n",
    "n = sp.Symbol('n', positive=True)\n",
    "x = n-1\n",
    "\n",
    "# y = 1/hn - 1/h1\n",
    "h1, hn = sp.symbols('h1 hn', positive=True)\n",
    "y = 1/hn - 1/h1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84ad3d64",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo numerico x e y\n",
    "\n",
    "for data in config:\n",
    "    data = data.calc_var(x, \"x\")\n",
    "    data = data.calc_var(y, \"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8fee50b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regressione\n",
    "\n",
    "for data in config:\n",
    "    data = data.reg_lin(stampa_param=True, plot_regressione=True, calc_residui=True,\n",
    "                            x_label=\"\", y_label=\"\", r_label=\"\",\n",
    "                            titolo_reg=\"\", titolo_residui=\"\",\n",
    "                            cd_A=4, cd_B=4, scala_barre=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc3ce36f",
   "metadata": {},
   "source": [
    "# Stima errore campionamento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "513736c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_max =\n",
    "w0_max =\n",
    "fc = 50     # [Hz]\n",
    "\n",
    "err_picco_max = A_max * (1 - np.cos(w0_max / (2*fc)))\n",
    "print(f\"errore massimo individuazione picco > {err_picco_max}\")"
   ]
  }
 ],
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