guia2-2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import random as rnd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.sparse import lil_matrix "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1000\n",
    "y = np.array([None]*N)\n",
    "\n",
    "def llenarY(N=100):\n",
    "    for n in range(N):\n",
    "      y[n] = math.sin(((2*math.pi*n)/N)) + math.cos(((20*math.pi*n)/N))+0.1*rnd.random()\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    f = 0\n",
    "    for i in range(N):\n",
    "        aux = x[i] - y[i]\n",
    "        f += aux**2\n",
    "        if i > 0:\n",
    "            aux = x[i]-x[i-1]\n",
    "            f += 0.1*aux**2\n",
    "    return f\n",
    "\n",
    "\n",
    "# gradiente  ∇f\n",
    "def grad(x):\n",
    "    g = np.array([None]*N)\n",
    "    for i in range(N):\n",
    "        g[i] = 2.0*(x[i]-y[i])\n",
    "        if i > 0:\n",
    "            g[i] += .2*(x[i]-x[i-1])\n",
    "        if i < N-1:\n",
    "            g[i] += .2*(x[i+1]-x[i])\n",
    "    return g\n",
    "\n",
    "\n",
    "def hessiano(x):\n",
    "    a = lil_matrix((N, N))\n",
    "    for c in range(N):\n",
    "        if (c-1 >= 0):\n",
    "            a[c, c-1] = -.2\n",
    "        if (1 <= c < N-1):\n",
    "            a[c, c] = 2.4\n",
    "        else:\n",
    "            a[c, c] = 2.2\n",
    "        if (c+1 < N):\n",
    "            a[c, c+1] = -.2\n",
    "    return a \n",
    "\n",
    "    # return np.array([\n",
    "    #     [7, -5, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    #     [-5, 12, -5, 0, 0, 0, 0, 0, 0, 0],\n",
    "    #     [0, -5, 12, -5, 0, 0, 0, 0, 0, 0],\n",
    "    #     [0, 0, -5, 12, -5, 0, 0, 0, 0, 0],\n",
    "    #     [0, 0, 0, -5, 12, -5, 0, 0, 0, 0],\n",
    "    #     [0, 0, 0, 0, -5, 12, -5, 0, 0, 0],\n",
    "    #     [0, 0, 0, 0, 0, -5, 12, -5, 0, 0],\n",
    "    #     [0, 0, 0, 0, 0, 0, -5, 12, -5, 0],\n",
    "    #     [0, 0, 0, 0, 0, 0, 0, -5, 12, -5],\n",
    "    #     [0, 0, 0, 0, 0, 0, 0, 0, -5, 7]\n",
    "    # ])\n",
    "\n",
    "\n",
    "# dirección del gradiente p\n",
    "def dirgrad(x):\n",
    "    vgrad = grad(x)\n",
    "    magGrad = np.sqrt(vgrad.dot(vgrad))\n",
    "    p = -vgrad/magGrad\n",
    "    return p\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Buggfix y forma de comparar una matriz con otra.\n",
    "# N = 10\n",
    "# a = a = lil_matrix((N, N))\n",
    "# for c in range(N):\n",
    "#     if (c-1 >= 0):\n",
    "#         a[c, c-1] = -5\n",
    "#     if (1 <= c < N-1):\n",
    "#         a[c, c] = 12\n",
    "#     else:\n",
    "#         a[c, c] = 7\n",
    "#     if (c+1 < N):\n",
    "#         a[c, c+1] = -5\n",
    "\n",
    "# b = np.array([\n",
    "#         [7, -5, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "#         [-5, 12, -5, 0, 0, 0, 0, 0, 0, 0],\n",
    "#         [0, -5, 12, -5, 0, 0, 0, 0, 0, 0],\n",
    "#         [0, 0, -5, 12, -5, 0, 0, 0, 0, 0],\n",
    "#         [0, 0, 0, -5, 12, -5, 0, 0, 0, 0],\n",
    "#         [0, 0, 0, 0, -5, 12, -5, 0, 0, 0],\n",
    "#         [0, 0, 0, 0, 0, -5, 12, -5, 0, 0],\n",
    "#         [0, 0, 0, 0, 0, 0, -5, 12, -5, 0],\n",
    "#         [0, 0, 0, 0, 0, 0, 0, -5, 12, -5],\n",
    "#         [0, 0, 0, 0, 0, 0, 0, 0, -5, 7]\n",
    "#     ])\n",
    "# aAsArray=a.toarray()\n",
    "# aAsArray==b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculos de phi\n",
    "def phiAlpha(x0, alpha, p):\n",
    "    paX = x0 + p * alpha\n",
    "    return f(paX)\n",
    "\n",
    "\n",
    "def phipAlpha(x0, alpha, p):\n",
    "    x = x0 + alpha * p\n",
    "    vgrad = grad(x)\n",
    "    return (np.dot(vgrad, p))\n",
    "\n",
    "\n",
    "def phipp(x0, alpha, p):\n",
    "    x = x0 + alpha * p\n",
    "    ahess = hessiano(x)\n",
    "    return np.dot(np.dot(ahess, p), p)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gradiente Conjugado\n",
    "\n",
    "def gradienteConjugado(x0, b, k=0, tol=1e-6):\n",
    "    A = hessiano(x0)\n",
    "    r = A.dot(x0)-b\n",
    "    p = r*-1\n",
    "    print(x0)\n",
    "    print(\"k, x0, alpha, beta, Ap\")\n",
    "    rDotr = np.dot(r, r)\n",
    "    AdotP = A.dot(p)\n",
    "    while np.linalg.norm(r) >= tol:\n",
    "        alpha = rDotr / np.dot(AdotP, p)\n",
    "        x0 = x0 + alpha*p\n",
    "        r1 = r + alpha * AdotP\n",
    "        b = (np.dot(r1, r1))/rDotr\n",
    "        p = -r1 + b*p\n",
    "        # print(x0, f(x0), alpha, b)\n",
    "        print(k, x0, alpha, b, AdotP)\n",
    "        r = r1\n",
    "        rDotr = np.dot(r, r)\n",
    "        AdotP = A.dot(p)\n",
    "        k += 1\n",
    "    return x0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Descenso de Gradiente\n",
    "from timeit import default_timer as timer\n",
    "\n",
    "def exhaustivoRefinado(p, xini, alpha=0, h=0.1, tol=1e-6):\n",
    "    \"\"\"Busqueda de minimo con metodo exhaustivo refinado. puedes cambiar el paso\n",
    "    Retorna f(a) y alpha\n",
    "    \"\"\"\n",
    "    k = 0\n",
    "    while h > tol:\n",
    "        while phiAlpha(xini, alpha+h, p) < phiAlpha(xini, alpha, p):\n",
    "            alpha = alpha + h\n",
    "            fnow = phiAlpha(xini, alpha, p)\n",
    "            # print(k, h, fnow)\n",
    "            k += 1\n",
    "        alpha = alpha-h\n",
    "        h = h / 10\n",
    "    return alpha\n",
    "\n",
    "def gradDescent(x0, k=0, tol=1e-4):\n",
    "    print(\"k, x^(k), p^(k), f(x^(k), θ, t\")\n",
    "    op = dirgrad(x0)\n",
    "    while np.linalg.norm(grad(x0)) >= tol:\n",
    "        p = dirgrad(x0)\n",
    "        alpha = exhaustivoRefinado(p, x0)\n",
    "        # print(f\"a: {alpha}\")\n",
    "        x0 = x0 + alpha*p\n",
    "        if k >= 1:\n",
    "            angulo = np.arccos(np.dot(op, p))\n",
    "            op = p\n",
    "            print(\n",
    "                f\"{k}, {x0}, {p} , {f(x0)}, {round(np.degrees(angulo),6)}, {timer()} \")\n",
    "        else:\n",
    "            print(f\"{k}, {x0}, {p} , {f(x0)}, - , {timer()}\")\n",
    "\n",
    "        k = k+1\n",
    "    return x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "# llenar Y \n",
    "llenarY(N=1000)\n",
    "b = [2*i for i in y]\n",
    "x0 = np.array([2*i for i in y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<==Grad Conjugado==>\n",
      "[ 2.00938501e+00  2.12602692e+00  2.08232880e+00  2.19179873e+00\n",
      "  2.14419796e+00  2.02519460e+00  1.96928308e+00  2.00558144e+00\n",
      "  2.05226147e+00  1.87537399e+00  1.77795824e+00  1.83739101e+00\n",
      "  1.65209564e+00  1.55982943e+00  1.48735592e+00  1.39799937e+00\n",
      "  1.43789992e+00  1.37429019e+00  1.19485066e+00  1.03121324e+00\n",
      "  9.29731445e-01  9.57530403e-01  7.57585517e-01  7.28451217e-01\n",
      "  5.11066549e-01  4.62890568e-01  2.62038626e-01  2.83194013e-01\n",
      "  3.57272450e-02 -1.06403521e-01 -8.57383644e-02 -1.49683613e-01\n",
      " -3.80641602e-01 -4.69182645e-01 -5.42219492e-01 -7.19397352e-01\n",
      " -7.51930340e-01 -8.48670019e-01 -9.73118299e-01 -8.85436260e-01\n",
      " -1.00906177e+00 -1.01474657e+00 -1.20254416e+00 -1.23250558e+00\n",
      " -1.20900752e+00 -1.19983783e+00 -1.36240227e+00 -1.28900286e+00\n",
      " -1.34262090e+00 -1.24250284e+00 -1.38082672e+00 -1.29409700e+00\n",
      " -1.27009228e+00 -1.29108878e+00 -1.15704247e+00 -1.18654056e+00\n",
      " -9.84889170e-01 -9.77794389e-01 -9.87640753e-01 -7.99226767e-01\n",
      " -7.71994280e-01 -7.27711909e-01 -5.19460096e-01 -5.21862890e-01\n",
      " -3.91018731e-01 -3.56823823e-01 -1.74004063e-01 -7.51182553e-02\n",
      "  1.21524284e-01  1.26856789e-01  2.70208965e-01  4.93758196e-01\n",
      "  6.85841848e-01  7.89650252e-01  9.53594115e-01  9.72724266e-01\n",
      "  1.07458933e+00  1.37329884e+00  1.49894571e+00  1.46769465e+00\n",
      "  1.61621298e+00  1.89760764e+00  1.88445473e+00  2.09976748e+00\n",
      "  2.21930469e+00  2.21662155e+00  2.32315534e+00  2.54508682e+00\n",
      "  2.66573090e+00  2.66423197e+00  2.84898697e+00  2.93015797e+00\n",
      "  2.88675725e+00  3.06379826e+00  2.98804470e+00  3.17282183e+00\n",
      "  3.22688197e+00  3.18568140e+00  3.26924269e+00  3.24147937e+00\n",
      "  3.27330164e+00  3.25370121e+00  3.19754133e+00  3.25148576e+00\n",
      "  3.20111348e+00  3.27377712e+00  3.09761252e+00  3.21280718e+00\n",
      "  3.13525580e+00  3.06102493e+00  3.04835057e+00  2.85337725e+00\n",
      "  2.84303813e+00  2.70012111e+00  2.76452591e+00  2.65388424e+00\n",
      "  2.49996826e+00  2.39339979e+00  2.30399366e+00  2.18341234e+00\n",
      "  2.12350237e+00  1.91585422e+00  1.79309591e+00  1.65879432e+00\n",
      "  1.56211302e+00  1.56838128e+00  1.47357108e+00  1.18845449e+00\n",
      "  1.12519971e+00  9.55973235e-01  9.41896595e-01  7.38730612e-01\n",
      "  6.85579656e-01  6.96317191e-01  5.04517734e-01  4.32293347e-01\n",
      "  3.13947664e-01  1.67022370e-01  1.83279031e-01  1.24154134e-01\n",
      " -1.21883852e-02 -3.79848161e-02 -1.72493861e-01 -1.47478403e-01\n",
      " -1.12536775e-01 -2.96516236e-01 -2.46659727e-01 -2.34483183e-01\n",
      " -3.71997248e-01 -3.03924055e-01 -3.58845511e-01 -1.88776376e-01\n",
      " -1.73208427e-01 -3.17266702e-01 -1.94842430e-01 -1.07033271e-01\n",
      " -4.59410860e-02 -4.60704660e-03  2.69837229e-02  1.87057695e-02\n",
      "  1.00731138e-01  3.32284659e-01  4.35701973e-01  4.64557674e-01\n",
      "  5.85829922e-01  6.53589631e-01  7.01760930e-01  8.62159998e-01\n",
      "  8.99980581e-01  1.20573882e+00  1.19127476e+00  1.30657489e+00\n",
      "  1.54746186e+00  1.67017065e+00  1.80375349e+00  1.95956877e+00\n",
      "  2.01965409e+00  2.08083246e+00  2.35961500e+00  2.37470089e+00\n",
      "  2.62747120e+00  2.74052732e+00  2.78934129e+00  2.82301827e+00\n",
      "  2.97621725e+00  3.01452152e+00  3.20593078e+00  3.26504817e+00\n",
      "  3.32691453e+00  3.49917136e+00  3.56311112e+00  3.73101305e+00\n",
      "  3.75321185e+00  3.74772571e+00  3.76302039e+00  3.85942322e+00\n",
      "  3.87859380e+00  3.87807695e+00  4.03409925e+00  4.01946226e+00\n",
      "  4.00539687e+00  3.99499860e+00  3.91230501e+00  3.88816411e+00\n",
      "  3.87696992e+00  3.84152358e+00  3.88833482e+00  3.78944750e+00\n",
      "  3.80426470e+00  3.72735752e+00  3.59454775e+00  3.50812237e+00\n",
      "  3.41750136e+00  3.43971894e+00  3.33896706e+00  3.23126356e+00\n",
      "  3.13201572e+00  2.94804704e+00  2.81830626e+00  2.88869860e+00\n",
      "  2.58645074e+00  2.48196475e+00  2.36355292e+00  2.30673721e+00\n",
      "  2.18137462e+00  2.06702953e+00  1.94057023e+00  1.81721701e+00\n",
      "  1.68419245e+00  1.64787194e+00  1.47112847e+00  1.42888134e+00\n",
      "  1.18441510e+00  1.17825060e+00  1.07093937e+00  8.18303440e-01\n",
      "  7.54090836e-01  7.09058679e-01  6.99989146e-01  4.89827994e-01\n",
      "  4.21395794e-01  4.43870758e-01  2.88832550e-01  3.09591133e-01\n",
      "  2.48022709e-01  1.61442027e-01  2.49515907e-01  4.38380185e-02\n",
      "  3.72800529e-02  8.45880274e-02  1.26565425e-01  1.97993586e-01\n",
      "  1.98355039e-01  2.04130733e-01  1.40719502e-01  1.47664310e-01\n",
      "  2.04942919e-01  2.22396391e-01  2.53675247e-01  4.12535276e-01\n",
      "  5.68835480e-01  4.93410060e-01  6.27927475e-01  6.34773584e-01\n",
      "  7.97197627e-01  8.77185096e-01  1.09600241e+00  1.10879226e+00\n",
      "  1.31499288e+00  1.34113989e+00  1.49614922e+00  1.65336712e+00\n",
      "  1.69662779e+00  1.85416831e+00  1.87922387e+00  2.17501182e+00\n",
      "  2.18566204e+00  2.24851702e+00  2.51234682e+00  2.54952439e+00\n",
      "  2.69593548e+00  2.82067533e+00  2.83650782e+00  2.96494904e+00\n",
      "  3.05521111e+00  3.31604313e+00  3.31116215e+00  3.46011257e+00\n",
      "  3.40151063e+00  3.64468991e+00  3.61240254e+00  3.68906175e+00\n",
      "  3.73857960e+00  3.90757785e+00  3.98257032e+00  3.87343897e+00\n",
      "  4.04726764e+00  4.05283788e+00  3.93842136e+00  3.97696689e+00\n",
      "  4.02016649e+00  4.04546688e+00  4.00433852e+00  4.00825648e+00\n",
      "  3.83891876e+00  3.92608455e+00  3.88376670e+00  3.82333275e+00\n",
      "  3.76794082e+00  3.66923070e+00  3.63612040e+00  3.42824482e+00\n",
      "  3.32415563e+00  3.21596985e+00  3.25646369e+00  3.20926393e+00\n",
      "  3.08007737e+00  2.82152574e+00  2.72753813e+00  2.62138842e+00\n",
      "  2.47120889e+00  2.36504632e+00  2.17903732e+00  2.24013984e+00\n",
      "  1.96917082e+00  1.80928815e+00  1.77112424e+00  1.55406096e+00\n",
      "  1.49377438e+00  1.40462575e+00  1.24978156e+00  1.01826966e+00\n",
      "  1.05344889e+00  8.05451097e-01  8.52055098e-01  5.69521865e-01\n",
      "  4.45125629e-01  4.73041743e-01  3.18718534e-01  3.52585057e-01\n",
      "  2.53631091e-01  1.21655045e-04 -7.03325995e-02 -1.17220406e-01\n",
      " -1.19789106e-01 -9.90031822e-02 -2.36510637e-01 -1.93709959e-01\n",
      " -2.73697780e-01 -3.26735446e-01 -2.67446938e-01 -2.49852268e-01\n",
      " -3.61680261e-01 -2.73329357e-01 -2.50832080e-01 -1.93933876e-01\n",
      " -2.80279852e-01 -2.29682886e-01 -1.68287080e-01 -5.68904491e-02\n",
      " -1.57309975e-02  3.55330299e-02  2.21860485e-01  1.71435503e-01\n",
      "  3.95917247e-01  4.11325896e-01  6.19529879e-01  7.14720099e-01\n",
      "  8.17339701e-01  8.34465240e-01  8.56553296e-01  1.03452998e+00\n",
      "  1.20917790e+00  1.29630266e+00  1.35218987e+00  1.59796548e+00\n",
      "  1.57273416e+00  1.80241746e+00  1.77551730e+00  1.89681396e+00\n",
      "  2.03676740e+00  2.12558075e+00  2.28978690e+00  2.39769980e+00\n",
      "  2.53660354e+00  2.56750479e+00  2.61876719e+00  2.75014646e+00\n",
      "  2.76829057e+00  2.89610716e+00  2.96035902e+00  3.15030992e+00\n",
      "  3.10775287e+00  3.07688843e+00  3.21959028e+00  3.20607070e+00\n",
      "  3.34734455e+00  3.28804476e+00  3.25199787e+00  3.34167948e+00\n",
      "  3.30218434e+00  3.22802143e+00  3.14006131e+00  3.15642030e+00\n",
      "  3.22484478e+00  3.21519276e+00  3.11167350e+00  3.10238633e+00\n",
      "  3.03548470e+00  2.88762165e+00  2.82485543e+00  2.79494739e+00\n",
      "  2.63367428e+00  2.41999431e+00  2.38432437e+00  2.24044052e+00\n",
      "  2.27468289e+00  2.07753407e+00  1.85044473e+00  1.78123921e+00\n",
      "  1.75179226e+00  1.60492530e+00  1.38540006e+00  1.18478269e+00\n",
      "  1.06478122e+00  1.07777704e+00  8.46158742e-01  7.76543828e-01\n",
      "  5.57718275e-01  4.03449434e-01  2.63030433e-01  1.36284127e-01\n",
      "  6.66388418e-02  5.06488415e-02 -1.25366225e-01 -3.79622759e-01\n",
      " -3.65390421e-01 -5.91422510e-01 -6.77397259e-01 -7.80858872e-01\n",
      " -8.65293237e-01 -9.32706521e-01 -9.96255454e-01 -1.06701588e+00\n",
      " -1.03618317e+00 -1.18269912e+00 -1.21406251e+00 -1.29458097e+00\n",
      " -1.25027208e+00 -1.20991251e+00 -1.33615890e+00 -1.28537372e+00\n",
      " -1.25531821e+00 -1.26659754e+00 -1.31179586e+00 -1.30306895e+00\n",
      " -1.17412295e+00 -1.13830123e+00 -1.21952146e+00 -1.10468570e+00\n",
      " -1.07189129e+00 -9.27165427e-01 -8.14176804e-01 -7.50418839e-01\n",
      " -8.05565874e-01 -5.94933806e-01 -4.49561318e-01 -3.72219052e-01\n",
      " -4.44492563e-01 -2.54581140e-01 -1.63976717e-01  4.98536996e-02\n",
      "  7.24949954e-02  2.59369916e-01  2.69691124e-01  3.21521165e-01\n",
      "  5.74960644e-01  7.35692178e-01  8.14135081e-01  8.96843636e-01\n",
      "  9.01038461e-01  1.04756865e+00  1.17465155e+00  1.33973875e+00\n",
      "  1.32282336e+00  1.55916644e+00  1.47774493e+00  1.66507481e+00\n",
      "  1.80235615e+00  1.85187194e+00  1.85347982e+00  1.99910644e+00\n",
      "  1.98320927e+00  1.99538440e+00  2.01722310e+00  2.12990926e+00\n",
      "  2.17760806e+00  2.14027205e+00  2.03002559e+00  2.18964965e+00\n",
      "  2.07760286e+00  2.02085581e+00  2.00336679e+00  2.08277418e+00\n",
      "  2.01222625e+00  1.87137256e+00  1.90318240e+00  1.79884852e+00\n",
      "  1.68204767e+00  1.74349236e+00  1.66003160e+00  1.55564017e+00\n",
      "  1.39823843e+00  1.30591989e+00  1.10386577e+00  1.15258413e+00\n",
      "  1.04155800e+00  8.98371033e-01  8.18339829e-01  5.86016609e-01\n",
      "  3.90713344e-01  4.20304235e-01  1.37801384e-01  1.51133018e-01\n",
      "  2.05065920e-02 -2.60691104e-01 -3.69064594e-01 -5.59699898e-01\n",
      " -7.08444920e-01 -6.62397538e-01 -8.12517454e-01 -9.57835304e-01\n",
      " -1.13589752e+00 -1.34889378e+00 -1.46049229e+00 -1.56699130e+00\n",
      " -1.61782452e+00 -1.67489858e+00 -1.73858657e+00 -1.89988731e+00\n",
      " -2.09683200e+00 -2.19474681e+00 -2.07557703e+00 -2.21905961e+00\n",
      " -2.26703640e+00 -2.33661381e+00 -2.50252326e+00 -2.36208374e+00\n",
      " -2.53876911e+00 -2.56142357e+00 -2.61575528e+00 -2.45161643e+00\n",
      " -2.62017588e+00 -2.57249034e+00 -2.55861160e+00 -2.56534269e+00\n",
      " -2.38982087e+00 -2.44674915e+00 -2.41232512e+00 -2.38673913e+00\n",
      " -2.23913317e+00 -2.26813084e+00 -2.09570352e+00 -2.07108954e+00\n",
      " -1.90896280e+00 -1.82449690e+00 -1.76647762e+00 -1.71001991e+00\n",
      " -1.58528343e+00 -1.53681410e+00 -1.42803945e+00 -1.28321186e+00\n",
      " -1.05798105e+00 -9.96875407e-01 -9.29826830e-01 -7.89413268e-01\n",
      " -6.21144879e-01 -5.37882393e-01 -3.79508249e-01 -3.94858909e-01\n",
      " -1.98953346e-01 -6.18258035e-02 -1.33151616e-01  1.62221386e-01\n",
      "  2.32112860e-01  1.60373569e-01  4.43300105e-01  3.99823375e-01\n",
      "  4.28093415e-01  6.26771662e-01  6.30201424e-01  6.10637217e-01\n",
      "  7.96110009e-01  7.16949442e-01  9.03072653e-01  8.88777021e-01\n",
      "  8.56967583e-01  9.72183694e-01  9.10602780e-01  1.02510667e+00\n",
      "  9.26835257e-01  9.04664161e-01  8.92368607e-01  9.23749426e-01\n",
      "  7.47172867e-01  7.55383796e-01  7.84805220e-01  5.93374614e-01\n",
      "  5.43450884e-01  5.99418416e-01  4.88785743e-01  4.40295748e-01\n",
      "  2.76819631e-01  9.71119864e-02  1.60263653e-01 -1.45854344e-01\n",
      " -9.24775484e-02 -1.84092546e-01 -3.33612145e-01 -4.53799949e-01\n",
      " -7.02500676e-01 -7.28513526e-01 -8.20166771e-01 -1.13836694e+00\n",
      " -1.08787559e+00 -1.31192990e+00 -1.41744877e+00 -1.61920384e+00\n",
      " -1.74385740e+00 -1.89047037e+00 -2.05309818e+00 -2.08737541e+00\n",
      " -2.24913484e+00 -2.31765012e+00 -2.48512849e+00 -2.51282602e+00\n",
      " -2.70475654e+00 -2.74932657e+00 -2.89873648e+00 -3.07109171e+00\n",
      " -3.06062583e+00 -3.04001713e+00 -3.22746813e+00 -3.29471404e+00\n",
      " -3.40872048e+00 -3.44232540e+00 -3.44917374e+00 -3.48163820e+00\n",
      " -3.39253118e+00 -3.46338817e+00 -3.43284716e+00 -3.50614104e+00\n",
      " -3.43861275e+00 -3.46972858e+00 -3.45590239e+00 -3.42168542e+00\n",
      " -3.38537260e+00 -3.43913355e+00 -3.29602833e+00 -3.29814668e+00\n",
      " -3.30628582e+00 -3.12935597e+00 -3.00856251e+00 -2.90352003e+00\n",
      " -2.80226535e+00 -2.72338958e+00 -2.61604880e+00 -2.66151060e+00\n",
      " -2.44500640e+00 -2.37365711e+00 -2.29063889e+00 -2.12873732e+00\n",
      " -2.06598680e+00 -1.89066902e+00 -1.89249002e+00 -1.76247135e+00\n",
      " -1.50687939e+00 -1.54060141e+00 -1.31375516e+00 -1.25615047e+00\n",
      " -1.00434253e+00 -9.42054828e-01 -8.32837891e-01 -8.58090559e-01\n",
      " -6.56803660e-01 -4.93083024e-01 -5.38821967e-01 -3.02277661e-01\n",
      " -2.07150351e-01 -2.73155644e-01 -8.89401289e-02 -7.82392401e-04\n",
      " -1.12552313e-01  1.14922290e-01  1.58955203e-01  2.02160704e-01\n",
      "  8.30261034e-02  1.06282566e-01  1.70739077e-01  1.36053759e-01\n",
      "  1.90186838e-01  2.55097040e-01  1.79323894e-01  8.58800411e-02\n",
      "  1.71298944e-01  6.60235196e-02  7.96340350e-02 -1.80139295e-02\n",
      "  7.38477344e-03 -1.53171498e-01 -2.47125263e-01 -3.04757752e-01\n",
      " -4.81293311e-01 -4.28669191e-01 -6.70493753e-01 -6.47022253e-01\n",
      " -7.90176342e-01 -8.41998889e-01 -1.10387457e+00 -1.10446159e+00\n",
      " -1.19593469e+00 -1.37241762e+00 -1.55484492e+00 -1.57765696e+00\n",
      " -1.83126800e+00 -1.79783130e+00 -1.97789324e+00 -2.13578753e+00\n",
      " -2.16713534e+00 -2.35566264e+00 -2.40485087e+00 -2.56328049e+00\n",
      " -2.70725118e+00 -2.86085302e+00 -3.02147262e+00 -3.06765059e+00\n",
      " -3.07060770e+00 -3.28859262e+00 -3.43154029e+00 -3.50282664e+00\n",
      " -3.53374123e+00 -3.66241892e+00 -3.64632848e+00 -3.69553322e+00\n",
      " -3.67272358e+00 -3.88149299e+00 -3.89427049e+00 -3.79760062e+00\n",
      " -3.91543598e+00 -3.95756233e+00 -3.83029157e+00 -3.98319199e+00\n",
      " -3.82197326e+00 -3.86658522e+00 -3.79073956e+00 -3.83281033e+00\n",
      " -3.68273859e+00 -3.74599379e+00 -3.67818370e+00 -3.53651975e+00\n",
      " -3.60312532e+00 -3.36397520e+00 -3.31364079e+00 -3.29408320e+00\n",
      " -3.07845359e+00 -3.00564558e+00 -3.01375066e+00 -2.86697322e+00\n",
      " -2.67015667e+00 -2.60991896e+00 -2.58891530e+00 -2.30500862e+00\n",
      " -2.26169107e+00 -2.12878114e+00 -2.06849858e+00 -1.85594420e+00\n",
      " -1.73692779e+00 -1.56346149e+00 -1.53203063e+00 -1.39393950e+00\n",
      " -1.33210203e+00 -1.18245338e+00 -9.59753799e-01 -8.97301225e-01\n",
      " -8.30461560e-01 -7.28736420e-01 -4.89798632e-01 -3.81393542e-01\n",
      " -3.87638421e-01 -3.90442621e-01 -2.49355520e-01 -1.48420310e-01\n",
      " -8.80890052e-03 -4.21599604e-02  1.08745790e-01  5.28191748e-02\n",
      "  1.82258630e-01  2.20889933e-01  2.44721947e-01  2.04935481e-01\n",
      "  9.83864998e-02  2.48048913e-01  2.38723878e-01  2.24836541e-01\n",
      "  1.77693954e-01  7.56123384e-02  3.51669339e-02  1.24801466e-01\n",
      " -5.50822824e-02 -1.24283429e-01 -1.38175157e-01 -2.39400104e-01\n",
      " -3.20310401e-01 -4.41061568e-01 -3.73160716e-01 -5.33780272e-01\n",
      " -6.48713184e-01 -7.53694089e-01 -8.18747863e-01 -1.01619179e+00\n",
      " -1.00298829e+00 -1.11569995e+00 -1.33334716e+00 -1.40208464e+00\n",
      " -1.55902182e+00 -1.69143718e+00 -1.83520329e+00 -1.93209883e+00\n",
      " -2.13533114e+00 -2.14696779e+00 -2.27646687e+00 -2.46018834e+00\n",
      " -2.54156544e+00 -2.51252609e+00 -2.70058572e+00 -2.87108353e+00\n",
      " -2.95761854e+00 -3.01617041e+00 -3.11104159e+00 -3.16317728e+00\n",
      " -3.23344971e+00 -3.17302895e+00 -3.37543858e+00 -3.41147877e+00\n",
      " -3.33896384e+00 -3.44978720e+00 -3.43970517e+00 -3.43591567e+00\n",
      " -3.54701308e+00 -3.58540921e+00 -3.59722285e+00 -3.47246880e+00\n",
      " -3.42377413e+00 -3.38700935e+00 -3.38342521e+00 -3.35634438e+00\n",
      " -3.35866407e+00 -3.31270436e+00 -3.17251899e+00 -3.18090402e+00\n",
      " -3.15282868e+00 -2.95444175e+00 -2.82683568e+00 -2.81850661e+00\n",
      " -2.60231315e+00 -2.59909962e+00 -2.50442700e+00 -2.38461727e+00\n",
      " -2.24174240e+00 -2.07846688e+00 -2.03627965e+00 -1.83518996e+00\n",
      " -1.74983944e+00 -1.55862230e+00 -1.54653706e+00 -1.28674891e+00\n",
      " -1.12193552e+00 -1.10286949e+00 -9.90727553e-01 -8.80697522e-01\n",
      " -5.92057817e-01 -4.46797751e-01 -4.45433179e-01 -2.05827882e-01\n",
      " -1.63862338e-01 -1.40632498e-02  3.01858728e-02  1.79652250e-01\n",
      "  3.51632686e-01  3.79930814e-01  4.30685108e-01  4.60171367e-01\n",
      "  6.93900564e-01  6.67645165e-01  7.59869447e-01  7.40697292e-01\n",
      "  8.87029193e-01  8.68915588e-01  9.40075719e-01  9.03609893e-01\n",
      "  8.92806395e-01  8.73974507e-01  1.02751114e+00  9.72861165e-01\n",
      "  9.71581007e-01  7.89724050e-01  8.52600825e-01  8.16838744e-01\n",
      "  7.18090910e-01  7.95842061e-01  7.26018035e-01  4.90892072e-01\n",
      "  5.79701199e-01  4.53956544e-01  3.71050646e-01  1.85874820e-01\n",
      "  2.17428660e-01 -2.24858260e-02 -4.85737115e-02 -7.27851827e-02\n",
      " -2.78562358e-01 -3.66258746e-01 -4.13612676e-01 -6.58529917e-01\n",
      " -6.60006059e-01 -7.79900448e-01 -9.61905358e-01 -9.98157055e-01\n",
      " -1.21959849e+00 -1.21948784e+00 -1.34167130e+00 -1.52263497e+00\n",
      " -1.59874169e+00 -1.74036058e+00 -1.80607324e+00 -1.81178627e+00\n",
      " -1.93861806e+00 -1.99690025e+00 -2.19417720e+00 -2.22059734e+00\n",
      " -2.24725180e+00 -2.29797053e+00 -2.46034533e+00 -2.47554604e+00\n",
      " -2.48905391e+00 -2.55292929e+00 -2.58962420e+00 -2.59028404e+00\n",
      " -2.60465098e+00 -2.57421296e+00 -2.56773387e+00 -2.41291733e+00\n",
      " -2.39110217e+00 -2.54416008e+00 -2.42641059e+00 -2.45089038e+00\n",
      " -2.33726921e+00 -2.20806797e+00 -2.13201570e+00 -2.14278579e+00\n",
      " -2.01036556e+00 -1.96422064e+00 -1.87563772e+00 -1.82001667e+00\n",
      " -1.67363691e+00 -1.58348389e+00 -1.30309187e+00 -1.34224120e+00\n",
      " -1.07324856e+00 -1.09590290e+00 -8.81814719e-01 -7.50013510e-01\n",
      " -5.64584761e-01 -4.16132017e-01 -2.74332770e-01 -2.52124203e-01\n",
      " -1.07653761e-01  3.50123996e-02  2.69719298e-01  3.69784245e-01\n",
      "  5.19822813e-01  5.49893968e-01  7.48772007e-01  8.74952085e-01\n",
      "  1.06848759e+00  1.13592439e+00  1.24879550e+00  1.36365196e+00\n",
      "  1.45859710e+00  1.53030390e+00  1.50397156e+00  1.72945200e+00\n",
      "  1.76436190e+00  1.88154604e+00  1.98391254e+00  1.85531291e+00\n",
      "  1.94251121e+00  2.10398780e+00  2.13825055e+00  2.12757038e+00]\n",
      "k, x0, alpha, beta, Ap\n",
      "0 [ 1.0169991   1.0476775   1.05714484  1.08091141  1.06565689  1.01955746\n",
      "  0.99449354  1.00447693  1.00445226  0.94623563  0.90522892  0.89483284\n",
      "  0.8358791   0.78239724  0.74247184  0.71236922  0.70907072  0.67601413\n",
      "  0.599391    0.52215171  0.47808616  0.45631527  0.39610781  0.34564837\n",
      "  0.2726085   0.21633729  0.15329044  0.11484377  0.02840196 -0.03696712\n",
      " -0.05135248 -0.09158069 -0.17621144 -0.23319367 -0.28169249 -0.34547624\n",
      " -0.3826249  -0.42737858 -0.4656746  -0.46412161 -0.49307083 -0.52590101\n",
      " -0.58588764 -0.61130896 -0.60632673 -0.61746931 -0.65806069 -0.65761189\n",
      " -0.65638106 -0.64548208 -0.6683692  -0.65373553 -0.63995417 -0.63046775\n",
      " -0.59523935 -0.57055408 -0.51220623 -0.49090649 -0.47432662 -0.41597962\n",
      " -0.38454296 -0.347705   -0.2809499  -0.24778417 -0.20529452 -0.16367446\n",
      " -0.09544628 -0.02781408  0.04168282  0.07726247  0.1432064   0.24389428\n",
      "  0.33432095  0.4010902   0.4626335   0.4949449   0.55731396  0.66979855\n",
      "  0.73427805  0.75228737  0.8219083   0.91998191  0.96566869  1.04099156\n",
      "  1.09815606  1.11994238  1.17386141  1.26324445  1.3215213   1.35159109\n",
      "  1.41506331  1.45357765  1.46634227  1.50762703  1.52102506  1.57437394\n",
      "  1.60496483  1.60633924  1.62455354  1.62774286  1.63257064  1.62424945\n",
      "  1.61080823  1.61636967  1.61388779  1.61308075  1.57892528  1.58818065\n",
      "  1.56897385  1.53765424  1.50694319  1.44606304  1.40918945  1.37165269\n",
      "  1.36566383  1.3234759   1.25552445  1.19918918  1.14962657  1.09847562\n",
      "  1.04767378  0.96703029  0.89597436  0.8336933   0.79185008  0.77459663\n",
      "  0.71824385  0.61678349  0.55237349  0.49380078  0.45235626  0.38459605\n",
      "  0.3493963   0.32814323  0.26437183  0.21167736  0.15421927  0.09987285\n",
      "  0.08416552  0.05440046  0.00494932 -0.02986892 -0.07036059 -0.07279493\n",
      " -0.07818273 -0.12498556 -0.12717521 -0.13227681 -0.16557352 -0.16435184\n",
      " -0.15705432 -0.10988937 -0.10261253 -0.13210496 -0.10094351 -0.05622122\n",
      " -0.02495994 -0.00327871  0.0095163   0.01838343  0.06534129  0.15344448\n",
      "  0.21054058  0.24166478  0.28775666  0.32504865  0.36232297  0.41910895\n",
      "  0.47705783  0.5712579   0.60899073  0.66626062  0.76242129  0.83671225\n",
      "  0.90468199  0.97085142  1.01058955  1.06283563  1.15421812  1.21187162\n",
      "  1.30062309  1.36473004  1.39406015  1.42436672  1.47758926  1.52353642\n",
      "  1.59078173  1.6338549   1.67556528  1.7398928   1.79309756  1.85215245\n",
      "  1.87505322  1.87715181  1.89083293  1.92324173  1.93858398  1.95593665\n",
      "  2.00129959  2.01108837  2.00436048  1.99156665  1.96326944  1.94663353\n",
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      " -2.07370367e-02  4.16615889e-02  2.86020553e-03 -8.94125166e-03]\n",
      "2 [ 1.00952129  1.05722592  1.04647245  1.08944892  1.06881128  1.01530881\n",
      "  0.98872706  1.00279463  1.01707079  0.94068922  0.89495926  0.90929065\n",
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      " -0.04636531 -0.08166064 -0.18494882 -0.23378564 -0.27487622 -0.3541946\n",
      " -0.37817866 -0.42496282 -0.47841108 -0.45056191 -0.5008622  -0.51415615\n",
      " -0.59497203 -0.61359351 -0.60536894 -0.60642786 -0.67222512 -0.6486098\n",
      " -0.66593867 -0.63004919 -0.68193381 -0.64905889 -0.63656726 -0.63965198\n",
      " -0.58410643 -0.58474341 -0.49989605 -0.48957079 -0.48615835 -0.40556005\n",
      " -0.38526568 -0.35763597 -0.26759953 -0.25628664 -0.19868201 -0.17263807\n",
      " -0.08976946 -0.03431889  0.05352002  0.06893396  0.13881141  0.24561904\n",
      "  0.33921642  0.39648572  0.47124106  0.49005926  0.54518944  0.67955631\n",
      "  0.74297839  0.74118227  0.8133867   0.93770924  0.9504446   1.04610831\n",
      "  1.10468458  1.11285781  1.16642194  1.26836305  1.32799435  1.33905633\n",
      "  1.42037638  1.4601879   1.45139812  1.52288427  1.50371721  1.58141813\n",
      "  1.60943688  1.59731838  1.6305274   1.62269829  1.63455433  1.62551089\n",
      "  1.60297502  1.62206486  1.60464757  1.62774721  1.55958703  1.5992441\n",
      "  1.56731469  1.53243     1.51729992  1.43349568  1.41723295  1.35779225\n",
      "  1.37538806  1.32471259  1.2517947   1.19752389  1.15092814  1.09364864\n",
      "  1.05599459  0.96098497  0.8965352   0.83138236  0.78509717  0.77966317\n",
      "  0.72912302  0.60256889  0.55937221  0.48366372  0.4640658   0.37526168\n",
      "  0.34527609  0.34028901  0.25639393  0.214519    0.15625513  0.09001038\n",
      "  0.08880875  0.05894288 -0.00206267 -0.02259124 -0.07987596 -0.07348126\n",
      " -0.06458698 -0.13936517 -0.12461096 -0.12290858 -0.17818506 -0.15566182\n",
      " -0.17088233 -0.10066082 -0.09287751 -0.14811052 -0.09803488 -0.05472968\n",
      " -0.02401236 -0.0029267   0.01219026  0.01359064  0.05655471  0.1610659\n",
      "  0.21456748  0.23563116  0.29094341  0.32617965  0.35524541  0.4271758\n",
      "  0.45982131  0.59077008  0.60050295  0.65853946  0.76932015  0.83518528\n",
      "  0.90242074  0.97592197  1.01023548  1.04877046  1.17028745  1.19599832\n",
      "  1.30829641  1.36710471  1.39410636  1.41617042  1.48422075  1.51290436\n",
      "  1.59794159  1.63259495  1.66775832  1.74574677  1.78504225  1.85953429\n",
      "  1.87503762  1.87485508  1.8847468   1.92677623  1.93874089  1.94494529\n",
      "  2.01038244  2.00914275  2.00251332  1.99468027  1.95842688  1.94480192\n",
      "  1.93779965  1.9236894   1.93866831  1.89866305  1.89839272  1.86117982\n",
      "  1.79904711  1.7544405   1.7131099   1.71503755  1.66874988  1.61559309\n",
      "  1.56276267  1.47661429  1.41651581  1.43003327  1.30029667  1.24119006\n",
      "  1.18421852  1.15072091  1.09087945  1.03301532  0.97040367  0.90851801\n",
      "  0.84572106  0.81873854  0.74014108  0.70715305  0.6011859   0.58516489\n",
      "  0.52975524  0.41668102  0.3785792   0.35553119  0.34216714  0.25045818\n",
      "  0.2144369   0.21545122  0.15093429  0.1518812   0.12324591  0.08697932\n",
      "  0.11370716  0.0295804   0.02158262  0.04248413  0.06426986  0.09604734\n",
      "  0.09889759  0.09939644  0.07327978  0.07608279  0.10114681  0.11217999\n",
      "  0.13219181  0.20586954  0.27533055  0.25433408  0.30979568  0.32341414\n",
      "  0.39606886  0.44358248  0.54037015  0.56127946  0.65097515  0.67542359\n",
      "  0.74819746  0.8222783   0.85238058  0.92274367  0.94962462  1.07664974\n",
      "  1.09476274  1.1320682   1.24775201  1.27849915  1.34698325  1.40609525\n",
      "  1.42258542  1.4817821   1.53385385  1.64781937  1.66054488  1.72270658\n",
      "  1.71189768  1.81208573  1.80990846  1.84409446  1.87389053  1.94966646\n",
      "  1.98415066  1.94730216  2.01708446  2.021404    1.97520477  1.98914113\n",
      "  2.00920195  2.01991244  2.00328446  1.99783123  1.9292563   1.95838059\n",
      "  1.94074503  1.91161068  1.88230238  1.83662011  1.81124622  1.71798803\n",
      "  1.66279115  1.61401427  1.62467816  1.60043318  1.53478236  1.4171786\n",
      "  1.36370151  1.30899989  1.23713964  1.18007256  1.09853618  1.1073293\n",
      "  0.98853991  0.90948913  0.87908682  0.78294574  0.74587401  0.69932715\n",
      "  0.62224149  0.51924425  0.51663435  0.41311726  0.41368815  0.29089055\n",
      "  0.22891306  0.2301153   0.16614179  0.17073603  0.12052218  0.00732211\n",
      " -0.03330564 -0.05650318 -0.05923604 -0.0555054  -0.11164262 -0.10130215\n",
      " -0.13565315 -0.15876515 -0.13544508 -0.12980151 -0.17305985 -0.13869616\n",
      " -0.12459265 -0.10244376 -0.13475871 -0.1137443  -0.08215392 -0.03112351\n",
      " -0.00728031  0.02275627  0.10233375  0.09588389  0.19069472  0.21278718\n",
      "  0.30556136  0.35699012  0.40508382  0.41773974  0.43486801  0.51739075\n",
      "  0.60090931  0.64707011  0.6831104   0.78901228  0.79535426  0.8917088\n",
      "  0.89327318  0.94950313  1.01664039  1.06562447  1.14282861  1.19957645\n",
      "  1.26390632  1.28447383  1.31245308  1.37097988  1.38826353  1.44609414\n",
      "  1.48444704  1.56582688  1.554133    1.54526422  1.60433884  1.60834921\n",
      "  1.66579578  1.64474456  1.63083057  1.66569367  1.64917571  1.61367231\n",
      "  1.57460749  1.58049999  1.60903856  1.6036486   1.55917683  1.54878586\n",
      "  1.51447392  1.44716268  1.41358015  1.39193261  1.31474708  1.21701428\n",
      "  1.18881689  1.12657098  1.12806471  1.03732424  0.9318309   0.89243639\n",
      "  0.87084127  0.79902426  0.69355943  0.59628317  0.5375384   0.52956777\n",
      "  0.42854034  0.38266309  0.28118331  0.20258467  0.13246463  0.0707783\n",
      "  0.03516079  0.01855854 -0.06570875 -0.17961323 -0.19138833 -0.29058727\n",
      " -0.33893652 -0.38953178 -0.43184208 -0.4660787  -0.49810761 -0.5298386\n",
      " -0.52485013 -0.58720568 -0.60827357 -0.64219153 -0.62540465 -0.6113362\n",
      " -0.66128703 -0.64314856 -0.62952123 -0.63464762 -0.65332003 -0.64663664\n",
      " -0.59089627 -0.57373142 -0.60216106 -0.55469721 -0.53152665 -0.46481356\n",
      " -0.40959068 -0.37948561 -0.3922126  -0.29962253 -0.22825907 -0.19183354\n",
      " -0.21198868 -0.13018115 -0.07763391  0.017736    0.04188723  0.1229621\n",
      "  0.13677282  0.16904216  0.28402281  0.36403342  0.40662681  0.44559672\n",
      "  0.45625276  0.52353482  0.58837714  0.66305695  0.67042144  0.76795683\n",
      "  0.74900139  0.83091734  0.89727221  0.9239919   0.93203247  0.99331603\n",
      "  0.99233924  0.99846506  1.01225642  1.06216303  1.08482216  1.06757106\n",
      "  1.025169    1.0844935   1.04045469  1.01248791  1.0053866   1.03520304\n",
      "  1.00317652  0.94215733  0.94648198  0.89908707  0.84793732  0.86614355\n",
      "  0.8284641   0.77558021  0.70139077  0.64942264  0.56161077  0.57031238\n",
      "  0.51906934  0.45106959  0.40316898  0.29474474  0.20396554  0.19883416\n",
      "  0.0797687   0.069903    0.00404341 -0.12394897 -0.1871571  -0.27761002\n",
      " -0.34654969 -0.33879305 -0.40689584 -0.48050712 -0.56916556 -0.67021277\n",
      " -0.72941699 -0.78106295 -0.80904301 -0.83815339 -0.87360431 -0.95134789\n",
      " -1.04365521 -1.08870659 -1.04773729 -1.10653359 -1.13443215 -1.17141913\n",
      " -1.23974573 -1.19284827 -1.26389898 -1.28095293 -1.29978619 -1.23834998\n",
      " -1.30220517 -1.2869983  -1.27960451 -1.27586724 -1.20378963 -1.22027063\n",
      " -1.20592832 -1.1887287  -1.12592329 -1.12660708 -1.05296888 -1.03047309\n",
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      "  8.27072671e-04  1.10545547e-03 -1.42050650e-03  4.22801585e-04\n",
      "  3.86953480e-03 -2.70971901e-03 -1.49103926e-03 -1.51777116e-03\n",
      "  1.27273309e-03  2.80194488e-03  3.27589617e-03 -3.95740458e-03\n",
      " -5.19400254e-03  3.85000621e-03  3.36405542e-03 -8.23575073e-04]\n",
      "3 [ 1.00947     1.05717667  1.0465278   1.08952509  1.06881694  1.01528953\n",
      "  0.98870435  1.00281121  1.01707158  0.94073911  0.89497858  0.9092631\n",
      "  0.82923358  0.78099079  0.74348037  0.70400891  0.71462236  0.68199942\n",
      "  0.59790525  0.51864562  0.46978973  0.47017549  0.38462043  0.3573715\n",
      "  0.26157606  0.22625101  0.13898923  0.13141723  0.02197142 -0.0463698\n",
      " -0.04639224 -0.08163985 -0.18489018 -0.23381261 -0.27492252 -0.35417125\n",
      " -0.37823362 -0.42499703 -0.47842757 -0.45053888 -0.50082992 -0.51413118\n",
      " -0.59504043 -0.61357817 -0.6054168  -0.60639811 -0.67225436 -0.64860353\n",
      " -0.66597546 -0.6300332  -0.68193698 -0.64908385 -0.63659756 -0.63967603\n",
      " -0.58413729 -0.58472471 -0.49989477 -0.48958459 -0.48611449 -0.40562813\n",
      " -0.38526447 -0.35761994 -0.26760168 -0.25629623 -0.19867204 -0.17271372\n",
      " -0.08975168 -0.03431643  0.05352076  0.06888319  0.13879424  0.24557034\n",
      "  0.33927755  0.39656152  0.47121163  0.49000055  0.54520791  0.67956041\n",
      "  0.74296137  0.74122925  0.81332835  0.93765787  0.95050784  1.04616331\n",
      "  1.10462891  1.11284699  1.16641158  1.26832507  1.32800774  1.33912472\n",
      "  1.42035029  1.46021429  1.45140585  1.52283912  1.50371032  1.58143819\n",
      "  1.60943201  1.59736359  1.63051789  1.62270779  1.63456036  1.62550228\n",
      "  1.60293969  1.62208442  1.60461952  1.6277576   1.55958783  1.59924358\n",
      "  1.5673318   1.5324792   1.51730617  1.43345315  1.41720114  1.35776902\n",
      "  1.37542892  1.32472129  1.25183747  1.19747598  1.15092707  1.09366706\n",
      "  1.05601311  0.96098411  0.896485    0.83129757  0.78513114  0.77968268\n",
      "  0.72917676  0.60256323  0.55934681  0.48361147  0.46403356  0.37524732\n",
      "  0.34528609  0.34027421  0.25645078  0.21450908  0.15618803  0.09001126\n",
      "  0.08878007  0.05896145 -0.0020486  -0.02265717 -0.07988171 -0.0734865\n",
      " -0.06462503 -0.13931768 -0.12463146 -0.12293254 -0.17821291 -0.15572956\n",
      " -0.17088025 -0.10063302 -0.09289763 -0.1481087  -0.09809175 -0.05476469\n",
      " -0.02394617 -0.00290319  0.01213232  0.01351779  0.05652197  0.16104861\n",
      "  0.21460364  0.23569036  0.29091378  0.3261773   0.35518055  0.4271504\n",
      "  0.45982223  0.59075324  0.60047414  0.65855261  0.76925446  0.83521744\n",
      "  0.90248944  0.97587831  1.01024316  1.04872294  1.17023532  1.19600838\n",
      "  1.30837045  1.36709271  1.39416275  1.41611742  1.48417738  1.51289784\n",
      "  1.59792991  1.63257854  1.66774112  1.74571955  1.78507126  1.85959706\n",
      "  1.87504087  1.87486458  1.88472582  1.92671856  1.93872241  1.94495712\n",
      "  2.01038341  2.00918671  2.00256725  1.99466163  1.95841608  1.9447526\n",
      "  1.93777647  1.92367473  1.93866836  1.8986922   1.89843098  1.86118804\n",
      "  1.79902937  1.75439343  1.71308101  1.71503899  1.6687907   1.615653\n",
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      "  4.66475345e-04 -4.81113378e-05 -2.22189660e-04  2.33977664e-04\n",
      " -9.06186228e-05  6.04410563e-05  1.25233831e-04 -1.83880502e-04\n",
      "  4.83347201e-05  1.14379828e-04 -2.00402979e-05  2.18308877e-04\n",
      " -3.28099667e-04 -1.34282218e-04 -4.55812755e-05  1.90569422e-04\n",
      "  2.02970366e-04  2.87882955e-05 -2.62667044e-04  1.10432323e-04\n",
      " -9.08029384e-05  1.14313030e-04  1.44867300e-06 -7.33441950e-05\n",
      " -1.69690852e-04  1.06870647e-04 -9.19814350e-05 -6.47920447e-05\n",
      " -2.62498309e-04 -2.19900086e-04  2.88622771e-04  1.20092513e-04\n",
      "  2.45508918e-04  1.13228507e-04 -4.05620919e-04 -4.27952878e-04\n",
      "  2.74531513e-04 -1.04800497e-04  2.40846277e-04  5.60225170e-05\n",
      "  8.74876186e-06 -1.61520406e-04  1.43709150e-04 -4.87421863e-04\n",
      "  1.29888336e-04 -2.62187662e-04  3.18724694e-04  1.07477989e-05\n",
      "  1.59137399e-04 -3.69430385e-04  1.15111059e-04 -3.30436508e-04\n",
      "  4.20995311e-04  1.30751877e-04  1.80239298e-04 -2.32135187e-04\n",
      " -1.54583972e-04 -2.59318833e-04  3.16260051e-04  8.84849059e-05\n",
      "  1.40856000e-04 -2.87066354e-04 -1.42354666e-05 -5.77078885e-05\n",
      "  2.19997888e-04  4.44557958e-05  8.55724746e-05  2.03793339e-04\n",
      " -6.94907475e-05  4.98948309e-06 -1.30061726e-04 -2.63808006e-04\n",
      "  2.47575343e-04  4.69710134e-04 -2.12868309e-04 -6.21820531e-05\n",
      " -1.04616071e-04 -1.38741207e-04  3.33181745e-04  2.04940660e-04]\n",
      "4 [ 1.00946392  1.05717739  1.04652919  1.08952873  1.06881707  1.01529108\n",
      "  0.98870958  1.00280699  1.01707148  0.94074371  0.89498295  0.90926376\n",
      "  0.82922777  0.78098826  0.74348107  0.70400836  0.71462602  0.68199858\n",
      "  0.59790822  0.51864667  0.46978947  0.47017196  0.38462303  0.35737141\n",
      "  0.26157925  0.2262517   0.13898847  0.13141079  0.02197326 -0.04636967\n",
      " -0.04639196 -0.08164159 -0.18488797 -0.23381065 -0.27492376 -0.35417849\n",
      " -0.37823537 -0.4250012  -0.47842739 -0.45053639 -0.50083138 -0.51413346\n",
      " -0.59503625 -0.61358203 -0.60541815 -0.6064049  -0.67225124 -0.64860364\n",
      " -0.6659787  -0.63003547 -0.68193758 -0.64908514 -0.63660201 -0.63968177\n",
      " -0.5841346  -0.58472782 -0.49989627 -0.48958183 -0.48611779 -0.40562649\n",
      " -0.38526832 -0.35761869 -0.2676014  -0.2562991  -0.19867527 -0.17271238\n",
      " -0.08975411 -0.03431852  0.05351564  0.06888291  0.13879139  0.24557159\n",
      "  0.33927883  0.3965622   0.47121086  0.49000305  0.5452091   0.67955527\n",
      "  0.74295972  0.74123056  0.81332896  0.93765585  0.95050831  1.04616488\n",
      "  1.10462744  1.1128456   1.16641234  1.26832083  1.32800879  1.33912695\n",
      "  1.42035604  1.46021232  1.45140333  1.52284203  1.50370834  1.58143775\n",
      "  1.60943429  1.59736336  1.63052373  1.6227063   1.63455989  1.62550043\n",
      "  1.60294089  1.62208244  1.60461725  1.62775782  1.55958866  1.59924632\n",
      "  1.56733361  1.53248055  1.51730715  1.43344915  1.41720086  1.35776949\n",
      "  1.3754269   1.32472405  1.25183682  1.19748002  1.15092593  1.09366694\n",
      "  1.05601371  0.96098073  0.89647973  0.83129844  0.78512898  0.77968467\n",
      "  0.72917545  0.60256633  0.55934762  0.48360346  0.46402822  0.37524764\n",
      "  0.34528504  0.34027683  0.256448    0.21450873  0.15618778  0.09000662\n",
      "  0.08878047  0.05895861 -0.00205309 -0.02265494 -0.07988448 -0.07349165\n",
      " -0.06462424 -0.13931952 -0.12462918 -0.12293857 -0.17822095 -0.15572653\n",
      " -0.17088252 -0.10063818 -0.0928988  -0.14811024 -0.09809082 -0.05476727\n",
      " -0.02394736 -0.00290395  0.01212735  0.01351476  0.05651826  0.1610456\n",
      "  0.21460431  0.23569255  0.29091795  0.32617012  0.35517724  0.42715006\n",
      "  0.45981717  0.59074906  0.60047311  0.65855032  0.7692562   0.83521663\n",
      "  0.90248904  0.97588112  1.01023932  1.04871973  1.17023351  1.19600926\n",
      "  1.30837192  1.36709745  1.39416006  1.41611896  1.48417482  1.51289282\n",
      "  1.59792742  1.63257586  1.6677391   1.74572228  1.78507289  1.85959853\n",
      "  1.87504345  1.87486635  1.8847236   1.92671327  1.93872025  1.94495763\n",
      "  2.01038671  2.0091888   2.00256976  1.9946646   1.9584115   1.94475075\n",
      "  1.93777289  1.92367177  1.9386701   1.89869495  1.89843392  1.86118738\n",
      "  1.79902654  1.75439321  1.71307805  1.71503887  1.66879424  1.61565045\n",
      "  1.56269557  1.47662028  1.41651501  1.43002497  1.30028914  1.241188\n",
      "  1.18413989  1.15072599  1.09088676  1.03303336  0.97036654  0.90851133\n",
      "  0.84568679  0.81876491  0.74012919  0.70714465  0.60120021  0.58518065\n",
      "  0.52971065  0.41664828  0.37855084  0.35550034  0.34216068  0.2504759\n",
      "  0.21440388  0.2153927   0.15095019  0.15184643  0.12324774  0.08701156\n",
      "  0.11367764  0.02953322  0.02152786  0.04239552  0.06427682  0.0960992\n",
      "  0.09893975  0.09940388  0.07325489  0.07605469  0.10107309  0.11210462\n",
      "  0.13219482  0.20585331  0.27536519  0.25434973  0.30977478  0.32330953\n",
      "  0.39606948  0.44353361  0.54040218  0.561278    0.65097068  0.67540596\n",
      "  0.74820314  0.82228234  0.85234611  0.92273472  0.94962281  1.07661963\n",
      "  1.09475167  1.13208595  1.24769574  1.27852824  1.34702434  1.40607767\n",
      "  1.42253117  1.48175703  1.53380796  1.64788008  1.66053661  1.72274697\n",
      "  1.71186657  1.81209726  1.80984982  1.84408734  1.87388749  1.94966063\n",
      "  1.98415696  1.9473701   2.0170902   2.02137437  1.97521541  1.98910067\n",
      "  2.00915946  2.01998243  2.00329122  1.99781693  1.92923126  1.958366\n",
      "  1.94073685  1.91164429  1.88233278  1.83664587  1.81126557  1.7179345\n",
      "  1.66272105  1.61394165  1.62472932  1.60049075  1.53483777  1.41717636\n",
      "  1.36365355  1.30897401  1.23709114  1.18007306  1.09854794  1.10731708\n",
      "  0.98855625  0.90950028  0.87900461  0.78293628  0.74592418  0.69927815\n",
      "  0.62228103  0.51918834  0.51663049  0.41313138  0.41368849  0.29084818\n",
      "  0.2288747   0.23002393  0.16620171  0.17080473  0.12052275  0.00731005\n",
      " -0.03340926 -0.0565633  -0.05924943 -0.0554893  -0.11161356 -0.10132312\n",
      " -0.13571249 -0.15873906 -0.13548216 -0.12981838 -0.17307589 -0.13869395\n",
      " -0.12460622 -0.10242263 -0.13480018 -0.11378407 -0.08219804 -0.0311584\n",
      " -0.00725674  0.02272795  0.10232349  0.09584877  0.19068166  0.21274389\n",
      "  0.30561841  0.35702846  0.40511785  0.41768858  0.43481822  0.51736118\n",
      "  0.60086488  0.64712262  0.68309128  0.78902375  0.79536823  0.89172437\n",
      "  0.8932336   0.94949028  1.01657846  1.06561051  1.14284626  1.19960572\n",
      "  1.26392615  1.28449079  1.3124398   1.37094842  1.38820842  1.44610219\n",
      "  1.48447876  1.5658487   1.55415451  1.54524079  1.60429705  1.60837244\n",
      "  1.66581993  1.64474244  1.63086936  1.66570491  1.64919004  1.61365299\n",
      "  1.57453608  1.58047244  1.6090319   1.60368613  1.55923794  1.54880125\n",
      "  1.51444987  1.44718106  1.41361536  1.39192717  1.31477162  1.21695882\n",
      "  1.18876408  1.12658992  1.12810915  1.03730056  0.93182724  0.8924077\n",
      "  0.87087137  0.79908576  0.69352765  0.59624293  0.53747724  0.52957955\n",
      "  0.42859011  0.3827055   0.28115532  0.20256462  0.13237229  0.07075039\n",
      "  0.03520941  0.01856648 -0.06565542 -0.17960008 -0.19143131 -0.29062289\n",
      " -0.33893272 -0.38958903 -0.43184824 -0.46612322 -0.49810293 -0.52983418\n",
      " -0.52483048 -0.58721989 -0.60831246 -0.64221879 -0.62541093 -0.61135372\n",
      " -0.66127401 -0.6431393  -0.62953213 -0.63465634 -0.65335553 -0.64663455\n",
      " -0.59091345 -0.57371563 -0.60217364 -0.55476549 -0.5315809  -0.46474962\n",
      " -0.40959362 -0.37949473 -0.39224351 -0.29959832 -0.22826534 -0.19178309\n",
      " -0.21203849 -0.13022008 -0.07769271  0.01779306  0.04193595  0.12295723\n",
      "  0.13670316  0.16902491  0.28399377  0.36409593  0.40669735  0.44559204\n",
      "  0.45619278  0.52352998  0.58832593  0.66312123  0.67043132  0.76793564\n",
      "  0.74896874  0.83096453  0.89723322  0.92405442  0.9320652   0.99332608\n",
      "  0.99231892  0.99845581  1.01223246  1.0622165   1.08482245  1.0676138\n",
      "  1.02518578  1.08448743  1.04041714  1.01250643  1.00537871  1.03520464\n",
      "  1.00321244  0.94220888  0.94643088  0.89905195  0.8479542   0.86615925\n",
      "  0.82849892  0.77567125  0.70135327  0.64937785  0.56158388  0.57030057\n",
      "  0.51910569  0.45117446  0.40313635  0.29476184  0.20392484  0.19877139\n",
      "  0.07981146  0.0699606   0.00405072 -0.12388723 -0.18724155 -0.27769188\n",
      " -0.34655803 -0.33878009 -0.40681672 -0.48043114 -0.56918171 -0.67026148\n",
      " -0.72948684 -0.78112262 -0.80902774 -0.83808742 -0.8735341  -0.95138866\n",
      " -1.04369291 -1.08876573 -1.04775853 -1.10645641 -1.13442284 -1.17143646\n",
      " -1.23974123 -1.19284371 -1.26396653 -1.28090976 -1.29983561 -1.23834189\n",
      " -1.30218673 -1.28702497 -1.27966078 -1.27584519 -1.20376918 -1.22028384\n",
      " -1.20589179 -1.18879247 -1.1259239  -1.12662863 -1.0529694  -1.03048541\n",
      " -0.95740775 -0.91359082 -0.88319769 -0.85239086 -0.79539746 -0.76596117\n",
      " -0.71206662 -0.63864243 -0.53558546 -0.49847707 -0.46176425 -0.39355482\n",
      " -0.31382444 -0.26661381 -0.19612613 -0.1893599  -0.10189781 -0.03864081\n",
      " -0.05266548  0.07241475  0.11053818  0.09348116  0.20936766  0.20243331\n",
      "  0.22071889  0.30572684  0.31414274  0.31298319  0.38846881  0.36809358\n",
      "  0.4439119   0.44348291  0.43400087  0.47969536  0.46142635  0.50441055\n",
      "  0.46597006  0.45305742  0.44739994  0.45390215  0.3806845   0.37844385\n",
      "  0.3837242   0.3022214   0.27606167  0.29326724  0.24605488  0.21546881\n",
      "  0.1380905   0.0575215   0.06661127 -0.05950492 -0.05139414 -0.09483796\n",
      " -0.16619907 -0.23148136 -0.34258087 -0.36697888 -0.418598   -0.55536171\n",
      " -0.5539071  -0.65214493 -0.71217684 -0.80673547 -0.87263125 -0.94554953\n",
      " -1.02161325 -1.04832039 -1.12135462 -1.16226091 -1.23752511 -1.2623938\n",
      " -1.347068   -1.37864383 -1.45002324 -1.52795272 -1.52994812 -1.52829667\n",
      " -1.60952585 -1.64867504 -1.701008   -1.7198165  -1.72516534 -1.73630198\n",
      " -1.70226895 -1.72826979 -1.72002541 -1.74779756 -1.72283919 -1.7332042\n",
      " -1.72697099 -1.71093522 -1.695823   -1.71207781 -1.65344702 -1.649147\n",
      " -1.64558585 -1.56645622 -1.5051114  -1.45206213 -1.40203595 -1.36104091\n",
      " -1.31350121 -1.32072884 -1.22769027 -1.18652348 -1.14230395 -1.06792812\n",
      " -1.0291515  -0.95195002 -0.94090549 -0.87646396 -0.76430688 -0.76082246\n",
      " -0.66255507 -0.62105962 -0.50940387 -0.47007332 -0.42119954 -0.4201283\n",
      " -0.32988838 -0.2545064  -0.2587743  -0.15667676 -0.109953   -0.1270031\n",
      " -0.0483055  -0.00796284 -0.04332702  0.0508032   0.07835479  0.09468554\n",
      "  0.04706922  0.05501285  0.08167878  0.07144039  0.0953355   0.12165155\n",
      "  0.08900141  0.04975071  0.07860736  0.03704896  0.03586735 -0.00481033\n",
      " -0.00351565 -0.07429846 -0.12220459 -0.15652805 -0.23234178 -0.22510615\n",
      " -0.32558353 -0.32942604 -0.39241735 -0.42869862 -0.54196457 -0.55550571\n",
      " -0.60178799 -0.68627843 -0.77146403 -0.79706457 -0.90502309 -0.90687163\n",
      " -0.98828187 -1.06304338 -1.08929736 -1.17284673 -1.20654273 -1.28141206\n",
      " -1.35400113 -1.43034207 -1.50583679 -1.53233352 -1.54391507 -1.64160809\n",
      " -1.71242083 -1.74974115 -1.77034081 -1.82563996 -1.82524621 -1.84567506\n",
      " -1.84518626 -1.93293877 -1.9426173  -1.90711132 -1.95471752 -1.97231968\n",
      " -1.92531186 -1.97996032 -1.91825309 -1.92921166 -1.89935816 -1.90938863\n",
      " -1.849253   -1.86795302 -1.83621758 -1.77573694 -1.79003    -1.68899667\n",
      " -1.65805372 -1.63944071 -1.54481991 -1.50613119 -1.50051837 -1.43134006\n",
      " -1.34069557 -1.3062204  -1.28435411 -1.16145421 -1.12805028 -1.06669384\n",
      " -1.02837002 -0.93125186 -0.86692472 -0.78720599 -0.7622405  -0.69952618\n",
      " -0.6623711  -0.58841434 -0.48633575 -0.44884895 -0.41334233 -0.35894589\n",
      " -0.25032096 -0.19590865 -0.19361711 -0.18930079 -0.12577699 -0.07323882\n",
      " -0.01098822 -0.01457707  0.04686471  0.03323095  0.08781918  0.10930842\n",
      "  0.11943247  0.10027549  0.0591972   0.11816542  0.11854735  0.11078175\n",
      "  0.086653    0.04058904  0.02235986  0.05189631 -0.02360924 -0.05979297\n",
      " -0.07249131 -0.11922373 -0.16118897 -0.21349276 -0.19541437 -0.26567047\n",
      " -0.32373031 -0.37552686 -0.41411641 -0.50012599 -0.50643663 -0.5621693\n",
      " -0.6610915  -0.7041911  -0.77877483 -0.84599482 -0.91597904 -0.96973663\n",
      " -1.06036357 -1.07797504 -1.14049806 -1.22566473 -1.26653507 -1.26492909\n",
      " -1.34997999 -1.43190355 -1.47744515 -1.50934704 -1.55386468 -1.5818235\n",
      " -1.61213479 -1.5965441  -1.68124895 -1.7012519  -1.67637733 -1.72045352\n",
      " -1.72012572 -1.72253434 -1.77070794 -1.79089604 -1.79300141 -1.73900633\n",
      " -1.71273068 -1.69489225 -1.69093062 -1.67914642 -1.67709867 -1.65271903\n",
      " -1.59201182 -1.58882829 -1.56941151 -1.47996703 -1.41798196 -1.40163641\n",
      " -1.30912398 -1.2962856  -1.25080013 -1.1911824  -1.1203028  -1.04373899\n",
      " -1.01223054 -0.92162964 -0.87137664 -0.78568969 -0.7637855  -0.64704918\n",
      " -0.56706026 -0.54799932 -0.49458047 -0.43333084 -0.30189712 -0.22914627\n",
      " -0.21386903 -0.11011345 -0.07835143 -0.01078659  0.01922986  0.09061842\n",
      "  0.16993118  0.19039282  0.21513083  0.23775484  0.33707272  0.33761789\n",
      "  0.37611495  0.37641694  0.43740631  0.43732014  0.46585375  0.45254812\n",
      "  0.44667445  0.44352124  0.50570861  0.48742838  0.4791286   0.40420995\n",
      "  0.42277166  0.40605496  0.36569202  0.39179492  0.35663628  0.25775863\n",
      "  0.2820062   0.22781475  0.18199281  0.10084184  0.09873561 -0.00315194\n",
      " -0.02413321 -0.04357486 -0.13483992 -0.18169071 -0.21415467 -0.32009914\n",
      " -0.33438224 -0.39246023 -0.47563745 -0.50566023 -0.60150112 -0.61435639\n",
      " -0.67333703 -0.75733462 -0.80150314 -0.86699767 -0.90066115 -0.9105712\n",
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      "  1.72531316e-05  1.77817084e-05 -6.00913089e-06  2.47249853e-05\n",
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      "  1.20433815e-05  1.20505249e-05  1.22345625e-05  1.81984553e-05\n",
      "  6.33195531e-06 -1.21370401e-05  2.08300508e-06  1.53733680e-06\n",
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      " -1.07447456e-05  2.29552838e-05 -9.10967693e-07  3.07621937e-05\n",
      "  6.00540597e-06  3.60271081e-06  9.74439422e-07  1.15355263e-05\n",
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      " -1.32761391e-05  1.53089300e-05  1.01778803e-05 -1.67145667e-05\n",
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      " -3.15200150e-06  1.93149959e-05  3.00903890e-05  1.46514161e-06\n",
      " -6.57608057e-06 -3.77870805e-07 -1.42665986e-05  1.53138938e-05\n",
      "  1.27047568e-05 -7.66159240e-06  1.15410746e-05 -3.60912513e-06\n",
      "  1.28279773e-05 -5.72033374e-06 -1.01599330e-05  5.20945119e-05]\n",
      "5 [ 1.00946382  1.05717731  1.04652919  1.08952835  1.06881748  1.01529166\n",
      "  0.98870949  1.00280733  1.01707151  0.94074373  0.89498326  0.90926382\n",
      "  0.82922747  0.78098797  0.74348136  0.70400866  0.71462556  0.68199877\n",
      "  0.59790823  0.51864701  0.46978966  0.47017202  0.38462259  0.35737153\n",
      "  0.26157969  0.22625172  0.13898795  0.13141094  0.02197312 -0.04636969\n",
      " -0.04639192 -0.08164151 -0.18488835 -0.23381039 -0.2749239  -0.35417889\n",
      " -0.37823598 -0.4250011  -0.47842742 -0.45053666 -0.50083157 -0.51413339\n",
      " -0.59503633 -0.61358188 -0.60541873 -0.60640493 -0.67225164 -0.64860369\n",
      " -0.66597866 -0.6300359  -0.68193786 -0.6490854  -0.6366024  -0.63968175\n",
      " -0.58413515 -0.58472783 -0.4998963  -0.48958215 -0.4861177  -0.40562665\n",
      " -0.38526807 -0.3576191  -0.26760152 -0.25629929 -0.19867546 -0.17271236\n",
      " -0.08975429 -0.03431918  0.05351544  0.06888257  0.13879159  0.24557178\n",
      "  0.33927859  0.39656174  0.47121132  0.49000347  0.54520875  0.67955521\n",
      "  0.74295951  0.74123016  0.81332929  0.93765629  0.95050786  1.04616443\n",
      "  1.10462782  1.11284562  1.16641192  1.26832125  1.32800853  1.33912707\n",
      "  1.42035623  1.46021242  1.45140337  1.52284194  1.5037086   1.58143764\n",
      "  1.60943427  1.59736376  1.63052364  1.6227067   1.63455957  1.62550056\n",
      "  1.6029408   1.62208222  1.60461729  1.62775762  1.5595889   1.59924654\n",
      "  1.56733384  1.53248046  1.51730688  1.4334495   1.41720077  1.35776944\n",
      "  1.37542691  1.32472376  1.25183712  1.19748018  1.15092627  1.09366677\n",
      "  1.05601329  0.96098034  0.89647986  0.83129836  0.785129    0.77968424\n",
      "  0.72917553  0.60256632  0.55934736  0.48360344  0.46402779  0.37524719\n",
      "  0.34528522  0.3402766   0.25644783  0.21450854  0.1561878   0.09000664\n",
      "  0.08878002  0.05895814 -0.00205323 -0.02265512 -0.07988468 -0.07349177\n",
      " -0.06462459 -0.13931957 -0.12462972 -0.12293889 -0.17822101 -0.15572697\n",
      " -0.17088271 -0.10063865 -0.09289923 -0.14811027 -0.0980908  -0.05476706\n",
      " -0.02394808 -0.00290462  0.01212742  0.01351451  0.05651797  0.16104546\n",
      "  0.214604    0.23569257  0.29091772  0.32617023  0.35517704  0.42714952\n",
      "  0.45981679  0.59074866  0.60047275  0.65855029  0.76925637  0.83521653\n",
      "  0.90248876  0.97588104  1.01023925  1.04871957  1.17023366  1.19600916\n",
      "  1.3083719   1.36709742  1.39416022  1.41611886  1.48417482  1.51289244\n",
      "  1.59792685  1.63257559  1.66773922  1.74572242  1.78507305  1.85959848\n",
      "  1.8750437   1.87486631  1.88472344  1.92671329  1.93871997  1.94495765\n",
      "  2.01038692  2.009189    2.00256983  1.99466454  1.95841167  1.94475039\n",
      "  1.93777264  1.92367172  1.93867008  1.89869515  1.89843384  1.86118733\n",
      "  1.79902659  1.75439303  1.71307822  1.71503892  1.66879374  1.61565062\n",
      "  1.5626958   1.47662048  1.4165147   1.43002473  1.30028886  1.24118772\n",
      "  1.18413988  1.15072601  1.09088603  1.0330334   0.97036632  0.90851151\n",
      "  0.84568655  0.81876462  0.74012931  0.70714469  0.60120008  0.58518029\n",
      "  0.52971044  0.4166482   0.37855023  0.35550036  0.34216013  0.25047537\n",
      "  0.21440396  0.2153923   0.1509501   0.15184614  0.12324764  0.08701126\n",
      "  0.11367699  0.02953291  0.02152737  0.04239537  0.06427679  0.09609873\n",
      "  0.09893987  0.09940404  0.07325467  0.07605407  0.10107275  0.11210412\n",
      "  0.13219449  0.20585303  0.27536501  0.25434918  0.3097747   0.32330932\n",
      "  0.39606921  0.44353308  0.54040195  0.56127784  0.6509707   0.67540611\n",
      "  0.74820286  0.82228204  0.85234632  0.92273422  0.94962278  1.07661944\n",
      "  1.0947513   1.13208603  1.24769571  1.27852849  1.34702361  1.40607766\n",
      "  1.42253112  1.48175701  1.53380773  1.64787998  1.6605365   1.72274719\n",
      "  1.71186647  1.81209711  1.80984974  1.84408718  1.87388717  1.94966112\n",
      "  1.98415689  1.9473702   2.01709024  2.02137456  1.97521513  1.98910079\n",
      "  2.00915963  2.01998206  2.003291    1.99781708  1.92923139  1.9583659\n",
      "  1.94073697  1.91164446  1.88233291  1.836646    1.81126517  1.71793418\n",
      "  1.66272116  1.61394164  1.62472922  1.60049057  1.53483786  1.4171767\n",
      "  1.36365342  1.30897383  1.23709092  1.18007256  1.09854805  1.10731695\n",
      "  0.98855594  0.90950012  0.87900481  0.78293612  0.74592384  0.69927784\n",
      "  0.62228115  0.51918834  0.51663035  0.41313116  0.41368789  0.29084768\n",
      "  0.22887497  0.23002378  0.16620176  0.17080415  0.12052252  0.00731011\n",
      " -0.0334097  -0.05656346 -0.0592499  -0.05548991 -0.11161381 -0.101323\n",
      " -0.13571259 -0.15873936 -0.1354827  -0.12981832 -0.17307613 -0.13869407\n",
      " -0.12460644 -0.10242303 -0.13480051 -0.11378441 -0.08219821 -0.03115895\n",
      " -0.00725715  0.02272765  0.10232323  0.09584852  0.19068156  0.21274415\n",
      "  0.30561849  0.35702808  0.40511794  0.41768852  0.434818    0.51736103\n",
      "  0.60086441  0.64712243  0.68309135  0.78902393  0.79536823  0.89172408\n",
      "  0.89323342  0.94949011  1.01657813  1.06561068  1.14284591  1.19960596\n",
      "  1.2639262   1.28449084  1.31243959  1.37094834  1.3882086   1.44610193\n",
      "  1.48447884  1.56584857  1.55415448  1.54524116  1.60429707  1.60837251\n",
      "  1.6658198   1.6447428   1.63086976  1.66570475  1.64918993  1.61365275\n",
      "  1.574536    1.58047243  1.60903185  1.60368616  1.55923795  1.54880165\n",
      "  1.5144505   1.44718115  1.41361547  1.39192699  1.31477141  1.21695894\n",
      "  1.18876423  1.12658963  1.12810871  1.03730056  0.93182768  0.89240793\n",
      "  0.87087122  0.79908543  0.69352743  0.59624319  0.53747736  0.52957936\n",
      "  0.4285899   0.3827054   0.28115512  0.2025645   0.13237224  0.07075019\n",
      "  0.03520924  0.01856653 -0.06565537 -0.17960002 -0.19143126 -0.29062309\n",
      " -0.33893323 -0.38958962 -0.43184826 -0.46612366 -0.4981029  -0.5298344\n",
      " -0.52483084 -0.58721991 -0.6083126  -0.64221903 -0.62541112 -0.61135397\n",
      " -0.66127395 -0.64313955 -0.62953225 -0.63465632 -0.65335583 -0.64663449\n",
      " -0.59091377 -0.57371614 -0.60217406 -0.55476526 -0.53158097 -0.46475017\n",
      " -0.40959405 -0.37949428 -0.39224349 -0.29959815 -0.22826569 -0.19178329\n",
      " -0.21203881 -0.13021976 -0.07769257  0.01779264  0.04193544  0.12295737\n",
      "  0.13670314  0.16902522  0.28399369  0.364096    0.40669696  0.44559238\n",
      "  0.45619287  0.52353013  0.58832575  0.6631209   0.67043114  0.76793603\n",
      "  0.74896875  0.83096465  0.89723333  0.92405485  0.93206501  0.99332637\n",
      "  0.992319    0.99845612  1.01223236  1.06221675  1.08482256  1.06761408\n",
      "  1.0251858   1.08448758  1.04041732  1.01250626  1.00537877  1.03520516\n",
      "  1.00321209  0.94220885  0.94643107  0.89905229  0.84795414  0.86615961\n",
      "  0.82849907  0.77567109  0.70135345  0.64937804  0.56158392  0.57030086\n",
      "  0.51910545  0.45117477  0.40313634  0.294762    0.20392497  0.19877147\n",
      "  0.07981157  0.06996063  0.00405056 -0.12388723 -0.18724185 -0.27769162\n",
      " -0.34655807 -0.33878017 -0.40681652 -0.48043121 -0.56918167 -0.67026149\n",
      " -0.72948718 -0.78112262 -0.80902771 -0.83808786 -0.87353409 -0.95138863\n",
      " -1.04369287 -1.08876547 -1.04775895 -1.10645665 -1.13442288 -1.17143605\n",
      " -1.23974138 -1.19284392 -1.26396659 -1.28091001 -1.29983566 -1.23834208\n",
      " -1.30218722 -1.28702494 -1.27966067 -1.27584531 -1.20376946 -1.22028389\n",
      " -1.20589183 -1.1887926  -1.12592395 -1.12662898 -1.0529693  -1.03048538\n",
      " -0.95740752 -0.9135908  -0.88319747 -0.85239122 -0.79539747 -0.76596124\n",
      " -0.71206674 -0.63864261 -0.53558541 -0.49847722 -0.46176382 -0.39355455\n",
      " -0.31382443 -0.26661355 -0.1961262  -0.18935987 -0.1018973  -0.038641\n",
      " -0.05266536  0.072415    0.11053837  0.09348113  0.20936795  0.20243363\n",
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      "  9.60235073e-07  9.01000554e-07  9.17967817e-07 -5.09737692e-07\n",
      "  2.18951981e-07  1.94328259e-06  1.14006977e-06  6.64682273e-07\n",
      "  5.51031356e-07 -1.78482359e-06  2.12043440e-06  1.53592645e-06\n",
      " -9.72924194e-07 -9.66536258e-07  3.98752000e-07  2.45698544e-06\n",
      " -1.36641767e-07  1.12776987e-06  1.77797860e-06  2.10978864e-06]\n",
      "6 [ 1.00946385  1.0571773   1.04652914  1.08952836  1.06881749  1.01529167\n",
      "  0.98870953  1.00280735  1.01707154  0.94074373  0.89498323  0.90926382\n",
      "  0.8292275   0.780988    0.74348135  0.70400865  0.71462558  0.68199873\n",
      "  0.59790826  0.51864701  0.46978969  0.47017202  0.38462259  0.35737153\n",
      "  0.26157967  0.22625171  0.13898798  0.13141093  0.02197312 -0.0463697\n",
      " -0.04639192 -0.08164153 -0.18488833 -0.23381045 -0.2749239  -0.35417889\n",
      " -0.37823598 -0.42500112 -0.47842744 -0.45053669 -0.50083158 -0.5141334\n",
      " -0.59503634 -0.61358191 -0.6054187  -0.60640496 -0.67225167 -0.64860372\n",
      " -0.66597867 -0.6300359  -0.68193791 -0.64908544 -0.63660238 -0.63968179\n",
      " -0.58413517 -0.58472786 -0.49989632 -0.48958216 -0.48611771 -0.40562663\n",
      " -0.38526809 -0.3576191  -0.26760157 -0.25629929 -0.19867544 -0.17271241\n",
      " -0.08975432 -0.03431918  0.0535154   0.06888258  0.1387916   0.24557176\n",
      "  0.33927856  0.39656176  0.47121132  0.49000345  0.54520877  0.67955521\n",
      "  0.74295949  0.74123017  0.81332928  0.93765628  0.95050786  1.04616442\n",
      "  1.10462779  1.11284563  1.16641196  1.26832122  1.32800857  1.33912705\n",
      "  1.4203562   1.46021245  1.45140339  1.52284194  1.50370859  1.58143767\n",
      "  1.60943427  1.59736374  1.63052366  1.62270667  1.63455962  1.62550053\n",
      "  1.60294078  1.62208224  1.60461727  1.62775765  1.5595889   1.59924656\n",
      "  1.56733384  1.53248045  1.5173069   1.43344949  1.4172008   1.35776943\n",
      "  1.3754269   1.32472377  1.2518371   1.1974802   1.15092627  1.09366677\n",
      "  1.05601325  0.96098035  0.89647986  0.83129837  0.78512898  0.77968424\n",
      "  0.7291755   0.60256628  0.55934736  0.48360344  0.4640278   0.37524717\n",
      "  0.34528517  0.34027658  0.25644782  0.21450853  0.15618779  0.09000664\n",
      "  0.08877999  0.05895812 -0.00205324 -0.02265517 -0.07988469 -0.07349178\n",
      " -0.0646246  -0.13931963 -0.12462976 -0.12293889 -0.17822101 -0.155727\n",
      " -0.17088277 -0.10063866 -0.09289926 -0.1481103  -0.09809079 -0.0547671\n",
      " -0.0239481  -0.00290466  0.01212737  0.01351452  0.05651797  0.16104544\n",
      "  0.21460399  0.23569251  0.2909177   0.32617024  0.35517703  0.42714948\n",
      "  0.45981675  0.59074863  0.60047273  0.6585503   0.76925635  0.83521653\n",
      "  0.90248875  0.97588099  1.01023926  1.0487196   1.17023365  1.19600917\n",
      "  1.30837188  1.36709739  1.39416023  1.41611886  1.4841748   1.51289243\n",
      "  1.59792682  1.63257557  1.66773922  1.74572242  1.78507304  1.8595985\n",
      "  1.87504367  1.87486631  1.88472346  1.92671329  1.93871999  1.94495764\n",
      "  2.01038691  2.00918901  2.00256982  1.99466454  1.95841167  1.9447504\n",
      "  1.93777264  1.92367172  1.93867008  1.89869512  1.89843383  1.86118733\n",
      "  1.79902659  1.75439306  1.71307823  1.71503889  1.66879373  1.61565061\n",
      "  1.56269581  1.47662048  1.41651471  1.43002471  1.30028884  1.2411877\n",
      "  1.18413986  1.150726    1.09088604  1.03303333  0.97036634  0.90851149\n",
      "  0.84568653  0.81876463  0.74012931  0.70714467  0.60120004  0.58518029\n",
      "  0.52971044  0.41664815  0.37855022  0.35550031  0.34216012  0.25047533\n",
      "  0.21440389  0.21539232  0.1509501   0.15184611  0.12324758  0.08701123\n",
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      "  6.41023004e-08 -1.01302358e-07 -5.00224070e-08 -1.65655269e-07\n",
      "  8.28115259e-08 -1.77454264e-07 -2.31926424e-07  4.34017359e-08\n",
      "  2.05412774e-08  2.88085866e-08 -9.82033751e-08 -1.12562774e-07\n",
      " -8.91817331e-08  4.31890223e-08 -4.86725923e-09  4.13771976e-08\n",
      "  7.33897722e-08 -9.75634413e-08 -2.04388513e-07  1.18921532e-07\n",
      " -2.88091356e-07  1.93229017e-07 -1.26489963e-07  2.87528045e-08\n",
      " -1.27144963e-07  9.51148764e-09 -1.41664788e-07 -7.55981272e-08\n",
      " -8.42881599e-08  1.60232021e-07  7.95233646e-08  1.40096199e-07\n",
      " -2.58565549e-07  1.14888014e-07 -1.80535969e-07  2.51556148e-07\n",
      " -1.09815877e-08  6.09143589e-08 -1.00252116e-07 -3.44770019e-08\n",
      " -7.20390292e-08  7.37697249e-08  7.58619169e-08  1.03998052e-07\n",
      "  1.43044820e-07 -5.93855243e-08 -2.34454320e-08  1.23383209e-07\n",
      " -5.33196589e-08  2.56339862e-07  5.68894990e-08 -4.10472044e-08\n",
      " -3.42331040e-08  2.33893570e-08  3.33431034e-08  1.43808477e-08\n",
      "  2.09771540e-07  1.67209284e-07  3.27706783e-07 -9.60225749e-08]\n",
      "0.3357986487825386\n"
     ]
    }
   ],
   "source": [
    "print(\"<==Grad Conjugado==>\")\n",
    "limpio = gradienteConjugado(x0, b)\n",
    "print(f(limpio))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "0-dimensional array given. Array must be at least two-dimensional",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "Cell \u001b[1;32mIn [88], line 8\u001b[0m\n\u001b[0;32m      6\u001b[0m         \u001b[39mprint\u001b[39m(k, f(x0), x0)\n\u001b[0;32m      7\u001b[0m     \u001b[39mreturn\u001b[39;00m x0\n\u001b[1;32m----> 8\u001b[0m limpio \u001b[39m=\u001b[39m newtonNDim(x0)\n\u001b[0;32m      9\u001b[0m \u001b[39mprint\u001b[39m(f(limpio))\n",
      "Cell \u001b[1;32mIn [88], line 4\u001b[0m, in \u001b[0;36mnewtonNDim\u001b[1;34m(x0, tol)\u001b[0m\n\u001b[0;32m      2\u001b[0m k \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\n\u001b[0;32m      3\u001b[0m \u001b[39mwhile\u001b[39;00m np\u001b[39m.\u001b[39mlinalg\u001b[39m.\u001b[39mnorm(grad(x0)) \u001b[39m>\u001b[39m tol:\n\u001b[1;32m----> 4\u001b[0m     x0 \u001b[39m=\u001b[39m x0 \u001b[39m-\u001b[39m np\u001b[39m.\u001b[39mdot(np\u001b[39m.\u001b[39;49mlinalg\u001b[39m.\u001b[39;49minv(hessiano(x0)), grad(x0))\n\u001b[0;32m      5\u001b[0m     k \u001b[39m=\u001b[39m k\u001b[39m+\u001b[39m\u001b[39m1\u001b[39m\n\u001b[0;32m      6\u001b[0m     \u001b[39mprint\u001b[39m(k, f(x0), x0)\n",
      "File \u001b[1;32m<__array_function__ internals>:180\u001b[0m, in \u001b[0;36minv\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "File \u001b[1;32mc:\\Users\\Daniel\\.conda\\envs\\baile\\lib\\site-packages\\numpy\\linalg\\linalg.py:546\u001b[0m, in \u001b[0;36minv\u001b[1;34m(a)\u001b[0m\n\u001b[0;32m    485\u001b[0m \u001b[39m\"\"\"\u001b[39;00m\n\u001b[0;32m    486\u001b[0m \u001b[39mCompute the (multiplicative) inverse of a matrix.\u001b[39;00m\n\u001b[0;32m    487\u001b[0m \n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m    543\u001b[0m \n\u001b[0;32m    544\u001b[0m \u001b[39m\"\"\"\u001b[39;00m\n\u001b[0;32m    545\u001b[0m a, wrap \u001b[39m=\u001b[39m _makearray(a)\n\u001b[1;32m--> 546\u001b[0m _assert_stacked_2d(a)\n\u001b[0;32m    547\u001b[0m _assert_stacked_square(a)\n\u001b[0;32m    548\u001b[0m t, result_t \u001b[39m=\u001b[39m _commonType(a)\n",
      "File \u001b[1;32mc:\\Users\\Daniel\\.conda\\envs\\baile\\lib\\site-packages\\numpy\\linalg\\linalg.py:197\u001b[0m, in \u001b[0;36m_assert_stacked_2d\u001b[1;34m(*arrays)\u001b[0m\n\u001b[0;32m    195\u001b[0m \u001b[39mfor\u001b[39;00m a \u001b[39min\u001b[39;00m arrays:\n\u001b[0;32m    196\u001b[0m     \u001b[39mif\u001b[39;00m a\u001b[39m.\u001b[39mndim \u001b[39m<\u001b[39m \u001b[39m2\u001b[39m:\n\u001b[1;32m--> 197\u001b[0m         \u001b[39mraise\u001b[39;00m LinAlgError(\u001b[39m'\u001b[39m\u001b[39m%d\u001b[39;00m\u001b[39m-dimensional array given. Array must be \u001b[39m\u001b[39m'\u001b[39m\n\u001b[0;32m    198\u001b[0m                 \u001b[39m'\u001b[39m\u001b[39mat least two-dimensional\u001b[39m\u001b[39m'\u001b[39m \u001b[39m%\u001b[39m a\u001b[39m.\u001b[39mndim)\n",
      "\u001b[1;31mLinAlgError\u001b[0m: 0-dimensional array given. Array must be at least two-dimensional"
     ]
    }
   ],
   "source": [
    "def newtonNDim(x0, tol=1e-4):\n",
    "    k = 0\n",
    "    while np.linalg.norm(grad(x0)) > tol:\n",
    "\n",
    "        A = hessiano(x0)\n",
    "        aAsArray = A.toarray()\n",
    "        x0 = x0 - np.dot(np.linalg.inv(aAsArray), grad(x0))\n",
    "        k = k+1\n",
    "        print(k, f(x0), x0)\n",
    "    return x0\n",
    "limpio = newtonNDim(x0)\n",
    "print(f(limpio))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<==Descenso de Gradiente==>\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'gradDescent' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn [14], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[39mprint\u001b[39m(\u001b[39m\"\u001b[39m\u001b[39m<==Descenso de Gradiente==>\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m----> 2\u001b[0m limpioDG \u001b[39m=\u001b[39m gradDescent(x0)\n",
      "\u001b[1;31mNameError\u001b[0m: name 'gradDescent' is not defined"
     ]
    }
   ],
   "source": [
    "print(\"<==Descenso de Gradiente==>\")\n",
    "limpioDG = gradDescent(x0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.538581852236683\n"
     ]
    }
   ],
   "source": [
    "# Evaluamos el gradiente condición de primer orden \n",
    "\n",
    "# gc = grad(limpio)\n",
    "# dg = grad(limpioDG)\n",
    "# print(gc)\n",
    "# print(dg)\n",
    "from scipy.sparse.linalg import splu\n",
    "A = hessiano(x0)\n",
    "\n",
    "aAsArray = A.toarray()\n",
    "limpioInv = np.dot(np.linalg.inv(aAsArray), b)\n",
    "print(f(limpioInv))\n",
    "# np.linalg.det(aAsArray)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "1.0272245758954355 1.047728992787289 1.047730830302571 1.0477289901917952\n",
      "1.085632255079729 1.0604626720906163 1.0604645169442941 1.0604626754547668\n",
      "1.0742882298075256 1.0631285252313165 1.0631303673884 1.063128528867755\n",
      "1.0747218603853175 1.0613305010290337 1.06133234333444 1.061330501904834\n",
      "1.0537269626539265 1.0541759276352871 1.054177767822877 1.054175931549719\n",
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      "1.0874318447937887 1.0566717142774085 1.0566735549579847 1.056671714818268\n",
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      "1.0923574161728697 1.0603141849030884 1.0603160023394282 1.0603141758382473\n",
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      "1.071568396023756 1.0461421130646762 1.046143935989169 1.0461421114681677\n",
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      "1.0437227579165085 1.0391434842321337 1.0391452617423285 1.0391434894637945\n",
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      "0.8716594568387693 0.8915201808976134 0.891521764803606 0.8915201837049385\n",
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      "0.8616703423916907 0.8488396637065788 0.8488411710900143 0.8488396555880748\n",
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      "0.4976757736660059 0.5102388395097991 0.5102397199848367 0.5102388407103089\n",
      "0.5629002449823313 0.5241289996159542 0.5241299237905581 0.5241290035627906\n",
      "0.49860302385690025 0.5225106712275276 0.5225115688313148 0.522510669847456\n",
      "0.5218894657445123 0.5304554009809609 0.5304563362193006 0.5304553945283436\n",
      "0.5648245388246032 0.5418264905792121 0.5418274102118865 0.5418264907227639\n",
      "0.5514104032892553 0.5439983644854423 0.5439993300612548 0.5439983676764483\n",
      "0.5266847179624312 0.5432054294775047 0.5432063713598764 0.5432054303850102\n",
      "0.5702422974642618 0.5490207749858439 0.5490217601918029 0.5490207780626029\n",
      "0.5082650936371483 0.546347513325645 0.5463484814661106 0.5463475179795322\n",
      "0.578832756421302 0.5589072279792362 0.5589082284546438 0.5589072276334154\n",
      "0.5432915951739741 0.5634967315454678 0.5634977126787135 0.5634967257721435\n",
      "0.5777082847437897 0.5761682767782033 0.5761692945999108 0.5761682761501399\n",
      "0.5922322035718047 0.5882238179979469 0.5882248340509041 0.5882238230906762\n",
      "0.6258484598313188 0.5986760097300691 0.5986770529342346 0.5986760178387608\n",
      "0.584088917674461 0.5982592267006829 0.5982602710432933 0.5982592357898222\n",
      "0.5879568893569485 0.603510578875672 0.6035116319027585 0.603510580987028\n",
      "0.6391003151168073 0.6149834054346028 0.6149844621706655 0.6149834028362655\n",
      "0.6143486921376278 0.6168094580001923 0.6168105258902324 0.6168094597732862\n",
      "0.613072012648473 0.6196198217352956 0.6196209065303742 0.6196198237645703\n",
      "0.6086881625440411 0.6250493062043547 0.6250503931213257 0.6250493122022934\n",
      "0.6594870288423127 0.6370232539561338 0.6370243656957324 0.6370232605033177\n",
      "0.6458699591194119 0.640011693918348 0.6400127969879382 0.6400117014687433\n",
      "0.652801844103723 0.6406568294978823 0.6406579657624956 0.6406568393739016\n",
      "0.6102094600549334 0.6364439694104462 0.6364450854499922 0.6364439753871316\n",
      "0.6381204423623481 0.6427249179622726 0.6427260638111474 0.6427249175332408\n",
      "0.6376428231279201 0.6508476503159173 0.6508487743760117 0.6508476497477071\n",
      "0.6978956523941571 0.6642523114552035 0.664253477534029 0.6642523126100881\n",
      "0.6352685574834198 0.6641996346021902 0.6642007787870083 0.6641996395588413\n",
      "0.7028486050276996 0.6757193946754056 0.675720581836816 0.6757193993377633\n",
      "0.6985085726805301 0.6763874746905372 0.6763886306670808 0.6763874768407105\n",
      "0.6233162703727811 0.6682071169651648 0.6682083152499072 0.6682071160077303\n",
      "0.6867005860108919 0.6779830911169626 0.6779842617932729 0.6779830934287291\n",
      "0.6992567307371899 0.6842720697688245 0.6842732892340265 0.6842720738168632\n",
      "0.6649353680533785 0.6845671915743491 0.6845683742263586 0.6845671914368662\n",
      "0.6876708504756164 0.692715041930362 0.6927162696899135 0.6927150384102638\n",
      "0.7150738846818794 0.702880566278011 0.7028817576309632 0.7028805605575213\n",
      "0.7449867847395554 0.7081687553513739 0.7081700001100433 0.7081687530550355\n",
      "0.6620151403027814 0.6987297324642054 0.6987309441003577 0.6987297328787409\n",
      "0.7022489344225282 0.7039765481042736 0.7039778126576368 0.7039765497328303\n",
      "0.6926165525071256 0.7099144108274189 0.7099156379771402 0.7099144127110403\n",
      "0.7326320097874744 0.7227714179979874 0.7227726987873856 0.7227714197708164\n",
      "0.761352017507264 0.7316841907707315 0.7316854300732786 0.7316841908239291\n",
      "0.745063746059405 0.7287298307130559 0.7287311265961661 0.7287298312037074\n",
      "0.6813192247000326 0.7192419019525881 0.719243158845129 0.7192419056412072\n",
      "0.7330741953410818 0.7249230499889695 0.7249243644913592 0.7249230524551769\n",
      "0.705781099784847 0.7273437400231724 0.7273450092507885 0.7273437421147841\n",
      "0.7437865873072105 0.7383894893917075 0.7383908175485496 0.7383894887063661\n",
      "0.7471360056800034 0.7472763938260788 0.7472776768768332 0.7472763958576105\n",
      "0.7507189664512763 0.7562194519210623 0.7562208046944174 0.7562194590798974\n",
      "0.7934420352835925 0.7673627168758236 0.7673640141557978 0.7673627193536332\n",
      "0.7857251566452422 0.7680742539421165 0.7680756153382846 0.7680742532553848\n",
      "0.738449046490069 0.7617254298285119 0.7617267342301547 0.7617254258011936\n",
      "0.757421706254283 0.7646871576429769 0.7646885280108607 0.7646871500714518\n",
      "0.7414619582505844 0.7705550554544766 0.7705563737365717 0.7705550518685781\n",
      "0.8251384964405983 0.7880601975556397 0.788061584005627 0.7880601911129012\n",
      "0.7725070171583642 0.7907340117861414 0.7907353433666637 0.7907340082261456\n",
      "0.8340717955843377 0.8006986241532379 0.8007000284958989 0.8006986217665026\n",
      "0.7604171685665089 0.7973139732904594 0.7973153141194643 0.7973139657797256\n",
      "0.8156862595710554 0.808688033716024 0.8086894480451413 0.808688028678235\n",
      "0.8434540727664835 0.8172628025041818 0.8172641608519859 0.8172627992196164\n",
      "0.8532195979769901 0.8153610681703924 0.8153624912252259 0.8153610603422502\n",
      "0.7703136232142922 0.7983159139043418 0.7983172816498889 0.7983159064109886\n",
      "0.7730331144952792 0.7924716703756427 0.7924731072686831 0.7924716657584054\n",
      "0.7689414657162212 0.7944028480049166 0.7944042350057914 0.7944028456110724\n",
      "0.8159615137359776 0.8065185789827514 0.8065200290161886 0.8065185774216801\n",
      "0.8151664292009401 0.8148571390818627 0.8148585390067223 0.8148571347065685\n",
      "0.8548543243534689 0.8230719751580782 0.8230734357175028 0.8230719741937084\n",
      "0.8052436797929846 0.8185738706526343 0.818575293688399 0.8185738736169439\n",
      "0.8236467946859727 0.8194078414576413 0.8194093222155984 0.8194078505697633\n",
      "0.801903300221729 0.8185462428206075 0.8185476865814665 0.8185462498760988\n",
      "0.8251665272120563 0.8243418301735519 0.8243433112374849 0.8243418290441819\n",
      "0.816159761676849 0.8298075279162258 0.8298089830120469 0.8298075289451152\n",
      "0.8670280144487965 0.8407323367158465 0.8407338289899737 0.8407323357533548\n",
      "0.8273822223576792 0.8411388712118637 0.8411403429877693 0.8411388710834182\n",
      "0.8190753630414991 0.8470480677936121 0.8470495705802918 0.8470480659037767\n",
      "0.9019026660841244 0.8641463494634972 0.864147831757008 0.8641463418690463\n",
      "0.8547212087838382 0.8661420891878153 0.8661436044268229 0.8661420881482846\n",
      "0.8715757690403175 0.8727061876729381 0.8727076938376322 0.8727061861733013\n",
      "0.8977085717550273 0.8797224587160023 0.8797239787920306 0.8797224510515114\n",
      "0.8575073983605925 0.8795442791256075 0.8795457925612615 0.879544267648315\n",
      "0.8929232303514579 0.8881808439431782 0.8881823707353138 0.8881808319602078\n",
      "0.9028526557238015 0.894920444933588 0.8949219783080763 0.8949204369156004\n",
      "0.8995794063252728 0.8984871586997728 0.8984887035329886 0.8984871543477125\n",
      "0.9160515562594568 0.9016169686807689 0.9016185279551102 0.9016169709888002\n",
      "0.8921401606547614 0.8989729507828869 0.8989745124343782 0.8989729535216258\n",
      "0.8713218749642444 0.8990620456495397 0.8990636248035159 0.8990620532011966\n",
      "0.9469268321235728 0.9102472140168053 0.9102487922227066 0.9102472241755484\n",
      "0.8955224717090516 0.9067605409998113 0.9067621373190915 0.9067605519706903\n",
      "0.9091179694520376 0.9077691064736564 0.9077706886658562 0.9077691118704871\n",
      "0.9228470862795792 0.9082381260345755 0.9082397270295315 0.9082381287376639\n",
      "0.868839768322615 0.9028635653721275 0.9028651480103919 0.9028635625880743\n",
      "0.951630711410413 0.9110985148119073 0.9111001246600051 0.911098514144669\n",
      "0.8723990916701353 0.9031205856036008 0.9031221809775467 0.9031205867949659\n",
      "0.9007159377348773 0.9074312537240339 0.907432879558084 0.9074312574951948\n",
      "0.8911394810862406 0.9144280486314766 0.9144296593631882 0.914428056099551\n",
      "0.9660231204469882 0.9307402787109204 0.9307419176362624 0.9307402847092319\n",
      "0.9540711023466916 0.9329393720808109 0.9329409917799811 0.9329393790238086\n",
      "0.8938394281496873 0.9266857778435066 0.9266874270692083 0.9266857840092331\n",
      "0.9317481872150749 0.9335707309464519 0.9335723539948853 0.9335707313384747\n",
      "0.9286510779660953 0.9411846964481927 0.9411863487212129 0.9411846963170771\n",
      "0.9732513714607359 0.9538121137921232 0.9538137415302009 0.9538121086360719\n",
      "0.989135821952938 0.9586638196401116 0.9586654767547381 0.9586638158252014\n",
      "0.906492018877919 0.9513267231349111 0.9513283639354212 0.9513267205632363\n",
      "0.9732299344561528 0.9619235073818789 0.9619251746386014 0.9619235059753978\n",
      "0.9959985631298194 0.9679977247020434 0.9679993739969276 0.967997719995257\n",
      "0.9767112139692384 0.9628716001964792 0.9628732724600298 0.9628715967612907\n",
      "0.9303295681339264 0.9522096320482063 0.9522112913653871 0.9522096266441458\n",
      "0.9691436715904133 0.9502996848208709 0.9503013621133226 0.9502996799310885\n",
      "0.9171930989884803 0.9408521371365671 0.9408538120513184 0.9408521365543006\n",
      "0.918731554007965 0.9408682091767321 0.9408698964839902 0.9408682082038407\n",
      "0.9442231996969069 0.9497389430564701 0.9497406278387317 0.9497389415317316\n",
      "0.9446996117659006 0.9608159774033117 0.9608176657353699 0.9608159715935518\n",
      "0.9987664254588493 0.9783395511884445 0.9783412427046025 0.978339545586433\n",
      "1.0162563157847453 0.9876923662332151 0.9876940675012497 0.9876923676303472\n",
      "0.9851277406160152 0.9856196072337144 0.9856213182771412 0.9856196104125021\n",
      "0.9699751378204177 0.9837435932682056 0.9837453066291034 0.9837436011132519\n",
      "1.0186105307481281 0.9873749662463607 0.9873766955638204 0.9873749771311351\n",
      "0.9427666128425894 0.9785121227545389 0.9785138427835625 0.9785121317022205\n",
      "1.0041918794994902 0.9839474817862706 0.9839492224727402 0.9839474938171595\n",
      "0.9800488414177411 0.9812850930078316 0.9812868182135944 0.9812851016591654\n",
      "0.9471630311254396 0.9791172087731446 0.979118951917191 0.9791172135977412\n",
      "1.0186892015466043 0.98973099874352 0.9897327204594191 0.9897309985252383\n",
      "0.9487503062362128 0.9887615009714068 0.9887632494251719 0.9887615022441885\n",
      "1.0221238485798876 1.0037964882096952 1.0037982116199244 1.0037964843663285\n",
      "1.033356153504099 1.011500530618799 1.0115022758005103 1.0115005208030443\n",
      "1.018461325132979 1.0104623143329117 1.0104640367463913 1.0104623041593381\n",
      "1.0136104057126498 1.0062244887014362 1.0062262406938518 1.0062244791261756\n",
      "0.9576376997269224 0.9990322923408071 0.9990340215012902 0.9990322834584242\n",
      "1.0459995309186427 1.0083979285415217 1.00839968806175 1.0083979212832719\n",
      "0.9653184886499154 1.0027229263030424 1.002724658999774 1.0027229152539723\n",
      "1.0561332316457708 1.012009685836566 1.0120114505136302 1.0120096798662954\n",
      "0.9773206426658153 1.0036470212297584 1.0036487735833057 1.003647023766828\n",
      "1.0128323825246457 1.0058149149776856 1.0058166934558106 1.0058149201077655\n",
      "0.997453115862971 1.0051758286562555 1.0051775878351124 1.005175831481951\n",
      "0.9803940235699997 1.0076258282642017 1.0076276043117327 1.0076258291037288\n",
      "1.0330772477191217 1.0209685506487747 1.0209703123568836 1.0209685489389977\n",
      "1.0479927172279215 1.029467793189463 1.0294695659334712 1.0294677892622164\n",
      "1.0695009066501697 1.0305570663006074 1.0305588294246713 1.0305570583991537\n",
      "1.0029931456347945 1.0160687981172187 1.016070566466945 1.0160687882356847\n",
      "0.9989944504945867 1.0068107847688168 1.0068125542458646 1.0068107751125712\n",
      "0.9956301560091793 1.0006792999989196 1.0006810721840753 1.0006792918366514\n",
      "0.9822291942525788 0.9965674679737276 0.9965692505219413 0.9965674628917205\n",
      "0.9820475782597953 0.9981909438505105 0.9981927247681944 0.9981909414024461\n",
      "1.0222679194236775 1.0062717614495758 1.0062735614994691 1.0062717651702322\n",
      "0.9883339726690272 1.007954125333848 1.0079559147003108 1.0079541272366401\n",
      "1.0054745656654878 1.017484547140072 1.0174863560981484 1.0174845511300934\n",
      "1.0468699524805316 1.0318189695125872 1.031820761841066 1.0318189692093886\n",
      "1.0441994444845688 1.0401329960321553 1.0401348072050334 1.0401329939802268\n",
      "1.050569553304291 1.0468204373046612 1.0468222372419365 1.0468204385493283\n",
      "1.0753121722541061 1.0520082419951031 1.0520100579676963 1.052008237216445\n",
      "1.049610882391875 1.0478744652675203 1.047876267216876 1.0478744618684965\n",
      "1.0223541000642273 1.0430461200269745 1.0430479455317334 1.043046118311197\n",
      "1.0317943564081509 1.046494579664208 1.0464963942903336 1.0464945820526852\n",
      "1.0874312881918013 1.0558231321566127 1.0558249684326522 1.0558231360519867\n",
      "1.0415221050324408 1.0525084248073109 1.0525102481841235 1.0525084291953632\n",
      "1.0843459295831475 1.053588247145033 1.0535900881053846 1.0535882520039075\n",
      "1.013531987602049 1.042365003208981 1.0423668290395864 1.0423650037807568\n",
      "1.0204859994906406 1.0426749593809288 1.0426768004324354 1.0426749620290883\n",
      "1.054454173432128 1.0518605077203196 1.0518623360509631 1.0518605052927994\n",
      "1.0736820397046671 1.0600085833208663 1.0600104207604855 1.0600085813007785\n",
      "1.0855331161661055 1.0626872756627257 1.0626891092124864 1.0626872739472024\n",
      "1.0333859124499165 1.0562276338749539 1.0562294692775296 1.0562276297060649\n",
      "1.0532932691383083 1.058904674836027 1.0589065110063756 1.058904672367387\n",
      "1.0800122908708756 1.0638262742349263 1.0638281154379492 1.06382627632034\n",
      "1.0655708263175563 1.0622734643074114 1.062275315283709 1.0622734744530793\n",
      "1.0659856340134413 1.0594017179294737 1.059403570331313 1.059401731840027\n",
      "1.0717355277504201 1.0538964172519372 1.0538982702521282 1.0538964283576098\n",
      "1.0164418533405872 1.0412554753410992 1.0412573231515558 1.041255485118068\n",
      "1.0300573495930985 1.0385399916551235 1.038541836579909 1.0385399945895186\n",
      "1.018614183686803 1.0392175612108556 1.0392194000364026 1.0392175620595374\n",
      "1.0561124838071723 1.0481364781203075 1.048138322249925 1.0481364808786497\n",
      "1.0572191196448006 1.0538649989982503 1.0538668369363773 1.053864998526353\n",
      "1.0919422845107716 1.058251872428887 1.0582537080798768 1.0582518677266775\n",
      "1.0264393264300804 1.049162575598596 1.0491644094818722 1.049162570213364\n"
     ]
    }
   ],
   "source": [
    "for i in range (N):\n",
    "    print(y[i], limpio[i], limpioDG[i], limpioInv[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4ab99072fe894e7598b7905f9af6f190",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graficar\n",
    "%matplotlib ipympl\n",
    "\n",
    "x = np.linspace(0,1000, 1000)\n",
    "plt.plot(x, y, label=\"F(x)\")\n",
    "plt.plot(x, limpio , label=\"Filtro GC\")\n",
    "# plt.plot(x, limpioDG , label=\"Filtro DG\")\n",
    "# plt.plot(x, limpioInv, label=\"Filtro  A^-1\")\n",
    "plt.xlabel('x(k)')\n",
    "plt.ylabel('f(x)')\n",
    "plt.title('')\n",
    "plt.legend(loc=1)\n",
    "plt.grid()\n",
    "plt.show()\n"
   ]
  }
 ],
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