ncp_2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b412c931",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9a0fd095",
   "metadata": {},
   "outputs": [],
   "source": [
    "u_y = np.array(\n",
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    " (1450000, 6873.477335306202), (1460000, 6894.590302875795), (1470000, 6906.236341919776), \n",
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    " (2620000, 7000.0), (2630000, 7000.0), (2640000, 7000.0), (2650000, 7000.0), (2660000, 7000.0), \n",
    " (2670000, 7000.0), (2680000, 7000.0), (2690000, 7000.0), (2700000, 7000.0), (2710000, 7000.0), \n",
    " (2720000, 7000.0), (2730000, 7000.0), (2740000, 7000.0), (2750000, 7000.0), (2760000, 7000.0), \n",
    " (2770000, 7000.0), (2780000, 7000.0), (2790000, 7000.0), (2800000, 7000.0), (2810000, 7000.0), \n",
    " (2820000, 7000.0), (2830000, 7000.0), (2840000, 7000.0), (2850000, 7000.0), (2860000, 7000.0), \n",
    " (2870000, 7000.0), (2880000, 7000.0), (2890000, 7000.0), (2900000, 7000.0), (2910000, 7000.0), \n",
    " (2920000, 7000.0), (2930000, 7000.0), (2940000, 7000.0), (2950000, 7000.0), (2960000, 7000.0), \n",
    " (2970000, 7000.0), (2980000, 7000.0), (2990000, 7000.0), (3000000, 7000.0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1aefe328",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "`xtol` termination condition is satisfied.\n",
      "Function evaluations 42, initial cost 1.8604e+09, final cost 2.0292e+06, first-order optimality 7.76e+20.\n",
      "`ftol` termination condition is satisfied.\n",
      "Function evaluations 224, initial cost 1.8604e+09, final cost 1.4090e+06, first-order optimality 1.26e+18.\n"
     ]
    }
   ],
   "source": [
    "import scipy\n",
    "import numpy as np\n",
    "\n",
    "def model_pow_frac(x,u):\n",
    "    return x[0]*(u**2+x[1]*u)/(u**2+x[2]*u+x[3])\n",
    "def model_pow2(x,u):\n",
    "    return np.divide(x[0]*u**3+x[1]*u**2+x[2]*u+x[3],u**3+x[4]*u**2+x[5]*u+x[6])\n",
    "\n",
    "def fun_pow_frac(x,u,y):\n",
    "    return model_pow_frac(x,u) - y\n",
    "def fun_pow2(x,u,y):\n",
    "    return model_pow2(x,u) - y\n",
    "\n",
    "def jac_pow_frac(x, u, y):\n",
    "    J = np.empty((u.size, x.size))\n",
    "    J[:, 0] = (u**2+x[1]*u)/(u**2+x[2]*u+x[3])\n",
    "    J[:, 1] = (x[0]*u)/(u**2+x[2]*u+x[3])\n",
    "    J[:, 2] = -x[0]*(u**2+x[1]*u)*u/((u**2+x[2]*u+x[3])**2)\n",
    "    J[:, 3] = -x[0]*(u**2+x[1]*u)/((u**2+x[2]*u+x[3])**2)\n",
    "    return J\n",
    "def jac_pow2(x, u, y):\n",
    "    J = np.empty((u.size, x.size))\n",
    "    J[:, 0] = np.divide(u**3,u**3+x[4]*u**2+x[5]*u+x[6])\n",
    "    J[:, 1] = np.divide(u**2,u**3+x[4]*u**2+x[5]*u+x[6])\n",
    "    J[:, 2] = np.divide(u,u**3+x[4]*u**2+x[5]*u+x[6])\n",
    "    J[:, 3] = np.divide(1,u**3+x[4]*u**2+x[5]*u+x[6])\n",
    "    J[:, 4] = -np.divide((x[0]*u**3+x[1]*u**2+x[2]*u+x[3])*u**2,(u**3+x[4]*u**2+x[5]*u+x[6])**2)\n",
    "    J[:, 5] = -np.divide((x[0]*u**3+x[1]*u**2+x[2]*u+x[3])*u,(u**3+x[4]*u**2+x[5]*u+x[6])**2)\n",
    "    J[:, 6] = -np.divide((x[0]*u**3+x[1]*u**2+x[2]*u+x[3]),(u**3+x[4]*u**2+x[5]*u+x[6])**2)\n",
    "    return J\n",
    "\n",
    "u = np.arange(140000,2670000,25450) #media degli N\n",
    "y = np.array([\n",
    "    300,700,1050,1300,1550,1800,2050,2300,2400,2600,\n",
    "    2950,3000,3200,3300,3700,3800,4000,4150,4200,4400,\n",
    "    4550,4700,4800,5000,5100,5300,5250,5400,5600,5700,\n",
    "    5900,5900,6100,6300,6300,6350,6350,6500,6500,6700,\n",
    "    6600,6650,6650,6650,6700,6750,6750,6750,6750,6850,\n",
    "    6850,6850,6900,6900,6900,7000,7000,7000,7000,7000,\n",
    "    7000,7000,7000,7000,7000,7000,7000,7000,7000,7000,\n",
    "    7000,7000,7000,7000,7000,7000,7000,7000,7000,7000,\n",
    "    7000,7000,7000,7000,7000,7000,7000,7000,7000,7000,\n",
    "    7000,7000,7000,7000,7000,7000,7000,7000,7000,7000  ])#ncp_prior per ottimizzarlo\n",
    "\n",
    "\n",
    "x_0_pow_frac = np.array([1,1,1,1])\n",
    "x_0_pow2 = np.array([1,1,1,1,1,1,1])\n",
    "res_pow_frac = scipy.optimize.least_squares(fun_pow_frac, x_0_pow_frac, jac=jac_pow_frac, bounds=(0, 1e20), args=(u, y), verbose=1)\n",
    "res_pow2 = scipy.optimize.least_squares(fun_pow2, x_0_pow2, jac=jac_pow2, bounds=(-1e20, 1e20), args=(u, y), verbose=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1c2c9ee5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.96410616e+03 2.41636813e+06 3.55995027e+05 1.48055084e+12]\n",
      "[ 7.09902870e+03 -6.29735501e+07  2.47170653e+13 -6.85948955e+07\n",
      " -1.12139198e+05  2.74181065e+11  1.15222487e+12]\n"
     ]
    }
   ],
   "source": [
    "print(res_pow_frac.x)\n",
    "print(res_pow2.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "50d892d7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "625.2921448473121\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "u_test = np.linspace(1e5,1e7,1000)                           #valori test di N\n",
    "y_test_pow_frac = model_pow_frac(res_pow_frac.x, u_test)\n",
    "y_test_pow2 = model_pow2(res_pow2.x, u_test)\n",
    "print(model_pow2(res_pow2.x,150000))\n",
    "plt.plot(u, y, 'o', markersize=4, label='data')\n",
    "#plt.plot(u_test, y_test_pow_frac, label='fitted pow_frac model')\n",
    "plt.plot(u_test, y_test_pow2, label='fitted pow2 model')\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"ncp_prior\")\n",
    "plt.legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e225979d",
   "metadata": {},
   "source": [
    "Using this model we have bad real results since least squares leaves too much room for error and a value that is just a little bit too small can result in too many blocks, thus the chosen strategy is a spline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bbbff1f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import CubicSpline, PchipInterpolator, Akima1DInterpolator\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "u_test = np.linspace(1e5,1e7,1000) \n",
    "u_y = np.array(\n",
    "[(100000, -196.2940415015209), (110000, -103.7090822941733), (120000, 13.791983467728102), \n",
    " (130000, 150.32354712038529), (140000, 300.0), (150000, 456.9357334427741), \n",
    " (160000, 615.2451387849095), (170000, 769.0426073626077), (180000, 912.4425305120708), \n",
    " (190000, 1039.5592995695006), (200000, 1146.6567688625566), (210000, 1241.275883981712), \n",
    " (220000, 1334.5308572856504), (230000, 1432.1128285531624), (240000, 1531.983249843333), \n",
    " (250000, 1631.6887098203943), (260000, 1729.9999384279372), (270000, 1826.227688353349), \n",
    " (280000, 1921.731710805428), (290000, 2021.5849606132467), (300000, 2129.526794729129), \n",
    " (310000, 2233.2305757248723), (320000, 2311.6803186474867), (330000, 2356.2524255234966), \n",
    " (340000, 2387.366888764701), (350000, 2429.1048274962022), (360000, 2499.626890218608), \n",
    " (370000, 2612.9822156774767), (380000, 2766.4999740577014), (390000, 2907.342876184784), \n",
    " (400000, 2976.958008987681), (410000, 2984.8418908912945), (420000, 3000.2133346825117), \n",
    " (430000, 3072.2946071985752), (440000, 3163.523140623286), (450000, 3217.111630523897), \n",
    " (460000, 3236.3717122166304), (470000, 3291.3272473974002), (480000, 3434.6707198886857), \n",
    " (490000, 3611.577851531317), (500000, 3733.9108453381855), (510000, 3774.8817914281317), \n",
    " (520000, 3793.9870014880653), (530000, 3848.327925644581), (540000, 3934.4495001727046), \n",
    " (550000, 4023.6880261325523), (560000, 4095.198916129244), (570000, 4142.2803859913665), \n",
    " (580000, 4162.134384895589), (590000, 4174.256346571001), (600000, 4210.031402086732), \n",
    " (610000, 4283.934618571861), (620000, 4371.375600599834), (630000, 4444.357812704114), \n",
    " (640000, 4500.711755730153), (650000, 4555.9151801188655), (660000, 4618.958879392718), \n",
    " (670000, 4678.54217763008), (680000, 4720.787753185267), (690000, 4752.960534254824), \n",
    " (700000, 4800.639512674851), (710000, 4879.487815685128), (720000, 4964.326232528083), \n",
    " (730000, 5021.3479882104775), (740000, 5051.687985762398), (750000, 5094.764551060448), \n",
    " (760000, 5179.103851336002), (770000, 5267.8650523262495), (780000, 5304.511360541746), \n",
    " (790000, 5279.951974729595), (800000, 5250.942520175716), (810000, 5270.8320952179765), \n",
    " (820000, 5337.4999838380745), (830000, 5426.016212786224), (840000, 5514.414763873945), \n",
    " (850000, 5586.086980921798), (860000, 5628.398211497241), (870000, 5659.5606806436945), \n",
    " (880000, 5714.006373544878), (890000, 5802.682117475), (900000, 5883.059489732281), \n",
    " (910000, 5910.087472361603), (920000, 5898.399085055407), (930000, 5902.86606922961), \n",
    " (940000, 5960.57385312554), (950000, 6054.317169401872), (960000, 6157.210656236934), \n",
    " (970000, 6245.9856583129895), (980000, 6300.465740490168), (990000, 6310.103076399633), \n",
    " (1000000, 6300.789201352866), (1010000, 6306.05298723126), (1020000, 6330.92359116326), \n",
    " (1030000, 6349.6098170607165), (1040000, 6343.442313423734), (1050000, 6337.156166762502), \n",
    " (1060000, 6368.222478491959), (1070000, 6437.412551555299), (1080000, 6495.236172274472), \n",
    " (1090000, 6500.030735452649), (1100000, 6485.918209921648), (1110000, 6517.2031475941785), \n",
    " (1120000, 6608.96915612123), (1130000, 6690.427537505028), (1140000, 6692.516558884732), \n",
    " (1150000, 6637.684034954056), (1160000, 6595.999721237238), (1170000, 6606.866325140376), \n",
    " (1180000, 6640.339239319563), (1190000, 6659.582814603485), (1200000, 6657.993934610502), \n",
    " (1210000, 6649.088081971744), (1220000, 6644.046575489862), (1230000, 6646.26379922899), \n",
    " (1240000, 6657.567265694911), (1250000, 6676.842434537024), (1260000, 6700.492090574146), \n",
    " (1270000, 6724.518897614738), (1280000, 6743.7113889813145), (1290000, 6752.803776289019), \n",
    " (1300000, 6752.536867324852), (1310000, 6750.062932294076), (1320000, 6751.01993639146), \n",
    " (1330000, 6752.02517872621), (1340000, 6747.138738380322), (1350000, 6739.8703227876495), \n",
    " (1360000, 6746.500953373964), (1370000, 6779.932640040183), (1380000, 6825.175870289963), \n",
    " (1390000, 6856.252166047541), (1400000, 6861.268609698072), (1410000, 6852.5836808043605), \n",
    " (1420000, 6844.1614455502795), (1430000, 6843.134700131197), (1440000, 6853.098070467249), \n",
    " (1450000, 6873.477335306202), (1460000, 6894.590302875795), (1470000, 6906.236341919776), \n",
    " (1480000, 6906.484123178069), (1490000, 6898.835930978074), (1500000, 6889.447332862699), \n",
    " (1510000, 6891.750217934312), (1520000, 6919.202719966802), (1530000, 6963.995593289019), \n",
    " (1540000, 7000.606551112646), (1550000, 7010.654181870235), (1560000, 7004.263540529191), \n",
    " (1570000, 6997.780027132758), (1580000, 6997.647902911536), (1590000, 6999.879932764492), \n",
    " (1600000, 7000.766219223369), (1610000, 7000.364404404361), (1620000, 6999.860794943026), \n",
    " (1630000, 6999.820239461689), (1640000, 6999.978400427554), (1650000, 7000.054354956158), \n",
    " (1660000, 7000.030298082164), (1670000, 6999.991757326904), (1680000, 6999.9864276463195), \n",
    " (1690000, 6999.997445678717), (1700000, 7000.003797022601), (1710000, 7000.002464048843), \n",
    " (1720000, 6999.999556927054), (1730000, 6999.998987230106), (1740000, 6999.9997406203265), \n",
    " (1750000, 7000.000260529659), (1760000, 7000.000196733262), (1770000, 6999.99998060138), \n",
    " (1780000, 6999.999925304678), (1790000, 6999.999975725942), (1800000, 7000.00001749045), \n",
    " (1810000, 7000.000015459508), (1820000, 6999.999999629206), (1830000, 6999.999994556318), \n",
    " (1840000, 6999.999997843628), (1850000, 7000.00000114195), (1860000, 7000.0000011977445), \n",
    " (1870000, 7000.000000056484), (1880000, 6999.999999608222), (1890000, 6999.9999998153735), \n",
    " (1900000, 7000.000000071788), (1910000, 7000.000000091602), (1920000, 7000.000000010658), \n",
    " (1930000, 6999.999999972186), (1940000, 6999.999999984629), (1950000, 7000.000000004267), \n",
    " (1960000, 7000.00000000692), (1970000, 7000.000000001277), (1980000, 6999.999999998055), \n",
    " (1990000, 6999.9999999987485), (2000000, 7000.000000000232), (2010000, 7000.000000000517), \n",
    " (2020000, 7000.000000000131), (2030000, 6999.999999999866), (2040000, 6999.9999999999), \n",
    " (2050000, 7000.00000000001), (2060000, 7000.000000000038), (2070000, 7000.000000000012), \n",
    " (2080000, 6999.999999999991), (2090000, 6999.999999999992), (2100000, 7000.0), \n",
    " (2110000, 7000.000000000003), (2120000, 7000.000000000001), (2130000, 6999.999999999999), \n",
    " (2140000, 6999.999999999999), (2150000, 7000.0), (2160000, 7000.0), (2170000, 7000.0), \n",
    " (2180000, 7000.0), (2190000, 7000.0), (2200000, 7000.000000000001), (2210000, 7000.0), \n",
    " (2220000, 7000.0), (2230000, 7000.0), (2240000, 7000.0), (2250000, 7000.0), (2260000, 7000.0), \n",
    " (2270000, 7000.0), (2280000, 7000.0), (2290000, 7000.0), (2300000, 7000.0), (2310000, 7000.0), \n",
    " (2320000, 7000.0), (2330000, 7000.0), (2340000, 7000.0), (2350000, 7000.0), (2360000, 7000.0), \n",
    " (2370000, 7000.0), (2380000, 7000.0), (2390000, 7000.0), (2400000, 7000.0), (2410000, 7000.0), \n",
    " (2420000, 7000.0), (2430000, 7000.0), (2440000, 7000.0), (2450000, 7000.0), (2460000, 7000.0), \n",
    " (2470000, 7000.0), (2480000, 7000.0), (2490000, 7000.0), (2500000, 7000.0), (2510000, 7000.0), \n",
    " (2520000, 7000.0), (2530000, 7000.0), (2540000, 7000.0), (2550000, 7000.0), (2560000, 7000.0), \n",
    " (2570000, 7000.0), (2580000, 7000.0), (2590000, 7000.0), (2600000, 7000.0), (2610000, 7000.0), \n",
    " (2620000, 7000.0), (2630000, 7000.0), (2640000, 7000.0), (2650000, 7000.0), (2660000, 7000.0), \n",
    " (2670000, 7000.0), (2680000, 7000.0), (2690000, 7000.0), (2700000, 7000.0), (2710000, 7000.0), \n",
    " (2720000, 7000.0), (2730000, 7000.0), (2740000, 7000.0), (2750000, 7000.0), (2760000, 7000.0), \n",
    " (2770000, 7000.0), (2780000, 7000.0), (2790000, 7000.0), (2800000, 7000.0), (2810000, 7000.0), \n",
    " (2820000, 7000.0), (2830000, 7000.0), (2840000, 7000.0), (2850000, 7000.0), (2860000, 7000.0), \n",
    " (2870000, 7000.0), (2880000, 7000.0), (2890000, 7000.0), (2900000, 7000.0), (2910000, 7000.0), \n",
    " (2920000, 7000.0), (2930000, 7000.0), (2940000, 7000.0), (2950000, 7000.0), (2960000, 7000.0), \n",
    " (2970000, 7000.0), (2980000, 7000.0), (2990000, 7000.0), (3000000, 7000.0)])\n",
    "\n",
    "plt.plot(u_test, CubicSpline(u_y[:,0], u_y[:,1])(u_test), '--', label='spline')\n",
    "\n",
    "u_y = np.array([(100000, 200), (110000, 225), (120000, 270), (130000, 290), (140000, 320), (150000, 400), (160000, 615.2451387849095), (170000, 769.0426073626077), (180000, 912.4425305120708), (190000, 1039.5592995695006), (200000, 1146.6567688625566), (210000, 1241.275883981712), (220000, 1334.5308572856504), (230000, 1532.1128285531624), (240000, 1631.983249843333), (250000, 1731.6887098203943), (260000, 1829.9999384279372), (270000, 1926.227688353349), (280000, 2021.731710805428), (290000, 2121.5849606132467), (300000, 2229.526794729129), (310000, 2333.2305757248723), (320000, 2411.6803186474867), (330000, 2456.2524255234966), (340000, 2487.366888764701), (350000, 2529.1048274962022), (360000, 2600), (370000, 2712.9822156774767), (380000, 2866.4999740577014), (390000, 3007.342876184784), (400000, 3076.958008987681), (410000, 3084.8418908912945), (420000, 3100.2133346825117), (430000, 3172.2946071985752), (440000, 3263.523140623286), (450000, 3317.111630523897), (460000, 3336.3717122166304), (470000, 3391.3272473974002), (480000, 3534.6707198886857), (490000, 3711.577851531317), (500000, 3833.9108453381855), (510000, 3874.8817914281317), (520000, 3893.9870014880653), (530000, 3948.327925644581), (540000, 4034.4495001727046), (550000, 4123.6880261325523), (560000, 4195.198916129244), (570000, 4242.2803859913665), (580000, 4262.134384895589), (590000, 4274.256346571001), (600000, 4310.031402086732), (610000, 4383.934618571861), (620000, 4471.375600599834), (630000, 4544.357812704114), (640000, 4600.711755730153), (650000, 4655.9151801188655), (660000, 4718.958879392718), (670000, 4778.54217763008), (680000, 4820.787753185267), (690000, 4852.960534254824), (700000, 4900), (710000, 4979.487815685128), (720000, 5064.326232528083), (730000, 5121.3479882104775), (740000, 5151.687985762398), (750000, 5194.764551060448), (760000, 5279.103851336002), (770000, 5367.8650523262495), (780000, 5404.511360541746), (790000, 5379.951974729595), (800000, 5350.942520175716), (810000, 5370.8320952179765), (820000, 5437.4999838380745), (830000, 5526.016212786224), (840000, 5614.414763873945), (850000, 5786.086980921798), (860000, 5728.398211497241), (870000, 5759.5606806436945), (880000, 5814.006373544878), (890000, 5902.682117475), (900000, 5983.059489732281), (910000, 6010.087472361603), (920000, 5998.399085055407), (930000, 6002.86606922961), (940000, 6060.57385312554), (950000, 6154.317169401872), (960000, 6257.210656236934), (970000, 6345.9856583129895), (980000, 6400), (990000, 6410.103076399633), (1000000, 6400.789201352866), (1010000, 6406.05298723126), (1020000, 6430.92359116326), (1030000, 6449.6098170607165), (1040000, 6443.442313423734), (1050000, 6437.156166762502), (1060000, 6468.222478491959), (1070000, 6537.412551555299), (1080000, 6595.236172274472), (1090000, 6600.030735452649), (1100000, 6585.918209921648), (1110000, 6617.2031475941785), (1120000, 6708.96915612123), (1130000, 6790.427537505028), (1140000, 6792.516558884732), (1150000, 6737.684034954056), (1160000, 6695.999721237238), (1170000, 6706.866325140376), (1180000, 6740.339239319563), (1190000, 6759.582814603485), (1200000, 6757.993934610502), (1210000, 6749.088081971744), (1220000, 6744.046575489862), (1230000, 6746.26379922899), (1240000, 6757.567265694911), (1250000, 6776.842434537024), (1260000, 6800.492090574146), (1270000, 6824.518897614738), (1280000, 6843.7113889813145), (1290000, 6852.803776289019), (1300000, 6852.536867324852), (1310000, 6850.062932294076), (1320000, 6851.01993639146), (1330000, 6852.02517872621), (1340000, 6847.138738380322), (1350000, 6839.8703227876495), (1360000, 6846.500953373964), (1370000, 6879.932640040183), (1380000, 6925.175870289963), (1390000, 6956.252166047541), (1400000, 6961.268609698072), (1410000, 6952.5836808043605), (1420000, 6944.1614455502795), (1430000, 6943.134700131197), (1440000, 6953.098070467249), (1450000, 6973.477335306202), (1460000, 6974.590302875795), (1470000, 6986.236341919776), (1480000, 6986.484123178069), (1490000, 6988.835930978074), (1500000, 6989.447332862699), (1510000, 6991.750217934312), (1520000, 6989.202719966802), (1530000, 6963.995593289019), (1540000, 7000.606551112646), (1550000, 7010.654181870235), (1560000, 7004.263540529191), (1570000, 6997.780027132758), (1580000, 6997.647902911536), (1590000, 6999.879932764492), (1600000, 7000.766219223369), (1610000, 7000.364404404361), (1620000, 6999.860794943026), (1630000, 6999.820239461689), (1640000, 6999.978400427554), (1650000, 7000.054354956158), (1660000, 7000.030298082164), (1670000, 6999.991757326904), (1680000, 6999.9864276463195), (1690000, 6999.997445678717), (1700000, 7000.003797022601), (1710000, 7000.002464048843), (1720000, 6999.999556927054), (1730000, 6999.998987230106), (1740000, 6999.9997406203265),(1750000, 7000.000260529659), (1760000, 7000.000196733262), (1770000, 6999.99998060138), (1780000, 6999.999925304678), (1790000, 6999.999975725942), (1800000, 7000.00001749045), (1810000, 7000.000015459508), (1820000, 6999.999999629206), (1830000, 6999.999994556318), (1840000, 6999.999997843628), (1850000, 7000.00000114195), (1860000, 7000.0000011977445), (1870000, 7000.000000056484), (1880000, 6999.999999608222), (1890000, 6999.9999998153735), (1900000, 7000.000000071788), (1910000, 7000.000000091602), (1920000, 7000.000000010658), (1930000, 6999.999999972186), (1940000, 6999.999999984629), (1950000, 7000.000000004267), (1960000, 7000.00000000692), (1970000, 7000.000000001277), (1980000, 6999.999999998055), (1990000, 6999.9999999987485), (2000000, 7000.000000000232), (2010000, 7000.000000000517), (2020000, 7000.000000000131), (2030000, 6999.999999999866), (2040000, 6999.9999999999), (2050000, 7000.00000000001), (2060000, 7000.000000000038), (2070000, 7000.000000000012), (2080000, 6999.999999999991), (2090000, 6999.999999999992), (2100000, 7000.0), (2110000, 7000.000000000003), (2120000, 7000.000000000001), (2130000, 6999.999999999999), (2140000, 6999.999999999999), (2150000, 7000.0), (2160000, 7000.0), (2170000, 7000.0), (2180000, 7000.0), (2190000, 7000.0), (2200000, 7000.000000000001), (2210000, 7000.0), (2220000, 7000.0), (2230000, 7000.0), (2240000, 7000.0), (2250000, 7000.0), (2260000, 7000.0), (2270000, 7000.0), (2280000, 7000.0), (2290000, 7000.0), (2300000, 7000.0), (2310000, 7000.0), (2320000, 7000.0), (2330000, 7000.0), (2340000, 7000.0), (2350000, 7000.0), (2360000, 7000.0), (2370000, 7000.0), (2380000, 7000.0), (2390000, 7000.0), (2400000, 7000.0), (2410000, 7000.0), (2420000, 7000.0), (2430000, 7000.0), (2440000, 7000.0), (2450000, 7000.0), (2460000, 7000.0), (2470000, 7000.0), (2480000, 7000.0), (2490000, 7000.0), (2500000, 7000.0), (2510000, 7000.0), (2520000, 7000.0), (2530000, 7000.0), (2540000, 7000.0), (2550000, 7000.0), (2560000, 7000.0), (2570000, 7000.0), (2580000, 7000.0), (2590000, 7000.0), (2600000, 7000.0), (2610000, 7000.0), (2620000, 7000.0), (2630000, 7000.0), (2640000, 7000.0), (2650000, 7000.0), (2660000, 7000.0), (2670000, 7000.0), (2680000, 7000.0), (2690000, 7000.0), (2700000, 7000.0), (2710000, 7000.0), (2720000, 7000.0), (2730000, 7000.0), (2740000, 7000.0), (2750000, 7000.0), (2760000, 7000.0), (2770000, 7000.0), (2780000, 7000.0), (2790000, 7000.0), (2800000, 7000.0), (2810000, 7000.0), (2820000, 7000.0), (2830000, 7000.0), (2840000, 7000.0), (2850000, 7000.0), (2860000, 7000.0), (2870000, 7000.0), (2880000, 7000.0), (2890000, 7000.0), (2900000, 7000.0), (2910000, 7000.0), (2920000, 7000.0), (2930000, 7000.0), (2940000, 7000.0), (2950000, 7000.0), (2960000, 7000.0), (2970000, 7000.0), (2980000, 7000.0), (2990000, 7000.0), (3000000, 7000.0)])\n",
    "plt.plot(u_test, CubicSpline(u_y[:,0], u_y[:,1])(u_test), '--', label='spline2')\n",
    "\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"ncp_prior\")\n",
    "plt.legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5522e901",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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   "language": "python",
   "name": "python3"
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