interpolation_gauss.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "\n",
    "pi = np.pi\n",
    "exp = np.exp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constants, points, range, bins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "#Constants:\n",
    "sigma = 1.0\n",
    "mi= 0.0\n",
    "\n",
    "#Range and points:\n",
    "n = 1000 #number of points\n",
    "n_test = 1000\n",
    "bins = 10 #number of bins\n",
    "x = np.linspace(-5.0, 5.0, num=n)\n",
    "\n",
    "l = np.linspace(-5.0,5.0,n_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define the gaussian function:\n",
    "def gauss (x):\n",
    "    g =[]\n",
    "        \n",
    "    for j in range(0,len(x)): \n",
    "                \n",
    "        g_i =  (1 / ( sigma * pow((2*pi),0.5)))* exp( -0.5 * pow ((x[j] - mi) / sigma, 2.0))\n",
    "        \n",
    "        g.append(g_i)\n",
    "    return g\n",
    "\n",
    "f = gauss(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3f658604c0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#Define the linear interpolation: \n",
    "# f is the distribuition\n",
    "# l is the point where the interpolated function is calculated\n",
    "\n",
    "def interpolate (f, x):\n",
    "    p=[]  \n",
    "    for i in range(0,len(x)-1):\n",
    "        dx = x[i+1] - x[i]\n",
    "        dy = f[i+1] - f[i]\n",
    "        coef_a = dy /dx\n",
    "        coef_b = -dy/dx * x[i] + f[i]\n",
    "        p.append((coef_a, coef_b, x[i], x[i+1]))\n",
    "    return p\n",
    "\n",
    "def interpolated_point(p,point):\n",
    "    for item in p:\n",
    "        if point >= item[2] and point <= item[3]:\n",
    "            return item[0]*point + item[1]\n",
    "\n",
    "\n",
    "        \n",
    "inter=[]\n",
    "real_points = gauss(l)\n",
    "coef = interpolate(f, l)\n",
    "\n",
    "for point in l:\n",
    "    inter.append(interpolated_point(coef, point))\n",
    "\n",
    "#plt.plot(l, inter)\n",
    "\n",
    "erro = []\n",
    "for i in range(0, len(l)):\n",
    "    err = inter[i] - real_points[i]\n",
    "    erro.append(err)\n",
    "     \n",
    "plt.plot(erro,\".\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cumulative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3f655edee0>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#Define the cumulative:\n",
    "def cumulative (coef, point):\n",
    "    integral_i =0\n",
    "    \n",
    "    for item in coef:\n",
    "        if point>= item[2] and point>= item[3]:\n",
    "            integral_i += item[0] /2 * (item[3]**2 - item[2]**2) + item[1] * (item[3] - item[2])\n",
    "        \n",
    "        elif point>= item[2] and point< item[3]:\n",
    "            integral_i += item[0] /2 * (point**2 - item[2]**2) + item[1] * (point - item[2])\n",
    "    #print (integral_i)       \n",
    "    return integral_i\n",
    "\n",
    "#A list of pairs (ci, xi):\n",
    "def cumulative_all_points(coef, x):\n",
    "    cumulative_all = []\n",
    "    for i in x:\n",
    "        c = cumulative(coef, i)\n",
    "        cumulative_all.append((c,i))\n",
    "    return cumulative_all\n",
    "\n",
    "cumulative_all = cumulative_all_points (coef, x)\n",
    "\n",
    "x_ii = []\n",
    "c_ii = []\n",
    "for i in range(0,n-1):\n",
    "    x_ii.append(cumulative_all[i][1])\n",
    "    c_ii.append(cumulative_all[i][0])\n",
    "\n",
    "plt.plot(x_ii, c_ii, \".\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  1.,   3.,  23., 115., 195., 255., 223., 128.,  46.,  10.]),\n",
       " array([-3.64578677, -3.00062819, -2.35546962, -1.71031105, -1.06515248,\n",
       "        -0.4199939 ,  0.22516467,  0.87032324,  1.51548181,  2.16064039,\n",
       "         2.80579896]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#Define the sampler:\n",
    "def sampler(cumulative_all, t):\n",
    "    sampler_list=[] \n",
    "    for j in range(len(cumulative_all)-1):\n",
    "        dc = cumulative_all[j+1][0] - cumulative_all[j][0]\n",
    "        dx = cumulative_all[j+1][1] - cumulative_all[j][1]\n",
    "        coefs_a = dx /dc\n",
    "        coefs_b = -dx/dc * cumulative_all[j][0] + cumulative_all[j][1]\n",
    "        sampler_list.append((coefs_a, coefs_b, cumulative_all[j][0], cumulative_all[j+1][0]))\n",
    "        \n",
    "    for item in sampler_list:\n",
    "        if t >= item[2] and t <= item[3]:\n",
    "            return item[0]*t + item[1]\n",
    "\n",
    "\n",
    "\n",
    "#A list of sampler point\n",
    "def sampler_points(cumulative_all, s_list):\n",
    "    sampl_points = []\n",
    "    for i in range(len(s_list)-1):\n",
    "        s = sampler(cumulative_all, s_list[i])\n",
    "        sampl_points.append(s)\n",
    "    \n",
    "    return sampl_points\n",
    "\n",
    "s_list = np.random.uniform(0,1.0,1000)\n",
    "samplerpoints = sampler_points(cumulative_all, s_list)\n",
    "\n",
    "plt.hist(samplerpoints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}