{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import numpy as np\n",
    "import time\n",
    "np.set_printoptions(precision=3)\n",
    "np.set_printoptions(suppress=True)\n",
    "plt.style.use(\"ggplot\")\n",
    "plt.rcParams[\"font.size\"] = 13"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Horner法で多項式の値を求める\n",
    "\n",
    "`coefs`: `[0次の係数, 1次の係数, ..., 最高次の係数]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_poly_value(coefs, x):\n",
    "    value = 0.0\n",
    "    size = len(coefs)\n",
    "    for i in range(size):\n",
    "        if i == 0:\n",
    "            value += coefs[size-i-1]\n",
    "        else:\n",
    "            value = value * x + coefs[size-i-1]\n",
    "            \n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_poly_value([2, 5, 3], -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 素直な解法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_poly_product(f_coefs, g_coefs):\n",
    "    \"\"\"\n",
    "    Parameters:\n",
    "        f_coefs: array_like. fの係数のリスト. [0次の係数, 1次の係数, ..., 最高次の係数]\n",
    "        g_coefs: array_like. gの係数のリスト. [0次の係数, 1次の係数, ..., 最高次の係数]\n",
    "    Returns:\n",
    "        h_coefs: ndarray. h=fgの係数のリスト. [0次の係数, 1次の係数, ..., 最高次の係数]\n",
    "    \"\"\"\n",
    "    f_size, g_size = len(f_coefs), len(g_coefs)\n",
    "    h_coefs = np.zeros([f_size+g_size-1], dtype=float)\n",
    "    \n",
    "    for i in range(f_size):\n",
    "        for j in range(g_size):\n",
    "            h_coefs[i+j] += f_coefs[i] * g_coefs[j]\n",
    "            \n",
    "    return h_coefs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12., 17., 10.,  3.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_poly_product([3, 2, 1], [4, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FFTを使った解法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FFTにライブラリを使用"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_poly_product_fft(f_coefs, g_coefs):\n",
    "    \"\"\"\n",
    "    Parameters:\n",
    "        f_coefs: array_like. fの係数のリスト. [0次の係数, 1次の係数, ..., 最高次の係数]\n",
    "        g_coefs: array_like. gの係数のリスト. [0次の係数, 1次の係数, ..., 最高次の係数]\n",
    "    Returns:\n",
    "        h_coefs: ndarray. h=fgの係数のリスト. [0次の係数, 1次の係数, ..., 最高次の係数]\n",
    "    \"\"\"\n",
    "    h_size = len(f_coefs) + len(g_coefs) - 1\n",
    "    h_fft_coefs = np.fft.fft(f_coefs, n=h_size) * np.fft.fft(g_coefs, n=h_size)\n",
    "    h_coefs = np.fft.ifft(h_fft_coefs)\n",
    "    \n",
    "    return np.real(h_coefs)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12., 17., 10.,  3.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_poly_product_fft([3, 2, 1], [4, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 速度比較\n",
    "\n",
    "$n = 2, 4, 8, \\ldots, 2^{15}$次多項式同士の積を計算する. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_mean_time(func, *array):\n",
    "    time_list = np.zeros([len(array[0])])\n",
    "    for i, a in enumerate(zip(*array)):\n",
    "        start_time = time.time()\n",
    "        func(*a)\n",
    "        time_list[i] = time.time() - start_time\n",
    "        \n",
    "    # remove slowest/fastest time\n",
    "    time_list.sort()\n",
    "    \n",
    "    return np.mean(time_list[1:-1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current n = 2\n",
      "Current n = 4\n",
      "Current n = 8\n",
      "Current n = 16\n",
      "Current n = 32\n",
      "Current n = 64\n",
      "Current n = 128\n",
      "Current n = 256\n",
      "Current n = 512\n",
      "Current n = 1024\n",
      "Current n = 2048\n",
      "Current n = 4096\n",
      "Current n = 8192\n",
      "Current n = 16384\n",
      "Current n = 32768\n"
     ]
    }
   ],
   "source": [
    "n_list = [2 ** i for i in range(1, 15+1)]\n",
    "sample_size = 20\n",
    "random_state = np.random.RandomState(2018)\n",
    "\n",
    "n_size = len(n_list)\n",
    "simple_mean_time, fft_mean_time = [], []\n",
    "\n",
    "for i, n in enumerate(n_list):\n",
    "    print(\"Current n = {}\".format(n))\n",
    "    sample_f_coefs = random_state.randint(low=-100, high=100, size=(sample_size, n))\n",
    "    sample_g_coefs = random_state.randint(low=-100, high=100, size=(sample_size, n))\n",
    "    \n",
    "    # simple\n",
    "    if n < 3000:\n",
    "        t = get_mean_time(get_poly_product, sample_f_coefs, sample_g_coefs)\n",
    "        simple_mean_time.append(t)\n",
    "    \n",
    "    # FFT\n",
    "    t = get_mean_time(get_poly_product_fft, sample_f_coefs, sample_g_coefs)\n",
    "    fft_mean_time.append(t)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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0tDS99tpratmyperWrasHH3xQJ0+ezLZtTEyMXnjhBd17772qXbu2WrRooW+/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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e63c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16, 9))\n",
    "plt.plot(n_list[:len(simple_mean_time)], simple_mean_time, color=\"red\", label=\"Simple method\")\n",
    "plt.plot(n_list, fft_mean_time, color=\"blue\", label=\"FFT method\")\n",
    "plt.xscale(\"log\", basex=2)\n",
    "plt.title(\"Time comparison: simple method vs interpolation + FFT\")\n",
    "plt.xlabel(r\"Size of $n$\")\n",
    "plt.ylabel(\"Average elapsed time (sec, sample: {:d})\".format(sample_size))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}