NumPy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ndarray 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 7.5, 8, 0, 1]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1 = [6, 7.5, 8, 0, 1]\n",
    "data1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6. ,  7.5,  8. ,  0. ,  1. ])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array(data1)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "다차원 배열 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3, 4], [5, 6, 7, 8]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = [[1,2,3,4], [5,6,7,8]]\n",
    "data2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4],\n",
       "       [5, 6, 7, 8]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.array(data2)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ndarray의 차원수"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ndarry의 행렬 형태"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2L, 4L)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "행렬의 형태가 안 맞는 경우도 생성은 된다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3], [5, 6, 7, 8]], dtype=object)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_ill_formed = [[1,2,3], [5,6,7,8]]\n",
    "arr3 = np.array(data_ill_formed)\n",
    "arr3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('O')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "0으로 초기화된 배열 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"null\" 값으로 되어있어 배열의 형태만 미리 지정하고자 하는 경우\n",
    "\n",
    "배열의 형태가 미리 지정되면 메모리 I/O가 훨씬 효율적이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  0.00000000e+000,   0.00000000e+000],\n",
       "        [  2.12274051e-314,   2.15749596e-314],\n",
       "        [  0.00000000e+000,   0.00000000e+000]],\n",
       "\n",
       "       [[  0.00000000e+000,   0.00000000e+000],\n",
       "        [  3.87491056e-297,   1.04979068e-319],\n",
       "        [  1.28822983e-231,   8.34402830e-309]]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty((2,3,2)) # 2x3x2 \"null\" 값을 갖는 행렬"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "순차적 배열 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(range(15))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 연습문제\n",
    "\n",
    "다음의 값을 갖는 1x10 행렬을 생성하시오.\n",
    "\n",
    "$$2^k , k=1,2, ... $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   2,    4,    8,   16,   32,   64,  128,  256,  512, 1024])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([2**k for k in range(1,11)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 자료형"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array([1,2,3])\n",
    "arr1.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "배열 생성 시점에서 자료형 명시"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.array([1,2,3], dtype=np.float64)\n",
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이미 생성된 배열의 자료형 변환"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "arr1_f64 = arr1.astype(np.float64)\n",
    "arr1_f64.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "부동소수점을 정수형으로 변환하면 소수점 정보 소실"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, -1])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([3.7, -1.2]).astype(np.int32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "문자열을 담은 배열을 변환할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(3.14) == float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.25, -3.14,  4.5 ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(['1.25', '-3.14', 4.5]).astype(np.float64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 배열과 스칼라 연산"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.,  3.],\n",
       "       [ 4.,  5.,  6.]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  1.41421356,  1.73205081],\n",
       "       [ 2.        ,  2.23606798,  2.44948974]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr ** 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "각 원소별로 연산 수행"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   4.,   9.],\n",
       "       [ 16.,  25.,  36.]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr * arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr - arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "list와 ndarray 연산 비교"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "can't multiply sequence by non-int of type 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-32-8e637aad1a64>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: can't multiply sequence by non-int of type 'list'"
     ]
    }
   ],
   "source": [
    "[1,2] * [1,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'hello hello hello '"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'hello ' * 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 1, 2]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2] * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1,2]) * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2\n",
       "1    4\n",
       "dtype: int64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas import Series\n",
    "Series([1,2]) * 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "순수 파이썬으로 배열의 원소 간 연산을 수행"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 6]\n"
     ]
    }
   ],
   "source": [
    "mat1 = [1,2]\n",
    "mat2 = [3,4]\n",
    "\n",
    "mat3 = []\n",
    "for i,v in enumerate(mat1):\n",
    "    mat3.append(mat1[i] + mat2[i])\n",
    "\n",
    "print(mat3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 색인과 슬라이싱"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "파이썬 list와 달리 arr의 슬라이스는 메모리를 효과적으로 활용하기 위해 원본의 객체를 참조한다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alist = range(10)\n",
    "piece = alist[:2]\n",
    "piece"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
     ]
    }
   ],
   "source": [
    "piece = [100,200]\n",
    "print(alist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before: [0 1 2 3 4 5 6 7 8 9]\n",
      "After: [ 0  1  2  3  4 12 12 12  8  9]\n"
     ]
    }
   ],
   "source": [
    "print('Before:', arr)\n",
    "arr[5:8] = 12\n",
    "print('After:', arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "복사본은 명시적으로 구한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 12, 12])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 12, 12])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8] is arr[5:8].copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "다차원 배열"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0,2] # 다차원 인덱싱"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d = np.array([[[1,2,3], [4,5,6]], \n",
    "                  [[7,8,9], [10,11,12]]])\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "old_values = arr3d[0].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[42, 42, 42],\n",
       "        [42, 42, 42]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0] = 42 # 스칼라 값을 브로드캐스팅\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0] = old_values\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "슬라이스 색인"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4, 12])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[1:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[1, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[2, :1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [4],\n",
       "       [7]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:, :1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 7])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### 도전과제\n",
    "\n",
    "학생 세 명이 각각 세 과목의 점수를 갖는다. \n",
    "\n",
    "1. 학생 세 명의 과목 점수를 ndarray로 표현하시오. 점수는 소수점을 포함할 수 있다.\n",
    "2. 각 학생의 평균 점수를 구하시오.\n",
    "3. 각 과목의 평균 점수를 구하시오."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 60.,  70.,  80.],\n",
       "       [ 75.,  85.,  95.],\n",
       "       [ 91.,  82.,  73.]], dtype=float32)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = np.array([[60,70,80],[75,85,95],[91,82,73]], dtype=np.float32)\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 70.,  85.,  82.], dtype=float32)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "student_means = np.array([np.mean(scores[0]), \n",
    "                          np.mean(scores[1]), \n",
    "                          np.mean(scores[2])])\n",
    "student_means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... 대신 각 행별로 연산을 수행하도록 지정"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 70.,  85.,  82.], dtype=float32)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(scores, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 75.33333588,  79.        ,  82.66666412], dtype=float32)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subject_means = np.array([np.mean(scores[:,0]), \n",
    "                          np.mean(scores[:,1]), \n",
    "                          np.mean(scores[:,2])])\n",
    "subject_means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... 대신 각 열별로 연산을 수행하도록 지정"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 75.33333588,  79.        ,  82.66666412], dtype=float32)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(scores, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "79.0"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 도전과제\n",
    "\n",
    "마방진(魔方陣)은 n<sup>2</sup>개의 수를 가로, 세로, 대각선 방향의 수를 더하면 모두 같은 값이 나오도록 n × n 행렬에 배열한 것이다. (위키백과, https://goo.gl/fWHxg0)\n",
    "\n",
    "마방진의 각 행의 합과 각 열의 합, 그리고 각 대각선의 합 M은 n에만 관계가 있고, 이 값은 다음과 같다.\n",
    "\n",
    "$$ M(n) = (n^3 + n) / 2 $$\n",
    "\n",
    "3x3 마방진 --> M(3) = 15\n",
    "\n",
    "다음 행렬이 마방진인지를 여부를 확인하시오.\n",
    "\n",
    "$$ \\begin{array}{ccc} 2 & 7 & 6 \\\\\n",
    "9 & 5 & 1 \\\\ \n",
    "4 & 3 & 8 \\end{array}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 7, 6],\n",
       "       [9, 5, 1],\n",
       "       [4, 3, 8]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "magic_matrix = np.array([[2,7,6],[9,5,1],[4,3,8]])\n",
    "magic_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 15, 15])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(magic_matrix, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 15, 15])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(magic_matrix, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(magic_matrix.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TODO: 반대방향 대각선"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 5, 8])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "magic_matrix.diagonal(axis1=1, axis2=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 불리언 색인"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], \n",
       "      dtype='|S4')"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names == 'Bob'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "불리언 색인은 실제 데이터와 관련이 없다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "some_arr = np.arange(7)\n",
    "some_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "some_arr[names=='Bob']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.06186249,  0.84748037, -1.92109529,  1.27647462],\n",
       "       [-1.026492  ,  2.22373553, -0.6111814 ,  0.31921399],\n",
       "       [ 1.93588875,  1.67774458,  0.33007255, -0.60620493],\n",
       "       [ 0.20390991,  0.29035578, -2.20870964, -0.55083674],\n",
       "       [-0.56964524, -0.14184054, -1.72120857,  0.07523899],\n",
       "       [-2.33672389, -0.84103908,  0.54296383, -0.31203884],\n",
       "       [ 2.00507355, -0.98749806, -1.2895552 ,  0.11870136]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.random.randn(7,4)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.06186249,  0.84748037, -1.92109529,  1.27647462],\n",
       "       [ 0.20390991,  0.29035578, -2.20870964, -0.55083674]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names=='Bob']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.06186249,  1.27647462],\n",
       "       [-1.026492  ,  0.31921399],\n",
       "       [ 1.93588875, -0.60620493],\n",
       "       [ 0.20390991, -0.55083674],\n",
       "       [-0.56964524,  0.07523899],\n",
       "       [-2.33672389, -0.31203884],\n",
       "       [ 2.00507355,  0.11870136]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[:, names=='Bob']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "조합 조건"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "and_mask = (names=='Bob') & (names=='Will')\n",
    "and_mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True,  True,  True, False, False], dtype=bool)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "or_mask = (names=='Bob') | (names=='Will')\n",
    "or_mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.84748037,  0.        ,  1.27647462],\n",
       "       [ 0.        ,  2.22373553,  0.        ,  0.31921399],\n",
       "       [ 1.93588875,  1.67774458,  0.33007255,  0.        ],\n",
       "       [ 0.20390991,  0.29035578,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.07523899],\n",
       "       [ 0.        ,  0.        ,  0.54296383,  0.        ],\n",
       "       [ 2.00507355,  0.        ,  0.        ,  0.11870136]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data<0] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 도전과제\n",
    "\n",
    "학생 20명의 수학 점수가 있다. \n",
    "\n",
    "1. 80점 이상만을 추출하시오.\n",
    "2. 30점 미만과 71점 이상의 점수만을 추출하시오. (p.134 참조)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([85, 99, 60, 29, 75,  9, 56, 12, 92,  9, 96, 98, 21, 37, 58, 95, 89,\n",
       "       21, 83, 57])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = np.random.randint(0, 101, size=20)\n",
    "scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 도전과제\n",
    "\n",
    "학생 10명이 국, 영, 수 점수를 갖는다. 점수는 국, 영, 수의 순서로 입력되어 있다. \n",
    "\n",
    "1. 국어 성적이 70점 이상인 학생들의 점수만을 출력하시오.\n",
    "2. 수학이 80점 이상이거나 영어가 60점 미만인 학생들의 점수만 출력하시오."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[97, 79, 36],\n",
       "       [90, 51, 62],\n",
       "       [65, 47, 56],\n",
       "       [98, 34, 82],\n",
       "       [12, 14, 59],\n",
       "       [70, 32, 25],\n",
       "       [26, 41, 86],\n",
       "       [65,  7, 98],\n",
       "       [80, 35, 29],\n",
       "       [ 1, 92, 47]])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = np.random.randint(0,101, size=(10,3))\n",
    "scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "문제 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[97, 79, 36],\n",
       "       [90, 51, 62],\n",
       "       [98, 34, 82],\n",
       "       [70, 32, 25],\n",
       "       [80, 35, 29]])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores[scores[:,0] >= 70]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "문제 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[97, 79, 36],\n",
       "       [65, 47, 56],\n",
       "       [12, 14, 59],\n",
       "       [70, 32, 25],\n",
       "       [80, 35, 29],\n",
       "       [ 1, 92, 47]])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores[(scores[:,1]>=80) | (scores[:,2]<60)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 팬시 색인"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.],\n",
       "       [ 1.,  1.,  1.,  1.],\n",
       "       [ 2.,  2.,  2.,  2.],\n",
       "       [ 3.,  3.,  3.,  3.],\n",
       "       [ 4.,  4.,  4.,  4.],\n",
       "       [ 5.,  5.,  5.,  5.],\n",
       "       [ 6.,  6.,  6.,  6.],\n",
       "       [ 7.,  7.,  7.,  7.]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.empty((8,4))\n",
    "for i in range(8):\n",
    "    arr[i]=i\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.,  4.,  4.,  4.])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  4.,  4.,  4.],\n",
       "       [ 3.,  3.,  3.,  3.]])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[4,3]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.,  7.,  7.,  7.],\n",
       "       [ 6.,  6.,  6.,  6.]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[-1,-2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "다차원 색인 배열"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23],\n",
       "       [24, 25, 26, 27],\n",
       "       [28, 29, 30, 31]])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(32).reshape((8,4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1,0], [1,0]] # (1,1), (0,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 5],\n",
       "       [2, 1]])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1,0]][:, [2,1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 축 바꾸기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[59, 10, 30, 26,  5],\n",
       "       [25, 56, 41, 74, 75],\n",
       "       [68, 82, 74,  6, 28]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = np.random.randint(0,100, size=(3,5))\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[97, 79, 36],\n",
       "       [90, 51, 62],\n",
       "       [98, 34, 82],\n",
       "       [70, 32, 25],\n",
       "       [80, 35, 29]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores[kor_gte_70]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[59, 25, 68],\n",
       "       [10, 56, 82],\n",
       "       [30, 41, 74],\n",
       "       [26, 74,  6],\n",
       "       [ 5, 75, 28]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "내적 (dot product) 구하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.56883137, -0.0108038 ,  0.02971338, -0.02314336,  0.22307224,\n",
       "         0.81325324],\n",
       "       [-0.0108038 ,  0.05020956, -0.10366799,  0.32133755,  0.19774149,\n",
       "         0.149565  ],\n",
       "       [ 0.02971338, -0.10366799,  1.60357044, -0.33555102, -1.38135662,\n",
       "        -0.54047262],\n",
       "       [-0.02314336,  0.32133755, -0.33555102,  2.13737972,  1.05704831,\n",
       "         0.96867586],\n",
       "       [ 0.22307224,  0.19774149, -1.38135662,  1.05704831,  1.58967579,\n",
       "         1.15603243],\n",
       "       [ 0.81325324,  0.149565  , -0.54047262,  0.96867586,  1.15603243,\n",
       "         1.749627  ]])"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6,3)\n",
    "np.dot(arr, arr.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7]],\n",
       "\n",
       "       [[ 8,  9, 10, 11],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(16).reshape((2,2,4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  8],\n",
       "        [ 4, 12]],\n",
       "\n",
       "       [[ 1,  9],\n",
       "        [ 5, 13]],\n",
       "\n",
       "       [[ 2, 10],\n",
       "        [ 6, 14]],\n",
       "\n",
       "       [[ 3, 11],\n",
       "        [ 7, 15]]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "축 번호를 지정해서 치환"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 8,  9, 10, 11]],\n",
       "\n",
       "       [[ 4,  5,  6,  7],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.transpose((1,0,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 유니버설 함수"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "순수 파이썬을 사용하면 함수 적용 시, 각각의 원소에 대해 작업을 수행해야 한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 4, 8, 16, 32, 64, 128, 256, 512]"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[2**k for k in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "유니버설 함수는 자동으로 각 원소에 대해 적용된다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0,\n",
       " 1.0,\n",
       " 1.4142135623730951,\n",
       " 1.7320508075688772,\n",
       " 2.0,\n",
       " 2.2360679774997898,\n",
       " 2.4494897427831779,\n",
       " 2.6457513110645907,\n",
       " 2.8284271247461903,\n",
       " 3.0]"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[n**0.5 for n in arr]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  1.        ,  1.41421356,  1.73205081,  2.        ,\n",
       "        2.23606798,  2.44948974,  2.64575131,  2.82842712,  3.        ])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   4.,   9.],\n",
       "       [ 16.,  25.,  36.]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.square(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.00000000e+00,   2.71828183e+00,   7.38905610e+00,\n",
       "         2.00855369e+01,   5.45981500e+01,   1.48413159e+02,\n",
       "         4.03428793e+02,   1.09663316e+03,   2.98095799e+03,\n",
       "         8.10308393e+03])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.97639043, -1.24504342,  1.08808156, -0.19151012,  2.05178953,\n",
       "       -0.21626345,  0.41969744,  0.24300959])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randn(8)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.04905818,  0.07870258,  0.71808672,  0.81026078, -0.71422444,\n",
       "        0.83527483, -1.2946444 , -0.88621981])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.random.randn(8)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.maximum?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.04905818,  0.07870258,  1.08808156,  0.81026078,  2.05178953,\n",
       "        0.83527483,  0.41969744,  0.24300959])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.maximum(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 배열을 사용한 데이터 처리"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ z=\\sqrt{x^2+y^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.  , -4.99, -4.98, -4.97, -4.96, -4.95, -4.94, -4.93, -4.92, -4.91])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "points = np.arange(-5,5, 0.01) # 균일하게 0.01 단위로 배치된 지점\n",
    "points[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xs, ys = np.meshgrid(points, points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 1000)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -5.  , -5.  , ..., -5.  , -5.  , -5.  ],\n",
       "       [-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],\n",
       "       [-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ys[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.07106781,  7.06400028,  7.05693985, ...,  7.04988652,\n",
       "         7.05693985,  7.06400028],\n",
       "       [ 7.06400028,  7.05692568,  7.04985815, ...,  7.04279774,\n",
       "         7.04985815,  7.05692568],\n",
       "       [ 7.05693985,  7.04985815,  7.04278354, ...,  7.03571603,\n",
       "         7.04278354,  7.04985815],\n",
       "       ..., \n",
       "       [ 7.04988652,  7.04279774,  7.03571603, ...,  7.0286414 ,\n",
       "         7.03571603,  7.04279774],\n",
       "       [ 7.05693985,  7.04985815,  7.04278354, ...,  7.03571603,\n",
       "         7.04278354,  7.04985815],\n",
       "       [ 7.06400028,  7.05692568,  7.04985815, ...,  7.04279774,\n",
       "         7.04985815,  7.05692568]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.sqrt(xs**2 + ys**2)\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "순수 파이썬으로 ... 안 하면 안 될까?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50.0\n",
      "50.0\n",
      "50.0\n",
      "49.9001\n",
      "49.9001\n",
      "49.9001\n",
      "49.8004\n",
      "49.8004\n",
      "49.8004\n",
      "49.9001\n",
      "49.9001\n",
      "49.9001\n",
      "49.8002\n",
      "49.8002\n",
      "49.8002\n",
      "49.7005\n",
      "49.7005\n",
      "49.7005\n",
      "49.8004\n",
      "49.8004\n",
      "49.8004\n",
      "49.7005\n",
      "49.7005\n",
      "49.7005\n",
      "49.6008\n",
      "49.6008\n",
      "49.6008\n",
      "50.0\n",
      "50.0\n",
      "50.0\n",
      "49.9001\n",
      "49.9001\n",
      "49.9001\n",
      "49.8004\n",
      "49.8004\n",
      "49.8004\n",
      "49.9001\n",
      "49.9001\n",
      "49.9001\n",
      "49.8002\n",
      "49.8002\n",
      "49.8002\n",
      "49.7005\n",
      "49.7005\n",
      "49.7005\n",
      "49.8004\n",
      "49.8004\n",
      "49.8004\n",
      "49.7005\n",
      "49.7005\n",
      "49.7005\n",
      "49.6008\n",
      "49.6008\n",
      "49.6008\n",
      "50.0\n",
      "50.0\n",
      "50.0\n",
      "49.9001\n",
      "49.9001\n",
      "49.9001\n",
      "49.8004\n",
      "49.8004\n",
      "49.8004\n",
      "49.9001\n",
      "49.9001\n",
      "49.9001\n",
      "49.8002\n",
      "49.8002\n",
      "49.8002\n",
      "49.7005\n",
      "49.7005\n",
      "49.7005\n",
      "49.8004\n",
      "49.8004\n",
      "49.8004\n",
      "49.7005\n",
      "49.7005\n",
      "49.7005\n",
      "49.6008\n",
      "49.6008\n",
      "49.6008\n"
     ]
    }
   ],
   "source": [
    "for x in xs[:3]:\n",
    "    for xn in x[:3]:\n",
    "        for y in ys[:3]:\n",
    "            for yn in y[:3]:\n",
    "                print(xn**2+yn**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pandas를 활용하지 않으면, matplotlib의 설정을 직접 수행해야 한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1122d6990>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7zKNfSGnBqeLBaYjqvNa8XkXXW2W16jNWprQ1VjYObkDNO8uOQ3V6oOnl8eKr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\nyxEpM9xmmWWWI1JmuM0yyyxHpPz/v1awQ4XArOkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111a36d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.imshow(z, cmap=plt.cm.gray)\n",
    "plt.colorbar()\n",
    "plt.title('Z sqrt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "배열 단위 분기 조건"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])\n",
    "yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])\n",
    "cond = np.array([True, False, True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nums1 = ['a','b']\n",
    "nums2 = ['x','y', 'z']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('a', 'x'), ('b', 'y')]"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zip(nums1, nums2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "순수 파이썬"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1.1000000000000001, 2.1000000000000001, True),\n",
       " (1.2, 2.2000000000000002, False),\n",
       " (1.3, 2.2999999999999998, True),\n",
       " (1.3999999999999999, 2.3999999999999999, True),\n",
       " (1.5, 2.5, False)]"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zip(xarr, yarr, cond)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1.1000000000000001, 2.1000000000000001, True)\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "test = zip(xarr, yarr,cond)[0]\n",
    "print(test)\n",
    "print(test[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1000000000000001"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test[0] if test[2] else test[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.1000000000000001, 2.2000000000000002, 1.3, 1.3999999999999999, 2.5]"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = [(x if c else y) for x,y,c in zip(xarr, yarr, cond)]\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "np.where로 배열 조건 처리하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.1,  2.2,  1.3,  1.4,  2.5])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = np.where(cond, xarr, yarr)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.17685648,  0.80864744, -0.32303124, -0.1522356 ],\n",
       "       [ 1.41983216, -0.71971288,  0.69867033,  1.73434949],\n",
       "       [ 0.06252835,  0.11799571, -2.19664267, -1.48046062],\n",
       "       [-0.55157242,  0.13686833, -0.77391849,  0.65758204]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(4,4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "0보다 큰 값만 골라내기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True, False, False],\n",
       "       [ True, False,  True,  True],\n",
       "       [ True,  True, False, False],\n",
       "       [False,  True, False,  True]], dtype=bool)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr>0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "0보다 큰 값은 2로, 그렇지 않은 값은 -2로 대체"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2,  2, -2, -2],\n",
       "       [ 2, -2,  2,  2],\n",
       "       [ 2,  2, -2, -2],\n",
       "       [-2,  2, -2,  2]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr>0, 2, -2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "0보다 큰 값은 2로, 그렇지 않은 값은 원래 값으로 둔다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.17685648,  2.        , -0.32303124, -0.1522356 ],\n",
       "       [ 2.        , -0.71971288,  2.        ,  2.        ],\n",
       "       [ 2.        ,  2.        , -2.19664267, -1.48046062],\n",
       "       [-0.55157242,  2.        , -0.77391849,  2.        ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# True면 2, False면 원래 값\n",
    "np.where(arr>0, 2, arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "중첩된 np.where 사용으로 여러 if ... elif ... else 처리"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.35114229,  0.97382945, -1.60897649,  0.44426907],\n",
       "       [ 0.15101789,  0.70438645,  0.64208516, -0.37943408],\n",
       "       [-1.00710536,  1.2099198 , -0.10111934,  0.04896735],\n",
       "       [ 1.50493227, -0.37021376,  2.43653421, -0.93062761]])"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(4,4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "조건 1) 0보다 큰 값은 2\n",
    "\n",
    "조건 2) (-1, 0] 은 -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.        ,  2.        , -1.60897649,  2.        ],\n",
       "       [ 2.        ,  2.        ,  2.        , -1.        ],\n",
       "       [-1.00710536,  2.        , -1.        ,  2.        ],\n",
       "       [ 2.        , -1.        ,  2.        , -1.        ]])"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr>0, 2, \n",
    "         np.where(arr>-1, -1, arr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 도전과제\n",
    "\n",
    "다음 배열을 활용해 5보다 작은 값은 모두 0으로 하고, 나머지는 원래 값을 갖는 새로운 배열을 생성하시오."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, 0],\n",
       "       [0, 0, 0, 5],\n",
       "       [5, 0, 0, 6],\n",
       "       [5, 6, 6, 5]])"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randint(1,7, size=(4,4))\n",
    "np.where(arr<5, 0, arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 도전과제\n",
    "\n",
    "각 학생은 3과목의 점수를 갖는다. \n",
    "\n",
    "\n",
    "1. 학생 10명의 점수를 scores 배열로 생성한다. 점수는 [0,100] 범위를 갖는다.\n",
    "\n",
    "2. 각 과목의 성적 등급을 다음의 기준으로 산출한다.\n",
    "\n",
    "A: [90, 100]\n",
    "\n",
    "B: [80, 90)\n",
    "\n",
    "C: [70, 80)\n",
    "\n",
    "D: [60, 70)\n",
    "\n",
    "F: [0, 60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[44, 48, 67],\n",
       "       [55, 49, 48],\n",
       "       [24, 75, 16],\n",
       "       [15, 57, 64],\n",
       "       [75, 84, 63],\n",
       "       [45, 11, 91],\n",
       "       [79, 25, 12],\n",
       "       [66, 37, 93],\n",
       "       [50, 54, 54],\n",
       "       [ 0, 89, 66]])"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = np.random.randint(0, 101, size=(10,3))\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([['F', 'F', 'D'],\n",
       "       ['F', 'F', 'F'],\n",
       "       ['F', 'C', 'F'],\n",
       "       ['F', 'F', 'D'],\n",
       "       ['C', 'B', 'D'],\n",
       "       ['F', 'F', 'A'],\n",
       "       ['C', 'F', 'F'],\n",
       "       ['D', 'F', 'A'],\n",
       "       ['F', 'F', 'F'],\n",
       "       ['F', 'B', 'D']], \n",
       "      dtype='|S1')"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(scores>=90, 'A', \n",
    "         np.where(scores>=80, 'B', \n",
    "                  np.where(scores>=70, 'C',\n",
    "                          np.where(scores>=60, 'D', 'F'))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 수학/통계 메서드"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.10474577,  0.29995521, -0.41528231, -0.5179343 ],\n",
       "       [-0.41227406, -1.54912985,  0.12543988,  0.03308258],\n",
       "       [-0.03451341,  0.20664698,  0.17310922, -0.86799997],\n",
       "       [ 1.02021137,  1.57854945,  0.55735632,  2.6181855 ],\n",
       "       [ 0.22875124,  0.72920747,  1.58232445, -0.76284121]])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5,4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12440493918226733"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.26051413,  0.25304585,  0.40458951,  0.10049852])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.68450179, -0.45072036, -0.13068929,  1.44357566,  0.44436048])"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "누적 합계 (누산)과 누적곱"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(1, 10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  6, 10, 15, 21, 28, 36, 45])"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cumsum(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([     1,      2,      6,     24,    120,    720,   5040,  40320,\n",
       "       362880])"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cumprod(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 연습문제\n",
    "\n",
    "원금 1000만원에 대한 연이자가 복리 3%이다. 1년마다 원리금을 10년간 구하시오.\n",
    "\n",
    "$$ 원리금 = 원금 * (1+r)^{yr} , yr = 1, 2, ... $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.03,  1.03,  1.03,  1.03,  1.03,  1.03,  1.03,  1.03,  1.03,  1.03])"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interests = np.array([0.03]*10)\n",
    "interests + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1030.        ,  1060.9       ,  1092.727     ,  1125.50881   ,\n",
       "        1159.2740743 ,  1194.05229653,  1229.87386542,  1266.77008139,\n",
       "        1304.77318383,  1343.91637934])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns = 1000 * (1+interests).cumprod()\n",
    "returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 불리언 배열을 위한 메서드"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "arr = np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, False,  True,  True,  True, False,  True,\n",
       "        True, False, False, False, False,  True,  True,  True, False,\n",
       "        True,  True, False, False, False,  True,  True,  True,  True,\n",
       "        True, False, False, False, False,  True,  True,  True, False,\n",
       "        True, False, False,  True,  True, False,  True,  True,  True,\n",
       "       False, False,  True, False,  True,  True,  True, False,  True,\n",
       "       False,  True, False,  True,  True, False, False,  True,  True,\n",
       "       False, False,  True,  True,  True, False, False, False, False,\n",
       "       False,  True, False, False, False,  True, False,  True, False,\n",
       "        True,  True, False, False,  True, False,  True,  True,  True,\n",
       "        True, False,  True,  True, False,  True,  True, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(arr > 0).sum() # 정수값 개수"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bools = np.array([False, False, True, False])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "True가 한 개라도 포함되었는 확인"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools.any()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "모두 True인지 확인"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools.all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 정렬"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.63787189,  0.29131189,  0.85162037,  0.77123274,  1.49470766,\n",
       "       -0.46191999,  1.27449963, -0.7649935 ])"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(8)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.7649935 , -0.46191999,  0.29131189,  0.63787189,  0.77123274,\n",
       "        0.85162037,  1.27449963,  1.49470766])"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "다차원 배열 정렬"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.93607022,  0.07204257,  0.83277371],\n",
       "       [-0.4529976 ,  1.93083172, -1.39372901],\n",
       "       [ 1.41266571,  0.36631619,  1.75150529],\n",
       "       [-0.99164063, -2.22595413,  1.5060838 ],\n",
       "       [-0.66738173,  0.17032224, -0.24093706]])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5,3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.93607022,  0.07204257,  0.83277371],\n",
       "       [-1.39372901, -0.4529976 ,  1.93083172],\n",
       "       [ 0.36631619,  1.41266571,  1.75150529],\n",
       "       [-2.22595413, -0.99164063,  1.5060838 ],\n",
       "       [-0.66738173, -0.24093706,  0.17032224]])"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.95978628, -0.77954971, -0.28099997],\n",
       "       [-0.34276346, -0.39929172, -1.44250929],\n",
       "       [-0.64172147, -0.35218453,  1.09828812],\n",
       "       [-0.94537208, -1.24468305, -0.60530107],\n",
       "       [ 0.22093413,  0.22972747,  0.57275975]])"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5,3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.95978628, -0.77954971, -0.28099997],\n",
       "       [-1.44250929, -0.39929172, -0.34276346],\n",
       "       [-0.64172147, -0.35218453,  1.09828812],\n",
       "       [-1.24468305, -0.94537208, -0.60530107],\n",
       "       [ 0.22093413,  0.22972747,  0.57275975]])"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort(1)\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 집합 함수"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "고유한 값 (=집합) 추출하기 == 중복 제거하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will'], \n",
       "      dtype='|S4')"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "np.unique(names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 난수 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy.random import normal # N() 정규분포에서 표본 추출\n",
    "from numpy.random import randn # N(0,1) 에서 표본 추출"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 158.5613324 ,  158.2898118 ,  159.50287137,  158.78068822],\n",
       "       [ 159.95333797,  161.15415924,  160.006222  ,  160.49918422],\n",
       "       [ 160.62129848,  157.23091994,  157.49804956,  162.59984107],\n",
       "       [ 160.27503054,  160.63938976,  159.2596997 ,  158.92198007]])"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = normal(160, 1.0, size=(4,4))\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.47213356, -1.56149105,  0.66219524,  0.22594747],\n",
       "       [-0.39088913,  0.42619626, -1.15171867,  1.75500927],\n",
       "       [ 0.07590816,  0.66165482, -0.13777658,  0.32154571],\n",
       "       [-2.00885841,  0.60784222, -0.50397334,  0.59111973]])"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "randn(4,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 예제: 계단 오르내리기"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"바닐라\" 파이썬으로 수행하기 (... 힘들고 느림)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, -1, -2, -3, -2, -3, -2, -3, -2, -1]\n"
     ]
    }
   ],
   "source": [
    "import random # 난수 생성을 위한 표준 모듈\n",
    "position = 0\n",
    "walk = [position]\n",
    "steps = 1000\n",
    "for i in range(steps):\n",
    "    step = 1 if random.randint(0,1) else -1\n",
    "    position += step\n",
    "    walk.append(position)\n",
    "    \n",
    "print(walk[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ndarray로 수행하기 (빠르고, 편리)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1  0  1  0 -1  0 -1 -2 -3 -4]\n"
     ]
    }
   ],
   "source": [
    "nsteps = 1000\n",
    "draws = np.random.randint(0,2, size=nsteps)\n",
    "steps = np.where(draws > 0 , 1, -1)\n",
    "walk = steps.cumsum()\n",
    "\n",
    "print(walk[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-11"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "35"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "117"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5000번 시뮬레이션"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1, ..., 0, 0, 0],\n",
       "       [1, 1, 1, ..., 0, 0, 1],\n",
       "       [0, 1, 1, ..., 1, 0, 0],\n",
       "       ..., \n",
       "       [0, 1, 1, ..., 1, 1, 0],\n",
       "       [0, 0, 1, ..., 1, 1, 1],\n",
       "       [0, 0, 1, ..., 1, 0, 0]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 1000\n",
    "# 0 또는 1\n",
    "# 5000 x 1000 행렬\n",
    "draws = np.random.randint(0,2, size=(nwalks, nsteps))\n",
    "draws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  1,  1, ..., -1, -1, -1],\n",
       "       [ 1,  1,  1, ..., -1, -1,  1],\n",
       "       [-1,  1,  1, ...,  1, -1, -1],\n",
       "       ..., \n",
       "       [-1,  1,  1, ...,  1,  1, -1],\n",
       "       [-1, -1,  1, ...,  1,  1,  1],\n",
       "       [-1, -1,  1, ...,  1, -1, -1]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# draw 행렬에서, 값이 0보다 크면 1, 아니면 -1\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.where?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "steps.cumsum?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000000,)"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "steps.cumsum().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 1000)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "steps.cumsum(1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "walks = steps.cumsum(1) # 누적합계는 애써 만들지 말고, 가져다 쓰자"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "127"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-143"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, ..., False,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.randint?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "random.randint?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 도전과제\n",
    "\n",
    "한국의 기업은 환율 변동에 민감하다. 원/달러 (KRW/USB) 환율은 정규 분포 범위에서 무작위로 변동된다고 할 때, 90일 간의 환율 변동을 시뮬레이션 하시오. 0일째의 환율은 1100원이라고 한다.\n",
    "\n",
    "참고: numpy.ndarray.cumprod 함수를 활용할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.85682393, -0.49415521, -1.46454241,  1.17986097, -3.01657982,\n",
       "        0.13987483,  0.24749857,  1.17470376, -0.09890397,  0.60632262])"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.random import randn\n",
    "randn(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1115.72032973,  1104.23800977,  1105.71363568,  1103.6121582 ,\n",
       "        1104.87908086,  1101.57914633,  1105.89720125,  1104.25810411,\n",
       "        1098.27833312,  1103.48640136,  1087.77965983,  1104.82416617,\n",
       "        1099.48014266,  1097.80643483,  1108.73291145,  1096.28455813,\n",
       "        1103.94612097,  1097.93219378,  1097.57035181,  1103.99775535,\n",
       "        1096.09151169,  1102.14155919,  1094.85175038,  1096.74810513,\n",
       "        1102.14534326,  1103.12946947,  1100.79792734,  1092.71802389,\n",
       "        1098.75955447,  1096.38124008,  1108.72276637,  1103.60407002,\n",
       "        1097.35425551,  1101.45028149,  1092.46981686,  1106.82298535,\n",
       "        1100.66893846,  1087.74931213,  1103.31794136,  1090.19566556,\n",
       "        1099.89370043,  1098.17728812,  1101.46680667,  1095.6577356 ,\n",
       "        1104.3272358 ,  1107.45835874,  1109.34875255,  1094.57577129,\n",
       "        1096.64454624,  1102.57284389,  1110.942322  ,  1104.26845907,\n",
       "        1100.86334193,  1098.63031619,  1100.93979185,  1097.08135051,\n",
       "        1095.73689487,  1098.56692807,  1103.29065229,  1098.36842868,\n",
       "        1096.15569978,  1104.82400081,  1098.20595503,  1093.57840325,\n",
       "        1090.38856653,  1107.93269545,  1092.22164338,  1104.22679353,\n",
       "        1098.68891755,  1102.41127731,  1100.08336961,  1106.38293259,\n",
       "        1105.74312952,  1100.57050538,  1104.76630905,  1106.50034859,\n",
       "        1104.8938878 ,  1098.12683586,  1094.68727707,  1100.21114899,\n",
       "        1102.6261339 ,  1097.91633329,  1095.78673552,  1104.73702944,\n",
       "        1098.2961329 ,  1101.00064987,  1105.69157062,  1092.66378124,\n",
       "        1101.15049566,  1101.81204614])"
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal(1100, 5, 90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### 도전과제\n",
    "\n",
    "성주는 주식 투자에 관심이 많다. 성주가 투자한 주식 10개는 각각 5천원에서 1000천원 범위의 임의의 값에서 시작한다고 하자. 주식은 하루에 30% 범위에서 가격이 변동할 수 있다.\n",
    "\n",
    "1. 주식 10개의 90일 간의 가격 변동값을 시뮬레이션한 결과를 적절한 방식의 자료구조로 표현하시오.\n",
    "\n",
    "2. 각 주식의 90일 평균값을 구하시오.\n",
    "\n",
    "3. 보유한 전체 주식의 각 날짜별 변동량의 평균을 구하시오."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "가격 변동률 모의값 생성 (90일, 10개 종목)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.23324529,  0.0434758 , -0.18469774],\n",
       "       [ 0.25409313, -0.06141993, -0.22739056],\n",
       "       [ 0.19959914,  0.01217642,  0.15033222],\n",
       "       [-0.23941651,  0.04368385,  0.10560161],\n",
       "       [-0.00979993, -0.07956693,  0.08204752]])"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "changes = np.random.uniform(low=-0.3, high=0.3, size=(90,10))\n",
    "changes[:5, :3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "주식 10개의 시작 모의 가격 생성"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([213, 638, 977,   7, 505, 780, 882, 406, 857, 803])"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start_prices = np.random.randint(5,1001, 10)\n",
    "start_prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 262.68124687,  665.73756024,  796.55031224],\n",
       "       [ 329.4267458 ,  624.84800287,  615.42229191],\n",
       "       [ 395.18004048,  632.45641543,  707.94009334]])"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stock_prices = start_prices * (1+changes).cumprod(0)\n",
    "stock_prices[:3,:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "각 종목의 90일 평균"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  167.53068585,  1507.02749068,  1410.53010033,     2.75458004,\n",
       "         125.52769225,   315.98711829,   628.45550576,   873.5069702 ,\n",
       "         356.80900904,   787.76269832])"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(stock_prices, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "일자별 전체 종목 평균"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 571.53996255,  514.55885971,  519.19390671,  489.25944672,\n",
       "        484.33342773,  483.72752053,  485.0267982 ,  496.60508208,\n",
       "        505.1586185 ,  482.08374973,  505.96691051,  492.45936105,\n",
       "        528.10521576,  556.55436184,  606.3448046 ,  587.81967025,\n",
       "        625.35489013,  660.81480261,  646.77216382,  696.85099424,\n",
       "        723.05836594,  789.53475287,  778.56135689,  785.13968763,\n",
       "        875.24304503,  903.23538576,  871.7944486 ,  885.34447962,\n",
       "        809.22300235,  853.37017496,  862.87897241,  855.69010317,\n",
       "        682.24608265,  767.02109013,  809.61906137,  701.74789718,\n",
       "        621.59375628,  639.60690415,  713.13740697,  840.10515612,\n",
       "        723.29301737,  699.33443044,  778.68684382,  770.06538713,\n",
       "        646.59274222,  585.14843022,  600.8863418 ,  680.09509994,\n",
       "        729.71614565,  731.61030171,  799.80526045,  842.92388563,\n",
       "        880.85787219,  801.03837064,  818.03032705,  779.72202911,\n",
       "        762.64236857,  802.20375591,  761.20663957,  768.93031251,\n",
       "        785.89735215,  733.51525366,  719.66129983,  716.13392231,\n",
       "        624.27420638,  534.23437543,  496.42917929,  504.14158573,\n",
       "        483.28736016,  487.26458183,  506.03111979,  451.57262994,\n",
       "        374.27457194,  394.28009649,  397.61325518,  373.76839377,\n",
       "        381.15581458,  376.10436246,  321.82024905,  331.00816775,\n",
       "        388.51753387,  395.91423235,  422.32245725,  424.39222701,\n",
       "        437.13418698,  403.03398624,  383.1188269 ,  389.825476  ,\n",
       "        356.63439589,  320.19431737])"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(stock_prices, axis=1)"
   ]
  }
 ],
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