chapter_03_2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0ab71ade",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "191c7a94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([('jin', 25, 67.), ('suho', 18, 77.)],\n",
       "      dtype=[('name', '<U10'), ('age', '<i4'), ('weight', '<f4')])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([('jin', 25, 67), ('suho', 18,77)], dtype=[('name', 'U10'), ('age', 'i4'), ('weight', 'f4')])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "33441f9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('suho', 18, 77.)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2712bcdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['jin', 'suho'], dtype='<U10')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr['name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "67158fad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([67., 77.], dtype=float32)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr['weight']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ee15d4a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype([('a', '<f4'), ('b', '<f8'), ('c', '<i4', (2, 2))])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 각 튜플은 (필드이름, 데이터타입, 서브배열의 shape)\n",
    "np.dtype([('a', 'f4'), ('b', np.float64), ('c', 'i4', (2, 2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "859c777c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype([('f0', '<i8'), ('f1', '<f4'), ('f2', 'S3')])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 콤마로 구분하는 dtype 문자열의 형태. 이 때 필드명은 기본 이름인 f0, f1 순으로 부여 (f#)\n",
    "np.dtype('i8, f4, S3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8f0175e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype([('col1', '<i4'), ('col2', '<f4')])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 필드 매개 변수 배열의 딕셔너리 형태\n",
    "np.dtype({'names': ['col1', 'col2'], 'formats': ['i4', 'f4']})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d5507535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('a', 'b')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 구조화된 데이터 타입에서 필드 이름의 튜플을 구할 수 있다\n",
    "c = np.dtype([('a', 'i8'), ('b', 'f4')])\n",
    "c.names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "97ab69e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mappingproxy({'a': (dtype('int64'), 0), 'b': (dtype('float32'), 8)})"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "83b4c097",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(1, 2., 3.), (4, 5., 6.)],\n",
       "      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '<f8')])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 파이썬 고유 타입인 튜플로 할당\n",
    "a = np.array([(1, 2, 3), (4, 5, 6)], dtype='i8, f4, f8')\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a994ab3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(1, 2., 3.), (7, 8., 9.)],\n",
       "      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '<f8')])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1] = (7, 8, 9)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "aaf700f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(0, 0., False, b''), (0, 0., False, b'')],\n",
       "      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '?'), ('f3', 'S1')])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 스칼라 값으로 할당\n",
    "a = np.zeros(2, dtype='i8, f4, ?, S1')\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9c99ff08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(7, 7.,  True, b'7'), (7, 7.,  True, b'7')],\n",
       "      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '?'), ('f3', 'S1')])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:] = 7\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0c6cec72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(0, 0., False, b'0'), (1, 1.,  True, b'1')],\n",
       "      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '?'), ('f3', 'S1')])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:] = np.arange(2)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e273ae68",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 배열 인덱싱의 기본 구문은 i:j:k\n",
    "# arr[i:j:k] i: 시작 인덱스, j: 끝 인덱스, k: 간격\n",
    "# 시작하는 인덱스 i부터 k를 더하여 인덱스 j-1까지의 요소를 선택"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6a09561a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "6b260a79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a11e4c1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6601ac0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 중요: 여기서 -1은 끝까지가 아니고, 끝에서 두번째를 의미\n",
    "arr[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "4d9364b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8, 9])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 배열의 끝에서 두번째부터 배열의 마지막 요소까지 선택\n",
    "arr[-2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2db0ee0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 간격을 -1로 주면 전체 요소를 역순으로 선택\n",
    "arr[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "05f1afdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 다차원 배열에서의 슬라이싱\n",
    "arr2 = np.arange(9).reshape(3, 3)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9d2431b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 0],\n",
       "       [5, 4, 3],\n",
       "       [8, 7, 6]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2[:, ::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "78482323",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2[:2, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "890b7c3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  4,  5],\n",
       "       [ 6,  7,  8],\n",
       "       [ 9, 10, 11]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 브로드캐스팅\n",
    "arr = np.array([[0, 1, 2],\n",
    "               [3, 4, 5],\n",
    "               [6, 7, 8],\n",
    "               [9, 10, 11]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "7ec4d1ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0],\n",
       "       [3, 3]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rows = np.array([[0, 0],\n",
    "                [3, 3]], dtype=np.intp)\n",
    "rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ccbf152d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2],\n",
       "       [0, 2]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns = np.array([[0, 2],\n",
    "                    [0, 2]], dtype=np.intp)\n",
    "columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2f0b9058",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2],\n",
       "       [ 9, 11]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# [[(0, 0), (0, 2)],\n",
    "#  [(3, 0), (3, 2)]\n",
    "arr[rows, columns]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "dcf051cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(15).reshape(3, 5)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "a6c6de25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, 13])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.array([0, 2])가 행을 뜻하고 3이 열을 뜻해, (0, 3), (2, 3)의 값을 선택한다\n",
    "arr[np.array([0, 2]), 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "85195935",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (5,) (3,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/30/4jg7fpg97lgc97y6qwzvprlm0000gn/T/ipykernel_3459/1005351094.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0marr1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0marr2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m13\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0marr1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0marr2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (5,) (3,) "
     ]
    }
   ],
   "source": [
    "# (5,1)배열과 (3, 1)배열은 브로드캐스팅할 수 없다.\n",
    "# 이때, newaxis를 사용해 차원을 증가시켜 shape을 동일하게 해서 브로드캐스팅한다.\n",
    "arr1 = np.array([1, 2, 3, 4, 5])\n",
    "arr2 = np.array([11, 12, 13])\n",
    "arr1 + arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5db8e1f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4],\n",
       "       [5]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1_nx = arr1[:, np.newaxis]\n",
    "arr1_nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f89adfb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11],\n",
       "       [12],\n",
       "       [13]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2_nx = arr2[:, np.newaxis]\n",
    "arr2_nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "494ba199",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 13, 14],\n",
       "       [13, 14, 15],\n",
       "       [14, 15, 16],\n",
       "       [15, 16, 17],\n",
       "       [16, 17, 18]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1_nx + arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "b31e0acf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 13, 14, 15, 16],\n",
       "       [13, 14, 15, 16, 17],\n",
       "       [14, 15, 16, 17, 18]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2_nx + arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "eabcee6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 불리언 배열로 인덱싱\n",
    "arr = np.arange(12).reshape(3, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "51ba2d4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [False, False,  True,  True],\n",
       "       [ True,  True,  True,  True]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind = arr > 5\n",
    "ind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "b909b7f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6,  7,  8,  9, 10, 11])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "35859d34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [False, False,  True,  True]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind[: -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "c9ae7240",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[ind[:, -1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "9d287875",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 인덱스와 슬라이싱을 동시에\n",
    "arr = np.arange(12).reshape(3, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "36da43c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  6],\n",
       "       [ 9, 10]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[np.array([1, 2]), 1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "2d9a4f63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [0, 2, 0],\n",
       "       [1, 1, 0]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 0이 아닌 요소를 행과 열을 나누어 인덱스를 반환\n",
    "arr = np.array([[1, 0, 0], [0, 2, 0], [1, 1, 0]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "fe6be1d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 1, 2, 2]), array([0, 1, 0, 1]))"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.nonzero(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "3eb644b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0],\n",
       "       [1, 1],\n",
       "       [2, 0],\n",
       "       [2, 1]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 전치행렬(transpose)를 사용해 행열 조합으로 인덱스를 나열할 수 있다\n",
    "np.transpose(np.nonzero(arr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "0e9f5e28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reduce() 메소드는 기본 축인 0축에 감소를 실행. axis=1로 설정하면 1축에 감소를 실행\n",
    "arr = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "7b6abdc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 7, 9])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.reduce(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "da03ddb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6, 15])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.reduce(arr, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "a648bbf7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  6, 10, 15])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# accumulate\n",
    "np.add.accumulate([1, 2, 3, 4, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "c196379c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1,   2,   6,  24, 120])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# multiply\n",
    "np.multiply.accumulate([1, 2, 3, 4, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "4e9f9601",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(12).reshape(3, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "3fd2a845",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  6,  8, 10],\n",
       "       [12, 15, 18, 21]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.accumulate(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "bdeeb926",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  3,  6],\n",
       "       [ 4,  9, 15, 22],\n",
       "       [ 8, 17, 27, 38]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.accumulate(arr, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "7f83ff7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(7)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "c65d9632",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 7, 5, 6])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arr에서 [0:3], [3:5], [5:6], [6:]에 해당하는 요서를 각각 더한 값을 반환\n",
    "# 즉, 0~2, 3~4, 5, 6 요소를 더한 값\n",
    "np.add.reduceat(arr, [0, 3, 5, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "fc1bacdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  2.,  3.],\n",
       "       [ 4.,  5.,  6.,  7.],\n",
       "       [ 8.,  9., 10., 11.],\n",
       "       [12., 13., 14., 15.]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.linspace(0, 15, 16).reshape(4, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "22774344",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12., 15., 18., 21.],\n",
       "       [12., 13., 14., 15.],\n",
       "       [ 4.,  5.,  6.,  7.],\n",
       "       [ 8.,  9., 10., 11.],\n",
       "       [24., 28., 32., 36.]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.reduceat(arr, [0, 3, 1, 2, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "1739778e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5,  6],\n",
       "       [ 8, 10, 12],\n",
       "       [12, 15, 18]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.multiply.outer([1, 2, 3], [4, 5, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "b9535846",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.arange(6).reshape(2,3)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "78bd7552",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.arange(4)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "47b99cd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  0,  0,  0],\n",
       "        [ 0,  1,  2,  3],\n",
       "        [ 0,  2,  4,  6]],\n",
       "\n",
       "       [[ 0,  3,  6,  9],\n",
       "        [ 0,  4,  8, 12],\n",
       "        [ 0,  5, 10, 15]]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.multiply.outer(arr1, arr2)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "db6a574b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3, 4)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "86007f79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 6)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = range(6)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "ec7692b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   1,   8,  27,  64, 125])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.power(arr1, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "08a672bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  8, 27, 16,  5])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = [1, 2, 3, 3, 2, 1]\n",
    "np.power(arr1, arr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "587cee95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 3, 2, 1],\n",
       "       [1, 2, 3, 3, 2, 1]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])\n",
    "arr3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "cd8fcbff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  8, 27, 16,  5],\n",
       "       [ 0,  1,  8, 27, 16,  5]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.power(arr1, arr3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "b9bd503e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(np.pi/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "e0fcf542",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(np.deg2rad(90))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "a7556462",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.5       , 0.70710678, 0.8660254 , 1.        ])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(np.array((0, 30, 45, 60, 90)) * np.pi/180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "9f1295d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f92650f0ac0>]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "arr = np.linspace(-np.pi, np.pi, 201)\n",
    "plt.plot(arr, np.sin(arr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b890aa82",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}