{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ad import adnumber\n",
    "\n",
    "x = adnumber(2.)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = 5.*x + 3\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y.d(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = 7.*x*x + 5.*x + 3\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y.d(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sin,pi\n",
    "\n",
    "x = adnumber(pi)\n",
    "y = sin(x)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y.d(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ad.admath import sin\n",
    "y = sin(x)\n",
    "y.d(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "from ad.admath import cos\n",
    "from math import pi\n",
    "\n",
    "numpy.random.seed(1)\n",
    "xrand = numpy.random.normal(scale=.1,size=10)\n",
    "xrand[0] = 0.\n",
    "for i in range(1,10): \n",
    "    xrand[i] = abs(xrand[i-1]) + abs(xrand[i]) + .02\n",
    "yrand = numpy.random.normal(scale=.42,size=10)\n",
    "\n",
    "def frantisek(x):\n",
    "#    print(x)\n",
    "    i = 0\n",
    "    while i < len(xrand) and xrand[i] <= x: \n",
    "        i += 1\n",
    "    if i>=len(xrand):\n",
    "        return 0\n",
    "    return (yrand[i]-yrand[i-1]) * ( \n",
    "        .5 - .5*cos((x - xrand[i-1])/(xrand[i]-xrand[i-1])*pi)\n",
    "    ) + yrand[i-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xx = numpy.arange(0.,xrand[9],xrand[9]/500)\n",
    "yy = [frantisek(x)*25. for x in xx]\n",
    "plt.plot(xx,yy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "yyd = []\n",
    "for x in xx:\n",
    "    xd = adnumber(x)\n",
    "    yd = frantisek(xd)\n",
    "    yyd.append(yd.d(xd))\n",
    "    \n",
    "plt.plot(xx,yy,xx,yyd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "def frantisek_dx(x):\n",
    "    xd = adnumber(x[0])\n",
    "    yd = frantisek(xd)\n",
    "    ret = numpy.empty((1,1))\n",
    "    ret[0,0] = yd.d(xd)\n",
    "    return ret\n",
    "\n",
    "minimize(fun=lambda x: frantisek(x[0]),\n",
    "        x0=[.5],\n",
    "        method='L-BFGS-B',\n",
    "        bounds=[(.4,.8)],\n",
    "        jac=frantisek_dx\n",
    "        )"
   ]
  }
 ],
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