{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 9\n",
    "Sperimentazione numerica relativa ll'interpolazione di dati e funzioni.\n",
    "\n",
    "Per stampare il grafico corrente si può impiegare: `print -dpng foo.png`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolante di Lagrange\n",
    "Calcola il polinomio di interpolazione in forma di Lagrange\n",
    "\n",
    "    yy = interpLagrange(x, y, xx)\n",
    "\n",
    "Input: \n",
    "- `x`:  vettore dei nodi di interpolazione, con elementi distinti\n",
    "- `y`:  vettore dei valori assunti dalla funzione nei nodi di interpolazione,\n",
    "- `xx`: vettore dei punti in cui si vuole valutare il polinomio interpolante.\n",
    "\n",
    "Output:\n",
    "- `yy`:  vettore contenente i valori assunti dal polinomio interpolante,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "function [yy] = interp_lagrange(x, y, xx)\n",
    "\n",
    "n = length(x);\n",
    "\n",
    "for j = 1:n\n",
    "    % calcolo coefficienti j-esimo polinomio fondamentale di Lagrange\n",
    "    x_zeri = [x(1:j-1) x(j+1:end)];\n",
    "    p = poly(x_zeri);\n",
    "    p = p / polyval(p, x(j));\n",
    "    % calcolo valori assunti dal polinomio\n",
    "    L(j,:) = polyval(p, xx);\n",
    "end\n",
    "\n",
    "yy = y * L;\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolante di Newton\n",
    "\n",
    "Calcola il polinomio di interpolazione in forma di Newton. Per la valutazione del polinomio si impiega l'algoritmo di Horner.\n",
    "\n",
    "    yy = interpNewton(x, y, xx)\n",
    "\n",
    "Input: \n",
    "- `x`:  vettore dei nodi di interpolazione con elementi distinti\n",
    "- `y`:  vettore dei valori assunti dalla funzione nei nodi di interpolazione,\n",
    "- `xx`: vettore dei punti in cui si vuole valutare il polinomio interpolante.\n",
    "\n",
    "Output:\n",
    "- `yy`:  vettore contenente i valori assunti dal polinomio interpolante,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "function [yy] = interp_newton(x, y, xx)\n",
    "\n",
    "% FASE 1 creazione della tabella delle differenze divise\n",
    "% Calcolo dei coefficienti del polinomio di Newton\n",
    "\n",
    "n = length(x);\n",
    "%for k = 2 : n % si calcolano n - 1 colonne (una per coeff.)\n",
    " %   y(k:n) = (y(k:n) - y(k-1:n-1))./(x(k:n) - x(1:n-k+1));\n",
    "%end\n",
    "for k = 1 : n-1\n",
    "    y(k+1:n) = (y(k+1:n) - y(k)) ./ (x(k+1:n) - x(k));\n",
    "end\n",
    "\n",
    "coeff = y; % diagonale della tabella delle differenze divise.\n",
    "\n",
    "% si ottiene il vettore dei coefficienti per cui vale p(x(i)) = y(i)\n",
    "% dove p(x) = c(1) + c(2)(x - x(1)) + ... + c(n)(x - x(1))...(x - x(n - 1))\n",
    "\n",
    "% FASE 2 applicazione algoritmo di Horner\n",
    "% Calcolo dei valori del polinomio di Newton nel vettore y.\n",
    "\n",
    "n = length(coeff);\n",
    "yy = coeff(n) * ones(size(xx)); \n",
    "\n",
    "for k = n - 1: -1 : 1\n",
    "    yy =  (xx - x(k)).*yy + coeff(k);\n",
    "end\n",
    "\n",
    "\n",
    "% Si ottiene yy(i) = p(xx(i))\n",
    "% dove p(x) = c(1) + c(2)(x - x(1)) + ... + c(n)(x - x(1))...(x - x(n - 1))\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [0, 1/4, 1/2, 3/4, 1];\n",
    "%x = [-1 -0.7 0.5 2];\n",
    "y = [];\n",
    "\n",
    "xx = linspace(min(x), max(x));\n",
    "cols = ['b-', 'c-', 'r-', 'g-', 'r-'];\n",
    "\n",
    "n = length(x);\n",
    "\n",
    "for j = 1:n\n",
    "    % calcolo coefficienti j-esimo polinomio fondamentale di Lagrange\n",
    "    x_zeri = [x(1:j-1) x(j+1:end)];\n",
    "    p = poly(x_zeri);\n",
    "    p = p / polyval(p, x(j));\n",
    "    % calcolo valori assunti dal j-esimo polinomio\n",
    "    L(j,:) = polyval(p, xx);\n",
    "    % rappresentazione grafica\n",
    "    figure(j)\n",
    "    hold on\n",
    "    plot(xx, L,cols(j))\n",
    "    plot(x, zeros(1,n), 'b-')\n",
    "    plot(x(j), 1, 'c*')\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k = 0:4\n",
    "    x(k + 1) = (k * pi) / 2;\n",
    "    y(k + 1) = sin(x(k + 1));\n",
    "end\n",
    "\n",
    "xx = linspace(min(x), max(x));\n",
    "yy = interp_lagrange(x, y, xx);\n",
    "figure(1)\n",
    "plot(xx, yy, \"r-\", x, y, '*', xx, sin(xx), 'b-')\n",
    "legend(\"interpolante di Lagrange\",\"punti di interpolazione\", \"y = sin(x)\");\n",
    "box off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k = 0:4\n",
    "    x(k + 1) = (k * pi) / 2;\n",
    "    y(k + 1) = cos(x(k + 1));\n",
    "end\n",
    "\n",
    "xx = linspace(min(x), max(x));\n",
    "yy = interp_lagrange(x, y, xx);\n",
    "figure(2)\n",
    "plot(xx, yy, \"r-\", x, y, '*', xx, cos(xx), 'b-')\n",
    "legend(\"interpolante di Lagrange\",\"punti di interpolazione\", \"y = cos(x)\");\n",
    "box off"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 3\n",
    "\n",
    "La temperatura T in prossimità del suolo subisce una variazione dipendente dalla latitudine L secondo la seguente tabella:\n",
    "\n",
    "$$\n",
    "\\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n",
    "\\hline L & -55 & -45 & -35 & -25 & -15 & -5 & 5 & 15 & 25 & 35 & 45 & 55 & 65 \\\\\n",
    "\\hline T & 3.7 & 3.7 & 3.52 & 3.27 & 3.2 & 3.15 & 3.15 & 3.25 & 3.47 & 3.52 & 3.65 & 3.67 & 3.52 \\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "Si vuole costruire un modello che descriva la legge $T = T(L)$ anche per latitudini non misurate. A tal fine si scriva uno script che fornisca la variazione di temperatura alle latitudini $L = \\pm 42$ utilizzando il polinomio interpolante.\n",
    "\n",
    "Visualizzare in un grafico i dati assegnati, il polinomio interpolante e le stime\n",
    "di T ottenute per $L = \\pm 42.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [-55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65];\n",
    "y = [3.7 3.7 3.52 3.27 3.2 3.15 3.15 3.25 3.47 3.52 3.65 3.67 3.52];\n",
    "\n",
    "xx = linspace(min(x), max(x), 200);\n",
    "figure(3)\n",
    "hold on\n",
    "[yy] = interp_newton(x, y, xx);\n",
    "l = length(yy);\n",
    "plot(xx, yy, 'b');\n",
    "plot(x, y, 'r*'); % dati sperimentali\n",
    "plot(42, yy(1), 'go'); % stima L = 42°\n",
    "plot(-42, yy(l), 'ro'); % stima L = -42°\n",
    "legend(\"interpolante di Newton\", \"dati\", \"stima L = 42°\", \"stima L = -42°\", ...\n",
    "    \"location\", \"southoutside\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 4\n",
    "\n",
    "Scrivere uno script che calcoli il polinomio interpolante un insieme di punti $P_i = (x_i , y_i), i = 1, \\dotsc, n + 1$, nella forma di Newton con $x_i$ scelti dall’utente come:\n",
    "- punti equidistanti in un intervallo $[a, b]$,\n",
    "- punti definiti dai nodi di Chebyshev nell’intervallo $[a, b]$, ossia\n",
    "\n",
    "$$\n",
    "x_{i}=\\frac{(a+b)}{2}+\\frac{(b-a)}{2} \\cos \\left(\\frac{(2 i-1) \\pi}{2(n+1)}\\right), \\quad i=1, \\ldots, n+1\n",
    "$$\n",
    "\n",
    "e y i = f (x i ) ottenuti dalla valutazione nei punti x i di una funzione test f :\n",
    "[a, b] → R. Testare lo script sulle funzioni\n",
    "\n",
    "- $f(x) = \\sin(x) - 2sin(2x)$,\n",
    "- $f(x) = \\sinh(x)$,\n",
    "- $f(x) = |x|$,\n",
    "- $x \\in [-\\pi, \\pi]$,\n",
    "- $x \\in [-2, 2]$,\n",
    "- $x \\in [-1, 1]$,\n",
    "- $f(x) = 1/(1 + x_2)$,\n",
    "- $x \\in [-5, 5]$ (funzione di Runge).\n",
    "\n",
    "Calcolare l’errore di interpolazione $r(x) = f (x) - p(x)$, tra la funzione test $f(x)$ e il polinomio di interpolazione $p(x)$. Visualizzare il grafico di $f(x)$ e $p(x)$, ed il grafico di $|r(x)|$. Cosa si osserva? Cosa accade all’aumentare del grado $n$ di $p(x)$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In questo esercizio si sfrutta l'interpolazione non per dedurre dati sperimentali ma per approssimare funzioni. Il grado generalmente è pari al numero di punti forniti meno uno ma in questo caso l'utente può scegliere anche il grado (per studiare la variazione della norma della funzione resto)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. Scegli il grado: troppo basso o troppo alto e l'approssimazione non sarà buona\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " grado: 3\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2. Indica l'intervallo [a,b] entro cui estrarre i nodi di interpolazione:\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " a: 2\n",
      " b: 4\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3. Definisci la strategia di calcolo dei nodi di interpolazione \n",
      " [1] Equispaziati \n",
      " [2] Chebyshev\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " strategia: 2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4. Scegli la funzione da interpolare \n",
      " [1] sin(x) - 2sin(2x) \n",
      " [2] sinh(x) \n",
      " [3] |x| \n",
      " [4] 1 / (1 + x^2)\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " funzione: 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "text = [\"1. Scegli il grado: troppo basso o troppo alto\" ...\n",
    "    \" e l'approssimazione non sarà buona\"];\n",
    "disp(text);\n",
    "n = input(\" grado: \");\n",
    "\n",
    "text = [\"2. Indica l'intervallo [a,b] entro cui estrarre\" ... \n",
    "    \" i nodi di interpolazione:\"];\n",
    "disp(text);\n",
    "a = input(\" a: \");\n",
    "b = input(\" b: \");\n",
    "\n",
    "text = [\"3. Definisci la strategia di calcolo dei nodi di\" ... \n",
    "    \" interpolazione \\n [1] Equispaziati \\n [2] Chebyshev\"];\n",
    "\n",
    "disp(text);\n",
    "scelta = input(\" strategia: \");\n",
    "switch scelta\n",
    "    case 1 % equispaziati\n",
    "        x = linspace(a, b, n + 1);\n",
    "    case 2 % Chebyshev\n",
    "        for i = 1 : n + 1\n",
    "            x(i) = (a + b)/2 + (b - a)/2 * cos(((2*i - 1)) ...\n",
    "                * pi / ((2 * (n + 1))));\n",
    "        end\n",
    "    otherwise\n",
    "        close all\n",
    "        return\n",
    "end\n",
    "\n",
    "text = [\"4. Scegli la funzione da interpolare \\n\" ...\n",
    "    \" [1] sin(x) - 2sin(2x) \\n [2] sinh(x) \\n\" ... \n",
    "    \" [3] |x| \\n [4] 1 / (1 + x^2)\"];\n",
    "disp(text);\n",
    "scelta = input(\" funzione: \");\n",
    "\n",
    "xx = linspace(a, b, 301);\n",
    "switch scelta\n",
    "    case 1\n",
    "        f = sin(xx) - 2 * sin(2 * xx); y = sin(x) - 2 * sin(2 * x);\n",
    "    case 2\n",
    "        f = sinh(xx); y = sinh(x); \n",
    "    case 3\n",
    "        f = abs(xx); y = abs(x); \n",
    "    case 4\n",
    "        f = 1 ./ (1 + xx.^2); y = 1 ./ (1 + x.^2);\n",
    "    otherwise\n",
    "      close all\n",
    "      return\n",
    "end\n",
    "\n",
    "\n",
    "yy = interp_newton(x, y, xx);\n",
    "\n",
    "figure(1)\n",
    "plot(xx, yy, \"b-\", x, y, \"ro\", xx, f, \"r--\");\n",
    "legend(\"Interpolante di Newton\", \"Dati\", \"Funzione test\", ...\n",
    "    \"location\", \"southoutside\");\n",
    "box off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_resto = abs(f - yy);\n",
    "figure(2);\n",
    "plot(xx, f_resto, \"b-\");\n",
    "legend(\"abs err. interpolazione\")\n",
    "box off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "norm_inf =  0.000044177\n"
     ]
    }
   ],
   "source": [
    "norm_inf = max(f_resto)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LLe =\n",
      "\n",
      "       3.10494      29.89431     508.71131   10759.64903\n",
      "\n",
      "LLc =\n",
      "\n",
      "   2.1044   2.4894   2.7278   2.9008\n",
      "\n"
     ]
    }
   ],
   "source": [
    "clc\n",
    "\n",
    "a = -1; \n",
    "b = 1; \n",
    "spacing = 200;\n",
    "xx = linspace(a, b, spacing);\n",
    "\n",
    "LLe = zeros(1,4);\n",
    "LLc = zeros(1,4);\n",
    "\n",
    "i=0;\n",
    "\n",
    "for n = 5:5:20  \n",
    "    i = i + 1;\n",
    "    \n",
    "    xe = linspace(a, b, n + 1);\n",
    "    xc = cos(((2*[0:n] + 1)) * pi / ((2 * (n + 1))));\n",
    "    \n",
    "    Le = zeros(1, spacing);\n",
    "    Lc = zeros(1, spacing);\n",
    "    \n",
    "    for j = 1 : n + 1\n",
    "        x_zeri = [xe(1:j-1) xe(j+1:end)];\n",
    "        p = poly(x_zeri);\n",
    "        pe = p / polyval(p, xe(j));\n",
    "    \n",
    "        Le = Le + abs(polyval(pe, xx));\n",
    "        \n",
    "        x_zeri = [xc(1:j-1) xc(j+1:end)];\n",
    "        p = poly(x_zeri);\n",
    "        pc = p / polyval(p, xc(j));\n",
    "        \n",
    "        Lc = Lc + abs(polyval(pc, xx));\n",
    "    end\n",
    "    \n",
    "    LLe(i) = max(Le);\n",
    "    LLc(i) = max(Lc);\n",
    "end\n",
    "\n",
    "LLe\n",
    "LLc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si nota come la costante di Lebesque assuma valori notevolmente più grandi quando si impiegano nodi equispaziati mentre quando si utilizzano i nodi di Chebyshev la costante risulta molto vicina all'unità. Si deduce che con il set di dati fornito l'indice di condizionamento è particolarmente elevato nel caso della scelta di nodi equispaziati. Qualsiasi algoritmo si scelga di impiegare, sarà difficile ottenere delle soluzioni accurate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "clc\n",
    "clearvars\n",
    "a = -1; b = 1;\n",
    "x = linspace(a, b, 22);\n",
    "\n",
    "xx = linspace(min(x), max(x), 301);\n",
    "f = @(z) sin(2 * pi * z);\n",
    "\n",
    "yy_es = f(xx);\n",
    "\n",
    "y = f(x);\n",
    "yy = interp_lagrange(x, y, xx);\n",
    "\n",
    "y_t = y + 0.0002 * randn(1, 22);\n",
    "yy_t = interp_lagrange(x, y_t, xx);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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X3FsJIT744AMhRHRCZdoMdLvd8/PzkXmIvsXIU+K6c0jynx9++OGMKcs9qTxTtba2dvv27ZH5mf0FR76FnEn5ZYUQt2/f7vf7i05hxrMj0xlfIOGkc0jjX3ziG8/Pz+W3jn6v+NRklU8+K+t+E1eG8V88WhqSbCJMXDfii51zSOZxQm5hjvkMh0Pf98vlcqFQ8DyvUChMbMXLipbcWZRKpagCIztNybePvEU2ya89JojPgPygGfMQ/+hFzZjyjPmZ8QUninqRjTwy/xRmTzk+nTkXyPgXl288ODj4/PPP5b5CfusZU5Nnv6L1ZOLKMOcvPvGVI4sdJiGQkLBoHzTtPDy002q1okBaCCsDFvJ/n332Wd7zANP87Gc/q1arNGCN4TjOz3/+8+W6crAyYH4cIQEAlEAvOwCAEggkAIASCCQAgBLSCqSLi4vBYJDSxAEA5kkrkDqdjryCGQAA80glkO7fv//FF1+kMWUAGXCcy/+ALKUSSC9evPj444/TmDKAtDmOCMPL/8gkZIlODQBek2kUIZOQpXwC6e7du/EbROYyD4uJShhO7C+hw5wDi3u9hsvNkxIeMnEjrw/W5QoRMnXicxuOPyvCaFPV5GsBUznCCaPVPBTCeb1aRyt8XvMGs+UWSFp4Y8ucRD4br3LIZCKWoCVHhk8Yf+CNCp5c4a/bLoDl5HMtu7t377569Sr7z13InFvd5RYb23BHtmFAD1crbrwyN21NTvxQSY/SPaZIKkc4QprCWTCqwzDKIXkemEyCTmKr7Dyr7mUUJbqi61LGx4gEGxP0sptkqc0sDC+bjTT1oBdHLJsrdMJDogikMQumUXyTDEV41QkijTkDkscJIaiDkt0bnKVOqr3ZTAxF6Ai2cOgggTQKQyINSSGQXltlu4qnGCUMWEUWBsgkrI6SXfID/kJBYR06cBJLkahYrQXP84IgUGc6QoggCDzPG5lgEATtdjv6p+u6iXyWyqwOJBlFl9fskgdISeFkLxRncU/QUqlUKBRGHvQ8r9VqLTSdbrd7bSDNOdkgCLrd7siMBUGwt7fneZ78Z6fTmWeulvgi6rC9ZCc3SVlwSDhA6P0Nm2hUuPM8r1wuCyF83+/3+0EQuK7b6XQ8z2s0Gp1OZzgcCiHa7fbR0VG/34/+KYSQ+/pCoRAduwyHw2azWSqV5HSCIJg42XK53Gq1oknJ4IneOxwOC4WCnDE5b9Lu7m6r1fI8Lwqq+ERarZbrup7ndbvddrvtum65XJafeO/evb/85S/RrPq+H5+r8TxWhL1HSFFYOM5lFnFUA1uk01TSpVgtM2Y4HPZ6vXa7Xa1WXddtNBr1et33/Vu3brmue+fOHdd1+/2+EEL+c39/P3pcxApoMm/a7XapVPJ9f+Jky+Wy67rxKcv3tlqtarUa5VMUfnF7e3v7+/vy7/GJ+L7f7XaPjo6EEAcHB6VSSX7iP//5z/isjsxVBgt5OfYGUiQUEwaoJzRpnQrrsMTyo46y9MZFjFf+bwoZA6VS6fz8XD7S6/U6nU6lUul0OvLBarUqhGi1WnLXX6/X5YMyq4QQlUql1+vV6/WotjY+2YlTFkIEQdBsNqNPmUjGpO/74xOpVqvytFO9Xj86OioUCtGhz/isTpwr1dhbsrusqL25caq/nQJKS6pSndOmKAtclUolCAJ5XkeeJfJ9X57gkX/Ej2P29/c3NzdlAW3+KUcPBkEgy30z3uu6rsytkYlUKhVZ4qtWq61Wq9FoRG8pl8vjs6o+ewNJXG47oUjzQt0aFdZhA9bGaWTY/O53v/vtb39bqVR835elrYODg36/73mePPVSr9d7vd7R0ZHneQcHB0KIW7dudTqdXq8nD2JGjnXkZIMgePToUb1ej09ZCLG3t9dsNmV4xE8djSiVStVqtdvtjk+kVCptbm5WKpXvvvtOFu7iXySa1aR6A6YuzMO7776by+eOEGEWXz+bTwHmoew6n9e+KK7X652fn4dh2O125SO7u7vdbjd6XIqejb+x3+/LP2ZMduJ7z8/PJ75rhvGJTPvEa1+ZiAR/O6uv9p1Za5FmKVSg8grvLHo540zITgeVSiXvGVFagr+dvYGUaUjQ/xsqyHA9XHT7UjOQMI8Efzt62WWCHuXIHa0iKM/SQKKGBqRKlzFJUIqlgZT0VRnm+Ui2T+Qnp8Oj6wYCAW+wMpDy2jg5JENOcln3HBGGwrm8ViSZhDlYGUg50euKyDBGLgXqkVYfmYR5EEgAUsPVs7AI6wIp3wt5cZAEANNYF0iAVXLvUCobYfQ5xzzsupZd7hunkB382DKRlbzWtzdOGoWkEeZiVyApgRv3ITO5rmnRJ1OkxpwsKtmpcHgEWIhTp5iTRYGUw2DYaegDC8skvvUlMuQ2CILornojVr9lQ+I3fZAT1OleEouzKJCUwiBZpE2tO8Mm2giTlchoyO3SE5a34Bt50PO8Vqslb8e3ykyuMgU5DyMPyrsFrj5jKrPmHBKnbQAjrD7kdjgcNptNeTfVQqEQ/TMIAtd1O52O53k3bty4f/9+dNM83/fl7fg2NzeFEP1+X96Jtd1uFwqFVqsV/TMIAt/3O51Oo9GQb+90OvJDoyBpt9tCiPF39fv9+Dzcu3fvj3/8YzRj8r2e58m7xC6/BBXGEVI+qKojVTacMV36wEje5UhmiRDC87xGo9Fut0ulku/7jUajXq//9NNP8Zt/y4BxXbff7/f7fSGE67p37tzZ3993XffWrVvyn67rDofDbrfreZ4MrShyhsOhvNO5jJbxd/V6vXa7Xa1WXdeV8/Cf//wnPmNyTqIsNJItgUSJDMhZ0ldtWLrkEQRBs9kUV7cbr1QqvV6vXq9PO58khGg0Gvv7+/V6XR4hyTe2Wi3f93u9XqfTqVQqnU7n/PxcCFEqlcanEJXafvzxRyHE+Lvks6VSSf5zzhkzjBUlOzVbi/IgScEZA1S2+riJQqEgT8bI3gH7+/vy2GX8tE3E9/2joyMhRKVS2dzclG/0fV/GTLvdrlQqQRDM391gnnfNM2OGsSKQlMUgWaTC9Luvjpw3WvS77u3tNZvNcrns+365XL5161an0+n1erIs1mg0fN+/c+dO/C2FQkGeZyoUCmtrawcHB/1+3/M813ULhUK9Xq9UKr7vu647ZyY9evRoxrsKhYKct/iM2cD8W5grfRRCVwskZ+Scippr1rTtMeNbmA+HwyAI4n0WCoWCPFUjg2q8M1sQBMPhsFwuy1NQ8vXRazzPq1Qqi87GjHfJeQiCID5ji04/Gwn+dgRS3sgkJOGN9UheOk7J1UqRQFqFDKQl4sdUBNIiFN/jKz570MTr9ejqL3XXrElzplEgYUSCv53pvezU3Sgv0f0PyXJUrgcAM5keSMpjQBISptA1soDFEEiACS4vonN1hkbp0gDXcsQURgeS0hslkDC5sstruym+4lOpxkQmB5IuKz1VOyRCHh6F3A0P2jI5kACoiUYYJjI2kFQffvQmzkNjdaxF0J2xgaQZTvNiReqfOAKuQyAByEEoaIRhlKGB5OhUrwMACGMDSUdJ3y0GVtGlT6ki5E1a53+953kLvR7LIZAA7enVhSd3nuedn59PvI3eNOMX/57/s669m9E8r7GEifdD4uwuoIXV77W3lE6n43nejRs37t+/Xy6XXdeVd3bwfb/f7wdB4Lru0dFRp9ORr/c8z/O8crlcKpVkcsjb6/m+H39LoVBotVrRPctlgMnPajQa8r4V0bNBEBwcHAghNjc3e71e9JqMF4VqDDxC0rd2weAM2Gba1upcXnHi9X9JPSuEaDQa9Xr9p59+kvHQ7/eHw+FwOOz1eu12u1qtuq7bbDbjISFf47runTt3XNcVQriuO/IW13Vv3boVf030WTL24s92Op1Go+G6br/fj16TzDLVmYGBBFjFyHpdKMKR/5J6dgZ5TFMqlc7Pz4UQvu93u912ux29oNvt1ut1IUS1Wu33+yNv6fV6nU6nUql0Oh05hbiRZxuNxv7+fr1e39zcXHThGMzEkp3OokMkio6wgawKKBioQRC0Wq2jo6P4g9HNZOWh1QhZx6tUKkEQjPeAGHnW93058Uql8pvf/Ca9L6IX0wJJzZV7To4jorI6J8Iwp9AR2q7yeapWq61Wq1Kp+L5frVZHnpXne+TxkOd58sFHjx7V6/Ver3d0dDTe704+KycYlewKhYLv+0EQjDw7HA6bzabsK/GLX/ziT3/6UxAEC/WzMJJpd4zVPZDCUIc7fkId+q8lcpvN5Y6xQRAMh8NFT954njfj/uXjz8qDKlnciz8b//T4a7TDLcyn03b71OkW1FCHGWuJ4zhCcAtzTXEL8ymM2Di5BTUAO5kVSDqLLq8ahoLO35iTvoMcgHEEklqiq00acbCHdGl9xhQYZ1AvO/134dEtqAU3/YRVwlBQFYBJgWRMWzEMhVB1cAaQHoe7UVjPnEACrGJek4VeduAckqK4HTVmM2wN4UKOEMYEknmtRQCwjSGBZKCQGzwDsIshgWRY+QK4hv59SsexFcOIQDJx4xSMecR0Zq4bVAWsZ0QgGYrTvACsQiABmqELD0xlQiCZWb4ALBRSFbCa9oFEaxEAzKB9IJktFJzmxSh6o8FUBBKgFUP7lAKCQAKgFDqX2kzXQHIc4TjCkaeQABiEmqS1tAwkWbQIQxE6FoylM/8bYm7U62A0LQPJNhwEQmJNgNn0C6Sojeg4Vzez4xACMAmbtK30C6RIeHXm0/gyBqd5YRuOBe2kXyBFjSdWWViFMeAwnn6BJOKZ5Jh/eARYiKqAnW7kPQPLCp1QWNReDB1hz5cFYCctj5BsxGle6zE6B8YjkAAdUJuGBXQNJFqLgNm4srCFVg2ks7Ozi4uLRGZlAVa2FulVCMBsK3VqePDgQbFYfPny5SeffLK9vR09/v7776+vrwsh1tfXP/3001XnEUKIq35HFnXkQAw/PGywfCAdHx8Xi8WnT58OBoMnT55EgTQYDNbX158/f57MDALWoyECSywfSGdnZxsbG0KIYrF4enoaPT4YDG7evPnkyZO33nqr2WzevHkzgdkEYKGQqoBdVjqHVCwW5R9bW1vRgxcXF2+//XatVltbW3v8+PG09zoxC32oI2w8gQQAxlvpHNJgMJB/xI+QarVarVYTQmxvbx8fH097b0ioLO6y3xGLDoCJlj9C2tjY+OGHH8TVSaPo8cPDw5OTkwRmDYAQwqFmBVssf4RUq9UODw+fPXt2enq6s7MjhDg5OXn48OHXX3/9+PHje/fuvXz58qOPPkpuVgFYh86lVnFWLJ2dnJwUi8XoZNK1j0t379599erVEh/HqknJzjrW/+Js9fZYNZCWs3QgsXEKwUKwDD83S8Aaul46yGZcssEe9CmFVQgkAGrjUvfW0CqQOHIHAHPpFEiUqiRupgmrOI5wwsvbQ8NsOgUSYBV6l4lYWSQMKd2Zj0ACoA0yyWzaBBKtxTjuT2gDfuUIZWpLaBNIeAMNRQDGIZAAJdGn9E3yeJGlYraVrvadpdARVOwA28RqASGjhI2nSSDRLhrDKTWz8ftGXm/6Ds1Sw1GyAwAogUDSFf2OABhGj0DiGg2wCoMcJmI/YDw9AgkAqAoYT4NAorU4DQMnAZhEg0DCVAyPNRRNDdiJQAIUwyAH2EqDQKK1CEAKBVUBkykfSLQWAcAOygcSZgvpd2QaOjfDWgQSoBD6lMJmBBIArdC51FxKB5LD1X0BjKGqaSqlAwnzYPg6ADMQSCagZ7whHE4gwWoEEgBACQQSAM1QpjaVwoFE+QLAFJSpjaTJLcwxWxgyfkVfsT7MIR1LYTMCCchTdG2sqEnB1bJgLYVLdgAwDcNjTaRqINFKBDATw2PNo2ggsaotin5HAHSnaCABlpCVJ04gAYJAMgkdYTUVhkI4oeOQRouhKmAeetkB+aO7NyDUPEJiSA0AWEjFQKL0tCQ6wsIy7CsMo2IgYWn0TtQR9/0CJAIJgLaoCphFvUCipxEAWEm5QKLotAo6wsI27DFMolwgAVahTykQIZAAaIyqgEnUCiRai6ujI6xe+L2AiFqBBACwFoFkHDrCwjIcZRpDrUBixUoE/Y60wSAHIEatQAKsQtMhGVQFTKFSINFaBACLqRRISAgdYQHoSKFAonwBqzDIIUHsPcygUCABwHKoCphBlUCitZgs+isC0I4qgYTEOQ49j5RGowEYQSAZyLm845sj/wYALRBIZpL958OQERqqYpBD0jjiNIAqgcTKlJRoR0e/I9iFxpf+1AgkWouwDM0FYJwagYTkRM1EOsIC0AuBZKaodMHBp4IY5ABMpEQgUb5IVrwvA2kEi4RUBfSmRCAhDUQRAL3kH0iUL9JD30U18bsAE+UfSEgRHWEB6INAArJFPxNgivwDifIFgKSEgqqAxvIOJFqLKaMHIwBd5B1ISBnDY1VDEwGYhkACskOfUmAGAgmAUTgG1VfOgcSqAyBZlKn1lWcgUb7IBv0YAWiBkp0FGB6rDBoHwAwEEpAVBjkAMxFIAEzD8FhN5RdIDieQAACvcYRkBXozqoBfAZiNQLICHWEBqI9AArLAIAfgWgQSABNxO3MNpRVIZ2dnFxcXs15B/1cAQEwqgfTgwYO//vWvDx8+PDk5GXnKcS57Y9InM2N0hAWQAbmTj3b1C0k+kI6Pj4vF4tOnT//whz+4rht/So4LlIdGXD0AFmGQA+wQ7eTlf4vu5JMPpLOzs42NDSFEsVg8PT1NfPoAACOlUrIrFovyj62trejBkcumOI4j/+dwoAQgBZSpMxbt5KOlvuhBUiqBNBgM5B/xI6SROQvDUP4vpHcDABgkvOrfuOjlG5MPpI2NjR9++EEIMRgM1tfXE58+lkdH2JxwjQbYIDrqWHqFd9I4QLl///7W1tbp6enOzk6tVnvj8xwhhHj33bvff/+KQ6PsMTwzeyzzPHGF9cw5jhChI0Np0WWfSiAJIU5OTorFYnQyacTdu3dfvXqVxudiNnaO2WOZ54xMytzS6/yNxGdF2t7eTmnKADA/mgMZW6UFxqWD7MJVVgEoi0CyDnfRzhRDYoG5EUgAgMSs0uQlkACYjDJ1plbrQkIgATAcZWpdEEj24bq2AJREINmICwdkwxGMgIFdVty3EEgATEdVQBMEEgDzURXIwOoXJSGQbES/IwAKIpCAVHAJO2BRBJKl6AibNpYwbLP6Ok8gATAfZWotEEgAgJUlcZsPAslWdISFZSiiqo9AshcdYVPETeGAxRFIQPIIexVRFUhTIus8gQQAWElSgxwIJAC2cDhGUhuBZC86wsIqMopk3Y5YUhOBBCSMazQoKN7LhO4myiKQrEZH2DSwVJUVVQXo35CspNZ5AgkAsILkBjkQSHajoQgrMU5MTQQSkCh2dUqKml4hPRoUdiPvGUDOOP+eLJansq4yKaTBoCyOkADYIgxFGAoOkRLkiCRLAgQSAEAJBJLtGB4L23ClQWURSEBiGBILrIJAAmAXqgLKIpDAlQUSw5KEXZyESwIEEhgeC0AJBBKQEIbEAqshkABYh+KqmggkCEFH2CSwDHVCmXplyQ6JlQgkAIASCCQIQUdYAAogkIAEMCRWO5RYFUQgAbARVQEFEUi4RL8jAPNKekisRCDhCv2OVkCcA6sjkICVMSQWSAKBBMBSHNeqhkACYCvK1MtJrSRAIOE1OsIuynGE47DcYJf0VngCCa/REXYhspkoW4q0s4HVEUjAMqKihRwSS+0HWB2BBMBiIVUBhRBIAIB5pXqVLAIJbwgFtafF0HUYVkl1hb+R4rQBc0UnjcIwvPoj3zkCtEcgAUsKQyEcx3FCoghIBCU7YCWkke4oUy8g5atkEUgAACUQSBhDR9j5OIJrqsIuaV+UhEACACiBQAJgPaoCaiCQAADXS3VIrEQgYQKusgogewQSJuMCBNdwUm8tAkrJYJ9AIAEAVQElEEgAgOukPCRWIpAwBXf4gWUoU+eOQMJU3Jl7qkxai4A6stkbEEjAwohqM1EVyBuBBACYJYMRSBKBhKnodwTbcOybLwIJWExmrUXANgQSAEAJBBJmoSPsOJaJwShTT5DhRUm4hTlmcUQoN086OQNIG0dImEoOtgmFI3vD0iEWQKoIJEw2MvSTI6RLDIk1HSXZHBFIuAYdYeNYGuZjeGxMxmfUCCQAwHQZlgQIJEwWNRPpdwQgGwQSpor3ZeDUiWBIrDUozOaFQMIsYXiZQ6QR7EFVIC8EEq5HvyPARhkOiZUIJMyBfkdCCIIZSBmBBMyH02hAylYNpLOzs4uLi0RmBQAUEQqqAjlY6Vp2Dx48KBaLL1++/OSTT7a3t6PH33///fX1dSHE+vr6p59+uuo8AgAylkdJYPlAOj4+LhaLT58+HQwGT548iQJpMBisr68/f/48mRmEIsLQ8k7PVn952CeXFX75QDo7O9vY2BBCFIvF09PT6PHBYHDz5s0nT5689dZbzWbz5s2bCcwmkCvLwxjIxkrnkIrFovxja2srevDi4uLtt9+u1Wpra2uPHz+e9l4nZpV5AIBU0Lk0cwsfIZ2cnHz77bfvvPOOEGIwGMgH40dItVqtVqsJIba3t4+Pj6dNJ6TDEgC1WXtcnFdJYOFA2t7elqeLjo+Pz87OxNVJo+gFh4eH6+vr8T4OMIMcvm7rFgogdcufQ6rVaoeHh8+ePTs9Pd3Z2RFCnJycPHz48Ouvv378+PG9e/devnz50UcfJTeryF/oCBvzyHE4oIdV8trSV93STk5OisVidDLp2selu3fvvnr1apXPRT7sHBxq57eGEMLa/iw5rfP5NP0IJF3ZuWu281tDCGFnIOW3wnPpICyCfkewDBcwzBKBhMVYd6sYDo+ArBBIwCzWBTBG2FcVyHGdX+ladgAAM1zGbq6DOzhCwmK4mSZsY8NRsqxMR7eHzuuYkEACprKxhxWQHwIJAGYxvioQddxxZBssv4MkAgkLs6cjrD3fFDaL4ieMkimnvqUEEhZnSb8jOnwD2aKXHQBcw/irOF41MkNZm8yrJUYgAcB15A7b6CPmUOT/BSnZYSmh4ad5hR2dfYGICis8gQRMQIdvIHsEEgDMwZK+PLkikABgLioUtVKiSEmAQMKSjB8tCCBjBBKWZ+q4UUVai4BtCCRglKlBixUZXBVQZJ0nkADAbsoMsSKQsAIj+x0ps3FCQYocSZiKQMJKDO53BCBjBBLwBiIWsxhXFXAUuGJQhEDCSgw+zQsgYwQS8BodvoEcEcvQZ5wAAAZvSURBVEgAsIgwdIRjVt1OFQQSACzAubpjkONofzpJtZIAgYRVhcKU07yOWhsnFBQfFKBMV4DlqdaLnUACgMVEfXmM63OXMwIJAKyk3hhwAglJoKEIy8hil3q7dL0RSEiG7uNJlRoeCGXFm160wRJHIAHAAi7714kwFI6+bRg1W2AEEpLBJRtgjzBUcGduAgIJUG40BrSge5laQQQSACyDqkDiCCQkRrVBdgAmUrYkQCAhOZp2/uYCDbCMsm1HAgkAlkTVLlkEEgAsT9mjjakUHs1LICFR2lXtFN44AdsQSEiYXn1h9ZpbqEi3RpjK6zyBBAC2ULZ/nUQgIWEaneZVfOMEbEMgwUYG3OsTCgm1aYQpjkCCdWQ/BtmVgViCPdQvCRBISJ7KNzV/3avOcUIR6nZCGlie+j3UCSRYylG7qQi9aHTqVGUEEiwVsvuAVXQYckcgIR2q1sIu50uHjRN6Ub8gpr4bec8AjKXy+VMnFNEBEsGEZISh+r0GFEcgwTphKBxyCDZxhBPqsMZTskNalD3NSzMWUBOBBADJULMRplELjEBCitTcPgGoiUBCulTreqRRaxE6Um2F1wuBBLuwv0C6VBvw4OjUAiOQkDKltk+GHwEKI5AAIFFKNcK0QiAhfWyfsIwqd2XVrSTAwFhkQYUrI+gyNhBIik6nj4QQHCEhA/LoSN6CiIMl2ECFAQ86diglkJCuy7vh5b196rhxArYhkAAgefk2wjRtgRFIyEjuB0kAFEcgIV3xk0ahk1OvH63GBsIYocjtlKmmA8DpZYfUxTLp8s4P+c4PYDjdentHCCRk4fXWkX3DTduNEyaQzTHWwPlQskO26PcNpErn/COQkLUsB7E7QuONE4YIM+3Oo8pFIpZCICFrdLcDUqJpb+8IgQRj6b5xwhg0wuZEpwbkQG6fpAWwutfnZEPttymOkGAmAg9KSWlM0uWlucLLU6W6dxgikJCPtMcMajowEJjfGxuQ44Qi1L0TK4EEE+nc8xXGSiEuLldzx3GMqAcQSMhPSs050gh2eOO6XFclO63XfQIJucp2iAaQsxRWeMe5jCOti3USvexgFG4LC8Ul3MU0dEIRRvfA1B1HSMhZgkM06FkHO0W97HTHERLyx7AkWOWyERa7yM9ycWLeVkMgwRDmbZwwmRPGx7Eu0RnByBWekh2UsOqwJG7BB93E1/mFO5wausKnFUgXFxeDwSCliWM5juK9cJbuBa58X1fVl7y51Fzyr1fYMFxmBs1d4dMKpE6n8+WXX6Y0cRjrukxynMv/3nhI7Y0TGDE6fmih3bfRK3wqgXT//v0vvvgijSnDfGEoQ2f8mfhluxxHXL7M3I0TtghDRzjzrMjGr/CpBNKLFy8+/vjjNKYMG8jQGcmk0Xbh5SZs8sYJg102qq7+kyv8jPEP8lnjV/i0RhE+e/ZMCPHpp59OfPbu3btpfCgAQBGvXr1a9C2Jdfs+OTn59ttv33nnnY8++ujaF3///ffxfzK0PhuOo/FVDMYr5xrV0rVe8lpjyedi6cWeWCBtb29vb2/P+WJWkVxovdhliSP6BhqlkdB8yWuNJZ+LpRc7A2OhjfFrGwMwCcezAAAlcKUGAIAScgskLuWQmbOzs4uLi7znwmr8BJlhUatg6d37/3322WdJz8xc/vznP/d6vV/+8pe5fLo9Hjx4MBgMDg8Pi8VisViMP/X++++fnJz87W9/+9e//sUPkZ4ZPwGSxdquiKV37/l0arh///7Lly8ZPJu24+PjYrH49OnTwWDw5MmTeDfIwWCwvr7+/Pnz/ObOCjN+AiSLtV0Rq+ze8ynZcSmHbJydnW1sbAghisXi6elp/KnBYHDz5s0nT548e/aMEkd6ZvwESBZruyJW2b3TqcFwUeFia2sr/vjFxcXbb79dq9XW1tYeP36cx6zZYtpPgMSxtusuu5LdQpdywCqiRS2EiE4tjrQZa7VarVYTQmxvbx8fH2c/k/aY9hMgcaztussukBa6lANWES3q4+Pjs7MzcVVDj7/m8PBwfX2dXyRtGxsb034CJGvGomZt1wVXajBZrVY7PDx89uzZ6enpzs6OEOLk5OThw4evXr3a2tp6/PjxvXv3Xr58yTFresZ/AqSEtd0AXKnBfCcnJ9M6HM94CgliOWeGtV1rBBIAQAn0sgMAKIFAAgAogUACACiBQAIAKIFAAgAo4f8D2KPIy3J1h/8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure\n",
    "plot( xx, yy, \"r-\", ...\n",
    "      x, y, \"bo\", ...\n",
    "      xx, yy_es, \"g--\")\n",
    "title(\"Interpolante di Newton con nodi equispaziati\")\n",
    "legend(\"intepolante di Newton\", \"dati sperimentali\", \"funzione test\")\n",
    "box off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure\n",
    "plot( xx, yy_t, \"r-\", ...\n",
    "      x, y, \"co\", ...\n",
    "      x, y_t, \"bo\", ...\n",
    "      xx, yy, \"g--\");\n",
    "title(\"Interp. di Newton con nodi equispaziati e perturbazione sui dati\")\n",
    "legend(\"intep. perturbato di Newton\", \"dati\", ...\n",
    "    \"dati perturbati\", \"interp. Newton\", \"location\", \"southoutside\")\n",
    "box off"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con il set di dati perturbato si verifica il **fenomeno di Runge**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "err_rel_dati =    3.932814314593389e-04\n"
     ]
    }
   ],
   "source": [
    "format long\n",
    "err_rel_dati = norm(y_t - y, inf) / norm(y, inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "err_rel_ris =    2.920313467184383e-01\n"
     ]
    }
   ],
   "source": [
    "err_rel_ris = norm(yy_t - yy, inf) / norm(yy, inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Esercizio 7\n",
    "\n",
    "Si calcoli il polinomio interpolatore nella forma di Newton di grado $n = 59$ della funzione $f(x) = log(x)$ nei nodi $x_i = 10 + i/59$, $i = 0, 1, \\dotsc, 59$. Si calcoli poi il polinomio interpolatore di grado $n = 59$ per i nodi $x_i = 10 + \\frac{i}{59}, i = 59, \\dotsc, 1, 0$, ossia ordinati in ordine inverso. \n",
    "\n",
    "Per entrambi i polinomi si visualizzi in un grafico in scala semilogaritmica il comportamento dell’errore di interpolazione in valore assoluto, commesso in $1000$ punti equispaziati sull’intervallo $[10, 11]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = linspace(10, 11, 1000);\n",
    "f = log(xx);\n",
    "\n",
    "x = linspace(10,11,60);\n",
    "y = log(x);\n",
    "yy = interp_newton(x, y, xx);\n",
    "\n",
    "figure\n",
    "plot( xx, yy,...\n",
    "      xx, log(xx), ...\n",
    "      x,y, \"*\")\n",
    "title(\"Confronto interpolatori di Newton\");\n",
    "box off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_t = fliplr(x); % flip array left to right\n",
    "y_t = log(x_t);\n",
    "yy_t = interp_newton(x_t, y_t, xx);\n",
    "\n",
    "figure\n",
    "plot( xx, yy_t,\"r\", ...\n",
    "      xx, log(xx), ...\n",
    "      x,y, \"o\")\n",
    "title(\"Confronto interpolatori di Newton con nodi invertiti\");\n",
    "box off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "err_ass = abs(f - yy);\n",
    "err_ass_t = abs(f - yy_t);\n",
    "\n",
    "figure\n",
    "semilogy( xx, err_ass, \"b.-\", ...\n",
    "          xx, err_ass_t, \"r.-\")\n",
    "warning (\"off\", \"Octave:negative-data-log-axis\");\n",
    "box off"
   ]
  }
 ],
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