{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python: basic features\n",
    "https://www.python.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, World!\n"
     ]
    }
   ],
   "source": [
    "print(\"Hello, World!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = 5\n",
    "b = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 + a * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a ** b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# different in python 3: a//b\n",
    "# for same behaviour run: from __future__ import division\n",
    "a / b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a / float(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a % b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a == b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a != b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a += 3\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 'hello', 5.5]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1, \"hello\", 5.5]\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.5"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 'hello', 5.5, 'how are you?']"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.append(\"how are you?\")\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "hello\n",
      "5.5\n",
      "how are you?\n"
     ]
    }
   ],
   "source": [
    "for x in a:\n",
    "    print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "element 0: 1\n",
      "element 1: hello\n",
      "element 2: 5.5\n",
      "element 3: how are you?\n"
     ]
    }
   ],
   "source": [
    "for i, x in enumerate(a):\n",
    "    print(\"element {}: {}\".format(i, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 'hello', 5.5, 'how are you?']"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0] = 10\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, 'bye')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = (-1, \"bye\")\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'bye'"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'tuple' object does not support item assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0mTraceback (most recent call last)",
      "\u001b[1;32m<ipython-input-22-c58040f40f7e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mb\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: 'tuple' object does not support item assignment"
     ]
    }
   ],
   "source": [
    "b[0] = 10\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x, y = b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'bye'"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'age': 23, 'name': 'Mary', 'sign': 'capricorn'}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = {\"name\":\"Mary\", \"age\":23, \"sign\":\"capricorn\"}\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[\"age\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'age': 23, 'job': 'student', 'name': 'Mary', 'sign': 'capricorn'}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[\"job\"] = \"student\"\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(a, b=4, c=5):\n",
    "    if a > 2 and b < 10:\n",
    "        return a\n",
    "    elif c == 5:\n",
    "        return b\n",
    "    else:\n",
    "        return a + b + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(4, 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(4, c=6, b=11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy: multi-dimensional arrays and scientific computing\n",
    "https://www.numpy.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0, 2, 4, 6, 8, 10, 12, 14, 16])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9L,)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  6,  8, 10, 12, 14, 16])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  6,  8, 10, 12])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  8, 12])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:7:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16, 14, 12, 10,  8,  6,  4,  2,  0])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  8, 10])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[0, 4, 5]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True,  True,  True,  True,  True,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a > 3\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  6,  8, 10, 12, 14, 16])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[b]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3L, 4L)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2],\n",
       "       [ 5,  6],\n",
       "       [ 9, 10]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:, 1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  4,  8],\n",
       "       [ 1,  5,  9],\n",
       "       [ 2,  6, 10],\n",
       "       [ 3,  7, 11]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 11, 12, 13],\n",
       "       [14, 15, 16, 17],\n",
       "       [18, 19, 20, 21]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   1,   4,   9],\n",
       "       [ 16,  25,  36,  49],\n",
       "       [ 64,  81, 100, 121]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,  20,  60, 120],\n",
       "       [ 40, 100, 180, 280],\n",
       "       [ 80, 180, 300, 440]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * [10, 20, 30, 40]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.84147098,  0.90929743,  0.14112001],\n",
       "       [-0.7568025 , -0.95892427, -0.2794155 ,  0.6569866 ],\n",
       "       [ 0.98935825,  0.41211849, -0.54402111, -0.99999021]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.5"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.5,  5.5,  9.5])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  7, 11])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(a, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2. ,  2.5,  3. ,  3.5,  4. ])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(2, 4, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.5,  2.5,  2.5],\n",
       "       [ 2.5,  2.5,  2.5]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.full((2, 3), 2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# matplotlib: plotting\n",
    "https://matplotlib.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#%matplotlib notebook\n",
    "#%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-5, 5, 50)\n",
    "y = np.sin(x)\n",
    "y2 = y ** 2\n",
    "y3 = -x / 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eQGJMkDYoDsbZJ+U1dSDAx5PB8VHM23rMKfMbeXt482DSg0wdOZWE0ASLfNep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\nwzCcwiQUwzAMwyn+H8vBtkf41GnwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x78818d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(x, y, label='sin')\n",
    "plt.plot(x, y2, '.', label='$\\sin^{2}$')\n",
    "plt.plot(x, y3, linewidth=3)\n",
    "plt.annotate('example text', xy=(0.5, -0.75))\n",
    "plt.xlabel(\"X axis\")\n",
    "plt.ylabel(\"Y axis\")\n",
    "plt.title(\"Example plot\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PjGVpehHfqgOpzovWRWEnECeEGCCEcAHmA6s1zmSzdDrBv+ckI6Xkgc92q7MXLGBfSR0v\nfHuQaUmhTE9SZy1r6a7JnUu0H/p8D9VqiXafaVoUpJQG4A/AV8B+YKmUMkfLTLYu0t+Dx6YP56fD\nVXywrUDrOHatzWDk3mXZ+Lq78LerErSO4/BcnfQ8P28Etc1tPLZyr5pb6yOtrxSQUn4ppRwspYyV\nUj6ldR57MG9UJJOGBPH0uv3kV6o2w+by4ncH2V9ax9OzE/H3dNE6jgIMC/Xh7smD+WJPKavVEu0+\n0bwoKKZ38uwFVyc99y7NokMNI5lcRkE1r244zJzUCC4b3l/rOMopbrtoIClRfvxlVQ7H1RLtXlNF\nwU7193Hj/66KZ9exGt7cdETrOHalsdXAPUuyCfNz5y8z1F5La+Ok1/Hc3BG0Gjp4cPluNYzUS6oo\n2LGZyWFMTQjhua8PkltWp3Ucu/HkF/spPNHEc3NH4O2mjta0RgMCPXl46jA2HKjg052F5/4GpZsq\nCnZMCMGTVyfg4+7M3Z9mqSM8TeD73ON8suMYt04YyOgB/lrHUc5i4dhoLhgUwJNr91FYrZZo95Qq\nCnYuwMuVZ+YkkVtWr47wPE9VDa088NkehoZ486fLB2sdRzkHnU7wzLXJ6ITg3qXZam6th1RRcAAX\nDwnmxnHRvL05n02H1I7wvpBS8uiKvdQ2t/Hc3BG4OqmjNW1BmJ87f70qnh1Hq3l1Q57WcWyCKgoO\n4pErhzEo2Iv7lmWrsxf64PNdxazPKePey4cwPMxH6zhKL8xKCWdmchjPf3uIXcdOaB3H6qmi4CDc\nnPW8OH8E1Y1tqmleLxWdaOKJ1TmMjvHndxMGah1H6SUhBE/OSiDU1427P81STfPOQRUFBxIf5st9\nlw9hfU4Zy9JV07yeMHQYufvTLIxS8uzcZPQ61ezOFvm4OfPCvBEUnWji8VWqacLZqKLgYH43YSDj\nBgbwxJocjqrdzuf0/LcHSS84wd9nJxLp76F1HOU8pMX4c+clcXyeWcyqrF/13VS6qKLgYHQ6wbNz\nk3HSCe5ekkV7h1HrSFZr86FK/rvhMHPTIrhqhDojwR7ceckgUqP78ecVe9Uy1TNQRcEBhfm58/fZ\niWQV1vDCtwe1jmOVKupbuXtJFoOCvHhiZrzWcRQTcdLreGHeCADuXpKFQb0p+hVVFBzU9KQw5qVF\n8soPh/k+V/WfP5XRKLlnSeeE5MvXj8TDxUnrSIoJRfp78OSsBDIKTvCf79Uy1V9SRcGB/fWqeIaH\n+nDPkmx1KX2KV388zOa8Sp6YGc+QEG+t4yhmcNWIcGanhPOf7w+xRZ3t/DOqKDgwN2c9ry4YiVFK\n7vh4F60G1QYj/Wg1z31zkOlJocwfFXnub1Bs1t+uTiA2yIs7P8mkuKZZ6zhWQxUFBxcd4Mm/5ySz\nu6jW4c+3rWlq44+fZBLRz52nZyeqs5btnKerE68tTKXNYOT2DzNUb7AuqigoXBEfwm0XDeTDbcdY\nmemYS/U6uuYRKhpa+c91Kar7qYOIDfLi2bmdb4qeWK32L4AqCkqX+68YwugYfx7+fA8Hj9drHcfi\n/rU+lx8OVPCXGfEkRfhpHUexoCviQ7jj4lg+3VnIJzuOaR1Hc6ooKEDnUr2Xr0/B09WJxR9m0NBq\n0DqSxXyWUcTrG4+wcGw0C8dGax1H0cCfLhvChLhAHl+VQ1ZhjdZxNKWKgtIt2MeN/1yXwtHKRoc5\nxjOjoJpHPt/D+NgAdYqaA9PrBC/NTyHYx5XbP8ygsqFV60iaUUVB+ZlxsQE8cuUwvso5zlNf7Nc6\njlkV1zRz2wcZhPm58d8bRuKsV78OjqyfpwuvLUilurGNOz/OdNiNbeq3QPmVWy4cwE0XxPDOlnze\nstPznRtbDfz2vXRaDUbe+s0o/DxctI6kWIGEcF+empXI1iNVPLLCMbsJq62ayq8IIfjztOGU1bbw\n1Jf7CfV1Z1pSqNaxTMZolNy7NJsDZXW8s2gUg4K9tI6kWJFrUyM4VtXIS9/nEeDlyoNThmodyaLU\nlYJyWnqd4Pl5IxgZ1Y97lmax82i11pFM5rlvDrI+p4xHpw1n0pBgreMoVuieywZz/ZgoXt1w2G6v\nls9EFQXljNyc9bx1YxoRfu789r108sobtI503l7dcJiXf8hj/qhIbr4gRus4ipUSQvC3qxK4MjGE\nJ7/Yz/IMxzl/RBUF5az6ebrw3s2jcdYLFv1vB+X1LVpH6rPXfzzMP9fnctWIMJ6apXYsK2d38mp5\nfGwADyzf7TCNI1VRUM4p0t+DdxaNoqqhjUXv7KTKBpfrvbXpCE+vy2VGchjPzlEnqCk94+qk540b\n0xge6sPvP9pFuh0No56JKgpKjyRF+PH6wlSOVDYw57WtNtVA7O3N+Tz5xX6mJYby/NxknNTSU6UX\nvFydePemUYT5unPzuzvJKanVOpJZqd8OpccuGhzEh7eMobKhlWv++xOHbKAdxrtb8vnb2n1MTQjh\nhfkjVEFQ+iTAy5X3bh6Np6sT817fxsaDFVpHMhv1G6L0SlqMP0tuG0eHlMx5fSuZx05oHemM3t96\nlCfW7OOK+P68dF2K2pymnJdIfw8+//14Ivq5c9O7O1m6s1DrSGahfkuUXhsW6sPyxePxdXfmhre2\ns+mQdb1rau8w8n9r9vGXVTlcPrw//7lO7VZWTCPU151li8d1Tz7/+6sDdrfBTf2mKH0SFeDBssXj\niA7w5OZ3d7J2d4nWkQAoq21h/hvbeGdLPjddEMPL14/ExUn9mCum4+3mzDuLRjEvLZKXf8jjniVZ\ndnVAlfptUfos2NuNT28dS0pkP/7wcSZPrM6hqU277qpb8iqZ9tImckvrePn6FB6fEa8KgmIWznod\n/7gmkfuvGMLKrBJufHsHtU3tWscyCfUbo5wXX3dn3r9lNIvGx/DuT0eZ8sImth+psmgGo1Hyyg95\nLHx7O/08XVj1hwuYnhRm0QyK4xFCcMfFg3hx/ggyj9VwxQsbWben1OaHk4StPYG0tDSZnp6udQzl\nNLYfqeL+z3ZzrLqJReNjeGDKEDxczNteq7S2mT+v2Mt3ueXMTA7j6dmJeLqqll6KZWUV1vDw53vY\nX1rHxMFB/HVmPDGBnlrH+hkhRIaUMu2ct1NFQTGlpjYD/1p/gHd/Okp0gAfPXJvM6AH+Jn+c0tpm\nXt1wmE93FCKR/HnacG4cF612KSuaMXQYeX9rAc99c5C2DiO/nxTL4omxuDnrtY4G2EhREELMAZ4A\nhgGjpZTnfLVXRcE2bDtSxQNdVw0T4gKZNyqSy4b3x9Xp/H5BympbeHVDHp/sKMQoJdemRnDHxYOI\n9PcwUXJFOT/H61p48ov9rMkuISbAg4emDuOSocEmmd+SUvb5jY+tFIVhgBF4HbhPFQX70tRm4M2N\n+SxNL6S4ppl+Hs5cnRLOvFGRDA3x6fH9tBo62F9az4pdRaoYKDZj06EK/rIqh/zKRrzdnLhsWH+m\nJIRw0eCgHl89tLR3kH70BJsOVbDpUCWzR4bz2wkD+5THJopCdwghNqCKgt3qMEq25FWyZGchX+8r\no71DkhzhS2q0P0HergR6uXT97UqQtyu1ze1kFdawu6iG7MJacsvqaO+QOOmEKgaKTWkzGNl0qIJ1\ne8v4Zt9xapvb8XTRc/HQYCYNCcbHzQkXJx0uTjpcnXS46PV0SMnO/Go25VWy/UgVrQYjznpBanQ/\nbhgTzYzkvi2iUEVBsUrVjW2syCzm811F5Fc20tR25vXdXq5OJIb7khzp11lEYvoR7O1mwbSKYjrt\nHUa2Haniyz1lfJ1TRlVj21lvPyjYiwlxgVwUF8ToAf7nvYDCaoqCEOJbIOQ0X3pUSrmq6zYbOEtR\nEELcCtwKEBUVlVpQUGCmtIqlNbUZqKxvo6KhhYr6NioaWvFw1pMc6cvAQC90qpupYoc6jJL8ygZa\n2o20Goy0GYy0dXT+bZSSpAhfQn3dTfqYPS0KZl+7J6WcbIL7eAN4AzqvFM47lGI1PFyciApwIipA\nDQcpjkOvEwwK9tY6xmmpzWuKoihKN02LghBilhCiCBgHfCGE+ErLPIqiKI7OKiaae0MIUQHY4qRC\nIFCpdQgLU8/Z/jna8wXbfc7RUsqgc93I5oqCrRJCpPdkkseeqOds/xzt+YL9P2c1p6AoiqJ0U0VB\nURRF6aaKguW8oXUADajnbP8c7fmCnT9nNaegKIqidFNXCoqiKEo3VRQURVGUbqooKIqiKN1UUVAU\nRVG6qaKgKIqidFNFQVEURemmioKiKIrSTRUFRVEUpZsqCoqiKEo3VRQURVGUbqooKIqiKN1UUVAU\nRVG6qaKgKIqidFNFQVEURenmpHWA3goMDJQxMTFax1AURbEpGRkZlT05o9lsRUEI8Q4wHSiXUiac\n5usCeBG4EmgCFkkpd53rfmNiYkhPTzd1XEVRFLsmhCjoye3MOXz0LjDlLF+fCsR1/bkVeNWMWRRF\nUZQeMFtRkFJuBKrPcpOrgPdlp22AnxAi1Fx5FNuQX9lIeX2L1jEcSn1LO/tL61CnMCqg7ZxCOFB4\nysdFXZ8r/eUNhRC30nk1QVRUlElDlNQ088iKPXQYJSE+boT6uhHi6971txtD+nuj0wmTPqbyc5UN\nrazOKmFFZjF7imvxdNHz4vwUJg/vr3U0u7e/tI7fvZ9O0YlmIv3dmTUinFkjIxgQ6Kl1NLuXX9lI\n0YkmympbKKttobSu8+/GVgMPTBlCarS/JrnMekazECIGWHuGOYW1wD+klJu7Pv4OeFBKedYJg7S0\nNGmqOYXKhlbmvraV8vpWYoO9KKttpqK+FeMp/ySTh/XnjYWpqjCYWHNbB1/vK2NlZjEbD1XSYZTE\nh/lw1Ygw1mSXsreklvuvGMLtE2PpnH5STO3rnDLuXpKFt5sTt14Uyw+55Ww5XImUMCLSj9kjw5me\nFIa/p4vWUe3O898c5MXvDv3scwGeLoT4ulHV0EZjq4FPbh1LQrivyR5TCJEhpUw75+00LAqvAxuk\nlJ90fXwAmCSl/NWVwqlMVRRqm9u57o1tHKls4INbxjAqprMqGzqMVDS0Ulrbwobccl76Po+7J8dx\n9+TB5/2YSqeapjam/2czRSeaCfN146qUcGalhDO4vzfQWTAeWL6bNdklXD0ijH9ck4Sbs17j1PZD\nSskrP+Tx768PkhzpxxsLU+nv4wZAWW0Lq7KKWZFZTG5ZPR4uej5bPJ7hYT4ap7YfX+eUcesHGcxI\nDmPBmChCfd0J9nHt/hkvqWlmzmtbaWnvYOniccQGeZnkcW2hKEwD/kDn6qMxwEtSytHnuk9TFIWm\nNgM3vr2D7KIa3rwxjUlDgk97Oykl9y3bzfJdRbz9mzQuHaaGM0zhniVZrMku4bUFqVwyNPi0V2E/\ne+GK8OWNG9O6X7iUvutNwc0pqeU37+wkyNuVVXdcgIuT2tZ0vg5XNHDVy1sYGOTJ0tvGnfHf/khF\nA3Nf34qzXseyxeOI6Odx3o/d06Jgtv/LQohPgK3AECFEkRDiFiHEYiHE4q6bfAkcAfKAN4HfmyvL\nqVoNHdz2QQa7jp3gxfkpZywIAEIInpqVQEK4D3cvySK/stESEe3a1zllrMgs5o6LBzF5eP8zDssJ\nIfjDJXG8vjCVQ+UNzHx5M9mFNRZOa1/KaluY+/pW1u4u4cEpQ3l+3oizXoHFh/ny91kJ7C+t45Uf\n8iyY1D41tBq47YMMXJx0vLog9az/9gODvHj/5jE0thpY8NZ2KupbLZbTnKuPrpNShkopnaWUEVLK\nt6WUr0kpX+v6upRS3iGljJVSJp5rLsEUDB1G7v40i02HKvnH7CSuTDz3Yic3Zz2vLUjFSSdY/EEG\nja0Gc8e0Wyca23hkxV6Gh/pwx8WDevQ9V8SHsPz28TjpdNzw1nYqGyz3y2FPOoySRf/bwZGKBt5c\nmMbtk3o2V3N5fAizU8J55Yc89hbXWiCpfZJScv+ybI5UNPDydSmE+7mf83uGh/nwv5tGc7yulYVv\nb6e2qd0CSR2ozYXRKHno8z2s21vGY9OHM3dUZI+/N6KfBy9dl8Kh8noeXL5bLd3ro8dX51DT1Ma/\n5yT3aihiWKgP798ymub2Dl7+Xr1j7YuTcwT/vDap16u6Hp8Rj7+nC/cty6bV0GGmhPbt9Y1HWLe3\njIenDmNi1JdiAAAgAElEQVT8oMAef19qdD/euDGVIxWNLHp3h0XelDpMUViaXshnGUXcdWkct1w4\noNffPyEuiPuvGMra3aW8tSnfDAnt27o9pazOLuGPl8b1adIyNsiLuWkRfLS9gMLqJjMktF+thg6e\n/+YgieG+TOvB1fEv+Xo48/TsRHLL6vnPd6oo99amQxX8a30u05JC+e2Evr32vHRdCtmFNTz15X4z\nJPw5hykKs0dG8NzcZO6eHNfn+1g8cSBTE0J4et1+fsqrNGE6+1bV0MqfV+4lIdyH2yfF9vl+7rp0\nMDoheP6bgyZMZ/8+3HaM4ppmHpwytM/Ley8d1p9rUyN49cfDam6nFwqrm/jjJ5nEBXvzr2uS+vzv\nPyUhhNcXpnHf5UNMnPDXHKYouDjpmD0y4rzWvAsheGZOMgODvHhg+W4MHUYTJrRff1mVQ11LO8/O\nGYGzvu8/ciG+biy6IIYVWcXkltWZMKH9qm9p55Uf8rhwUCAXxvV82OJ0Hps+nCAvV+5blk1LuxpG\n6on/W7sPQ4fktYWpeLqe317hy4b3t8ieEYcpCqbi5erEA1cMoehEM+tzyrSOY/XW7i7hiz2l3D15\nMENCvM/7/m6fGIu3qxPPrD9ggnT2781N+VQ3tvHAlPN/h+nr7sw/rknkUHnDrzZeKb92uKKBb/cf\n56YLB9jUDnFVFPpg8rD+DAj05M2NR9Sk81nUNrXzl1U5JEf4cttFA01yn34eLiyeFMt3ueXsPHq2\n1lpKZUMrb206wrTEUJIi/Exyn5OGBDMvLZLXfzysViOdw9ub83HW67hxXLTWUXpFFYU+0OkEt1w4\ngOyiWnbkqxemM1mSfozqxjaempWI03kMG/3STeMHEOztyj/X5aqifBYvf59Hq8HIvZebdjf+o9OH\n4enqxBsbj5j0fu1JVUMryzOKuGZkOIFerlrH6RVVFPrompER+Hu68KZaiXRaHUbJB9sKGD3A36T9\nWwDcXfTcNTmO9IITfJ9bbtL7theF1U18tL2AuWmRDDRRm4STfNycmZMayZd7SimvUx1tT+eDbQW0\nGozccqFprpAtSRWFPnJ30bNwbDTf7j/O4YoGreNYnQ0HyimsbuY342LMcv9z0yIZEOjJv9YfoMOo\nrhZ+6blvDqITgrsu7ftqu7NZOC4ag1HyyY7Cc9/YwbS0d/D+1gImDwtmULBpC7IlqKJwHhaOi8bF\nSaf2LZzGe1sL6O/jyuXx5ukX5azXce/lgzlwvJ5VWcVmeQxbtb+0jpVZxdx0wQBCfM3TL2pAoCcT\nBwfx0fYC2tUqvJ9ZvquI6sY2fjvB9q4SQBWF8xLo5co1IyP4fFeRar9wivzKRjYerOCGMdHntQT1\nXK5MCCUh3Idnvz6odtqe4t9fHcDb1YnbJ/Z9T0hP/GZ8NOX1rXydc9ysj2NLjEbJ25vySYrwZcwA\nbc5DOF+qKJynWy4cQKvByAdbe3T8qUP4YGsBznrB/NE9byXSFzqd4N7Lh1Bc06xemLocqWjgu9xy\nfjdhIL4ezmZ9rImDg4ny9+C9rUfN+ji25Lvcco5UNvLbCQNt9hwQVRTO06BgLyYPC+aDbQVqQw/Q\n2GpgWUYhUxNCCfY2f6vriXFBhPu5szRdjW0DLMsoQq8TzDNzQQbQ6wQLxkaxI7+a/aVqMyHAmxuP\nEO7nzpUJIVpH6TNVFEzgdxMGUt3YxvJdRVpH0dzKrGLqWwz8Zrxl1mbrdIJrUyPYnFdJcU2zRR7T\nWhk6jCzPKOLiIUEWKcjQOeHv6qTjfXWlTFZhDTuOVnPzhQNMugTb0mw3uRUZPcCfpAhf3tqUj9GB\nV8JIKXn/pwLiw3wYGdXPYo97bWoEUsLyDMcuypsOVVJe38qcNPNfJZzk5+HC1SPCWZlZbLHWztbq\nzU1H8HZzYl4vOjBbI1UUTEAIwe8mDCS/spFv9zvu2Pb2/GoOHK/nN+NiLDqeGunvwfjYAD7LKHLo\norw0vZAATxcuGXrmg6PMYeG4aJrbO1iW4bhDeIXVTazbU8r1Y6LwOs8eR1pTRcFEpiaEEO7nzpub\nHHeX5/tbj+Ln4czMEWEWf+y5aZEcq25iu4PuMK9qaOXb/ceZlRJu1hVfp5MQ7ktadD8+2FbgsEX5\n7c356ITgpvG9b41tbVRRMBEnvY5F42PYefQEeeX1WsexuNLaZr7KOc68tMizHjNoLlMSQvB2c2KZ\ng044r8wqob1DWnTo6FQ3jo+hoKqJHw9VaPL4Wmpp72D5riKmJYWabV+IJamiYEJXpYShE7Ays0Tr\nKBb3yfZjGKVkwVhtmn+5OeuZkRzGl3tLqWtxrLFtKSXL0gtJjvA1SSfavpgSH0KQt6tDLs3ecKCc\n+hYD14yM0DqKSaiiYELB3m5cMCiQlVnFDtWordXQwcc7jnHp0GAi/T00yzE3LZKWdiNrs0s1y6CF\nvcV15JbVa3aVAJ3nlVw/OoofDpRTUNWoWQ4trMgsJtDLlfGxAVpHMQlVFExsVko4RSeaySg4oXUU\ni/k65ziVDW0sNFOfo55KjvBlcH8vh5vwXJpeiKuTjhnJlp/LOdX1Y6LQC8HH249pmsOSapva+SG3\ngpnJYTa9DPVU9vEsrMjl8SG4OetYkek4/XhWZRUT6uvGhF4cSG4OQgjmpEaSeayGQ8cdY16npb2D\nVVnFTEkIwdfdvDuYz6W/jxuThgSxOrvEYSacv9xbSluHkatTtC3IpqSKgol5uTpx+fAQvthTSpvB\n/huF1TS18ePBCmYkh6HTab+t/+qUcJx0gmUOsmfh633HqWsxMFfDoaNTzUgOo7S2xWEOQFqZWczA\nIE8STdweXkuqKJjB1Slh1DS18+NB+1+JsW5vGe0dkpkaD12cFOTtyiVDg/l8V5FDdO9cll5IuJ87\n4wZax3j2ZcP74+6sZ3W2/S+2KK5pZnt+NVePCLfZPkeno4qCGUyIC8Lf04WVDtDSeXVWCQODPIkP\n89E6Src5aZFUNrSx4YB9F+XimmY251VybWqEVVylAXi4OHHZ8P58uafU7ovy6qzOwneVBvtyzEkV\nBTNw1uuYnhTKt/uOU2/HyyPLalvYll/FzOQwq3qnNGlIEIFernbfJG95RhFSdrb5sCYzk8M40dTO\n5kOVWkcxq5WZxYyM8iM6wFPrKCZ1zqIghLhACOHZ9d8LhBDPCSFs6yRqDVydEk6rwcj6vWVaRzGb\ntbtLkBKrGTo6yVmv45qR4XyfW055vX0eF2k0SpZlFHLBoABNlwGfzkWDg/B1d7brIaT9pXUcOF7P\n1SnhWkcxuZ5cKbwKNAkhkoF7gcPA+2ZNZQdSIv2IDvCw6yGkNdklJIb7mvwMYFOYkxZBh1F2X+Lb\nm51HqymsbmZOqnVMMJ/KxUnHlYkhfJVTRnObfbaTX5lZjJNOMC0xVOsoJteTomCQnTuxrgJellK+\nAmizbdKGCCG4akQ4Px2u4rgdHm6eX9lIdlGt1V0lnDQo2JvhoT6s2W2fG9nW7C7BzVnHZcPNc9zp\n+ZqRHEZTWwff5dpfg0ijUbIqq4SLBgcR4OWqdRyT60lRqBdCPAwsAL4QQugAbRdE24irR4QhJXb5\nbnVNdglCwPRk632nNCM5jOzCGgqrm7SOYlKGDiPr9pRx6bD+eFppR84xAwII9nZllR3+7G/Lr6Ks\nrsUuh46gZ0VhHtAK3CKlLAMigGfMmspODAzyIjnC1+6GkKSUrMoqZnSMP6G+7lrHOaPpSZ0Fa62d\nXS1sO1JNVWMbM5KstyDrdYIZyWH8eKCC2mb7WmyxKrMETxc9lw2zzqu083XOoiClLJNSPiel3NT1\n8TEppZpT6KGrU8LJKamzqx22+0rrOFzRqEmL7N6I9PcgOdKPtbvt693qmuzOF6VJQyx7bkJvzUwO\no63DyFd2tNiipb2DL/eUckVCCO4ulu8GbAlnLApCiM1df9cLIepO+VMvhFAHsvbQ9KQw9DphV1cL\nq7NLcNIJrkyw3neqJ81ICiWnpI4jFQ1aRzGJNoOR9TllXe1UrPtFKSnCl+gAD1Zl28/P/g+55dS3\nGrh6hH0OHcFZioKU8sKuv72llD6n/PGWUlrPTiUrF+TtyoWDAlmZaR/9YIxGydrsUi4aHEQ/Txet\n45zTNDsbQtqSV0ltc3v30Jg1E0JwVXIYWw9XUW4niy1WZBYT5G0/HVFPpyf7FCaf5nO/MU8c+3R1\nShjFNc1kHLP9zqkZx05QXNNstauOfinU151RMf3sZghpTXYJPm5OTIgL0jpKj8wcEYZR2kdRrm1u\nZ8OBCmYk2U9H1NPpyTP7ixDiVSGEpxCivxBiDTDD3MHsyWXDQ3B10rHWDjbzrM6y7qWQpzMjOYyD\nxxs4UGbb8zot7R18ve84UxJCcHGyjRelQcHeDAv1sYuNbF/llNHWYbT6ubTz1ZOfrIl0bljLAjYD\nH0spr+3JnQshpgghDggh8oQQD53m65OEELVCiKyuP3/pVXob4eXqxKXDgvliTxkdNjyE1N5h5Ms9\npUy24qWQpzM1IRSdwOavFn48WEFDq4HpSbb1onTViDCyCms4VmXbS4PX7i4l0t+d5Aj76Yh6Oj0p\nCv2A0XQWhlYgWvSg0Y0QQg+8AkwFhgPXCSGGn+amm6SUI7r+/F/Po9uW6UlhVDa0sv1IldZR+mxL\nXiVVjW02M3R0UpC3K2MHBrB2d6lNn4i3dncp/p4uNjeeffLwn9U2POFc1dDKlrxKpidZV58vc+hJ\nUdgGrJdSTgFGAWHAlh5832ggT0p5RErZBnxK565oh3TxkGA8XfSsseF3q6u7xrMnDrGN8exTzUgO\nI7+ykZwS21w419Rm4Nt9x5maEGJz49nhfu6kRfez6SGkdXs7r/Jn2NhVWl/05KdrspTyHQApZbOU\n8o/Ar4aCTiMcOLVNZVHX535pvBBitxBinRAi/nR3JIS4VQiRLoRIr6iwzXbI7i56Jg/v33X+gO21\nFG5p7+DrnM7xbFcn614KeTpT4kNw0gmbnfD8Prec5vYOmxs6OmnmiM55ndwy2yzKa3d3togfFmr/\nHX56snntmBCinxBitBDiIiHERSZ8/F1AlJQyCfgPsPIMGd6QUqZJKdOCgmzvXepJM5I6D9/ZnGd7\nLYU3HCinodXAzGTbXJ/dz9OFCwYFdnV2tb0hpLXZpQR5uzJ6gL/WUfrkysRQ9DrBGhu8Wjhe18L2\n/GpmOMDQEfRsSepvgY3AV8Bfu/5+ogf3XQyc2sIxoutz3aSUdVLKhq7//hJwFkJoe9CvGU0YHIiP\nmxNrs23v3erq7BICvVwZZ2Pj2aeakRxG0YlmsgprtI7SK/Ut7Xx/oJxpXS+stijQq3Nt/5ps25vX\n+XJPKVLCDCvu82VKPRk+uovOuYQCKeXFQArQk9+qnUCcEGKAEMIFmA+sPvUGQoiQk5PWQojRXXls\ndyb2HFyd9FwRH8LXOWW0tNtOS+H6lna+21/OtMQQm31RArg8vj8uep3NDSF9u/84bQajzb8ozUgO\n41h1E9lFtVpH6ZU12SUMDfFmULD9Dx1Bz4pCi5SyBUAI4SqlzAWGnOubpJQG4A90XlnsB5ZKKXOE\nEIuFEIu7bnYtsFcIkQ28BMyXtvY2opdmJIdR32pgow2d3/zt/uO0Gmx/fbaPmzMXDQ7ii92lNrW7\nfG12KWG+bqRE9tM6ynm5Ij4EF73OproGF51oYtexmu4VVI6gJ0WhSAjhR+d4/zdCiFVAQU/uXEr5\npZRysJQyVkr5VNfnXpNSvtb13y9LKeOllMlSyrFSyp/6+kRsxfjYAPw9XWyqz//qrBLC/dwZGWXb\nL0rQOQRQVtdCeoFt7C6vbWpn46EKpieHWc05zH3l6+7MpCFBrN1dYjP7db7o+j11hFVHJ/VkonmW\nlLJGSvkE8BjwNnC1uYPZKye9jqkJIXy77zhNbQat45zTicY2Nh2qZHpyqF1Msk0e1h83Z53NTHiu\nzymlvUPaRK+jnpiRHEZ5fSs78qu1jtIja3eXkhzhS1SAdR15ak69WvAspfxRSrm6a9+B0kfTk8Jo\nbu/g+9xyraOc07q9ZRiM0uY2rJ2Jp6sTk4f1Z+3uEtoM1r80eEVmMQMCPUkMt49dtJOH9cfDRW8T\nexbyKxvZU1xrs8uA+8q2dsHYidED/An2drWJd6urs4uJDfJkeKj9NMadPTKcE03tVj+vU1zTzLYj\n1cxKCbeLqzTo3K9z2fD+rNtbavVF+WSvsml2cpXWU6ooaECvE0xLCuWHAxXUt1jvqVRltV3rs5Pt\na332hLggAjxdWJFp3W0XVnWdwWFvvftP7tfZYuX7ddbuLmVUTD/C/Kz3dEFz6Mk+hTuFELY/w2hl\npieF0WYw8s0+6z3YvHOjF3YzdHSSs17HjOQwvtl/3GqPipRSsmJXMWnR/exuPPuiwUH4ujtb9RDS\nweP1HDhe73BDR9CzK4X+wE4hxNKurqf285ZRQyOj/Aj3c7fqNfNrdpeSEO7DwCAvraOY3KyU8M5T\nzPZa579/Tkkdh8ob7PJweBenzsUW1rxfZ212CToBUxNDtI5icT1ZffRnII7OVUeLgENCiL8LIWLN\nnM2uCSGYnhTKxoMV1DRZ37x9QVUj2YU1drsULynCl4GBnny+yzqHkFZkFuOi19nNqqNfmpEcRmOb\ndS62kFKyZncpYwcGEOztpnUci+vRnELXhrKyrj8GOttpfyaE+JcZs9m9GclhGIySdVZ4sPnJSfDp\ndjZ0dJIQglkp4WzPr6bohHX1+Td0GFmVVcLFQ4Pw87D+I0/7YuzAAIK8Xa1yI9ve4jryKxsdasPa\nqXoyp3CXECID+BedLbMTpZS3A6nANWbOZ9fiw3yIC/ZiaXrhuW9sYWuyOyfZwu14ku3k0MwqK3th\n2nK4isqGVmbZ4dDRSXqdYFpiKN8fKLe6xRZL0wtxcdJxZYJ9XqWdS0+uFPyB2VLKK6SUy6SU7QBS\nSiMw3azp7JwQgnmjIsk8VsPB49ZzVOSBss5JNnt/pxTp78GomH6syCy2qiZtK3YV4ePmxMVDg7WO\nYlYzkjsXW3ydYz2LLVraO1iZVcyVCSH4ejhrHUcTPZlTeFxKedq2FlLK/aaP5Fhmj4zAWS9YstN6\nrhZWZxej1wmuTLT/d0qzUiLIK29gb7F19PlvbDXwVc5xpiWF2eS5Fb0xMsqPiH7uVrUKad3eUupb\nDMwbFaV1FM2ofQoa8/d04fLhIXy+q4hWg/YrMTqMkpWZJYyPDSDQy1XrOGY3LTEUF73OavYsfJVT\nRnN7B7NH2u/Q0UlCCGYmh7E5r5LjdS1axwHg0x2FRAd4MHagbZ5bYQqqKFiBeaMiOdHUbhV7FjYc\nKKe4ppnrRzvGOyVfD2cuGRrM6uwSDFZwIt6KzGIi+nUeX+kI5o2KpMMo+XSH9lfK+ZWNbM+vZm5a\npF1t1uwtVRSswIWDAgn3c7eKIaQPtxUQ7O3K5OH9tY5iMbNGhlPZ0MomjXfYHq9rYUtepV21tTiX\n6ABPLhocxCc7jmlelJemF6LXCa5NjdA0h9ZUUbACOp1gTloEm/MqKazWbnlkYXUTGw5WMH90FM42\ndjj8+bh4SDB+Hs6s1HgIaXVWCUaJXW5YO5sFY6Ioq2vhOw33LLR3GPkso4iLhwTT38fx9iacynF+\n863cnLTOk0uXZRRpluHjHcfQCcF1oyPPfWM74uKkY1piKF/llNHQql07888zi0mO8CXWDneQn80l\nQ4MJ9XXjw209OqbFLH7ILaeivpV5oxzrZ/90VFGwEuF+7kyIC+Kz9EJNDiBpNXSwZGchlw4NJtTX\nfvcmnMnskeG0tBtZr9FGwtyyOvaX1tn13oQzcdLruG50FJsOVZJf2ahJhqXphQR7u3LxkCBNHt+a\nqKJgReaPiqSktoVNhyzf0nn93jKqG9tYMDba4o9tDUZG9SPK34PlGl2pLc8oQq8Tdr835Ezmj4rE\nSSf4eLvlrxbKalv4Preca1MjcHKgYdMzUf8CVmTysP74e7poMuH84bYCogM8uHBQoMUf2xoIIZg/\nOpKtR6rYW2zZg+XrWtr5dEchU+JDCHCAZcCnE+zjxuXx/VmWUWTxJnnLdxVhlDA3TQ0dgSoKVsXF\nScfslHC+3X+cyoZWiz1ublkdO4+e4IYxUTZ/DvD5uGFMNF6uTrz242GLPu7H249R32pg8UTH7jG5\nYEw0NU3t3eciW4LRKFmaXsjYgf7EBHpa7HGtmSoKVmbeqEjaOzp76VvKR9uO4eKkY06qY79T8nV3\n5oaxUXy5p5SCKsuMbbe0d/D25nwuHBRIYoR9HLnZV+NiAxgY5MmHFhxC2pZfRUFVE/MdeAfzL6mi\nYGXi+nuTGt2PT3ces0g/noZWAysyi5meFEo/T/vsyNkbt1wwACedjjc2HrHI463ILKaivpXbJzn2\nVQJ0DuEtGBNN5rEaiw3hLdlZiI+bE1MSHO/chDNRRcEKzUuL5HBFI7uOnTD7Y63MLKah1eCwE8y/\nFOzjxjWp4SzLKKK83rytFzqMktd/PExiuC/jYwPM+li24prUCNycdXxkgauF2qZ21u0t4+qUcNyc\n7bvPVG+oomCFpiWF4umi592fzPuLIaXkw20FDA/1ISXSz6yPZUtuvSiW9g4j7245atbH+SqnjKNV\nTdw+KdZhdjCfi6+7MzOTw1iZWUKdmVtqL0k/RpvBqCaYf0EVBSvk6erEjeNjWJNdwu6iGrM9zq5j\nJ8gtq2fB2Gj1onSKAYGeTE0I4YOtBWZ7YZJS8uqGwwwI9OSKeDV0caoFY6Npbu8w67xaTVMbr/xw\nmAlxgSSEO/Zczi+pomClfj8plgBPF578Yr/Z5hY+3HYML1cnrhrhmGvjz2bxxFjqWw18vP2YWe5/\nS14Ve4prufWigegdeMXX6SRF+JEU4cuH2wrM9rP/0nd51Le08+i0YWa5f1umioKV8nZz5u7LBrMj\nv5qvzdA9Nb+ykS92lzJ7ZDierk4mv39blxThx4WDAnl7c75Z1s2/9uNhgr1dHaJFdl8sGBvNofIG\ns/zsH61s5INtR5mbFsnQEB+T37+tU0XBil03KpJBwV78Y10ubQbTdZCUUvLI53twddbxh4sHmex+\n7c3iibFU1Lea/KyFPUW1bM6r5OYLB9j9QTp9NSslnCH9vXl8VY7Jj+v8x7pcnPU6/nT5YJPer71Q\nRcGKOel1PHLlUPIrG026GuOzjCK2HqnioalDCXbwjpBnc8GgABLDfXlj4xGT9qN67cfDeLs5ccMY\ntTb+TJz1Op6+JpHj9S08+/VBk93vjvxq1ueUsXhiLMHe6mf/dFRRsHIXDwnmgkEBvPjdIWqbzv8d\nU1VDK099uZ+06H5cpzbsnJUQgsUTY8mvbOSrHNM0ysuvbOTLvaUsGBuNt5tjngHcUyOj+nHj2Gje\n23qUTBMszzYaJU99sY8QHzd+N2Hg+Qe0U6ooWDkhBI9eOZza5nZe/uHQed/fk1/sp7HVwNOzEx26\npUVPTUkIISbAg1c3HDbJ1cJrGw7jrNdx0wUx5x/OAdx3xRD6e7vx8Od7aD/PQ3jW7C4hu6iW+64Y\ngruLGrY7E1UUbMDwMB+uHRnBez8VcKyq74fwbDxYwYrMYm6fGEtcf28TJrRfep3grslx7Cmu5ekv\n95/Xfa3ILGJJeiELxkSroYse8nZz5q9XxZNbVs9bm/L7fD8t7R38a/0B4sN8mO2A7cl7QxUFG3Hf\nFUPQ6wT/XJ/bp+9vbuvg0ZV7GBjoye/V5HKvzEqJYNH4GN7anM8HfTwIZvuRKh78bA9jB/rz0NSh\nJk5o366ID+GK+P688O3BPvekemdLPsU1zTw6bZi6Qj4HVRRsRH8fN269aCBf7Cklo6C619//wncH\nKaxu5qlZiWpLfx88Nn04lw4N5vFVe/nhQO+OjTxS0cBtH2YQ4e/O6wvScHFSv3a99deZCTjrdTy6\nYm+v9y5UNrTy3x8OM3lYMONjHbM1fG+on04bctvEgQR7u/LQ8j0c7cUJVftK6nhrUz5z0yIYp3rs\n9IleJ3jpuhSGhfrwh492sb+0rkffV93Yxs3v7kQnBO8uGo2vh5pc7osQXzcemDKEzXmVrMzq+RLh\n2qZ27l+WTXN7Bw9NVRvVekIVBRvi4eLEs3OTKa9vZdpLm1ieUXTOd01NbQYe/nw3fu7OPHKl+qU4\nH56uTrz9m1F4uzlz87s7OV539oZ5rYYObvsgnZLaFt68MZWoAA8LJbVPN4yJJiXKj7+t3U9pbfM5\nb78jv5qpL25k06FKHp8xnEHBjnX2dV+ZtSgIIaYIIQ4IIfKEEA+d5utCCPFS19d3CyFGmjOPPZgQ\nF8S6uyYQH+7LvcuyuevTrNP256lpauOl7w5xwT++J7uolsdnxuPnoVpjn68QXzfeXpRGbXM7t7y3\nk6Y2w2lvJ6Xkgc92s/PoCZ6dk0xqtL+Fk9ofvU7w9OxEGloNTHpmA4+t3Eth9a8XXhg6jDz39QHm\nv7EVFycdy28fz43jYiwf2EYJc/UWEULogYPAZUARsBO4Tkq575TbXAncCVwJjAFelFKOOdv9pqWl\nyfT0dLNktiUdRsmrG/J4/ttDhPq68eL8FFKj+1FW28Lbm4/w8fZjNLZ1cOnQYG6fFEtajHpRMqXv\nc4/z2/fSmTg4iGtSI3719Z351by3tYD7rxjCHWpi36SOVDTw+o9H+Dyz8xjNGUmhLJ4Uy9AQHwqr\nm7jr00x2Havh2tQInpgZj5dq4wKAECJDSpl2ztuZsSiMA56QUl7R9fHDAFLKp0+5zevABinlJ10f\nHwAmSSnPeB6fKgo/l1Fwgrs+zaS0toWJg4PYdKjiV78oinm899NRHl+dc8avz02L4J/XJKkOtGZy\n8g3QR9uP0dTWwYS4QLKOdXYVfmp2IjOTVaPHU1lDUbgWmCKl/G3XxwuBMVLKP5xym7XAP6SUm7s+\n/g54UEqZ/ov7uhW4FSAqKiq1oMByx/XZgrqWdv6yci/f5ZYzKyWc300YSKS/Gr+2hJKaZhpbfz2E\n5BUVVokAAAN7SURBVKTXERPgoQqCBdQ0tfHB1gLe31bAgEBPnp2TrH7+T6OnRcEmrquklG8Ab0Dn\nlYLGcayOj5szL8xP0TqGQwrzc9c6gsPz83DhzkvjuPPSOK2j2AVzTjQXA6ceaRTR9bne3kZRFEWx\nEHMWhZ1AnBBigBDCBZgPrP7FbVYDN3atQhoL1J5tPkFRFEUxL7MNH0kpDUKIPwBfAXrgHSlljhBi\ncdfXXwO+pHPlUR7QBNxkrjyKoijKuZltotlchBAVgC3ONAcClVqHsDD1nO2foz1fsN3nHC2lDDrX\njWyuKNgqIUR6T2b+7Yl6zvbP0Z4v2P9zVm0uFEVRlG6qKCiKoijdVFGwnDe0DqAB9Zztn6M9X7Dz\n56zmFBRFUZRu6kpBURRF6aaKggaEEPcKIaQQwq6PgRJCPCOEyO1qi75CCOGndSZzOVebeHsjhIgU\nQvwghNgnhMgRQtyldSZLEULohRCZXb3b7I4qChYmhIgELgeOaZ3FAr4BEqSUSXS2UX9Y4zxm0dUm\n/hVgKjAcuE4IMVzbVGZnAO6VUg4HxgJ3OMBzPukuYL/WIcxFFQXLex54ALD7yRwp5ddSypMtRLfR\n2dvKHo0G8qSUR6SUbcCnwFUaZzIrKWWplHJX13/X0/kiGa5tKvMTQkQA04C3tM5iLqooWJAQ4iqg\nWEqZrXUWDdwMrNM6hJmEA4WnfFyEA7xAniSEiAFSgO3aJrGIF+h8U2fUOoi52ETrbFsihPgWCDnN\nlx4FHqFz6MhunO35SilXdd3mUTqHGz6yZDbF/IQQXsBy4G4pZZ3WecxJCDEdKJdSZgghJmmdx1xU\nUTAxKeXk031eCJEIDACyuw5eiQB2CSFGSynLLBjRpM70fE8SQiwCpgOXSvtd/+yQLeCFEM50FoSP\npJSfa53HAi4AZnYdI+wG+AghPpRSLtA4l0mpfQoaEUIcBdKklLbYWKtHhBBTgOeAiVLKCq3zmIsQ\nwonOifRL6SwGO4HrpZRnPqvTxonOdzbvAdVSyru1zmNpXVcK90kpp2udxdTUnIJiTi8D3sA3Qogs\nIcRrWgcyh67J9JNt4vcDS+25IHS5AFgIXNL1/zar6x20YuPUlYKiKIrSTV0pKIqiKN1UUVAURVG6\nqaKgKIqidFNFQVEURemmioKiKIrSTRUFRVEUpZsqCoqiKEo3VRQURVGUbv8Pz1sLODNitz0AAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7881438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2, sharex=True)\n",
    "ax[0].plot(x, y)\n",
    "ax[1].plot(x, y2)\n",
    "ax[1].set_ylabel('y axis')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SY6fzdDJzyY2dqc9k70iSEvNWLzf2Qq/+vp+db689c8QPAIWh8QNAYWj8AFAYGj8AFIbG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x89c30b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y, x = np.mgrid[0:20, 0:30]\n",
    "z = (x - 4)**2+ y**2\n",
    "plt.figure()\n",
    "plt.pcolormesh(x, y, z)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# SciPy: extra modules for scientific computation\n",
    "https://www.scipy.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x, a, b, c):\n",
    "    return a * np.exp(-b * x) + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 60\n",
    "x = np.linspace(0, 5, n)\n",
    "y = f(x, 5, 2, 0.5) + 2 * np.random.rand(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "popt, pcov = curve_fit(f, x, y)\n",
    "perr = np.sqrt(np.diag(pcov))\n",
    "y_fit = f(x, *popt)\n",
    "msd = np.sum((y - y_fit) ** 2) / n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+tLsKtvze7kiUUsotmrjbdYGM+yB3FRzNrTNLB55SSjmRJm6wEnebTrDhidq3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\nuJVSys9o4lZKKT/z/wFJZJ4qlQPoeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8d0acc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pnames = ['a', 'b', 'c']\n",
    "results = ''\n",
    "for name, value, error in zip(pnames, popt, perr):\n",
    "    results += '{} = {:.2f}$\\pm${:.2f}\\n'.format(name, value, error)\n",
    "results += 'MSD = {:.2f}'.format(msd)\n",
    "    \n",
    "plt.plot(x, y, '.', label='data')\n",
    "plt.plot(x, y_fit, label='fit: $ae^{-bx} + c$')\n",
    "plt.annotate(results, xy=(0.7, 0.55), xycoords='axes fraction')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}