04_Function_Sol.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Functions and Classes: Exercise Solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Functions\n",
    "Define the following functions and show some sample outputs.  \n",
    "1) Factorial of n: $1 \\times 2 \\times \\cdots \\times n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def factorial(n):\n",
    "    \"\"\"factorial of n\"\"\"\n",
    "    f = 1\n",
    "    for i in range(n):\n",
    "        f = f * (i+1)\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def factorial(n:int):\n",
    "    \"\"\"factorial of n\"\"\"\n",
    "    if n < 0 or type(n)!=int:\n",
    "        print('n should be non-negative integer.')\n",
    "        return\n",
    "    elif n==0:\n",
    "        return 1\n",
    "    else:\n",
    "        return factorial(n-1)*n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n should be non-negative integer.\n"
     ]
    }
   ],
   "source": [
    "factorial(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n",
      "2\n",
      "6\n",
      "24\n",
      "120\n",
      "720\n",
      "5040\n",
      "40320\n",
      "362880\n"
     ]
    }
   ],
   "source": [
    "for n in range(10):\n",
    "    print(factorial(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) For a circle of radius r (default r=1), given x coordinate, return possible y coordinates (i.e., both positive and negative)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def circley(x, r=1):\n",
    "    \"\"\"y coordinate for given x for a circle of radius r\"\"\"\n",
    "    if abs(x) > r:\n",
    "        return\n",
    "    elif abs(x) == r:\n",
    "        return 0.\n",
    "    else:\n",
    "        y = np.sqrt(r**2 - x**2)\n",
    "        return y, -y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n",
      "0.0\n",
      "(0.5999999999999999, -0.5999999999999999)\n",
      "(0.8, -0.8)\n",
      "(0.916515138991168, -0.916515138991168)\n",
      "(0.9797958971132712, -0.9797958971132712)\n",
      "(1.0, -1.0)\n",
      "(0.9797958971132712, -0.9797958971132712)\n",
      "(0.9165151389911681, -0.9165151389911681)\n",
      "(0.8, -0.8)\n",
      "(0.6000000000000003, -0.6000000000000003)\n",
      "(2.1073424255447017e-08, -2.1073424255447017e-08)\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "X = np.linspace(-1.2, 1.2, 13)\n",
    "for x in X:\n",
    "    print(circley(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n",
      "0.0\n",
      "(0.5999999999999999, -0.5999999999999999)\n",
      "(0.7999999999999999, -0.7999999999999999)\n",
      "(0.916515138991168, -0.916515138991168)\n",
      "(0.9797958971132712, -0.9797958971132712)\n",
      "(1.0, -1.0)\n",
      "(0.9797958971132712, -0.9797958971132712)\n",
      "(0.916515138991168, -0.916515138991168)\n",
      "(0.7999999999999999, -0.7999999999999999)\n",
      "(0.5999999999999999, -0.5999999999999999)\n",
      "0.0\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "for i in range(-6, 7):\n",
    "    print(circley(0.2*i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Draw a star-like shape with n vertices, every m-th vertices connected, with default of n=5 and m=2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def star(n=5, m=(n-1)//2, r=1):\n",
    "    \"\"\"Draw a star with n>=5 vertices.\"\"\"\n",
    "    if n < 3:\n",
    "        print('n should be 3 or more.')\n",
    "        return\n",
    "    if m == None:\n",
    "        m = (n-1)//2\n",
    "    xy = np.zeros((n+1, 2))\n",
    "    th = 2*np.pi*m/n\n",
    "    for i in range(n):\n",
    "        xy[i] = [r*np.sin(i*th), r*np.cos(i*th)]\n",
    "    xy[-1] = xy[0]\n",
    "    plt.plot(xy[:,0], xy[:,1])\n",
    "    plt.axis('square')\n",
    "    plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 40 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "M = 7\n",
    "for n in range(5, 5+N):\n",
    "    for m in range(1, min((n+1)//2, M)):\n",
    "        plt.subplot(M, N, (m-1)*N + n-4)\n",
    "        star(n, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "4) Any function of your interest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Classes\n",
    "1) Define the `Vector` class with the following methods and test that they work correctly.  \n",
    "* `norm`, `normalize`: as in the previous class (use L^p norm, with default p=2).\n",
    "* `scale(s)`: multiply each component by scalar s.\n",
    "* `dot(v)`: a dot product with another vector v."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Vector:\n",
    "    \"\"\"A class for vector calculation.\"\"\"\n",
    "    default_p = 2\n",
    "    \n",
    "    def __init__(self, arr):  # make a new instance\n",
    "        self.vector = np.array(arr)     # array is registered as a vector\n",
    "    \n",
    "    def norm(self, p=None):\n",
    "        \"\"\"Give the L^p norm of a vector.\"\"\"\n",
    "        if p == None:\n",
    "            p = self.default_p\n",
    "        y = self.vector ** p\n",
    "        z = np.sum(y) ** (1/p)\n",
    "        return(z)\n",
    "    \n",
    "    def normalize(self):\n",
    "        u = self.vector/self.norm()\n",
    "        self.vector = u\n",
    "    \n",
    "    def scale(self, s):\n",
    "        u = s * self.vector\n",
    "        self.vector = u\n",
    "    \n",
    "    def dot(self, v):\n",
    "        return(np.sum(self.vector * v.vector))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = Vector([0, 1, 2])\n",
    "x.vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 6])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.scale(3)\n",
    "x.vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = Vector([1, 2, 3])\n",
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) Save the class Vector as a module `vector.py`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Import the module and test how it works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import importlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'vector' from '/Users/doya/Dropbox (OIST)/Python/ComputationalMethods/vector.py'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(vector) # This is needed after updating a module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = vector.Vector([0, 1, 2])\n",
    "x.vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.norm(p=1)"
   ]
  },
  {
   "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}