Mètodes iteratius.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "driven-satisfaction",
   "metadata": {},
   "source": [
    "# Mètodes iteratius\n",
    "Biel Nebot Cabrera"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "arctic-indianapolis",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "\n",
    "def plotFuncio(f,xmin,xmax):\n",
    "    x = np.linspace(xmin,xmax,1000)\n",
    "    y = [f(i) for i in x]\n",
    "    plt.plot(x,y); plt.grid(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "young-center",
   "metadata": {},
   "source": [
    "## Cerca àuria\n",
    "Es defineix la funció $f_1(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fantastic-parish",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f1(x):\n",
    "#     return (x**3)+924*math.exp(-x)\n",
    "    return -x**3+math.exp(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "technical-shock",
   "metadata": {},
   "source": [
    "I s'executa l'algoritme especificant l'interval d'estudi $[x_1, x_2]$ i el nombre d'iteracions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "growing-stomach",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It. 0    x1 = -1     x2 = 0     x3 = -0.618     x4 = -0.382  \n",
      "It. 1    x1 = -0.618     x2 = 0     x3 = -0.382     x4 = -0.2361  \n",
      "It. 2    x1 = -0.618     x2 = -0.2361     x3 = -0.4721     x4 = -0.382  \n",
      "It. 3    x1 = -0.618     x2 = -0.382     x3 = -0.5279     x4 = -0.4721  \n",
      "It. 4    x1 = -0.5279     x2 = -0.382     x3 = -0.4721     x4 = -0.4377  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def cercaAuria(funcio,x1,x2,iteracions):\n",
    "    x1_Orig, x2_Orig = x1, x2\n",
    "\n",
    "    x3 = x2-((math.sqrt(5)-1)/2)*(x2-x1)\n",
    "    x4 = x1+((math.sqrt(5)-1)/2)*(x2-x1)\n",
    "    \n",
    "    print(\"It. 0    x1 = {}     x2 = {}     x3 = {}     x4 = {}  \".format(round(x1,4),round(x2,4),round(x3,4),round(x4,4)))\n",
    "\n",
    "    for k in range(1,iteracions+1):\n",
    "        if funcio(x3) < funcio(x4):\n",
    "            x1, x2, x3, x4 = x1, x4, x4 - ((math.sqrt(5)-1)/2)*(x4 - x1), x3            \n",
    "        else:\n",
    "            x1, x2, x3, x4 = x3, x2, x4, x3 + ((math.sqrt(5)-1)/2)*(x2-x3)\n",
    "            \n",
    "        # prints i plots\n",
    "        print(\"It. {}    x1 = {}     x2 = {}     x3 = {}     x4 = {}  \".format(k,round(x1,4),round(x2,4),round(x3,4),round(x4,4)))\n",
    "        plt.plot([x1, x2],[funcio(x1), funcio(x2)],\"--\",color=(random.random(),random.random(),random.random()))\n",
    "    plotFuncio(funcio,x1_Orig,x2_Orig)\n",
    "\n",
    "    \n",
    "    \n",
    "# Crida a la funció   \n",
    "cercaAuria(f1,-1,-0,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "attended-consent",
   "metadata": {},
   "source": [
    "## Bisecció\n",
    "Es defineix la funció $f_2(x)$ i la seva derivada $f^{'}_2(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dated-synthetic",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f2(x):\n",
    "    return -x**3+math.exp(x)\n",
    "def Df2(x):\n",
    "    return -3*x**2+math.exp(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "indian-plenty",
   "metadata": {},
   "source": [
    "I s'executa l'algoritme especificant l'interval d'estudi  $[x_1, x_2]$ i el nombre d'iteracions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "accurate-trout",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It. 0    x1 = -1     x2 = 0\n",
      "It. 1    x1 = -0.5     x2 = 0\n",
      "It. 2    x1 = -0.5     x2 = -0.25\n",
      "It. 3    x1 = -0.5     x2 = -0.375\n",
      "It. 4    x1 = -0.5     x2 = -0.4375\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def Biseccio(funcio,funcioDerivada,x1,x2,iteracions):\n",
    "    x1_Orig, x2_Orig = x1, x2\n",
    "    \n",
    "    print(\"It. 0    x1 = {}     x2 = {}\".format(x1,x2))\n",
    "\n",
    "    for k in range(1,iteracions+1):\n",
    "        if funcioDerivada((x1+x2)/2) > 0:\n",
    "            if funcioDerivada(x1) < 0:\n",
    "                x1, x2 = x1, (x1+x2)/2\n",
    "            elif funcioDerivada(x1) > 0:\n",
    "                x1, x2 = (x1+x2)/2, x2\n",
    "        elif funcioDerivada((x1+x2)/2) < 0:\n",
    "            if funcioDerivada(x1) < 0:\n",
    "                x1, x2 = (x1+x2)/2, x2\n",
    "            elif funcioDerivada(x1) > 0:\n",
    "                x1, x2 = x1, (x1+x2)/2\n",
    "        else:\n",
    "            print(\"òptim!\")\n",
    "            return (x1+x2)/2\n",
    "            \n",
    "        # prints i plots\n",
    "        print(\"It. {}    x1 = {}     x2 = {}\".format(k,round(x1,4),round(x2,4)))\n",
    "        plt.plot([x1, x2],[funcio(x1), funcio(x2)],\"--\",color=(random.random(),random.random(),random.random()))\n",
    "    plotFuncio(funcio,x1_Orig,x2_Orig)\n",
    "\n",
    "    \n",
    "    \n",
    "# avaluem    \n",
    "Biseccio(f2,Df2,-1,0,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "referenced-observation",
   "metadata": {},
   "source": [
    "## Newton\n",
    "Es defineix la funció $f_3(x)$, la seva derivada primera $f^{'}_3(x)$ i la seva derivada segona $f^{''}_3(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "moved-attack",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f3(x):\n",
    "    return x**3+799*math.exp(-x)\n",
    "def Df3(x):\n",
    "    return 3*x**2-799*math.exp(-x)\n",
    "def DDf3(x):\n",
    "    return 6*x+799*math.exp(-x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "requested-commerce",
   "metadata": {},
   "source": [
    "I s'executa l'algoritme especificant el punt de sortida $x_1$ i el nombre d'iteracions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "joint-verification",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It. 0    x1 = -20\n",
      "It. 1    x1 = -19.0\n",
      "It. 2    x1 = -18.0\n",
      "It. 3    x1 = -17.0\n",
      "It. 4    x1 = -16.0\n",
      "It. 5    x1 = -15.0\n",
      "It. 6    x1 = -14.0\n",
      "It. 7    x1 = -13.0\n",
      "It. 8    x1 = -12.0\n",
      "It. 9    x1 = -11.0\n",
      "It. 10    x1 = -10.0\n",
      "It. 11    x1 = -9.0\n",
      "It. 12    x1 = -8.0001\n",
      "It. 13    x1 = -7.0001\n",
      "It. 14    x1 = -6.0002\n",
      "It. 15    x1 = -5.0005\n",
      "It. 16    x1 = -4.0008\n",
      "It. 17    x1 = -3.0014\n",
      "It. 18    x1 = -2.0019\n",
      "It. 19    x1 = -1.002\n",
      "It. 20    x1 = -0.0006\n",
      "It. 21    x1 = 0.9994\n",
      "It. 22    x1 = 1.9695\n",
      "It. 23    x1 = 2.7793\n",
      "It. 24    x1 = 3.1781\n",
      "It. 25    x1 = 3.2352\n",
      "It. 26    x1 = 3.236\n",
      "It. 27    x1 = 3.236\n",
      "It. 28    x1 = 3.236\n",
      "It. 29    x1 = 3.236\n",
      "It. 30    x1 = 3.236\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def Newton(funcio,funcD,funcDD,x1,iteracions):\n",
    "   \n",
    "    print(\"It. 0    x1 = {}\".format(round(x1,4))); plt.scatter(x1,funcio(x1),color=(random.random(),random.random(),random.random()))\n",
    "    memoryX = [x1]\n",
    "    \n",
    "    for k in range(1,iteracions+1):\n",
    "        x1 = x1 - funcD(x1)/funcDD(x1)\n",
    "        print(\"It. {}    x1 = {}\".format(k,round(x1,4))); memoryX.append(x1)\n",
    "                 \n",
    "        # prints i plots\n",
    "        plt.scatter(x1,funcio(x1),color=(random.random(),random.random(),random.random()))\n",
    "    plotFuncio(funcio,min(memoryX),max(memoryX))\n",
    "    \n",
    "# avaluem    \n",
    "Newton(f3,Df3,DDf3,-20,30)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "exclusive-newton",
   "metadata": {},
   "source": [
    "## Nelder i Mead\n",
    "Es defineix la funció $f_4(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fabulous-facial",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f4(punt):\n",
    "    x, y = punt[0], punt[1]\n",
    "    return -4*x-14*y+x**2+y**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "numerical-marshall",
   "metadata": {},
   "source": [
    "Funcions complementàries per l'algoritme:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "connected-reggae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fi(p1,p2,a):\n",
    "    return p1+a*(p2-p1)\n",
    "\n",
    "def beBaixa(vg,llista_v):\n",
    "    # centre de gravetat de la cara de l’hipertetraedre oposada a vg\n",
    "    v = np.array([0,0])\n",
    "    for punt in llista_v:\n",
    "        if np.linalg.norm(punt-vg) > 0.000001:\n",
    "            v = v + punt\n",
    "    return (1/(len(llista_v)-1))*v\n",
    "\n",
    "def puntOrdenatsPetit_a_Gran(funcio,llistPunts):\n",
    "    llistaImatges = [funcio(punt) for punt in llistPunts]\n",
    "\n",
    "    indexMax = llistaImatges.index(max(llistaImatges))\n",
    "    puntMax = llistPunts.pop(indexMax)\n",
    "    llistaImatges.pop(indexMax)\n",
    "    \n",
    "    \n",
    "    indexMin = llistaImatges.index(min(llistaImatges))\n",
    "    puntMin = llistPunts.pop(indexMin)\n",
    "    llistaImatges.pop(indexMin)\n",
    "\n",
    "    return [puntMin, llistPunts[0], puntMax]\n",
    "\n",
    "# def puntOrdenatsPetit_a_Gran_v2(funcio,llistPunts):\n",
    "#     llistaImatges = [funcio(punt) for punt in llistPunts]\n",
    "\n",
    "#     indexMax = llistaImatges.index(max(llistaImatges))\n",
    "#     puntMax = llistPunts.pop(indexMax)\n",
    "#     llistaImatges.pop(indexMax)\n",
    "    \n",
    "    \n",
    "#     indexMin = llistaImatges.index(min(llistaImatges))\n",
    "#     puntMin = llistPunts.pop(indexMin)\n",
    "#     llistaImatges.pop(indexMin)\n",
    "    \n",
    "#     index2Max = llistaImatges.index(max(llistaImatges))\n",
    "#     punt2Max = llistPunts.pop(index2Max)\n",
    "\n",
    "#     return [puntMin, punt2Max, puntMax]\n",
    "\n",
    "def ordenaTriangle(diccionariTriangle):\n",
    "    vs, vh, vg = puntOrdenatsPetit_a_Gran(f4,list(diccionariTriangle.values))\n",
    "    return {\"vs\": vs, \"vh\": vh, \"vg\": vg}\n",
    "    \n",
    "def plotIteracio(puntsTriangle):\n",
    "    col = (random.random(),random.random(),random.random())\n",
    "    plt.plot([puntsTriangle[0][0],puntsTriangle[1][0]],[puntsTriangle[0][1],puntsTriangle[1][1]],\"-\",color=col)\n",
    "    plt.plot([puntsTriangle[1][0],puntsTriangle[2][0]],[puntsTriangle[1][1],puntsTriangle[2][1]],\"-\",color=col)\n",
    "    plt.plot([puntsTriangle[2][0],puntsTriangle[0][0]],[puntsTriangle[2][1],puntsTriangle[0][1]],\"-\",color=col)\n",
    "    plt.scatter([puntsTriangle[0][0],puntsTriangle[1][0],puntsTriangle[2][0]],[puntsTriangle[0][1],puntsTriangle[1][1],puntsTriangle[2][1]],s=30,color = col)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acting-aerospace",
   "metadata": {},
   "source": [
    "I s'executa l'algoritme especificant tres punts $P_1$, $P_2$ i $P_3$ i el nombre d'iteracions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "african-peeing",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It. 0    vs = [8 5]   vh = [ 6 12]   vg = [10 10]\n",
      "v =  [7.  8.5]\n",
      "vr =  -49.0\n",
      "It. 1    vs = [1.  5.5]   vh = [8 5]   vg = [ 6 12]\n",
      "It. 1    f(vs) = -49.75   f(vh) = -13   f(vg) = -12\n",
      "v =  [4.5  5.25]\n",
      "vr =  20.25\n",
      "It. 2    vs = [1.  5.5]   vh = [5.25  8.625]   vg = [8 5]\n",
      "It. 2    f(vs) = -49.75   f(vh) = -39.796875   f(vg) = -13\n",
      "v =  [3.125  7.0625]\n",
      "vr =  -34.421875\n",
      "[0.6875  8.09375]\n",
      "It. 3    vs = [0.6875  8.09375]   vh = [1.  5.5]   vg = [5.25  8.625]\n",
      "It. 3    f(vs) = -50.0810546875   f(vh) = -49.75   f(vg) = -39.796875\n",
      "v =  [0.84375  6.796875]\n",
      "vr =  -17.9326171875\n",
      "It. 4    vs = [3.046875  7.7109375]   vh = [0.6875  8.09375]   vg = [1.  5.5]\n",
      "It. 4    f(vs) = -51.39862060546875   f(vh) = -50.0810546875   f(vg) = -49.75\n",
      "v =  [1.8671875  7.90234375]\n",
      "vr =  -41.53973388671875\n",
      "It. 5    vs = [1.43359375 6.70117188]   vh = [3.046875  7.7109375]   vg = [0.6875  8.09375]\n",
      "It. 5    f(vs) = -52.58988571166992   f(vh) = -51.39862060546875   f(vg) = -50.0810546875\n",
      "v =  [2.24023438 7.20605469]\n",
      "vr =  -49.32062911987305\n",
      "It. 6    vs = [1.43359375 6.70117188]   vh = [1.46386719 7.64990234]   vg = [3.046875  7.7109375]\n",
      "It. 6    f(vs) = -52.58988571166992   f(vh) = -52.2901885509491   f(vg) = -51.39862060546875\n",
      "v =  [1.44873047 7.17553711]\n",
      "vr =  -48.25051760673523\n",
      "It. 7    vs = [2.24780273 7.4432373 ]   vh = [1.43359375 6.70117188]   vg = [1.46386719 7.64990234]\n",
      "It. 7    f(vs) = -52.74213449656963   f(vh) = -52.58988571166992   f(vg) = -52.2901885509491\n",
      "v =  [1.84069824 7.07220459]\n",
      "vr =  -52.69715766608715\n",
      "It. 8    vs = [2.24780273 7.4432373 ]   vh = [2.2175293  6.49450684]   vg = [1.43359375 6.70117188]\n",
      "It. 8    f(vs) = -52.74213449656963   f(vh) = -52.69715766608715   f(vg) = -52.58988571166992\n",
      "v =  [2.23266602 6.96887207]\n",
      "vr =  -51.87954968214035\n",
      "It. 9    vs = [1.83312988 6.83502197]   vh = [2.24780273 7.4432373 ]   vg = [2.2175293  6.49450684]\n",
      "It. 9    f(vs) = -52.944936614483595   f(vh) = -52.74213449656963   f(vg) = -52.69715766608715\n",
      "v =  [2.04046631 7.13912964]\n",
      "vr =  -52.36707345768809\n",
      "It. 10    vs = [2.1289978  6.81681824]   vh = [1.83312988 6.83502197]   vg = [2.24780273 7.4432373 ]\n",
      "It. 10    f(vs) = -52.94980400870554   f(vh) = -52.944936614483595   f(vg) = -52.74213449656963\n",
      "v =  [1.98106384 6.8259201 ]\n",
      "vr =  -52.292080404935405\n",
      "It. 11    vs = [2.11443329 7.1345787 ]   vh = [2.1289978  6.81681824]   vg = [1.83312988 6.83502197]\n",
      "It. 11    f(vs) = -52.9687935946713   f(vh) = -52.94980400870554   f(vg) = -52.944936614483595\n",
      "v =  [2.12171555 6.97569847]\n",
      "vr =  -52.81810978478461\n",
      "It. 12    vs = [1.97742271 6.90536022]   vh = [2.11443329 7.1345787 ]   vg = [2.1289978  6.81681824]\n",
      "It. 12    f(vs) = -52.99053357856155   f(vh) = -52.9687935946713   f(vg) = -52.94980400870554\n",
      "v =  [2.045928   7.01996946]\n",
      "vr =  -52.9488376446634\n",
      "It. 13    vs = [1.97742271 6.90536022]   vh = [2.0874629  6.91839385]   vg = [2.11443329 7.1345787 ]\n",
      "It. 13    f(vs) = -52.99053357856155   f(vh) = -52.985690677097125   f(vg) = -52.9687935946713\n",
      "v =  [2.03244281 6.91187704]\n",
      "vr =  -52.90093307591377\n",
      "It. 14    vs = [2.07343805 7.02322787]   vh = [1.97742271 6.90536022]   vg = [2.0874629  6.91839385]\n",
      "It. 14    f(vs) = -52.99406731908637   f(vh) = -52.99053357856155   f(vg) = -52.985690677097125\n",
      "v =  [2.02543038 6.96429405]\n",
      "vr =  -52.99855636081603\n",
      "It. 15    vs = [1.96339786 7.01019424]   vh = [2.07343805 7.02322787]   vg = [1.97742271 6.90536022]\n",
      "It. 15    f(vs) = -52.99855636081603   f(vh) = -52.99406731908637   f(vg) = -52.99053357856155\n",
      "v =  [2.01841795 7.01671106]\n",
      "vr =  -52.98007022447614\n",
      "It. 16    vs = [1.96339786 7.01019424]   vh = [1.99792033 6.96103564]   vg = [2.07343805 7.02322787]\n",
      "It. 16    f(vs) = -52.99855636081603   f(vh) = -52.998477453566316   f(vg) = -52.99406731908637\n",
      "v =  [1.9806591  6.98561494]\n",
      "vr =  -52.9847253475486\n",
      "It. 17    vs = [2.02704857 7.00442141]   vh = [1.96339786 7.01019424]   vg = [1.99792033 6.96103564]\n",
      "It. 17    f(vs) = -52.99924882587764   f(vh) = -52.99855636081603   f(vg) = -52.998477453566316\n",
      "v =  [1.99522322 7.00730782]\n",
      "vr =  -52.997073323499926\n",
      "It. 18    vs = [1.99657178 6.98417173]   vh = [2.02704857 7.00442141]   vg = [1.96339786 7.01019424]\n",
      "It. 18    f(vs) = -52.99973771319001   f(vh) = -52.99924882587764   f(vg) = -52.99855636081603\n",
      "v =  [2.01181017 6.99429657]\n",
      "vr =  -52.99590664420961\n",
      "It. 19    vs = [1.98760402 7.00224541]   vh = [1.99657178 6.98417173]   vg = [2.02704857 7.00442141]\n",
      "It. 19    f(vs) = -52.999841297770004   f(vh) = -52.99973771319001   f(vg) = -52.99924882587764\n",
      "v =  [1.9920879  6.99320857]\n",
      "vr =  -52.997837771037176\n",
      "It. 20    vs = [2.00956823 6.99881499]   vh = [1.98760402 7.00224541]   vg = [1.99657178 6.98417173]\n",
      "It. 20    f(vs) = -52.99990704462921   f(vh) = -52.999841297770004   f(vg) = -52.99973771319001\n",
      "v =  [1.99858613 7.0005302 ]\n",
      "vr =  -52.99971441256677\n",
      "It. 21    vs = [1.99757895 6.99235096]   vh = [2.00956823 6.99881499]   vg = [1.98760402 7.00224541]\n",
      "It. 21    f(vs) = -52.99993563076479   f(vh) = -52.99990704462921   f(vg) = -52.999841297770004\n",
      "v =  [2.00357359 6.99558298]\n",
      "vr =  -52.9994953102675\n",
      "It. 22    vs = [1.99558881 6.99891419]   vh = [1.99757895 6.99235096]   vg = [2.00956823 6.99881499]\n",
      "It. 22    f(vs) = -52.99997936237631   f(vh) = -52.99993563076479   f(vg) = -52.99990704462921\n",
      "v =  [1.99658388 6.99563258]\n",
      "vr =  -52.99967402431654\n",
      "It. 23    vs = [2.00307606 6.99722378]   vh = [1.99558881 6.99891419]   vg = [1.99757895 6.99235096]\n",
      "It. 23    f(vs) = -52.999982830491035   f(vh) = -52.99997936237631   f(vg) = -52.99993563076479\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def NelderMead(funcio,P1,P2,P3,iteracions):\n",
    "    # vàlid per R2\n",
    "    vs, vh, vg = puntOrdenatsPetit_a_Gran(funcio, [P1,P2,P3])\n",
    "    \n",
    "    # prints i plots\n",
    "    print(\"It. 0    vs = {}   vh = {}   vg = {}\".format(vs,vh,vg))\n",
    "    plotIteracio([vs,vh,vg])\n",
    "    \n",
    "    for k in range(1,iteracions+1):\n",
    "        dicc_triangle = {\"vs\": vs, \"vh\": vh, \"vg\": vg}\n",
    "\n",
    "        v = beBaixa(vg,[vs,vh,vg])\n",
    "        print(\"v = \",v)\n",
    "        vr = fi(v, vg, -1)\n",
    "        print(\"vr = \",f4(vr))\n",
    "        # CAS 1\n",
    "        if funcio(vr) < funcio(vs):\n",
    "            ve = fi(v,vg,-2)\n",
    "            # CAS 1a\n",
    "            if funcio(ve) < funcio(vs):\n",
    "                dicc_triangle[\"vg\"] = ve \n",
    "            # CAS 1b\n",
    "            else:\n",
    "                dicc_triangle[\"vg\"] = vr\n",
    "        # CAS 2\n",
    "        elif funcio(vs) <= funcio(vr) and funcio(vr) < funcio(vh):\n",
    "            dicc_triangle[\"vg\"] = vr\n",
    "        # CAS 3\n",
    "        elif funcio(vh) <= funcio(vr) and funcio(vr) < funcio(vg):\n",
    "            dicc_triangle[\"vg\"] = vr\n",
    "            vc = fi(v, dicc_triangle[\"vg\"], 1/2)\n",
    "            print(vc)\n",
    "            # CAS 3a\n",
    "            if funcio(vc) < funcio(dicc_triangle[\"vg\"]):\n",
    "                dicc_triangle[\"vg\"] = vc\n",
    "            # CAS 3b\n",
    "            else:\n",
    "                dicc_triangle[\"vh\"] = fi(vs, dicc_triangle[\"vh\"], 1/2)\n",
    "                dicc_triangle[\"vg\"] = fi(vs, dicc_triangle[\"vg\"], 1/2)\n",
    "        # CAS 4\n",
    "        else:\n",
    "            vc = fi(v, dicc_triangle[\"vg\"], 1/2)\n",
    "            # CAS 3a\n",
    "            if funcio(vc) < funcio(dicc_triangle[\"vg\"]):\n",
    "                dicc_triangle[\"vg\"] = vc\n",
    "            # CAS 3b\n",
    "            else:\n",
    "                dicc_triangle[\"vh\"] = fi(vs, dicc_triangle[\"vh\"], 1/2)\n",
    "                dicc_triangle[\"vg\"] = fi(vs, dicc_triangle[\"vg\"], 1/2)\n",
    "        \n",
    "        nouTriangle = list(dicc_triangle.values())\n",
    "        vs, vh, vg = puntOrdenatsPetit_a_Gran(funcio, nouTriangle)\n",
    "        fs, fh, fg = funcio(vs), funcio(vh), funcio(vg)\n",
    "    \n",
    "    \n",
    "        plotIteracio([vs,vh,vg])\n",
    "        print(\"It. {}    vs = {}   vh = {}   vg = {}\".format(k,vs,vh,vg))\n",
    "        print(\"It. {}    f(vs) = {}   f(vh) = {}   f(vg) = {}\".format(k,funcio(vs),funcio(vh),funcio(vg)))\n",
    "    plt.grid()\n",
    "\n",
    "\n",
    "# avaluem\n",
    "\n",
    "v0 = np.array((8, 5))\n",
    "v1 = np.array((10, 10))\n",
    "v2 = np.array((6,12))\n",
    "\n",
    "NelderMead(f4,v0,v1,v2,23)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "structured-panel",
   "metadata": {},
   "source": [
    "Els tres punts del triangle són $v_s$, $v_h$ i $v_g$."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}