CHAP_07.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "CHAP-07.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyPHZz5hC0CrYYOhfY7w9cos",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/metamath1/noviceml/blob/master/CHAP_07.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bbZPqgO3Iku7"
      },
      "source": [
        "# 7장 그림 및 예제 코드"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rfbVWzytIcPa"
      },
      "source": [
        "# 기본적인 import들\n",
        "# 이후 그래프 그리는 코드에는 중복으로 적지 않음.\n",
        "# 다른 곳으로 그래프 그리는 코드를 복사-붙이기 할 때는 \n",
        "# 이 import 코드와 함께 복사-붙이기 해야함\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib as mpl\n",
        "import matplotlib.font_manager as mfm\n",
        "from matplotlib.patches import Rectangle, Circle, PathPatch, Arc\n",
        "from mpl_toolkits.mplot3d import Axes3D \n",
        "import mpl_toolkits.mplot3d.art3d as art3d\n",
        "\n",
        "# numpy 출력 형식 지정\n",
        "np.set_printoptions(precision=4, linewidth=150)\n",
        "\n",
        "# matplotlib 스타일 지정\n",
        "mpl.style.use('bmh')\n",
        "mpl.style.use('seaborn-whitegrid')\n",
        "style = plt.style.library['bmh']\n",
        "# 스타일 컬러를 쉽게 쓸 수 있도록 리스트 저장\n",
        "style_colors = [ c['color'] for c in style['axes.prop_cycle'] ]\n",
        "\n",
        "# 그림을 로컬 폴더에 저장하고 싶으면 True로 수정 \n",
        "file_print = False"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uQiv0PdTIv3Z"
      },
      "source": [
        "from matplotlib.text import Text, TextPath\n",
        "from matplotlib.transforms import Affine2D\n",
        "\n",
        "# https://matplotlib.org/3.1.1/gallery/mplot3d/pathpatch3d.html\n",
        "def text3d(ax, xyz, s, zdir=\"z\", size=None, angle=0, usetex=False, **kwargs):\n",
        "    '''\n",
        "    Plots the string 's' on the axes 'ax', with position 'xyz', size 'size',\n",
        "    and rotation angle 'angle'.  'zdir' gives the axis which is to be treated\n",
        "    as the third dimension.  usetex is a boolean indicating whether the string\n",
        "    should be interpreted as latex or not.  Any additional keyword arguments\n",
        "    are passed on to transform_path.\n",
        "\n",
        "    Note: zdir affects the interpretation of xyz.\n",
        "    '''\n",
        "    x, y, z = xyz\n",
        "    if zdir == \"y\":\n",
        "        xy1, z1 = (x, z), y\n",
        "    elif zdir == \"x\":\n",
        "        xy1, z1 = (y, z), x\n",
        "    else:\n",
        "        xy1, z1 = (x, y), z\n",
        "\n",
        "    text_path = TextPath((0, 0), s, size=size)\n",
        "    trans = Affine2D().rotate(angle).translate(xy1[0], xy1[1])\n",
        "\n",
        "    p1 = PathPatch(trans.transform_path(text_path), **kwargs)\n",
        "    ax.add_patch(p1)\n",
        "    art3d.pathpatch_2d_to_3d(p1, z=z1, zdir=zdir)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DNzW5P_XI3Tw"
      },
      "source": [
        "from matplotlib.patches import FancyArrowPatch\n",
        "from mpl_toolkits.mplot3d import proj3d\n",
        "\n",
        "class Arrow3D(FancyArrowPatch):\n",
        "    \"\"\"\n",
        "    https://stackoverflow.com/questions/22867620/putting-arrowheads-on-vectors-in-matplotlibs-3d-plot\n",
        "    \"\"\"\n",
        "    def __init__(self, xs, ys, zs, *args, **kwargs):\n",
        "        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)\n",
        "        self._verts3d = xs, ys, zs\n",
        "\n",
        "    def draw(self, renderer):\n",
        "        xs3d, ys3d, zs3d = self._verts3d\n",
        "        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
        "        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))\n",
        "        FancyArrowPatch.draw(self, renderer)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nH-86BkWJfPL",
        "outputId": "17458563-f3d1-4f4a-9da0-d5afeaca808f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "# 데이터 파일 사용을 위한 github repo 복사\n",
        "# !주의! \n",
        "# 구글 colab 환경에서 실행하는 경우만 실행하세요.\n",
        "# 로컬환경에서는 실행하지 마세요.\n",
        "!git clone -l -s https://github.com/metamath1/noviceml.git noviceml"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'noviceml'...\n",
            "warning: --local is ignored\n",
            "remote: Enumerating objects: 32, done.\u001b[K\n",
            "remote: Counting objects:   3% (1/32)\u001b[K\rremote: Counting objects:   6% (2/32)\u001b[K\rremote: Counting objects:   9% (3/32)\u001b[K\rremote: Counting objects:  12% (4/32)\u001b[K\rremote: Counting objects:  15% (5/32)\u001b[K\rremote: Counting objects:  18% (6/32)\u001b[K\rremote: Counting objects:  21% (7/32)\u001b[K\rremote: Counting objects:  25% (8/32)\u001b[K\rremote: Counting objects:  28% (9/32)\u001b[K\rremote: Counting objects:  31% (10/32)\u001b[K\rremote: Counting objects:  34% (11/32)\u001b[K\rremote: Counting objects:  37% (12/32)\u001b[K\rremote: Counting objects:  40% (13/32)\u001b[K\rremote: Counting objects:  43% (14/32)\u001b[K\rremote: Counting objects:  46% (15/32)\u001b[K\rremote: Counting objects:  50% (16/32)\u001b[K\rremote: Counting objects:  53% (17/32)\u001b[K\rremote: Counting objects:  56% (18/32)\u001b[K\rremote: Counting objects:  59% (19/32)\u001b[K\rremote: Counting objects:  62% (20/32)\u001b[K\rremote: Counting objects:  65% (21/32)\u001b[K\rremote: Counting objects:  68% (22/32)\u001b[K\rremote: Counting objects:  71% (23/32)\u001b[K\rremote: Counting objects:  75% (24/32)\u001b[K\rremote: Counting objects:  78% (25/32)\u001b[K\rremote: Counting objects:  81% (26/32)\u001b[K\rremote: Counting objects:  84% (27/32)\u001b[K\rremote: Counting objects:  87% (28/32)\u001b[K\rremote: Counting objects:  90% (29/32)\u001b[K\rremote: Counting objects:  93% (30/32)\u001b[K\rremote: Counting objects:  96% (31/32)\u001b[K\rremote: Counting objects: 100% (32/32)\u001b[K\rremote: Counting objects: 100% (32/32), done.\u001b[K\n",
            "remote: Compressing objects: 100% (27/27), done.\u001b[K\n",
            "remote: Total 80 (delta 12), reused 19 (delta 4), pack-reused 48\u001b[K\n",
            "Unpacking objects: 100% (80/80), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iVp-Ha7pJhla"
      },
      "source": [
        "# 구글 colab 환경일 경우 그래프에 한글 폰트 사용을 위한 설정\n",
        "path = 'noviceml/font/NanumBarunGothic.ttf'\n",
        "fontprop = mfm.FontProperties(fname=path, size=18)\n",
        "\n",
        "# !주의!\n",
        "# 아래 라인은 LaTeX 폰트 설치를 위한 것입니다.\n",
        "# 노트북을 실행할 때 마다 colab 환경에 폰트를 설치해야 합니다.\n",
        "# 처음 설치시 시간이 오래 걸립니다. 그림 17, 18을 랜더링 할 필요가 없다면\n",
        "# 이 라인은 주석 처리하고 실행하세요.\n",
        "!apt install texlive-fonts-recommended texlive-fonts-extra cm-super dvipng \n",
        "\n",
        "# 로컬 환경일 경우 다음 한글 폰트 사용을 위한 설정을 주석 해제하세요.\n",
        "# https://financedata.github.io/posts/matplotlib-hangul-for-ubuntu-linux.html\n",
        "# 아래 코드의 주석 제거 후 경로를 유저 컴퓨터의 폰트 파일 경로로 수정하세요.\n",
        "# path = '/usr/share/fonts/truetype/nanum/NanumBarunGothic.ttf'\n",
        "# fontprop = mfm.FontProperties(fname=path, size=18)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2edubHIuI-0T"
      },
      "source": [
        "# 행렬\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p3VsAulKJAIT"
      },
      "source": [
        "## 행렬에 대한 연산: 덧셈, 스칼라 곱셈, 곱셈"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ti00bTPJJB74"
      },
      "source": [
        "### 덧셈"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dsb4XemsI85w",
        "outputId": "6fb48424-d34f-4ff9-da01-a0348ace5979",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A = np.matrix([[1,2],[3,4]])\n",
        "B = np.matrix([[10,20],[30,40]])\n",
        "\n",
        "A+B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[11, 22],\n",
              "        [33, 44]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jrkekv5GJEKD"
      },
      "source": [
        "### 스칼라 곱셈"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xlRAvsxUJDNY",
        "outputId": "29f36084-b838-41c6-fb92-e984b93d7c1f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "3*B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[ 30,  60],\n",
              "        [ 90, 120]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Vd5VO5iJIJD"
      },
      "source": [
        "### 곱셈"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PKiQUEIVJGxA",
        "outputId": "e54886fe-43b4-470f-a556-fb2c1fd03674",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A = np.array([[1,2,3], [4,5,6]]) #-----[1]\n",
        "B = np.array([[2,1], [1,2], [1,1]])\n",
        "\n",
        "np.dot(A,B) #-----[2]\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 7,  8],\n",
              "       [19, 20]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3PFAmn7TJKnd"
      },
      "source": [
        "### 단위행렬"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2CtDzV9XJJaw",
        "outputId": "541f645e-ebc8-4205-bed8-8a2fdb3918fd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "A = np.matrix([[2, 4], [4, 2]])\n",
        "I = np.matrix(np.eye(2))\n",
        "\n",
        "print(A*I)\n",
        "print(I*A)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[2. 4.]\n",
            " [4. 2.]]\n",
            "[[2. 4.]\n",
            " [4. 2.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UoHJ1J1IJQgc"
      },
      "source": [
        "### 대각행렬과 역행렬"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5MI5-kK6JL-o",
        "outputId": "3709c2f7-9629-4c0b-bfca-58490b5ec397",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "D = np.matrix(np.eye(3)*np.array([2,1,4]))\n",
        "D.I"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[0.5 , 0.  , 0.  ],\n",
              "        [0.  , 1.  , 0.  ],\n",
              "        [0.  , 0.  , 0.25]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gp3xZNBeJR3Y",
        "outputId": "b4c43104-b755-4aae-e074-446af2a678ce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "D.I*D"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[1., 0., 0.],\n",
              "        [0., 1., 0.],\n",
              "        [0., 0., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cgOYttg_JNpb"
      },
      "source": [
        "### 대칭행렬과 대각화"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vgonT8_AJS8I",
        "outputId": "8a2d1e73-2a66-482a-a2b2-7435ff200774",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A = np.matrix([[2, 4], [4, 2]])\n",
        "X = np.matrix([[ 0.7071, -0.7071], [ 0.7071,  0.7071]])\n",
        "D = X.I*A*X\n",
        "D\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[ 6.0000e+00, -1.3122e-16],\n",
              "        [-8.5947e-18, -2.0000e+00]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GRN7Npf2JXgW"
      },
      "source": [
        "# 벡터 "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DoML-uyiJZe6"
      },
      "source": [
        "## 그림 7-1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xr5y-6qnJV5Q",
        "outputId": "38287675-dc4a-4e89-cc1c-db99635498fd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "from matplotlib import cm\n",
        "\n",
        "fig = plt.figure()\n",
        "fig.set_size_inches((15,5))\n",
        "\n",
        "ax1 = fig.add_subplot(1, 3, 1, projection='3d')\n",
        "ax2 = fig.add_subplot(1, 3, 2, projection='3d')\n",
        "ax3 = fig.add_subplot(1, 3, 3, projection='3d')\n",
        "\n",
        "ax1.xaxis.set_tick_params(labelsize=15)\n",
        "ax1.yaxis.set_tick_params(labelsize=15)\n",
        "ax1.zaxis.set_tick_params(labelsize=15)\n",
        "\n",
        "ax2.xaxis.set_tick_params(labelsize=15)\n",
        "ax2.yaxis.set_tick_params(labelsize=15)\n",
        "ax2.zaxis.set_tick_params(labelsize=15)\n",
        "\n",
        "ax3.xaxis.set_tick_params(labelsize=15)\n",
        "ax3.yaxis.set_tick_params(labelsize=15)\n",
        "ax3.zaxis.set_tick_params(labelsize=15)\n",
        "\n",
        "x, y, z = 0, 1, 2\n",
        "P = np.array([1.5, 1.8, 1])\n",
        "\n",
        "Q = np.array([2.1, 3.2, 3])\n",
        "O = (0, 0, 0)\n",
        "\n",
        "axis_length = Q + 0.5\n",
        "\n",
        "def draw_vector(ax, P, Q, elev, azim, title=''):\n",
        "    \n",
        "    arrow = Arrow3D([P[x], Q[x]], [P[y], Q[y]], [P[z], Q[z]], lw=2, color='k',\n",
        "                   mutation_scale=20, arrowstyle=\"-|>\" )\n",
        "    ax.add_artist(arrow)\n",
        "    ax.axis('off')\n",
        "    \n",
        "    ax.plot3D([Q[x], Q[x]], [0, Q[y]], [0,0], '--', color=\"gray\")\n",
        "    ax.plot3D([P[x], P[x]], [0, P[y]], [0,0], '--', color=\"gray\")\n",
        "\n",
        "    ax.plot3D([0, Q[x]], [Q[y], Q[y]], [0,0], '--', color=\"gray\")\n",
        "    ax.plot3D([0, P[x]], [P[y], P[y]], [0,0], '--', color=\"gray\")\n",
        "\n",
        "    ax.plot3D([P[x], P[x]], [P[y], P[y]], [0, P[z]], '--', color=\"gray\") #p로의 세로선\n",
        "    ax.plot3D([Q[x], Q[x]], [Q[y], Q[y]], [0, Q[z]], '--', color=\"gray\") #p로의 세로선\n",
        "\n",
        "    ax.plot3D([0, P[x]], [0, P[y]], [0,0], '--', color=\"gray\")\n",
        "    ax.plot3D([0, Q[x]], [0, Q[y]], [0,0], '--', color=\"gray\")\n",
        "\n",
        "    ax.plot3D([0, P[x]], [0, P[y]], [P[z], P[z]], '--', color=\"gray\")\n",
        "    ax.plot3D([0, Q[x]], [0, Q[y]], [Q[z], Q[z]], '--', color=\"gray\")\n",
        "\n",
        "    ax.plot3D([P[x], Q[x]], [0, 0], [0,0], lw=2, color='k')\n",
        "    ax.plot3D([0,0], [P[y], Q[y]], [0,0],  lw=2, color='k')\n",
        "    ax.plot3D([0,0], [0, 0], [P[z], Q[z]], lw=2, color='k')\n",
        "\n",
        "    # 축 그리기 \n",
        "    ax.plot3D([O[x], axis_length[0]], [0, 0], [0, 0], color='k', alpha=0.2)\n",
        "    ax.text(axis_length[0]+0.5, 0, 0, '$x$', fontsize=18)\n",
        "    \n",
        "    ax.plot3D([0,0], [O[y], axis_length[1]], [0, 0], color='k', alpha=0.2)\n",
        "    ax.text(0, axis_length[1]+0.2, 0, '$y$', fontsize=18)\n",
        "    \n",
        "    ax.plot3D([O[x], 0], [O[y], 0], [O[z], axis_length[2]], color='k', alpha=0.2)\n",
        "    ax.text(0, 0, axis_length[2]+0.1, '$z$', fontsize=18)\n",
        "    \n",
        "    ax.plot([O[x]], [O[y]], [O[z]], 'o', color='k')\n",
        "\n",
        "    # 콤포넌트 그리기\n",
        "    ax.text(P[x]+(Q[x]-P[x])-0.3, -0.4, 0, '$v_1$', fontsize=18)\n",
        "    ax.text(-0.4, P[y]+(Q[y]-P[y])-0.8, 0, '$v_2$', fontsize=18)\n",
        "    ax.text(0, 0.1,  P[z]+(Q[y]-P[z])/2,   '$v_3$', fontsize=18)\n",
        "\n",
        "    ax.set_title(title, fontproperties=fontprop)\n",
        "    ax.set_xlabel('$x$', fontsize=20)\n",
        "    ax.set_ylabel('$y$', fontsize=20)\n",
        "    ax.set_zlabel('$z$', fontsize=20)\n",
        "    \n",
        "    ax.set_xlim((0, 2.5))\n",
        "    ax.set_ylim((0, 3.5))\n",
        "    ax.set_zlim((0, 3.5))\n",
        "    \n",
        "    ax.view_init(elev, azim)\n",
        "    \n",
        "draw_vector(ax1, P, Q, 20, 30, '벡터와 벡터의 요소')  \n",
        "draw_vector(ax2, P-0.5, Q-0.5, 20, 30, '이동된 벡터와 벡터의 요소') \n",
        "draw_vector(ax3, O, Q, 20, 30, '위치 벡터') \n",
        "\n",
        "plt.subplots_adjust(hspace=0.05, wspace=0.0)\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-1.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-1.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1080x360 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DF8xSXi3JmP2"
      },
      "source": [
        "## 그림 7-2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gz1b54kTJa3o",
        "outputId": "6c324511-9193-4a1c-90cb-1bca5e38fa26",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 460
        }
      },
      "source": [
        "fig = plt.figure(figsize=(7,7))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "ax.xaxis.set_tick_params(labelsize=18)\n",
        "ax.yaxis.set_tick_params(labelsize=18)\n",
        "ax.set_xlabel(r'$x$', fontsize=25)\n",
        "ax.set_ylabel(r'$y$', fontsize=25)\n",
        "ax.grid(False)\n",
        "\n",
        "a = np.array( [[1, 1],[2, 3]] )\n",
        "da = a[1]-a[0]\n",
        "\n",
        "b = np.array( [[1, 1],[3, 2]] )\n",
        "db = b[1]-b[0]\n",
        "\n",
        "\n",
        "vec_a = FancyArrowPatch(a[0], a[1], lw=2, color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax.add_patch(vec_a)\n",
        "\n",
        "vec_b = FancyArrowPatch(b[0], b[1], lw=2, color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax.add_patch(vec_b)\n",
        "\n",
        "a_ = a + db # + db[1]\n",
        "vec_a_ = FancyArrowPatch(a_[0], a_[1], lw=1, color='k', mutation_scale=20, arrowstyle=\"-|>\", ls='--')\n",
        "ax.add_patch(vec_a_)\n",
        "\n",
        "b_ = b + da\n",
        "vec_b_ = FancyArrowPatch(b_[0], b_[1], lw=1, color='k', mutation_scale=20, arrowstyle=\"-|>\", ls='--')\n",
        "ax.add_patch(vec_b_)\n",
        "\n",
        "dc = da+db\n",
        "c = a.copy()\n",
        "c[1,:] = c[0,:]+dc\n",
        "vec_c = FancyArrowPatch(c[0], c[1], lw=2, color='white', mutation_scale=30, arrowstyle=\"-|>\", ec='gray')\n",
        "ax.add_patch(vec_c)\n",
        "\n",
        "# 가로 선\n",
        "ax.plot( (0, a[0,0]),(a[0,1], a[0,1]), lw=1, color='k' )\n",
        "ax.plot( (0, a[1,0]),(a[1,1], a[1,1]), lw=1, color='k' )\n",
        "ax.plot( (0, a_[1,0]),(a_[1,1], a_[1,1]), lw=1, color='k' )\n",
        "\n",
        "# 세로 선\n",
        "ax.plot( (a[0,0], a[0,0]), (0, a[0,1]), lw=1, color='k' )\n",
        "ax.plot( (b[1,0], b[1,0]), (0, b[1,1]), lw=1, color='k' )\n",
        "ax.plot( (b_[1,0], b_[1,0]), (0, b_[1,1]), lw=1, color='k' )\n",
        "\n",
        "vec_ay = FancyArrowPatch((0.0, a[0,1]), (0.0, a[1,1]), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_ay)\n",
        "\n",
        "vec_by = FancyArrowPatch((0.0, a[1,1]), (0.0, a[1,1]+db[1]), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_by)\n",
        "\n",
        "vec_cy = FancyArrowPatch((0.5,c[0,1]), (0.5,c[1,1]), lw=1, color='white', mutation_scale=20, arrowstyle=\"<|-|>\", ec='gray')\n",
        "ax.add_patch(vec_cy)\n",
        "\n",
        "vec_ax = FancyArrowPatch((a[0,0], 0.0), (b[1,0], 0.0), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_ax)\n",
        "\n",
        "vec_bx = FancyArrowPatch((b[1,0], 0.0), (a[1,1]+da[0], 0.0), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_bx)\n",
        "\n",
        "vec_cx = FancyArrowPatch((c[0,0],0.5), (c[1,0],0.5), lw=1, color='white', mutation_scale=20, arrowstyle=\"<|-|>\", ec='gray')\n",
        "ax.add_patch(vec_cx)\n",
        "\n",
        "ax.text(1.2, 2, r\"$\\mathbf{a}$\", fontsize=25)\n",
        "ax.text(3.5, 2.9, r\"$\\mathbf{a}'$\", fontsize=25)\n",
        "ax.text(2, 1.2, r\"$\\mathbf{b}$\", fontsize=25)\n",
        "ax.text(2.8, 3.5, r\"$\\mathbf{b}'$\", fontsize=25)\n",
        "ax.text(2.5, 2.3, r\"$\\mathbf{c}$\", fontsize=25)\n",
        "\n",
        "ax.text(0.5, 2.5, r\"$c_2$\", fontsize=20)\n",
        "ax.text(0.0, 2.0, r\"$a_2$\", fontsize=20)\n",
        "ax.text(0.0, 3.5, r\"$b_2$\", fontsize=20)\n",
        "\n",
        "ax.text(2.5, 0.5, r\"$c_1$\", fontsize=20)\n",
        "ax.text(2.0, 0.0, r\"$b_1$\", fontsize=20)\n",
        "ax.text(3.5, 0.0, r\"$a_1$\", fontsize=20)\n",
        "\n",
        "plt.axis('equal')\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-2.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-2.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DMTR2C82Jqmw"
      },
      "source": [
        "## 그림 7-3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fXR0OV7yJngQ",
        "outputId": "b89bd146-bde4-41e7-9cad-c4a9730d6bcb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 460
        }
      },
      "source": [
        "fig = plt.figure(figsize=(7,7))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "ax.xaxis.set_tick_params(labelsize=18)\n",
        "ax.yaxis.set_tick_params(labelsize=18)\n",
        "ax.set_xlabel(r'$x$', fontsize=25)\n",
        "ax.set_ylabel(r'$y$', fontsize=25)\n",
        "ax.grid(False)\n",
        "\n",
        "a = np.array( [[1, 1],[2, 3]] )\n",
        "da = a[1]-a[0]\n",
        "\n",
        "b = np.array( [[1, 1],[3, 2]] )\n",
        "db = b[1]-b[0]\n",
        "\n",
        "vec_a = FancyArrowPatch(a[0], a[1], lw=2, color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax.add_patch(vec_a)\n",
        "\n",
        "vec_b = FancyArrowPatch(b[0], b[1], lw=2, color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax.add_patch(vec_b)\n",
        "\n",
        "minus_b = b.copy()\n",
        "minus_b[1,:] = minus_b[0,:]-db\n",
        "vec_minus_b = FancyArrowPatch(minus_b[0], minus_b[1], ls='--', lw=1, color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax.add_patch(vec_minus_b)\n",
        "\n",
        "a_ = a - db # + db[1]\n",
        "vec_a_ = FancyArrowPatch(a_[0], a_[1], lw=1, color='k', mutation_scale=20, arrowstyle=\"-|>\", ls='--')\n",
        "ax.add_patch(vec_a_)\n",
        "\n",
        "b_ = minus_b + da\n",
        "vec_b_ = FancyArrowPatch(b_[0], b_[1], lw=1, color='k', mutation_scale=20, arrowstyle=\"-|>\", ls='--')\n",
        "ax.add_patch(vec_b_)\n",
        "\n",
        "db_ = minus_b[1]-minus_b[0]\n",
        "dc_ = da+db_\n",
        "c_ = a.copy()\n",
        "c_[1,:] = c_[0,:]+dc_\n",
        "vec_c_ = FancyArrowPatch(c_[0], c_[1], lw=2, color='white', mutation_scale=30, arrowstyle=\"-|>\", ec='gray', ls='--')\n",
        "ax.add_patch(vec_c_)\n",
        "\n",
        "dc = da-db\n",
        "c = b.copy()\n",
        "c[0,:] = c[1,:]\n",
        "c[1,:] = c[0,:]+dc\n",
        "\n",
        "vec_c = FancyArrowPatch(c[0], c[1], lw=2, color='white', mutation_scale=30, arrowstyle=\"-|>\", ec='gray')\n",
        "ax.add_patch(vec_c)\n",
        "\n",
        "# 세로 선\n",
        "ax.plot( (a[0,0], a[0,0]), (-0.5, a[0,1]), lw=1, color='k' )\n",
        "ax.plot( (a[1,0], a[1,0]), (-0.5, a[1,1]), lw=1, color='k' )\n",
        "ax.plot( (b[1,0], b[1,0]), (-0.5, b[1,1]), lw=1, color='k' )\n",
        "\n",
        "# 가로 선\n",
        "ax.plot( (a[0,0], 4), (a[0,1], a[0,1]), lw=1, color='k' )\n",
        "ax.plot( (b[1,0], 4), (b[1,1], b[1,1]), lw=1, color='k' )\n",
        "ax.plot( (a[1,0], 4), (a[1,1], a[1,1]), lw=1, color='k' )\n",
        "\n",
        "vec_ay = FancyArrowPatch((4.0, a[0,1]), (4.0, a[1,1]), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_ay)\n",
        "\n",
        "vec_by = FancyArrowPatch((3.5, b[0,1]), (3.5, b[1,1]), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_by)\n",
        "\n",
        "vec_cy = FancyArrowPatch((3.5, c[0,1]), (3.5,c[1,1]), lw=1, color='white', mutation_scale=20, arrowstyle=\"<|-|>\", ec='gray')\n",
        "ax.add_patch(vec_cy)\n",
        "\n",
        "vec_bx = FancyArrowPatch((a[0,0], -0.5), (b[1,0], -0.5), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_bx)\n",
        "\n",
        "vec_ax = FancyArrowPatch((a[0,0], 0.0), (a[1,0], 0.0), lw=1, mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(vec_ax)\n",
        "\n",
        "vec_cx = FancyArrowPatch((c[0,0],0.0), (c[1,0],0.0), lw=1, color='white', mutation_scale=20, arrowstyle=\"<|-|>\", ec='gray')\n",
        "ax.add_patch(vec_cx)\n",
        "\n",
        "ax.text(1.2, 2, r\"$\\mathbf{a}$\", fontsize=25)\n",
        "ax.text(-0.7, 1.0, r\"$\\mathbf{a}'$\", fontsize=25)\n",
        "ax.text(2, 1.2, r\"$\\mathbf{b}$\", fontsize=25)\n",
        "ax.text(0, 0.3, r\"$-\\mathbf{b}$\", fontsize=25)\n",
        "ax.text(0.5, 2.5, r\"$-\\mathbf{b}'$\", fontsize=25)\n",
        "\n",
        "ax.text(2.4, 0.1, r\"$c_1$\", fontsize=20)\n",
        "ax.text(1.4, 0.1, r\"$a_1$\", fontsize=20)\n",
        "ax.text(1.9, -0.8, r\"$b_1$\", fontsize=20)\n",
        "\n",
        "ax.text(3.2, 2.5, r\"$c_2$\", fontsize=20)\n",
        "ax.text(4.0, 2.0, r\"$a_2$\", fontsize=20)\n",
        "ax.text(3.2, 1.5, r\"$b_2$\", fontsize=20)\n",
        "\n",
        "ax.text(0, 1.5, r\"$\\mathbf{a}+(-\\mathbf{b})$\", fontsize=20)\n",
        "ax.text(2.5, 2.5, r\"$\\mathbf{c}$\", fontsize=25)\n",
        "\n",
        "plt.axis('equal')\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-3.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-3.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rD1n3EDgJt0T"
      },
      "source": [
        "## 그림 7-4"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fhtrdH3qJrvI",
        "outputId": "656c3833-bba1-4b5a-ec65-25d92027b3b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        }
      },
      "source": [
        "fig = plt.figure(figsize=(15,7))\n",
        "ax1 = fig.add_subplot(1, 2, 1)\n",
        "ax2 = fig.add_subplot(1, 2, 2)\n",
        "\n",
        "ax1.xaxis.set_tick_params(labelsize=18)\n",
        "ax1.yaxis.set_tick_params(labelsize=18)\n",
        "ax1.set_xlabel(r'$x$', fontsize=25)\n",
        "ax1.set_ylabel(r'$y$', fontsize=25)\n",
        "\n",
        "ax2.xaxis.set_tick_params(labelsize=18)\n",
        "ax2.yaxis.set_tick_params(labelsize=18)\n",
        "ax2.set_xlabel(r'$x$', fontsize=25)\n",
        "ax2.set_ylabel(r'$y$', fontsize=25)\n",
        "\n",
        "a = np.array([0, 0])\n",
        "b = np.array([3, 3])\n",
        "vec_a = FancyArrowPatch((0, 0), (3, 0) , lw=1, mutation_scale=20, arrowstyle=\"-\", color='k', ls='--')\n",
        "ax1.add_patch(vec_a)\n",
        "\n",
        "vec_b = FancyArrowPatch((3, 0), (3, 3) , lw=1, mutation_scale=20, arrowstyle=\"-\", color='k', ls='--')\n",
        "ax1.add_patch(vec_b)\n",
        "\n",
        "c = np.array( [a, b] )\n",
        "dc = c[1]-c[0]\n",
        "vec_c = FancyArrowPatch(c[0], c[1], lw=2, mutation_scale=20, arrowstyle=\"-|>\", color='gray')\n",
        "ax1.add_patch(vec_c)\n",
        "\n",
        "ax1.plot(*a, 'o', color='k')\n",
        "ax1.plot(*b, 'o', color='k')\n",
        "\n",
        "ax1.text(-0.2,-0.2, r\"$\\mathbf{a}$\", fontsize=20)\n",
        "ax1.text(3.1, 3.1, r\"$\\mathbf{b}$\", fontsize=20)\n",
        "ax1.text(1.5, 1.7, r\"$\\mathbf{c}$\", fontsize=20)\n",
        "ax1.set_title(\"L2 거리\", fontsize=20, fontproperties=fontprop)\n",
        "ax1.set_xlim(-1, 4)\n",
        "ax1.set_ylim(-1, 4)\n",
        "\n",
        "ax2.plot((0, 0), (0, 1), lw=2, color='gray')\n",
        "ax2.plot((0, 1), (1, 1), lw=2, color='gray')\n",
        "ax2.plot((1, 1), (1, 3), lw=2, color='gray')\n",
        "# ax2.plot((1, 3), (3, 3), lw=2, color='gray')\n",
        "vec_a = FancyArrowPatch((1, 3), (3, 3) , lw=2, mutation_scale=20, arrowstyle=\"-|>\", color='gray')\n",
        "ax2.add_patch(vec_a)\n",
        "\n",
        "ax2.plot((0, 2), (0, 0), lw=2, ls='--', color='gray')\n",
        "ax2.plot((2, 2), (0, 1), lw=2, ls='--', color='gray')\n",
        "ax2.plot((2, 3), (1, 1), lw=2, ls='--', color='gray')\n",
        "vec_b = FancyArrowPatch((3, 1), (3, 3) , lw=2, mutation_scale=20, ls='--', arrowstyle=\"-|>\", color='gray')\n",
        "ax2.add_patch(vec_b)\n",
        "\n",
        "ax2.plot(*a, 'o', color='k')\n",
        "ax2.plot(*b, 'o', color='k')\n",
        "ax2.text(-0.2,-0.2, r\"$\\mathbf{a}$\", fontsize=20)\n",
        "ax2.text(3.1, 3.1, r\"$\\mathbf{b}$\", fontsize=20)\n",
        "ax2.set_title(\"L1 거리\", fontsize=20, fontproperties=fontprop)\n",
        "ax2.set_xlim(-1, 4)\n",
        "ax2.set_ylim(-1, 4)\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-4.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-4.pdf\", format='pdf', bbox_inches='tight')\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1080x504 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "msAzJk5dJw5H"
      },
      "source": [
        "## 그림 7-5"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7sclxe84Ju7A",
        "outputId": "69142187-508a-45c1-e257-89f7cb72316b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        }
      },
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True)\n",
        "fig.set_size_inches((15,7))\n",
        "\n",
        "ax1.xaxis.set_tick_params(labelsize=18)\n",
        "ax1.yaxis.set_tick_params(labelsize=18)\n",
        "ax1.set_xlabel(r'$x$', fontsize=25)\n",
        "ax1.set_ylabel(r'$y$', fontsize=25)\n",
        "ax1.grid(False)\n",
        "\n",
        "ax2.xaxis.set_tick_params(labelsize=18)\n",
        "ax2.yaxis.set_tick_params(labelsize=18)\n",
        "ax2.set_xlabel(r'$x$', fontsize=25)\n",
        "ax2.set_ylabel(r'$y$', fontsize=25)\n",
        "ax2.grid(False)\n",
        "\n",
        "l1 = lambda x1, x2 : np.abs(x1) + np.abs(x2)\n",
        "l2 = lambda x1, x2 : np.sqrt(x1**2 + x2**2)\n",
        "\n",
        "x = np.linspace(-1, 1, 100)\n",
        "X1, X2 = np.meshgrid(x, x)\n",
        "\n",
        "L1 = l1(X1,X2)\n",
        "L2 = l2(X1,X2)\n",
        "\n",
        "ax1.contour(X1, X2, L1)\n",
        "ax1.set_title(\"L1 거리 함수\", fontsize=20, fontproperties=fontprop)\n",
        "ax1.axis('equal')\n",
        "\n",
        "ax2.contour(X1, X2, L2)\n",
        "ax2.set_title(\"L2 거리 함수\", fontsize=20, fontproperties=fontprop)\n",
        "ax2.axis('equal')\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-5.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-5.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1080x504 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OHmEql8BJ0Ux"
      },
      "source": [
        "## 그림 7-6"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sxYea5OOJyNw",
        "outputId": "0d4f64bd-5d34-4c2d-dd43-17025e9a09e9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fig = plt.figure(figsize=(16,5))\n",
        "ax1 = fig.add_subplot(1, 3, 1)\n",
        "ax2 = fig.add_subplot(1, 3, 2)\n",
        "ax3 = fig.add_subplot(1, 3, 3)\n",
        "\n",
        "\n",
        "a = np.array([(1, 0.5), (2.5, 0.5)])\n",
        "da = a[1]-a[0]\n",
        "vec_a = FancyArrowPatch(a[0], a[1], lw=1, \n",
        "                        color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax1.add_patch(vec_a)\n",
        "\n",
        "b = np.array([(1, 0.5), (2.2, 1.7)])\n",
        "db = b[1]-b[0]\n",
        "vec_b = FancyArrowPatch(b[0], b[1], lw=1, \n",
        "                        color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax1.add_patch(vec_b)\n",
        "ax1.plot(*a[0], '.', color='k')\n",
        "\n",
        "theta = 180*np.arccos(np.dot(da,db) / (np.linalg.norm(da)*np.linalg.norm(db)))/np.pi\n",
        "e = Arc((1, 0.5), 0.5, 0.5, angle=0, theta1=0, theta2=theta,\n",
        "        color='k',linewidth=1, fill=False, zorder=2)\n",
        "ax1.add_patch(e)\n",
        "ax1.text(1.3, 0.6, r\"$\\theta$\", fontsize=20)\n",
        "ax1.text(2.5, 0.4, r\"$\\mathbf{a}$\", fontsize=20)\n",
        "ax1.text(2.2, 1.7, r\"$\\mathbf{b}$\", fontsize=20)\n",
        "ax1.text(1.3, 0.2, r\"$\\mathbf{a}\\cdot\\mathbf{b}>0$\", fontsize=20)\n",
        "ax1.axis('off')\n",
        "ax1.set_xlim(0.5, 3)\n",
        "ax1.set_ylim(0, 2.5)\n",
        "\n",
        "##################################################################################\n",
        "a = np.array([(1, 0.5), (2.5, 0.5)])\n",
        "da = a[1]-a[0]\n",
        "vec_a = FancyArrowPatch(a[0], a[1], lw=1, \n",
        "                        color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax2.add_patch(vec_a)\n",
        "\n",
        "b = np.array([(1, 0.5), (1, 2.)])\n",
        "db = b[1]-b[0]\n",
        "vec_b = FancyArrowPatch(b[0], b[1], lw=1, \n",
        "                        color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax2.add_patch(vec_b)\n",
        "ax2.plot(*a[0], '.', color='k')\n",
        "\n",
        "theta = 180*np.arccos(np.dot(da,db) / (np.linalg.norm(da)*np.linalg.norm(db)))/np.pi\n",
        "e = Arc((1, 0.5), 0.5, 0.5, angle=0, theta1=0, theta2=theta,\n",
        "        color='k',linewidth=1, fill=False, zorder=2)\n",
        "ax2.add_patch(e)\n",
        "ax2.text(1.2, 0.7, r\"$\\theta$\", fontsize=20)\n",
        "ax2.text(2.5, 0.4, r\"$\\mathbf{a}$\", fontsize=20)\n",
        "ax2.text(1, 2, r\"$\\mathbf{b}$\", fontsize=20)\n",
        "ax2.text(1.3, 0.2, r\"$\\mathbf{a}\\cdot\\mathbf{b}=0$\", fontsize=20)\n",
        "ax2.axis('off')\n",
        "ax2.set_xlim(0.5, 3)\n",
        "ax2.set_ylim(0, 2.5)\n",
        "\n",
        "##################################################################################\n",
        "a = np.array([(1, 0.5), (2.5, 0.5)])\n",
        "da = a[1]-a[0]\n",
        "vec_a = FancyArrowPatch(a[0], a[1], lw=1, \n",
        "                        color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax3.add_patch(vec_a)\n",
        "\n",
        "b = np.array([(1, 0.5), (0.5, 1.7)])\n",
        "db = b[1]-b[0]\n",
        "vec_b = FancyArrowPatch(b[0], b[1], lw=1, \n",
        "                        color='k', mutation_scale=20, arrowstyle=\"-|>\")\n",
        "ax3.add_patch(vec_b)\n",
        "ax3.plot(*a[0], '.', color='k')\n",
        "\n",
        "theta = 180*np.arccos(np.dot(da,db) / (np.linalg.norm(da)*np.linalg.norm(db)))/np.pi\n",
        "e = Arc((1, 0.5), 0.5, 0.5, angle=0, theta1=0, theta2=theta,\n",
        "        color='k',linewidth=1, fill=False, zorder=2)\n",
        "ax3.add_patch(e)\n",
        "ax3.text(1.2, 0.7, r\"$\\theta$\", fontsize=20)\n",
        "ax3.text(2.5, 0.4, r\"$\\mathbf{a}$\", fontsize=20)\n",
        "ax3.text(0.5, 1.7, r\"$\\mathbf{b}$\", fontsize=20)\n",
        "ax3.text(1.3, 0.2, r\"$\\mathbf{a}\\cdot\\mathbf{b}<0$\", fontsize=20)\n",
        "ax3.axis('off')\n",
        "ax3.set_xlim(0.5, 3)\n",
        "ax3.set_ylim(0, 2.5)\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-6.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-6.pdf\", format='pdf', bbox_inches='tight')\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1152x360 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LwuUZVZUJ1cw"
      },
      "source": [
        "def cube2d(ax, origin, dx=1, dy=1, dc=0.1, axis='off', hidden=False):\n",
        "    x0, y0 = origin\n",
        "    \n",
        "    if hidden==False:\n",
        "        ax.plot((x0, x0+dx), (y0, y0), lw=2, color='k')\n",
        "        ax.plot((x0+dx, x0+dx), (y0, y0+dy), lw=2, color='k')\n",
        "        ax.plot((x0+dx, x0), (y0+dy, y0+dy), lw=2, color='k')\n",
        "        ax.plot((x0, x0), (y0+dy, y0), lw=2, color='k')\n",
        "\n",
        "    ax.plot((x0, x0+dc), (y0+dy, y0+dy+dc), lw=2, color='k')\n",
        "    ax.plot((x0+dx, x0+dx+dc), (y0+dy, y0+dy+dc), lw=2, color='k')\n",
        "    ax.plot((x0+dx, x0+dx+dc), (y0, y0+dc), lw=2, color='k')\n",
        "    \n",
        "    ax.plot((x0+dc, x0+dx+dc), (y0+dy+dc, y0+dy+dc), lw=2, color='k')\n",
        "    ax.plot((x0+dc, x0+dx+dc), (y0+dy+dc, y0+dy+dc), lw=2, color='k')\n",
        "    ax.plot((x0+dx+dc, x0+dx+dc), (y0+dy+dc, y0+dc), lw=2, color='k')\n",
        "    \n",
        "    ax.axis(axis)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w454oWbMJ4eB"
      },
      "source": [
        "# 행렬을 이용한 데이터 표현"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1WjIn7flJ5ns"
      },
      "source": [
        "## 그림 7-7"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t1d8AlqTJ3Ag",
        "outputId": "269add62-cdc5-4a20-c3d1-04ab3e812d58",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 411
        }
      },
      "source": [
        "fig = plt.figure(figsize=(7,7))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "    \n",
        "cube2d(ax, (0, 0))\n",
        "cube2d(ax, (0.1, 0.1), hidden=True)\n",
        "cube2d(ax, (0.2, 0.2), hidden=True)\n",
        "\n",
        "width = FancyArrowPatch((0, -0.1), (1, -0.1), lw=2,  mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(width)\n",
        "\n",
        "height = FancyArrowPatch((-0.1, 0), (-0.1, 1), lw=2,  mutation_scale=20, arrowstyle=\"<|-|>\", color='k')\n",
        "ax.add_patch(height)\n",
        "\n",
        "ax.text(0.4, -0.2, \"width\", fontsize=25)\n",
        "ax.text(-0.25, 0.4, \"height\", fontsize=25, rotation=90)\n",
        "\n",
        "ax.text(-0.03, 1.05, \"R\", fontsize=25)\n",
        "ax.text(0.07, 1.15, \"G\", fontsize=25)\n",
        "ax.text(0.17, 1.25, \"B\", fontsize=25)\n",
        "\n",
        "ax.set_xlim(-0.3, 1.4)\n",
        "ax.set_ylim(-0.3, 1.4)\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-7.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-7.pdf\", format='pdf', bbox_inches='tight')\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ADH5eVizJ8ih"
      },
      "source": [
        "## 그림 7-8"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EzIHItxJJ6xg",
        "outputId": "7aae9444-c862-434d-ff3c-795790fb5548",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        }
      },
      "source": [
        "im = plt.imread(\"noviceml/img/old_python.png\")\n",
        "print(im.shape)\n",
        "\n",
        "fig = plt.figure(figsize=(7,7))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "ax.xaxis.set_tick_params(labelsize=18)\n",
        "ax.yaxis.set_tick_params(labelsize=18)\n",
        "\n",
        "ax.imshow(im)\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-8.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-8.pdf\", format='pdf', bbox_inches='tight')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(256, 272, 4)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xMj7w9u7KKQW"
      },
      "source": [
        "## 그림 7-9"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kaeSod38KAzZ"
      },
      "source": [
        "R = im[:,:,0]\n",
        "G = im[:,:,1]\n",
        "B = im[:,:,2]\n",
        "A = im[:,:,3]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hND0K0buKLXI",
        "outputId": "8e602ae2-ab13-4afe-9e16-514cd4d8990f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 233
        }
      },
      "source": [
        "fig = plt.figure(figsize=(15,7))\n",
        "ax1 = fig.add_subplot(1, 4, 1)\n",
        "ax2 = fig.add_subplot(1, 4, 2)\n",
        "ax3 = fig.add_subplot(1, 4, 3)\n",
        "ax4 = fig.add_subplot(1, 4, 4)\n",
        "\n",
        "ax1.imshow(R)\n",
        "ax1.set_title(\"Red\")\n",
        "ax2.imshow(G)\n",
        "ax2.set_title(\"Green\")\n",
        "ax3.imshow(B)\n",
        "ax3.set_title(\"Blue\")\n",
        "ax4.imshow(A)\n",
        "ax4.set_title(\"Alpha\")\n",
        "\n",
        "plt.show()\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-9.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-9.pdf\", format='pdf', bbox_inches='tight')\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1080x504 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JTLkr02HKOCh"
      },
      "source": [
        "## 문서를 행렬로 표현하기"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ofkGR07qKMBo"
      },
      "source": [
        "docs = [\n",
        "'This is the first document',\n",
        "'This is the second document',\n",
        "'And the third one',\n",
        "'Is this the first document']\n",
        "\n",
        "V = ['<NULL>', 'and', 'document', 'first', 'is', 'one', 'second', 'the', 'third', 'this']"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3kxX83oVKQBo",
        "outputId": "02a12feb-cc83-4785-b0c6-f0e9a477ae43",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "pre_docs = list(map(lambda x : x.lower().split(), docs))\n",
        "pre_docs\n",
        "\n",
        "D = [[V.index(w) for w in doc] for doc in pre_docs ]\n",
        "\n",
        "print(D)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[9, 4, 7, 3, 2], [9, 4, 7, 6, 2], [1, 7, 8, 5], [4, 9, 7, 3, 2]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k-lEDnEIKQ0Z"
      },
      "source": [
        "N = max([len(doc) for doc in pre_docs])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Piyr133tKR55",
        "outputId": "69d11dca-8015-4ee6-c52d-66d82ff4fc98",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "N"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CuDWDUpIKSyV",
        "outputId": "5fbed8f5-bed1-49a9-edaa-03cc9e14f16e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "N = max([len(doc) for doc in pre_docs]) #-----[1]\n",
        "pre_docs = [doc + ['<NULL>']*(N-len(doc)) for doc in pre_docs] #-----[2]\n",
        "pre_docs\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[['this', 'is', 'the', 'first', 'document'],\n",
              " ['this', 'is', 'the', 'second', 'document'],\n",
              " ['and', 'the', 'third', 'one', '<NULL>'],\n",
              " ['is', 'this', 'the', 'first', 'document']]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H9kJVcCbKTqJ",
        "outputId": "ef0e529e-de0f-49de-a262-202cb00cec06",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "D = [[V.index(w) for w in doc] for doc in pre_docs ]\n",
        "D = np.array(D)\n",
        "D"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[9, 4, 7, 3, 2],\n",
              "       [9, 4, 7, 6, 2],\n",
              "       [1, 7, 8, 5, 0],\n",
              "       [4, 9, 7, 3, 2]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uJJfOHHBKWIz"
      },
      "source": [
        "# 넘파이"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x0qRGDe5KZp7"
      },
      "source": [
        "## 그림 7-10"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xFi_pvAxKUpB",
        "outputId": "b313159a-1f8a-4d59-800e-0e81b1d9ab09",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fig = plt.figure(figsize=(16,5))\n",
        "\n",
        "np.random.seed(1)\n",
        "\n",
        "ax1 = fig.add_subplot(141, projection='3d')\n",
        "ax2 = fig.add_subplot(142, projection='3d')\n",
        "ax3 = fig.add_subplot(143, projection='3d')\n",
        "ax4 = fig.add_subplot(144, projection='3d')\n",
        "\n",
        "k = 2.3\n",
        "rx, ry = 2, 2\n",
        "\n",
        "###############################################################################################\n",
        "offset_x, offset_y, offset_z = 0, 0, 1.5\n",
        "d = 5\n",
        "i = 0\n",
        "j = 1\n",
        "\n",
        "text3d(ax1, (i*k+offset_x+.6, d+offset_z, j*k+offset_y+.4), \"{}\".format(np.random.randint(10)), \n",
        "       zdir=\"y\", size=1.5, usetex=True, ec=\"k\", fc=\"#FFFFFF\")\n",
        "bottom, left = i*k+offset_x, j*k+offset_y\n",
        "rect = Rectangle((bottom, left), rx, ry, alpha=.8, facecolor='gray', edgecolor='k')\n",
        "ax1.add_patch(rect)\n",
        "art3d.pathpatch_2d_to_3d(rect, z=d+offset_z, zdir='y')\n",
        "            \n",
        "ax1.set_xlim(0, 7)\n",
        "ax1.set_ylim(0, 7)\n",
        "ax1.set_zlim(0, 7)\n",
        "ax1.view_init(20, -50)\n",
        "ax1.set_title(\"0D tensor: scalar\", fontsize=18)\n",
        "ax1.axis('off')\n",
        "###############################################################################################\n",
        "\n",
        "###############################################################################################\n",
        "offset_x, offset_y, offset_z = 0, 0, 1.5\n",
        "d = 5\n",
        "i = 0\n",
        "\n",
        "for j in range(3):\n",
        "    text3d(ax2, (i*k+offset_x+.6, d+offset_z, j*k+offset_y+.4), \"{}\".format(np.random.randint(10)), \n",
        "           zdir=\"y\", size=1.5, usetex=True, ec=\"k\", fc=\"#FFFFFF\")\n",
        "    bottom, left = i*k+offset_x, j*k+offset_y\n",
        "    rect = Rectangle((bottom, left), rx, ry, alpha=.8, facecolor='gray', edgecolor='k')\n",
        "    ax2.add_patch(rect)\n",
        "    art3d.pathpatch_2d_to_3d(rect, z=d+offset_z, zdir='y')\n",
        "            \n",
        "ax2.set_xlim(0, 7)\n",
        "ax2.set_ylim(0, 7)\n",
        "ax2.set_zlim(0, 7)\n",
        "ax2.view_init(20, -50)\n",
        "ax2.set_title(\"1D tensor: vector\", fontsize=18)\n",
        "ax2.axis('off')\n",
        "###############################################################################################\n",
        "\n",
        "###############################################################################################\n",
        "offset_x, offset_y, offset_z = -1, 0, 1.5\n",
        "d = 3\n",
        "\n",
        "for i in range(3):\n",
        "    for j in range(3):\n",
        "        text3d(ax3, (i*k+offset_x+.6, d+offset_z, j*k+offset_y+.4), \"{}\".format(np.random.randint(10)), \n",
        "               zdir=\"y\", size=1.5, usetex=True, ec=\"k\", fc=\"#FFFFFF\")\n",
        "        bottom, left = i*k+offset_x, j*k+offset_y\n",
        "        rect = Rectangle((bottom, left), rx, ry, alpha=.8, facecolor='gray', edgecolor='k')\n",
        "        ax3.add_patch(rect)\n",
        "        art3d.pathpatch_2d_to_3d(rect, z=d+offset_z, zdir='y')\n",
        "            \n",
        "ax3.set_xlim(0, 7)\n",
        "ax3.set_ylim(0, 7)\n",
        "ax3.set_zlim(0, 7)\n",
        "ax3.view_init(20, -50)\n",
        "ax3.set_title(\"2D tensor: matrix\", fontsize=18)\n",
        "ax3.axis('off')\n",
        "###############################################################################################\n",
        "\n",
        "###############################################################################################\n",
        "offset_x, offset_y, offset_z = 0, 0, 1.5\n",
        "\n",
        "for d in range(0, 5, 2):\n",
        "    for i in range(3):\n",
        "        for j in range(3):\n",
        "            # print(d)\n",
        "            text3d(ax4, (i*k+offset_x+.6, d+offset_z, j*k+offset_y+.4), \"{}\".format(np.random.randint(10)), \n",
        "                   zdir=\"y\", size=1.5, usetex=True, ec=\"k\", fc=\"#FFFFFF\")\n",
        "            bottom, left = i*k+offset_x, j*k+offset_y\n",
        "            rect = Rectangle((bottom, left), rx, ry, alpha=.8, facecolor='gray', edgecolor='k')\n",
        "            ax4.add_patch(rect)\n",
        "            art3d.pathpatch_2d_to_3d(rect, z=d+offset_z, zdir='y')\n",
        "            \n",
        "ax4.set_xlim(0, 7)\n",
        "ax4.set_ylim(0, 7)\n",
        "ax4.set_zlim(0, 7)\n",
        "ax4.view_init(20, -50)\n",
        "ax4.set_title(\"3D tensor\", fontsize=18)\n",
        "ax4.axis('off')\n",
        "###############################################################################################\n",
        "\n",
        "\n",
        "plt.subplots_adjust(hspace=0.05, wspace=0.0)\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-10.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-10.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1152x360 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v5hvVXggLIG1"
      },
      "source": [
        "## 넘파이 어레이ndarray"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9AzzrKwSKdqr",
        "outputId": "22381320-7b95-489c-e8ad-aa3c9db8fb3a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A = np.array([1,2,3,4])\n",
        "A\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ndLOUiZvLJhK",
        "outputId": "c08972f2-17a4-444c-ac31-945d4b5b49f4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "B = np.array([[1,2],[3,4]])\n",
        "B\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [3, 4]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aU11StytLKPJ",
        "outputId": "b326aaaa-30ef-4f27-c2cd-870160964ffc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(4,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A7TLntLrLLC6",
        "outputId": "cf76611a-f75a-44ed-db68-6f20e3dc26b0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "B.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-5WrsXV_LL3p",
        "outputId": "d302c8e0-634c-4d46-d8b4-89c91be510e4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A.reshape(1,4)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3, 4]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HHmrtXr_LM_x",
        "outputId": "321f0c41-7a8e-418c-f111-e62d1b6952e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A.reshape(1,4).shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 4)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BCN5IRbwLOCx",
        "outputId": "72552601-af29-49b8-c5cf-08bab005cf97",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "A.reshape(4,1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1],\n",
              "       [2],\n",
              "       [3],\n",
              "       [4]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aPzSyXPpLO9Z",
        "outputId": "9c9d2a9f-1717-4b56-875d-57d84792c2b9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A.reshape(4,1).shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(4, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QgwZRL9VLP0p",
        "outputId": "c0729372-afed-41f2-a80a-607221ca7b36",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "np.random.rand(3,2) # 0에서 1사이의 무작위 소수로 채워진 3행 2열 ndarray 생성"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.9579, 0.5332],\n",
              "       [0.6919, 0.3155],\n",
              "       [0.6865, 0.8346]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GFcIbvDZLRKp",
        "outputId": "fdf3b1f4-4641-4246-e05e-732c7f454001",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "np.ones((3,2)) # 모두 1로 채워진 3행 2열 ndarray 생성"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 1.],\n",
              "       [1., 1.],\n",
              "       [1., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IE0N01oWLSMJ",
        "outputId": "72ecc2cb-a156-470d-cedd-b215a158cadc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.ones_like(A) # A라는 ndarray와 모양은 같고 모두 1로 채워진 ndarray 생성"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 1, 1, 1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SCScxbKILTPB",
        "outputId": "0464c3b9-6d4b-4855-9349-bb473877c838",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "np.zeros((3,2)) # 모두 0으로 채워진 3행 2열 ndarray 생성"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0.],\n",
              "       [0., 0.],\n",
              "       [0., 0.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "epMufx52LUTB",
        "outputId": "f7849b21-a463-45ed-8529-9c91550a2f16",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.zeros_like(A) # A라는 ndarray와 모양은 같고 모두 0으로 채워진 ndarray 생성"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 0, 0])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dMGsQjoqLVH5",
        "outputId": "cbd32c0b-3347-4b14-bcf9-378fa287ecdb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "np.full((3,2), 10) # 모두 10으로 채워진 3행 2열 ndarray 생성"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[10, 10],\n",
              "       [10, 10],\n",
              "       [10, 10]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-9xECmeaLWap",
        "outputId": "9d5e3f6e-89dd-49dc-ab2f-7d40e9d3f5d6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.arange(10) # 0부터 9까지 순차적인 자연수로 ndarray를 생성"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9YTJ3iwDLYo-"
      },
      "source": [
        "## 넘파이 어레이 연산"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GPUNFGZqLXd5"
      },
      "source": [
        "np.random.seed(12)\n",
        "\n",
        "A = np.random.randint(0,9,4).reshape(2,2)\n",
        "B = np.random.randint(0,9,4).reshape(2,2)+1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OtgN5PWJLaK5",
        "outputId": "8ded7bc1-b290-4d0e-c6fc-ecbace808766",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[6, 1],\n",
              "       [2, 3]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OAiCTi1DLa-X",
        "outputId": "57abae44-bec7-448e-f99f-336eb9f48645",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4, 1],\n",
              "       [7, 2]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lNF1fvv_LcMB",
        "outputId": "2aa45291-3a08-4464-d63c-3b6e3460403e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A+B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[10,  2],\n",
              "       [ 9,  5]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TfsA1MNVLdvy",
        "outputId": "371f357c-605d-402f-970f-582877ff8297",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A-B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2,  0],\n",
              "       [-5,  1]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Iy8VYMELeuh",
        "outputId": "55181827-f535-464b-bf53-ff30a4f2bfa0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A/B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.5   , 1.    ],\n",
              "       [0.2857, 1.5   ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pcBVrcoZLfnZ",
        "outputId": "6b6efc69-5451-43a3-cca5-a4f425aa0cfd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A*B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[24,  1],\n",
              "       [14,  6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4zyGN1p8Lgmx",
        "outputId": "39491693-f955-49ee-86b0-cc290120091e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "np.dot(A,B)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[31,  8],\n",
              "       [29,  8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Td58RvlGLhdB"
      },
      "source": [
        "def cube2d2(ax, origin, dx=1, dy=1, dc=0.1, label='', fc=10, la=1.0, \n",
        "            hidden=(None,), **kwargs):\n",
        "    x0, y0 = origin\n",
        "    \n",
        "    if 'F' not in hidden : # hidden !='F':\n",
        "        ax.plot((x0, x0+dx), (y0, y0), **kwargs)                   # F,아래쪽\n",
        "        if 'L' not in hidden : #hidden!='L':\n",
        "            ax.plot((x0, x0), (y0+dy, y0), **kwargs)               # F, 왼쪽\n",
        "        if 'U' not in hidden : #hidden!='U':\n",
        "            ax.plot((x0+dx, x0), (y0+dy, y0+dy), **kwargs)         # F, 위쪽\n",
        "        if 'R' not in hidden :# hidden!='R':\n",
        "            ax.plot((x0+dx, x0+dx), (y0, y0+dy), **kwargs)         # F, 오른쪽\n",
        "    \n",
        "    if 'U' not in hidden : # hidden!='U':\n",
        "        ax.plot((x0+dc, x0+dx+dc), (y0+dy+dc, y0+dy+dc), **kwargs)     # U, 위쪽\n",
        "        if 'L' not in hidden : # hidden!='L':\n",
        "            ax.plot((x0, x0+dc), (y0+dy, y0+dy+dc), **kwargs)          # U, 왼쪽\n",
        "        if 'R' not in hidden : # hidden!='R':\n",
        "            ax.plot((x0+dx, x0+dx+dc), (y0+dy, y0+dy+dc), **kwargs)    # U, 오른쪽\n",
        "    \n",
        "    if 'R+' not in hidden and 'R' not in hidden : # hidden!='R':\n",
        "        ax.plot((x0+dx, x0+dx+dc), (y0, y0+dc), **kwargs)          # R, 아래쪽\n",
        "        ax.plot((x0+dx+dc, x0+dx+dc), (y0+dy+dc, y0+dc), **kwargs) # R, 오른쪽\n",
        "    \n",
        "    ax.text(x0 + 0.5 * dx, y0 + 0.5 * dy, label,\n",
        "            ha='center', va='center', fontsize=fc, alpha=la)\n",
        "    \n",
        "box_solid  = dict(c='k', lw=2, alpha=1.0,)\n",
        "box_gray   = dict(c='k', lw=2, alpha=0.2,)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1FWuS9OFLkUS"
      },
      "source": [
        "## 그림 7-11"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AZHbbn1TLi0R",
        "outputId": "c111a07f-7308-4f12-a794-59eacff3b6f4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fig = plt.figure(figsize=(16,5))\n",
        "\n",
        "np.random.seed(1)\n",
        "\n",
        "ax1 = fig.add_subplot(141, projection='3d')\n",
        "ax2 = fig.add_subplot(142, projection='3d')\n",
        "ax3 = fig.add_subplot(143, projection='3d')\n",
        "\n",
        "k = 2.3\n",
        "rx, ry = 2, 2\n",
        "axis_length = 8\n",
        "\n",
        "###############################################################################################\n",
        "offset_x, offset_y, offset_z = -3, -2, 1.5\n",
        "d = 5\n",
        "i = 0\n",
        "j = 2\n",
        "for i in range(3):\n",
        "    text3d(ax1, (i*k+offset_x+.6, d+offset_z, j*k+offset_y+.4), \"{}\".format(np.random.randint(10)), \n",
        "           zdir=\"y\", size=1.5, usetex=True, ec=\"k\", fc=\"#FFFFFF\")\n",
        "    bottom, left = i*k+offset_x, j*k+offset_y\n",
        "    rect = Rectangle((bottom, left), rx, ry, alpha=.8, facecolor='gray', edgecolor='k')\n",
        "    ax1.add_patch(rect)\n",
        "    art3d.pathpatch_2d_to_3d(rect, z=d+offset_z, zdir='y')\n",
        "\n",
        "axis0 = Arrow3D([offset_x-0.5, offset_x-0.5+axis_length], [d+offset_z, d+offset_z], [d, d], \n",
        "                mutation_scale=20, lw=1, arrowstyle=\"-|>\", color=\"k\")\n",
        "ax1.add_artist(axis0)\n",
        "\n",
        "ax1.text(offset_x-1+axis_length/2, d+offset_z, d+0.3, \"0\", fontsize=15)\n",
        "\n",
        "ax1.set_xlim(0, 7)\n",
        "ax1.set_ylim(0, 7)\n",
        "ax1.set_zlim(0, 7)\n",
        "ax1.set_xlabel('x')\n",
        "ax1.view_init(20, -50)\n",
        "# ax1.view_init(0, -90)\n",
        "ax1.set_title(\"1D tensor: vector\", fontsize=18)\n",
        "ax1.axis('off')\n",
        "###############################################################################################\n",
        "\n",
        "###############################################################################################\n",
        "offset_x, offset_y, offset_z = -1, 0, 1.5\n",
        "d = 3\n",
        "for i in range(3):\n",
        "    for j in range(3):\n",
        "        text3d(ax2, (i*k+offset_x+.6, d+offset_z, j*k+offset_y+.4), \"{}\".format(np.random.randint(10)), \n",
        "               zdir=\"y\", size=1.5, usetex=True, ec=\"k\", fc=\"#FFFFFF\")\n",
        "        bottom, left = i*k+offset_x, j*k+offset_y\n",
        "        rect = Rectangle((bottom, left), rx, ry, alpha=.8, facecolor='gray', edgecolor='k')\n",
        "        ax2.add_patch(rect)\n",
        "        art3d.pathpatch_2d_to_3d(rect, z=d+offset_z, zdir='y')\n",
        "\n",
        "axis0 = Arrow3D([offset_x-0.5, offset_x-0.5], [left, left], [d+axis_length/2, d-axis_length/2], \n",
        "                mutation_scale=20, lw=1, arrowstyle=\"-|>\", color=\"k\")\n",
        "ax2.add_artist(axis0)\n",
        "ax2.text(offset_x-2, left, d, \"0\", fontsize=15)\n",
        "\n",
        "axis1 = Arrow3D([offset_x-0.5, offset_x-0.5+axis_length], [left, left], [d+axis_length/2, d+axis_length/2], \n",
        "                mutation_scale=20, lw=1, arrowstyle=\"-|>\", color=\"k\")\n",
        "ax2.add_artist(axis1)\n",
        "ax2.text(offset_x-1+axis_length/2, left, d+axis_length/2+0.3, \"1\", fontsize=15)\n",
        "\n",
        "\n",
        "ax2.set_xlim(0, 7)\n",
        "ax2.set_ylim(0, 7)\n",
        "ax2.set_zlim(0, 7)\n",
        "ax2.view_init(20, -50)\n",
        "# ax2.view_init(0, -90)\n",
        "ax2.set_title(\"2D tensor: matrix\", fontsize=18)\n",
        "ax2.axis('off')\n",
        "###############################################################################################\n",
        "\n",
        "###############################################################################################\n",
        "offset_x, offset_y, offset_z = 0, 0, 1.5\n",
        "\n",
        "for d in range(0, 5, 2):\n",
        "    for i in range(3):\n",
        "        for j in range(3):\n",
        "            text3d(ax3, (i*k+offset_x+.6, d+offset_z, j*k+offset_y+.4), \"{}\".format(np.random.randint(10)), \n",
        "                   zdir=\"y\", size=1.5, usetex=True, ec=\"k\", fc=\"#FFFFFF\")\n",
        "            bottom, left = i*k+offset_x, j*k+offset_y\n",
        "            rect = Rectangle((bottom, left), rx, ry, alpha=.8, facecolor='gray', edgecolor='k')\n",
        "            ax3.add_patch(rect)\n",
        "            art3d.pathpatch_2d_to_3d(rect, z=d+offset_z, zdir='y')\n",
        "\n",
        "\n",
        "axis0 = Arrow3D([offset_x-0.5, offset_x-0.5], [0+offset_z, 0+offset_z+5], [3+axis_length/2, 3+axis_length/2], \n",
        "                mutation_scale=20, lw=1, arrowstyle=\"-|>\", color=\"k\", zorder=10)\n",
        "ax3.add_artist(axis0)\n",
        "ax3.text(offset_x, offset_z+1, 3.8+axis_length/2, \"0\", fontsize=15)\n",
        "\n",
        "axis1 = Arrow3D([offset_x-0.5, offset_x-0.5], [0+offset_z, 0+offset_z], [3+axis_length/2, 3-axis_length/2], \n",
        "                mutation_scale=20, lw=1, arrowstyle=\"-|>\", color=\"k\", zorder=10)\n",
        "ax3.add_artist(axis1)\n",
        "ax3.text(offset_x-0.5, 0, 3.5, \"1\", fontsize=15)\n",
        "\n",
        "axis2 = Arrow3D([offset_x, offset_x+axis_length], [0+offset_z, 0+offset_z], [0-0.5, 0-0.5], \n",
        "                mutation_scale=20, lw=1, arrowstyle=\"-|>\", color=\"k\", zorder=10)\n",
        "ax3.add_artist(axis2)\n",
        "ax3.text(offset_x+0.5+axis_length/2, -1, 0, \"2\", fontsize=15)\n",
        "\n",
        "ax3.set_xlim(0, 7)\n",
        "ax3.set_ylim(0, 7)\n",
        "ax3.set_zlim(0, 7)\n",
        "ax3.view_init(20, -50)\n",
        "# ax3.view_init(0, 0)\n",
        "ax3.set_title(\"3D tensor\", fontsize=18)\n",
        "ax3.axis('off')\n",
        "###############################################################################################\n",
        "\n",
        "plt.subplots_adjust(hspace=0.05, wspace=0.0)\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-11.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-11.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1152x360 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kp-rZV2bLno5"
      },
      "source": [
        "### 축 순서 바꾸기"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1vRirQE-Llc2",
        "outputId": "90afa503-f607-4062-ea57-0cc6f453cb29",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "A = np.arange(1, 7).reshape(2, 3) \n",
        "A\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "upIFlRAkLp-D",
        "outputId": "281f980d-e1c0-4b77-e5a6-97d5bfaaebfe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "A.transpose(1, 0) "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 4],\n",
              "       [2, 5],\n",
              "       [3, 6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3qT-OEiaLqup",
        "outputId": "7ecfde0a-f585-4b46-ce2d-f3b7087b0d63",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A = np.arange(1, 13).reshape(2, 2, -1)\n",
        "A"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 1,  2,  3],\n",
              "        [ 4,  5,  6]],\n",
              "\n",
              "       [[ 7,  8,  9],\n",
              "        [10, 11, 12]]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1-nEfwcfLrhy",
        "outputId": "3b5d070e-6fd9-48b2-cf20-ae81df24ce54",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        }
      },
      "source": [
        "A.T"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 1,  7],\n",
              "        [ 4, 10]],\n",
              "\n",
              "       [[ 2,  8],\n",
              "        [ 5, 11]],\n",
              "\n",
              "       [[ 3,  9],\n",
              "        [ 6, 12]]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nAwA0uNTLshx",
        "outputId": "369da2c7-82a3-40e1-faf8-2d07e947a2f4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A = np.arange(1, 13).reshape(2, 2, -1)\n",
        "A.transpose(1,0,2)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 1,  2,  3],\n",
              "        [ 7,  8,  9]],\n",
              "\n",
              "       [[ 4,  5,  6],\n",
              "        [10, 11, 12]]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "luhl6E_RLvaF"
      },
      "source": [
        "## 인덱싱"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gppUdnfSLt3Z",
        "outputId": "faee0f78-01b7-429f-92a4-0fe73a083fad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A = np.arange(30).reshape(5,6)\n",
        "A\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3,  4,  5],\n",
              "       [ 6,  7,  8,  9, 10, 11],\n",
              "       [12, 13, 14, 15, 16, 17],\n",
              "       [18, 19, 20, 21, 22, 23],\n",
              "       [24, 25, 26, 27, 28, 29]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JTlcQQV1LwnS",
        "outputId": "4e23f69f-7dd6-4650-91a4-56e2ac3f5057",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A[0,2]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DV8_8iSbLxYB",
        "outputId": "1d62836f-27c7-45d7-83e4-d5fa162164f5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A[2,3]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "15"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "odPr5Nw-LyYJ",
        "outputId": "041dd421-f1f6-42fd-ca50-9a6d30c40a6e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A[:, 0::2]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  2,  4],\n",
              "       [ 6,  8, 10],\n",
              "       [12, 14, 16],\n",
              "       [18, 20, 22],\n",
              "       [24, 26, 28]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AkvRlns-LzUx",
        "outputId": "a9628872-caa2-48d1-eb13-0a2b7fcf8484",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.array([A[0,1], A[1,2], A[2,3], A[3,1], A[4,0]])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  8, 15, 19, 24])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QytnFdm_L0GM",
        "outputId": "8f883451-e850-4559-9d22-766a78714247",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A[[0,1,2,3,4], [1,2,3,1,0]] # A[np.arange(4), [1,2,3,1,0]]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  8, 15, 19, 24])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0-gUjZNNL04Z",
        "outputId": "e5a83383-700f-48b9-a432-ac99bcbfa92f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A > 20"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[False, False, False, False, False, False],\n",
              "       [False, False, False, False, False, False],\n",
              "       [False, False, False, False, False, False],\n",
              "       [False, False, False,  True,  True,  True],\n",
              "       [ True,  True,  True,  True,  True,  True]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pqdJ-voQL15Z",
        "outputId": "7543aca7-b2cd-447e-b8f4-6007592cb58b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A[A > 20]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([21, 22, 23, 24, 25, 26, 27, 28, 29])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8ZSO_NQrL4Zt"
      },
      "source": [
        "## 브로드캐스팅"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DTneFH5DL2sy",
        "outputId": "faa76ba2-6972-400b-aa2a-7ea8a7775a2b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A = np.array([1,2,3])\n",
        "A * 2\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 4, 6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o3yu5rKZL7EC"
      },
      "source": [
        "## 그림 7-12"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PPtpawldL5up",
        "outputId": "e4215577-d8f3-48ba-fc4f-29966842b6c4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        }
      },
      "source": [
        "fig = plt.figure(figsize=(12,4))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "cube2d2(ax, (0,0),   0.1, 0.1, 0.05, '1', 40, 1.0, hidden=('R',), **box_solid)\n",
        "cube2d2(ax, (0.1,0), 0.1, 0.1, 0.05, '2', 40, 1.0, hidden=('R',), **box_solid)\n",
        "cube2d2(ax, (0.2,0), 0.1, 0.1, 0.05, '3', 40, 1.0, hidden=(None,), **box_solid)\n",
        "\n",
        "ax.text(.42, .08, r'$\\times$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "b_pos = 0.5\n",
        "cube2d2(ax, (0+b_pos,0),   0.1, 0.1, 0.05, '2', 40, 1.0, hidden=('R',), **box_gray)\n",
        "cube2d2(ax, (0.1+b_pos,0), 0.1, 0.1, 0.05, '2', 40, 0.2, hidden=('R',), **box_gray)\n",
        "cube2d2(ax, (0.2+b_pos,0), 0.1, 0.1, 0.05, '2', 40, 0.2, **box_gray)\n",
        "\n",
        "ax.text(.92, .08, '=', ha='center', va='center', fontsize=30)\n",
        "\n",
        "cube2d2(ax, (0+b_pos*2,0),   0.1, 0.1, 0.05, '2', 40, 1.0, hidden=('R',), **box_solid)\n",
        "cube2d2(ax, (0.1+b_pos*2,0), 0.1, 0.1, 0.05, '4', 40, 1.0, hidden=('R',), **box_solid)\n",
        "cube2d2(ax, (0.2+b_pos*2,0), 0.1, 0.1, 0.05, '6', 40, 1.0, **box_solid)\n",
        "\n",
        "ax.axis('off')\n",
        "ax.axis('equal')\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-12.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-12.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k1H0bp-nMA1F"
      },
      "source": [
        "np.random.seed(2)\n",
        "\n",
        "m, n = 4, 3\n",
        "A = np.random.randint(0, 10, m*n).reshape(m,n)\n",
        "b = np.random.randint(0, 10, n)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cbClEC2-L8UR",
        "outputId": "3a9af4d9-a752-4ba8-c4cb-e97add534dc6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "A"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[8, 8, 6],\n",
              "       [2, 8, 7],\n",
              "       [2, 1, 5],\n",
              "       [4, 4, 5]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QTS4GJ4lMClB",
        "outputId": "93ba4078-050a-4c53-8216-60039bc37449",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([7, 3, 6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3TW49JlgMDSh",
        "outputId": "528ef16e-9457-4b5c-df38-efd35be20158",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "A*b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[56, 24, 36],\n",
              "       [14, 24, 42],\n",
              "       [14,  3, 30],\n",
              "       [28, 12, 30]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UflJ6MKaMFct"
      },
      "source": [
        "## 그림 7-13"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r0JVyAh7MEJ5",
        "outputId": "b23604d5-01a6-43af-ce3a-486a4fddf8ba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fig = plt.figure(figsize=(16,5))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "dy = 0.1\n",
        "dx = 0.0\n",
        "for j in range(m) :\n",
        "    for i in range(n):\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('R', 'U'), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :    \n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('U',), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=(None,), **box_solid)    \n",
        "\n",
        "ax.text(.43, .22, r'$\\times$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "dx = 0.5        \n",
        "for j in range(m) :\n",
        "    for i in range(n):\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 0.2, hidden=('R', 'U'), **box_gray)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 0.2, hidden=('U',), **box_gray)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 1.0, hidden=(None,), **box_solid) \n",
        "\n",
        "ax.text(.93, .22, r'$=$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "C = A*b\n",
        "dx = 1.0       \n",
        "for j in range(m) :\n",
        "    for i in range(n):\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('R', 'U'), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :    \n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('U',), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=(None,), **box_solid)  \n",
        "                \n",
        "ax.axis('off')\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-13.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-13.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1152x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "40zyKmbdMGqh"
      },
      "source": [
        "np.random.seed(3)\n",
        "\n",
        "m, n = 4, 3\n",
        "b = np.random.randint(0, 10, n+1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YKuQAQA9MJgZ",
        "outputId": "f40371d7-5944-4656-e382-984449f6420e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([8, 9, 3, 8])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iAbk4GJoMLzL"
      },
      "source": [
        "## 그림 7-14"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m0Gk8aSBMKdZ",
        "outputId": "078dfe45-0fa9-4eac-84c7-2fbe77bc7b28",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fig = plt.figure(figsize=(12,5))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "dy = 0.1\n",
        "dx = 0.0\n",
        "for j in range(m) :\n",
        "    for i in range(n):\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('R', 'U'), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :    \n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('U',), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=(None,), **box_solid)    \n",
        "\n",
        "ax.text(.43, .22, r'$\\times$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "dx = 0.5        \n",
        "for j in range(m) :\n",
        "    for i in range(n+1):\n",
        "        if i < n+1-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 0.2, hidden=('R', 'U'), **box_gray)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 0.2, hidden=('U',), **box_gray)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 1.0, hidden=(None,), **box_solid) \n",
        "\n",
        "ax.axis('off')                \n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-14.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-14.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uUKLpOYgMP9h",
        "outputId": "ce9ec78c-d53f-4218-af14-cd9d60a2515c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "C = A * b[:, np.newaxis] #-----[1]\n",
        "C\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[64, 64, 48],\n",
              "       [18, 72, 63],\n",
              "       [ 6,  3, 15],\n",
              "       [32, 32, 40]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RGwPXbBiMSuA"
      },
      "source": [
        "## 그림 7-15"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "swIF7qo4MRna",
        "outputId": "0aefebe2-b59b-49ad-8ad8-53db01ee4ba0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fig = plt.figure(figsize=(16,5))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "dy = 0.1\n",
        "dx = 0.0\n",
        "for j in range(m) :\n",
        "    for i in range(n) :\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('R', 'U'), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :    \n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=('U',), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, A[::-1,:][j,i], 40, 1.0, hidden=(None,), **box_solid)    \n",
        "\n",
        "ax.text(.43, .22, r'$\\times$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "dx = 0.5        \n",
        "for j in range(m) :\n",
        "    for i in range(n) :\n",
        "        if i == 0 :\n",
        "            style = box_solid\n",
        "            la = 1.0\n",
        "        else :\n",
        "            style = box_gray\n",
        "            la = 0.2\n",
        "        \n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                if i == 0 :\n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[::-1][j], 40, la, hidden=('R+', 'U'), **style)\n",
        "                else :\n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[::-1][j], 40, la, hidden=('R', 'U'), **style)\n",
        "            else :\n",
        "                if i == 0 : \n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[::-1][j], 40, la, hidden=('R+',), **style)\n",
        "                else :\n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[::-1][j], 40, la, hidden=('R',), **style)\n",
        "        else :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[::-1][j], 40, la, hidden=('U',), **style)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[::-1][j], 40, la, hidden=(None,), **style) \n",
        "\n",
        "ax.text(.93, .22, r'$=$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "C = A * b.reshape(-1,1)  \n",
        "dx = 1.0       \n",
        "for j in range(m) :\n",
        "    for i in range(n):\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('R', 'U'), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :    \n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('U',), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=(None,), **box_solid)    \n",
        "\n",
        "ax.axis('off')\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-15.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-15.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4sAAAEeCAYAAAAjJ4C6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOydd7gkVdGH37OB3SWzRIlLLBAJCp+BICCSkSgSFEQQQREVVBQVCYqKghFRREFUkiRJInwqKAKKCfkIFiwLu+S85IVdON8fdYbpmTv33rn3Tk/PdNf7PDx093b31Jk73ef86tSpCjFGHMdxHMdxHMdxHCfLuKINcBzHcRzHcRzHcXoPF4uO4ziO4ziO4zjOAFwsOo7jOI7jOI7jOANwseg4juM4juM4juMMwMWi4ziO4ziO4ziOMwAXi47jOI7jOI7jOM4AXCw6juM4juM4juM4A3Cx6DiO4ziO4ziO4wzAxaLjOI7jOI7jOI4zABeLjuM4juM4juM4zgBcLDqO4ziO4ziO4zgDcLHoOI7jOI7jOI7jDMDFouM4juM4juM4jjMAF4uO4ziO4ziO4zjOAFwsOo7jOI7jOI7jOANwseg4juM4juM4juMMwMWi4ziO4ziO4ziOM4AJRRvQb4QQJgP/AdYo2hbH6SAvAAvHGF8r2hCns4QQ/gxsWrQdBfBP4OCijegC44G1geeBGQXb0g0CsA7wRIzx8qKNcTpLCCFgY6x1irbFcTrIi8CKMcYnizZkNPjM4ggIISwC/A4Xik75WABYumgjnM4SQtgCeEfRdhTEkkUb0AUmACsBiwELF2xLNxgHrAgsm/5zSkQIYTxwCi4UnfIxP7Bx0UaMlhBjLNqGviCEsDQmFNcHHga2jjHeVqxV+RFCWAi4GHg38CywU4zxT8ValR8hhInAGcAHgLnAB2KMvy7WqvxI3tuvA5+rHYsxhuIscjpNCGE34FxgPuA84IMxxleKtSo/QghbAxcBCwJ/BbaLMc4u1qr8SFEuq2N/35eAu2OMc4u1Kj/SO3p1YAqwGjArxnhTsVY5nSKEMAn4BfA+4GVg7xjjJcValR8hhHHAycCngAh8PMZ4arFW5UsI4dPASWn368AXY4lFSAhhb+AsYGI6NDHGOK9Ak0aNh6G2QQhhFeAaYFXgbkwo3leoUTkSQlgS+C2wIfAosG2M8ZZircqPEMICwAXAdlg45i4xxt8Xa1V+hBAmAKcBBwDz8PdA6QghfAT4ETYTcwrwyTKHGKdO+UxgEubU2y3G+FKxVuVHemethj27zwPTY4yvFmtVfjQJ4znAfdi7yykByTl9CbAl1XBOz4c5p99PdZzTJwKfTYcOjzF+t0CTcieE8Ange9lj/SoUwcNQhyWEsD5wIyYU/wlsUnKhuBLwF0wozgA2LrlQnAr8HhOKTwBblFwoTsFmXw7AZiN2KtYip5ME40uYM2AccDTwiZILxY8Dv8SE4tnAjiUXiotgSyEmAM9gM4plForzA4IJxRcAxYViaUjO6WsxofgosFnJheICwKWYUHwB2L7kQnECJow/iz23HyizUEx98FeoC8Uji7SnU7hYHIIQwmbAn7C1XH/AhMRjxVqVHyGEtTFhvAa2wHyTGOM9xVqVHyGE5YHrgbcDs7D2/r1Yq/IjhLAocDUmEJ8GtowxXlWsVU6nSGFN3wO+goU1HRJj/GrJw3yOB36AJXn5DrBvyYXTVMxxOQ54Erin5I6AhTGhOAGbcbqrn73zTiMhhGmYc3oDquGcXhwbS26LOac3r4Bz+mJgfyzBy04xxrMLNSpH0prbHwNfAl4FDogxfqtYqzqDh58NQghhF2ydzyQsRHHfGOPLxVqVHyGEjYArsEQJf8Ye6meKtSo/QghrYqHFKwC3A9vEGB8s1qr8CCG8AQvPWxd4EGvv7cVa5XSKFNZ0FrAX8AqwT4zxomKtyo8kjE/Fsp1GbO3L14u1Kl9CCEth7yuAR8r8vgIIISwGrIxlP30KuK/Mjo+qEUJYB+uTlsWc09vGGB8p1qr8CCGsgDlr1wJmYsuZ7irWqvxIz+9lwCbY87tDjPGvxVqVHylU/mxgNyxUfs8Y42XFWtU5XCy2IIRwIPATzHv7I+Cwknurd8AE8RTgN9jC8jnFWpUfIYS3YmsyF8dmUt8TY3yqWKvyI4SwOiaMp2EhXFvHGGcVapTTMUIIC2KhxVsDzwE7xxivLdaq/EiJTs4FdsfCmg6JMf6sWKvyJYSwHLBM2n0gxvhokfbkTQpNXDHtPhZjvL9Ie5zOEkLYGHNOL0o1nNNrYX3w8lTDOb0s5ghYB3gAa+8dxVqVHykC4lJgc2xpwHtijNcXalSH8TDUDCnW+PPAT7Hv5jjg0JILxf2wH/kU4GfAHiUXilsDf8SE4pXAViUXim/BwnymAX/HQm1dKJaEEMISWFjT1sDjWFhTmYXiAph3fndsze0eZRaKqU9aCROKEZtdK7tQXJa6UHzQhWK5CCHsiOUJWBRzTm9TcqH4NqwPXh5zTr+z5EJxdeAGTCj+FwstLrNQXBq4DhOKD2N/31IJRXCx+DqZNMZfxzrlQ2OMx5Y57CWEcAQWujYea/dBZV4PEkLYC/NmLoCl6N41xvhisVblR6qxdx2wFObVfFeM8YlCjXI6RghhRWwQ8lYsO+TGMcZ/FWpUjqT1Pn8GtgBmY2FrvynWqvxIfdIqwBLAa9j6xL4s6NwOSRivCLwhHZpZ5rDEKpKc078BJmNO+bI7p7fBnNNTqY5z+gbMOX0zsGmZndOpUsINwJuB6VgffGuxVuWDi0VeD2s6CzgcS2O8V5nr3aRO+URMHIOlMf5CyYXxYcA5WL2bk4EPlbwm2e5YGMhC2Nrb98QYny/WKqdThBDeiHVSAtwKbBRjvLtYq/Ijza79FXgL8AiWMfHPxVqVHylRwmrY7MurWMbTMs++BGx94pKYs/Yed2yVixDCZ6g7p78GfKTkzum9Mef0/FTDOf0uzDm9JOac3rLMz3AIYT2sD14V+BcmFO8t1qr8qLxYzKQx/gDVSWP8Myydb1XSGB8PfB9LlHBkjPEzJc8geDC2BnU+rMbe+8tcjL1qhBDeQT2s6XpMOD1crFX5kRJh3ISJpxmYMC6l9xZed14K5uiZC2iZHT1JGK+OJVerCePZxVrldIrUB38TqGWF/FSMsezF2D+BOacnYEXoy+6cfi9wFfbOOpeSO6dDCO/EolyWwWaOS10pASqe4CalIb8SK53wBCYUy1w6YQo2y7QTtt5n9zKXTkiDkB9iGRNfAz4cYzyzWKvyI3nnv4iVTgCrsXdCmTvlqhFC2A64EPNWX45lXCtzTcGNsXYuBtyCrW8qbaccQpiECadJWEa9u8vs6EnOy9Wx3/NcYHqZZ1+qRvr7no6VTpgH7F/y0gkBOB4rnQDmnC5F6YTBCCEcgmWmDlgZo0+V3Bm/M3A+9o6+EJtwKW2lhBqVFYupxt7VwBuxNMbbxBi1WKvyI9XYuwzYFKuxt0OM8aZircqPlMb4V1gijNKlMW4mU2Pv45gw/liM8bRirXI6SQjh/cDPsff2mZQ/jGsnzEs9P1bvdseSe6vnx2ZPJ2I1ye4u+d93Pqym7yTgZay9pR90VYX0ez4PeA/2e949xvi7Yq3Kj+ScPhX4CDZDflAFnNNHY4kgwQTy18rsnA4hHIA5P8YBp1HyBJhZKikWK1pj72qqlcb4N1gijFKmMc5StRp7VSSE8Cms6DzAicBRJe+UP4SVL5oAXII5e8ocxrUQtvZlPFZ8fkaZByEpymV16sJ4epn/vlXDa+zxvhjj5cValR/JOf194FDMOf3RGONPirUqP5IwPhL4Rjp0PFDqBJjNVE4seo29ctfYS2mMr8KyUz2CCeMyr2+qVI29qpE6qROAo9Khz8QYTx7ikr4nhFDrlAOWMfHgkoc1LYplPQ1Y1Me9ZR6EpHfWapgwfg5LZlNaYVw1WtTY2zrGeGexVuVHixp7O8YY/1KoUTmSnNO/APbEnNN7xxgvLtaq/EjC+FvAEVjyrU/EGE8p1qruUymxmGrsXYyVTrgS8/6Udn1ESmP8Oyw71c2Yd6/M2alWxoTxalga463LnJ0q1di7Eiud8BiwXZlLJ1SNtN7nx8CBWFjTATHGXxRrVX4kYXwS1imDieSjSy6clgBWSruPA/eXvL2LYMJ4HFb+5N4yOwKqRghhDSyKaRpWY2+bCjmnH8bK+ZTZOb0Q5pzeigo4p1OysTOwBJhzgf1ijOcVa1UxVEYspjTGZ2FhL7/Akp2UNuwlpTH+DZad6hpsvUCZ1/usi3VSy2BpjLcreSKMFbG/qwD3YsJ4erFWOZ0ihemdC+xMvfj8lcValR9pvc+ZwL5YWNMRMcbvFWtVvoQQlgGWS7sPlTmjLbxeJ3MlbAb1CWBWmYVx1QghbIAJpyWBv2EzbGV2Tq+C9cGrAndjwrjMzuklMef0/2DO6W1jjP8u1qr8SJUSLgC2wyol7Bpj/N9irSqOSojFVGPve1gndTKWoaq03sxUY+8crHTCecAHS55Rb1MsY+IiwLXALjHGZ4u1Kj9Sjb1rsIHmrdhLu9QDzSqRZl8uA96Jzb7sEGO8sVir8iNlAL0Y2B4LazqgzBkTAUIIKwBLpd1ZMcbHi7Qnb9IMzPJp9+EY40NF2uN0luScvhRYEHPavrfkzun1sKitqjinV8L+rpVwTqdKCVcA7wCexP6+pa2U0A6lrrPoNfb4ASWvsZcyJl6DCcWLsPInZRaKtRp7y1GBGntVI802/QkTig8Bm5ZcKNYcPNsDz2NhTaUViqlPWhkTihFLZFN2obg8daF4vwvFcpGpsbcgFg2xU8mFYqVq7IUQ1saKzwvmnN645EKxVr/4HcAsYJOqC0UosVhMYU0/xlL71tb7lLbeTRqEHI21OWBpjD9ZcmH8IWxGYjKWxnjPGOOcYq3Kj1Rj7w9YzbnLsLAXL15dEkIIq2Kd8nrAXVjx+duKtSo/UpbmG6h7b7cseWr9cdh66qlYqO3dMcani7UqP1KfNA1YGhPG95Z5UF1FUo29X2PO6e9jNefK7JzeGXNOL4zV2Cu7c3ojTDgthwnkUjunU6WEG7CSerdjwvi/xVrVG5RSLKY0xr/G6t3MAXYreb2bWhrj47FByMExxtIWY0+DkCOxhcfjsXZ/tMwZ9UIIH8AE4hRsbdfuZS7GXjVCCG/GOqlVgH9g3syZxVqVHylL803A2sD9WHtvLtaq/EjJitbABpnzAI0xPlesVfmR+qRVsazjr2GlMUqbdbxqpD74y8CPMOf0Fyl/MfYDMOf0JMwpv1eZ64KGELYHfo85py/FlruU1jmdKiX8BVgR65veGWN8oFireofSrVn0GnvlrrGXBiHfBD5NRdIYV63GXtUIIWyOdcYLY53zbiUXEhti5YuWBO7E1r+UtlNO7+jVsQiIV7AZxTJHQIzHZlAXxITx9BjjC8Va5XSKFjX2Dokxnl6sVfnRosbeccBxZe6DQwj7Yk7p8ZhT/uAY47xircqPEMJWWD3fBbC+aY8yV0oYDaUSixVMY1ypGnspjfHPsIyJpU9jnDqprwGfT4c+HWP8doEmOR0mhLAbloxqEnA+loyqzN7qrbB31kJYxsTtSh6KORkTivNhWW3vLnkW7olYe6dQAWFcNVIyqrOwGnsvY87pstfYOwk4HHNOHxZj/GGxVuVLCOEILBEkmED+QsmF8V5YhYSJwC+BA8v8jh4tpRGLTWmMq1Jj77dUJ43x/Fjinu2xNMa7xRivKdaq/Ehha6cBB2Brbj8UY/xlsVY5nSSEcBAWzjQO+CG2xrjModR7YgPNSdi7epcyh1Kn1OurYf3s89gMW5n/vllhPAcTiqVdv1Y1Uo29i4F3Y87pnWKM1xVqVI60qLG3b4zx/GKtyo/knP468Ll06IgY43eGuKTvCSF8nHoCzG8Dny1zKPVYKIVY9Bp7lUhjfDmwEZYIY/uSr2+qVI29qpE65aOwovMAxwBfKbn39mNYpzwe+23vW3LhtDDmuByHLYeYUeZBSHLmrY6NKV7AhHFpw9aqhtfYK3eNvSbn9DzMOf2rYq3Kj9QHHwt8OR36HPCtMvfBY6XvxWJTjb0/Yg91mbNTVarGXghhOcwRsDaWxnibMmenaqqx9zRW2Li0pROqRgpr+jbwSSys6WMxxh8Xa1W+hBCOxQQxWL3bw8vcKSfn1jTMW/0kMLPk7V0Im0EdBzwL3FNmYVw1mmrszcD64LI7p2s19p7AnNOlLZ2QnNPnATthzundY4xXFWtVfqQ11acAh2Brbg+KMZ5RrFW9T1+LxVRj73wsccCFWNrmMq/3eQfm3VsMS2e8U8mzUwkmjFcE7sA6qTInwngDtuZ2PeBBrL23F2uV0ylSopMzgX2w9VzvjzFeWKxV+ZG8tz8EPpoOfTHG+LUCTcqdEMJSwApp99Eyv68AQgiLAStjwvgp4L4yC+OqkWrsXY05p/+DRW2V2Tm9PNbeN2LO6a1jjFqsVfkRQlgUc05vijmnd4gx3lSsVfmR1tz+CngvFiq/Z4zxsmKt6g9Cv77XgxWvLu1Ly6k0d2GdVFdKJ4QQIkCMMXTj86pKCOF5LNtaFTkByzZXZiZja6oBrsPEU5mZAGyMhen9NsZ4f7c+OISwAUCM8Z/d+syqkZw9c7HQcccpE89gky1/7saHlWGM1c8zi6XNoOdUnk1ijI8XbYTTcaoqFKH8QhFsrQ/Ai5RfKIIl3orAS90Uik53iDHGFLLnOGVjsxjjf4o2op/oW7EYY3zZHF/9rdZHQhm8EyOhwu11oVhiqvJ7hobfdCVmgEII86BS7e3P0CRnRFTlnVXhMUfV2utCcYSMK9oAx3Ecx3Ecx3Ecp/dwseg4juM4juM4juMMwMWi4ziO4ziO4ziOMwAXi47jOI7jOI7jOM4AXCw6juM4juM4juM4A3Cx6DiO4ziO4ziO4wzAxaLjOI7jOI7jOI4zABeLjuM4juM4juM4zgAmFG1APyAiawD7AhsDAiwGjAeeBmYBfwMuVtVrCzOyw1StzSIyP7ALsCewFrAc5kx5HLgduBL4uao+X5iRjtMmFXx+JwNTgQWByVhbAzAPeAV4AZitqs8VZmQHqVp7nf6k2/2qiPwQ+Fjm0HGqemwn7t3m51eqvYMhIhOBm4H1M4e3UNXr2rh2eWA/YFPgTVjfNR8wG3go3fcK4EpVfbWzljuDEWKMRdswakIIESDGGPK4v4gsDnwf2BvriIfj38CBqvrvPOzJu73QW23uRnsBRGQL4ExgpWFOfRzYX1V/m4cd3Wpvr3xu1aja8wtdeUdPAFbAhFM7vAjMVNUX87AnhLABQIzxn3ncv2rt7bXPrRpjeX673a+KyObAH2l8741IPHl7O4OIHAM02zGkWExC++vAoZjzazjuAQ5W1T+0a5ePsUaPh6EOgogsDdwA7EP9YZwH/Au4DLgEuBF4KXPZm4EbRWTLLpraMSra5n2AP9D4gr8DuBy4Fngic3xJ4FIR2b57FjpOe1Tt+U3ea6FROEVMIM1O/z0PvJb59/ntUlmoW3Z2iqq11+lfut2visgCwM9oz0HWcarW3qEQkXWBL47wmgWAa4BPUBeKEZuNvQK4GPgz8GzmslWBa0Rk37Ha7AyPh6EOzhlYx1zjdOBoVX00e1L6kR8KnIB9n5OB80VkdVV9ulvGdohKtVlENsE8gbUX7s3AQap6a+ac+YD9sdmaSVh7zxSRNfuprU4lqNTziw3MJmf2nwAeUtW52ZNEZBywFLAs9qyPA1YRkdv6LIypau11+pCC+tWvA6uMxe7RUrX2DkWKfDgTmDjCS7+JLZmocRnwKVW9t+n+E7EQ1e9iIfjjgJ+KyE2qOn3UhjvD4jOLLRCRDYGs1+ccVf1I86ALQFVfUNVvAp/PHF4cODhnMztK1dqcBlSnYrHwANcDm2Zf8ACq+oqq/gRb/1VjKeDDXTHUcdqggs/v/MAimUNPqerMZuEEoKqvqeojwIOZwxMwD39fULX2Ov1JEf2qiGwKfDztzgIeHuk9RkvV2tsGnwfekrb/2s4FKSIm2/dcD+zWLBQBVHWuqv4ME9415gM+MyprnbZxsdia7Zr2T2rjmlOBlzP7W3fOnK5QtTZ/AFgnbb8E7Kmqrwx2sqpeAJwGnIy94K/K3ULHaZ+qPb+LNO0PEMUteBwLbaqxcOfMyZ2qtdfpT7raryYnyhnUZ/W+iCV46hZVa++giMibgKPT7iu0H4q6NY1rFL8zXASEql6ECeXsPZwc8TDU1izftH/ncBeo6ksich/1MLBlO2xT3lStzQdmtk9X1WG9c6p6SI72OM5YqNrzO1/T/pzhLlDV10TkZeqhnCMNlSqSqrXX6U+63a+eAKyWtm8Czga+Oob7jZSqtbclIjIeCz+tvae+A8xo8/IR912Z81ZM2/3Ud/UlPrPYmua0xgu2ed2UzPYLHbKlW1SmzSnsYZPMoXOLssVxOkRlnt9Es+e53b4se95rg57Ve1StvU6f0e1+VUQ2xhKigEVIHKiqXUvvX7X2DsORwIZp+y4GZkIdiqr1XX2Ji8XW3Ny0v95wF6SkEVnvRvM9ep0qtXkr6r/92fSP3Y4zGFV6fmHg4GBKy7MypPVF2dm1fhpgVK29Tv/RtX5VRKZg4Zi1z/uKqrY7I9UpqtbelojIG4Fj0m7EROywkQ8ZRtx3JVbLbPdT39WXeBhqay7F1oQsnfaPEpFrVXUoz+zB1L/PiKU17ieq1OZ1M9t3ZtuYEoVsidUyWxB4DKtFd7WqPtVVKx2nfar0/AI8A8ylLobeAAxXgH5JGlPNPzHYiT1I1drr9B/d7Fe/AqyRtm8BThyVxWOjau0dQCb8dFI69ENV/ctI7qGqfxOR/1AXiUeIyDmq+tJg14jIbjQ6Ok8fyWc6I8fFYgtUdY6IfBS4COtstwQuEZFPqOrM7LnJ4/Mp7GGu8V1V/UfXDO4AFWvzmzLbdwGIyDuwhefrtLwC5ojIKcCxquoeeqenqNjzW1uPNwurtQWwkIisCtzfnGCiqZREjUfzKlSfB1Vrr9OXdKVfFZG3A4en3XnAAao6b3Qmj4mqtbcVnwbemrbvA44a5X0OBv6Eic43Ar8XkY+o6u3Zk1Jpjv2B72UOX6KqF4/yc502CTH2SsjzyAkhRIAYYy6FSVOh1dOox1BH4FbgfszLuySwAfWQoFexLFdHDePRHxV5txd6q815tVdE7gTWTLvfwzx1p9Oe8+TfwHatShKMlW78fXvpc6tG1Z5f6Mo7eipWfzC7pOIlLBtfxJ7p+TP/HjHhlC0r0TFCCBsAxBj/mcf9q9beXvvcqjGS57cb/aqITE7n1j7nBFX9UtM592HPCMBxqnpsG58PeHtHgoismWyrJdDaWlX/N/Pv04Bs+YstVPW6Ie73buAcGkv8/BdLlDMHmIqV5chmdT4LOKTdsFcfY40eX7M4BKp6Dlb49ASsQw7YVPmOwK7Y4uYpWIf8K2AtVf1cHoOublGRNmdfNqsBP8Je8FdgteqWwDxc04BDaEzR/GasgHk21bPj9AQVeX5fJ4V0/R9Wa6zWhilYqYlFqRduBngKuD0v4dQNqtZep6/oRr96HHXhdAeN0RHdpmrtfZ0UvXAGdaF4RlYojgZV/T0WOXEk8HQ6vCb2Xe4GbE79O/8tsIGq7j/C9ZHOKPEw1CEQkeWx2PD3MfR3FbB6O+uJyDGqekk37MuDirR5ocz2Dun/n1TV7zedNxM4TUTOBX4HvCMd3wwLheinNV5OBajI8/s6IjIfsBywGI3r81oxFZgiIg+p6uzcjcuBqrXX6Sty7VdF5K1Y2COYo+QAVX251bldomrtzXI49XY8BBwx1huKyGKYGD6A4RN4bQ+sKSJfw4Rq/4ZI9gk+szgIIvI2LHxrH2zQ9TSW8Wk9zLsxBfMY7Us9E9M6wMUi8u1u29sJKtTm+Zv2z23xgn8dVX0W2AvIrvn59CCnO04hVOj5BV7P5vpGTBQFLKT2IcwDfwsWIvV/WChUbX3QFGDVJKr7iqq11+k7cutXRWQSlkilNhP3XVX92xhs7QRVay8AIrIGjTOch6jqM2O852rY++tQ7J31ErY84m1YxMQkzEn2XuDqdNkqwE+xGVqf+MoZ/4JbICJLAZdh3luwuOmtVPWBplNnAjNF5Gzgm8Bn0vHDReQ2VT2jKwZ3gIq1+WUaX/QnD3eBqs4SkQuAD6ZDa4nIyqp671DXOU43qNjzW0t0sBr1wdQc4O7mZC/YWr6ngKeSYKpli11aROaoal9kCK1ae52+JM9+9RjMUQJwD3D0WI3tAFVrbzb8tDbzd66qXj7Ge07B+q7austHgXer6m1Npz6EJXC7SEQ+DvwgHd8D6+++PBY7nKHxmcXWfBHLJge2tmfPFoOu10lT4EcCWc/PV0Rk4iCX9CJVanM25fyLwL/avO6apv23dcac3iCE4Osw+5cqPb9gpSOyzs4ZLYRTA+n7yGYgXFZE+iXhQNXaOyghhAnA+tTXcjm9QS79qohsAHw27dbq+PVCZt+qtRfgE8DGafvxtD9WDgHWyuwf1EIoNqCqpwAXZA59RkSW6IAtuRJCWHb4s3oTF4tNJM/JvplD16nqrcNdlwZfP80cWhZ4Z4fNy4UKtjkbMvHECOLd/9u0v3TLs/qEYHwzc6jnX7bOQCr4/AIsntl+bqiaXE1kZ9YmUs8a2+tUrb0tCSHMBwiW0Kev21JCOt6vpjW6P6fuKDlNVf80ags7S6Xam0JFT8gcOqxDkQofzGzPGMFM5U8y21OAnTtgS8cJIeyT2V2/MEPGiIvFgaxGPZQL4KYRXNucxnvDsZvTFarW5umZ7UmDnjWQZ5v2F+iALYWQvPNnUPdgEmPseDkQpytU6vlN6eSzs+AjqXva7KHv+We4au0djBDCZEwoTsZKwdxSrEVOE3n0q1+mXs/wDuph871AZdqbIhJ+Rj3s9heqen4H7jsJWDdz6K8juLzn+64QwieBszOHfleULWPF1ywOpHl25emWZ7Xmuab9xVue1XtUrc23Y9m0ABYXkUltZhlrHmiNaVF3UYQQ5gfOx8opvMjAhfpOf1G157e53xpJgepXh7lXL1K19g4ghLAA5sEnmy4AACAASURBVBSZgInlmQxsm1MsefSr789svxF4XkRGYtMxInJMZn/IWn8jpErtXZHGqJP9RGS/Ed7j2mxbVDVg/U02NL4UfVcIIQBfBb6QPR5j7MsSVeAzi61oDu9ZuOVZrVmoaf/5MdrSLarW5psz27X1L+0wrWn/oY5Y00VCCIth2cR2xBJhbFmsRU4HqNrz29zhjmStbfO5/SA4qtbeBkIICwNrYO/qZ4G76MN2VIA8+tVeXmNbpfbmZVfp+q4UtfUTTCi+ipUC6Xv60suYM81JId7U8qzWNC+4HzTBRI9RtTb/DssmWCsouxuNiT4Go3k910hCJgonLa7+HVYu4QFgmxjjHeYEc/qYqj2/zYldhqvJlWVy0/7cMdrSDarW3tdJzq2VscHqU8B9Mcbo76yeJI9+9Z50z5GwKvWx7ZM0rtvtZKKYKrV3LqAjvGYiVt6ixv0t7JmNRQrUZlv7uu9KofLnALtif8f3xRgvDyH0RZbxoQgx9m8tyxBCBIgxdrTnEJH/YmsjwH7Iy7VTR0ZEzseKYddYVVVndMquvNoLvdnmnNubtftpYDVVfWqI86cAM4Bl0qFbVPXNnbQpz/aGENbAZhSnYQvst4kxzsr7c506VXt+Idd39NrUB2mvAbeq6rCzTSKyCo3rO2/rZKHrEMIGADHG5vU0Y6Jq7U33XgpYIe0+FmO8vxuf69QZ6fPbC/2qiNxHvQzDcap6bLvXens7h4hMw2q+1mgZEisivwO2SbsREFW9u437n4hl9K6xpar+cahrch5jLQJcCmyGhRbvGGP8S96f2y08DLU1Z2a2F6CN+jkisjlWMLTG9Z0cdHWBqrX5OOqhTIsBP01ZJQfjROoveKjX+Ol50sDqL5hQvBnYtCYUndJQtef3ycz2OGDYovMishCNwun5TgqnnKlUe1MURE0oPpgVik5PU5l+NVG19uZBtu8KwCmpruygiMiawMczh+4F/pyDbW0RQlgG+BMmFB8G3lkTimXBxWJrTsHCAWocKCLnJ09JAyIyUUQOBq6g/n3OAz6fu5WdpVJtVtU7aHxR7wpcLiIrZM8TkakicjpwWObwTcBZ+Vs5dkII7wKuA5bE6jttGWP0wtzlo1LPL/AYVhS7xhIiskpKPd+AiAQRWRJLkFIjAg/mbGMnqUR7UzmfFbG6kgAzY4yPFGmT0z5V6VdrVK29OXEBjRm8twauFpEBIakiMk5E9sCEWTYx3+dVdSSJvzpGCGFV4AZgPeBuYOMY47Clq/oND0MdBLG0TddS77TAOtw7sExsc7AshBvQmN3qVeAQVc3WL+sIeU9l91qbu9De8cBFNNbneRX4O+YdWgp4KxZ7X2MG8C5Vndlpezrd3hDCe7G0zfMB5wL7xxgHFPIuQ4hEP1C15xdyf0dPxhKfTGz6p5ewdX4RW8szP42O0QjM6lCNsAbyDI8se3tTBsGVsRmaCMyIMc7O+3OdwRnN81t0v9rtsMyqtXcEdk2jjTDUdO7SmFO7eR3iPZgAewGYiiURWqzpnONV9RjaIIcx1vrY2tWlgX8B28UYH8v7c4vAZxYHQVUV+2FehHVcYFPka2PpknfDFipnB10KvDuPQVc3qFqb05qfPYDjqaejHw+8HfMQbkzjC/5yYKM8hGKnCSEcAvwaE4o/AD7QSig65aGCz+8cTAg3p1ufghVtXxQr3J7t5+YAd+chnPKmzO0NIYwHVscGgq8Cdw8mFJ3epsz9aiuq1t48UNVHgf8BTqexNNCqwLbA7sAWNArFB4D3tSsUO00IYTNshnNp4I/AFq2EYlnwmcU2EJG1gL2ATal3aBOxTE4PYVPoVwFXqGpuX2g3vRO90OYut3cVYB9gB2ytzJJYKuYHMY/X+ap6Q542dKK9yTt/NLaWAuBLwNfiEA96Gbxe/UDVnl/o6jt6MuZ5XhArkD0BE8qvYrNuLwDPtJP0Zyx0a8arTO1NqeZXx2ZE5wLTY4xDZnH0mcXuMNbnt4h+tciZtqq1dxi7ptHmzGLTdSti9SY3w2Yap2IOsdnAo1jehf8FLlTVEWV37lR7Qwi7AOdh794LMWf8oOvByzDGcrHYR3h7y81Y2xtCGAd8HzgUy5j40RjjT/L+XKc9qvg9V63NVRMxY21vCGESJhQnYWsy7x5q0NWpz3Xao4LPr7e3xHTIIX8gVkdxHPBj4OMxxiEzU5fhe/Y6i45TAkII8wG/APbEZhb2jjFeXKxVjuM4rQkhTMGE4kSs/tr0GGNf1YF0HKcapKitzwFfT4eOA44bKmqrTLhYdJw+J4SwELZObSvgOWDnGOO1xVrlOI7TmhDCgli21vHYO+ue4bzzjuM4RZCitk4GPoXlAzgsxvjDYq3qLi4WHaePCSEsCVyJLQ5/DNg2xvjvYq1yHMdpTSpevQoWxjUbuDfG+FqxVjmO4wwkhDARqwX5fmxN9b4xxvOLtar7uFh0nD4lhLAScDUg2ELyrWOM04u1ynEcpzUhhMWxZBwBeAKYVZUwLsdx+osQwgJYHcjtsKRhu8YY/7dYq4rBxaLj9CEhhLUxobgccCs2o/hwsVY5juO0JoSwNLB82n04xvhQkfY4juMMRghhKha19XbMsbV9jPHvxVpVHC4WHafPCCFsBFyBlUO4HtjJa5I5jtOrhBCWx+qRAdxf5npkjuP0N+l9dTXwRmAWFrWlxVpVLOOGP8VxnF4hhLA98HtMKF4KbONC0XGcXiQY0zChGLH1iS4UHcfpSUIIawI3YkLxdmCjqgtFcLHoOH1DCGFf4DKsQO0ZwHtjjC8Va5XjOM5AUgbBVYHFsbqv02OMTxVrleM4TmtCCG8F/gKsgAnGd8YYHyzWqt7AxaLj9AEhhMOxOorjgW8AH44xzivWKsdxnIGEEMZjNRQXAeYBd8UYny3WKsdxnNaEELYG/og5t64EtnLnVh0Xi47Tw6Qwrm8A306HjogxHuUZBB3H6UVSqnkBFgReATTG+EKxVjmO47QmhLA3lgdiAeCXWNbTF4u1qrfwBDeO06OEECYApwEHYN75D8UYf1WsVY7jOK0JIUzGZhTnA+YAd8cYXynWKsdxnNaEEA4DvoeV8zkZONLrvg7ExaLj9CAhhCnAecBOwEvY+sTfFmuV4zhOa0II82NCcQJWk2y6h8o7jtOLhBACcBxwdDp0ZIzxWwWa1NO4WHScHiOEsCiWyGZT4GlghxjjTcVa5TiO05oQwkLAatjSlmeBe9w77zhOL5LWVP8QOBhLvvXhGOOZxVrV27hYdJze40/AusCDWGmM2wu2x3EcZzAWwmYUA/AUcJ+vqXYcp4c5H9gdC5XfM8Z4WcH29DwuFh2n91gXUKwQ7KyijXEcxxmERYFlgOeAx2KM9xdsj+M4znDsDjwDvCfGeH3RxvQDpRCLIYRKeTG9vaXn78D2McYnijbE6TwV/D0TQtigaBu6xG4Athym9EwEdsDWVP8hxvhIwfY4OVG1d5a3t/Q8gkVt3Vq0If1CKcSi45SMd8UYny/aCMdxnCGYCzwPPO1C0XGcPmKjGOO9RRvRT5RCLMYYK+HGrXl/vL3lJNNeF4olpiq/Z2j4Tf+zaFu6QW1GsWrtdcpNVd5ZFR5zVK29LhRHyLiiDXAcx3Ecx3Ecx3F6DxeLjuM4juM4juM4zgBcLDqO4ziO4ziO4zgDcLHoOI7jOI7jOI7jDMDFouM4juM4juM4jjMAF4uO4ziO4ziO4zjOAFwsOo7jOI7jOI7jOANwseg4juM4juM4juMMYELRBvQDIrIIsB/wbmB9YHFgIjAbmAHcBJytqqUpxCwiawD7AhsDAiwGjAeeBmYBfwMuVtVrCzNylIhI7NCtVlbV+zp0L8fpGCKyNPbOehfwRmAJIAIPA7cBF2DP75zCjOwgIjIRmAosDEym3rfNBV7C3luzVfW1YizsLFVrr9O/iEgADgNOxH6rAMep6rGjvN/i2Nhkc2A9bDw2BXgGeBT4B3A1cKGqvjIW24exoyvjCBGZDOwDbANsiL3La+2tjcV+rarXdciethGR+YFdgD2BtYDlsEmox4HbgSuBn6vq8yO451TgfcDW2Hh7SWAS1t5HgJuB3wKXquq8jjXGGZIQY6d+790nhBABYowhj/unl9wngK8AC7VxyZXAgar6aB725N1eeP1F/H1gb6Cdz/k31uZ/d9qWvNrbq2KxG3/fXvrcqtGl53c8cBxwBDagGIq7gANU9Ya87OnSO/oNwNIMHykzB5g5koHLSAkhbAAQY8zFcVi19vba51aNsT6/yWn1c2Dbpn8asVgUkQnA54AvURedQ/Eo8ElVPb/dzxhJe7sxjhCRvYHvYYJpOP4K7Kuq09v94LH8fUVkC+BMYKVhTn0c2F9VfzvM/cYBn8X+vgu2YcJM4MOq+vs2zgV8jDUWXCwOQuqUf45557PMxDzzc4FpwLo0dtrTgY1V9bFO29SFgdfSwJ+wmcQa84BbgQeAV7FByptpHIjOAXZU1T900p4cxeJ5o7x0JeDtaXsusKyqPtEZq/xFVna68PxOBC7HPNBZ7gIUmA97X70h828vA9vm5ZXuwjt6NWx2LcscrF0Be09NzPxbBO5W1ec6bQ/kK2Kq1t5e/NyqMUYxsSNwBq2FzojEYnKCnQe8t+mfpmPvt5eARbGZxiWazvmiqn6tnc8ZoVjMdRwhIl/BhFOWR4BbgBeB5bGxWPZ5fwIbf97VjiGj/fuKyD7Ar2icULgDuAcTeuvQ+HeYB+w8mGBMf9/zgd2b/mkGcCf2fluGgWPPCLxfVc9tx24fY40eD0MdnC/QKBTvAD6qqn/OniQi0zDPz07p0GrAacCuXbCx05xBo1A8HTi6eaZURBYADgVOwH5Dk4HzRWR1VX26W8aOFlXda6TXpIHa9ZlDJ3VSKDpOB/g2jULxFuAQVf1b7UDqlPcCTsEGV5OAS0VkbVV9oJvGdoDlaRROLwKzVPWF2oH03C4GrIiF0QdgVRG5I88QtZyoWnudPkREpgAnAx/NHP43NtAfLUfQKBRvxN5t/9f02eOAnYEfA0ulwyeIyF+ax25jJc9xhIi8n0ah+ADwceAyVY2Z85bCxmEfToeWAM4VkQ2z53USEdkEm1GsCZ+bgYNU9dbMOfMB+2NRapOwceKZIrLmIGPE42gUin8HDlXVvzd99kLAZ7DvZlyy4UwRuUFVZ3Wgec4geIKbFojIssDRmUN3AZu0etmk8IHdgD9mDu8iIuvkamSHEZENge0zh85R1Y+0CqlV1RdU9ZvA5zOHFwcOztnMIvkwtn4T4F4sNNlxegIRWRP4WObQbcA7s0IRQFVfVdWzsbCw2nrFhYGvdsXQDpHW8SyVOfQScFdWOAGoalTVp4C7gdr6vfHAsl0xtENUrb1Of5Kik/5Jo1A8BXjHGO45ETgqc+huYOtmoQigqq+p6iXAjtisU40vjPbzO8yw44j0rH8nc+gJbPx5abMAVNXHVPUg4KzM4bcAO3TU6rpt44BTsSgVMOG7aVYoJrteUdWfYGtLayxFXdRm77kMFn5a42Zgs2ahmO77nKoeQ+PfcxLwqVE0xxkBLhZb80HsB1jjU0PNmKnqq8CXmw7v1OrcHma7pv2T2rjmVCw8oMbWnTOnd0jeuxMzhz6uqi8VZY/jtOBjNL7PPzZU6GESkd/KHNpXRFbMy7gcaA5tm5Xewy1Joirr+Fo8eb/7haq11+lPVsASnYAlWdpVVQ9T1ZeHuGY43o7Nltf4UbOTpJkkNLIzeO9KURWFMYJxxK40Pu9fVtWZw9z+SzSK451HZ+WwfAALMQVzWO05VMSCql6ARdqdjAnFq1qc9n7q4hPgE22Mr76DiegazUsvnA7jYrE1m2e2n8Ayaw3HTdjDU2PtThrUBZZv2r9zuAvSA31f5lBZvdcnU++sLh1uobbjFMBWme27VPX6Qc+scwq2lgSsL9it41blRzYcc06bSVweo3FAtWhnTcqVqrXX6W9uBNZX1d904F4jHpu0OG8i7SWJyZN2xxGbZ7YjcM5wN05LCO7OHMpr/HlgZvt0VX14uAtU9RBV/Yyq/kxVb2txyqpATfw/3BwNM8g9X8ES+tQYLsmOM0ZcLLbmQGAjLIb6oHbSj6dzZmcOLZ6TbXnRPPhoJxsVNC42HtLb14+IyJaYNw0sbO/wAs1xnAGkLIHZtcY3tnNdSsL1j8yhvoiGSOt+stkQ23rvpDTrL2YO9YV4qlp7nb7mNeAbWBhhp9aQdWJsAgWOT0Y4jvgy8DasJMV+qvpMmx/zZGa74+PPFGK8SeZQW0llhkNVP6aqC2LvuJEs38r+Lvo2cUy/4AluWpC8NCNK9pBiubPZn3LJPpcjNzftrwcMmd00JbrJziY236OvSWFbp2YOnaSq9xZlj+MMwlQaO8tHRnDtrdQz863fMYvypTmcbO4Irn0JWCBtz98Zc3Knau11+hRV/Rfwrw7f9u/YDFvtHbcecGEb162e2f5vXhmBh2Ok44iUJ2I05deWzmzn0datqE8wzabD470UqjyScOWVM9ttZX91Ro/PLHaO5hTG/ynKkFFyKY0vqKOSAB6Kg6k7HCLwszwMK5BDgDXS9uM0rjdwnF5lJF7WrDd6sZRsoMxkiziPT8kzykzV2uuUDFV9BCsJVOMgERkypFRE/gebnatxeh62tUnu44g065ddc57H+HPdzPad2Yg7EdlQRD4nIqeIyM9F5JsisreITM3BDkTkTcBbM4cuyeNznDouFjvHR5v2Ly7EilGiqnOwNtTWuGwJXCIiA2LBRWSKiBwFfDNz+Luq+o/mc/uVlKI5m7r6hDyLWzvOGHiKxrVpy43g2uZQrVXGbk7uNCd2GUniluY+b1LLs3qLqrXXcZo5HHvPgc2g/UlENmo+SUSCiOwG/Jb6b/9m4AddsXKgPd0aRxxEY6TgRTl8xpsy23cBiMg7RORWbPb3G1hJtQ9i2U3PAR4UkW+lKLSOkMakF1J3is7CSnQ4OeJhqB1ARDYGPpQ5dJmq3l6UPaNFVS8RkQ9g2asWxNYwvSe9DO7Hwp+WBDagPsh8FVu4fdTAO/Y1R1BfED8L+FGBtjjOoKjqPBFRYM10aMAgagia14g0F3zvOVQ1isgc6uv4RjIQaRbHPe8wrVp7HacZVZ2R1v1dhDm01gJuEJH7gP9i6xEXxUJUs8uBfgvsq6ojCd3uJLmPI0RkVRrHX/+hddbRsZIN+5wtIvtjM7ZD6YjJWF3ELUVku1al2IYjRUMsgyXC2RETxrV+ajqwo6rOHuRyp0N4xzFGRGQF4Hzq3+UL9HHNF1U9B3sZn4CtdwnYC3hHLKXzJtgAJAK/AtZS1c+1kwSoX0hesE9mDp3kBa2dHie7vngVEdliuAtERGjMvAftJ48omuyanEnJgz8kqX5Zc/sKTac/AqrWXsdpQFVvwUTiR4AH0+FpWM3Y3bFoqJpQvBF4l6rukOqOdp1ujCNEZBEsBLO2HvlV4JDmeowdIutIXA0TvhOAK7Aa3UtgkQvTsNDbbIKjNwPnj6R8SQpnjcAr6V7XAp9OdszA6nyvq6o6yvY4I8DF4hgQkWWxshrZsK8D+jkJiogsD3wX+BwDvdJZApbd6yIR2bUbtnWRD1NPcT0bOKNAWxynHU5r2j8lDSRaksTGrxgoHia3OL0Xebxpf8WhBiLp31Zm4HrOfsmiV7X2Ok4DIjIFOBpb/jJcqP1GwDki8tmULboIch1HiMjCmFDLRod8QVX/OsglYyXroNoB6ys+qarvUdWrVPVJVX1FVWeq6mnJrpsy12wG7N8BO/6FzWhe5vWuu4eLxVGSvPI3UC9AC/BZVf11QSaNGRF5G5YdcR/MY/Q0cAw2s7gwJh6nAftSz4S1DnCxiHy72/bmQRpkZdNanzZcAWDHKRpV/T/g7MyhNwLXicgGzeeKyOZYJ74hA7PI9cVvPQ0SsjMGk4E1RGRAxs8kjAXzvs9p+ue+iIioWnsdJ0tKaHMjtv5vUSxx0+mYAFkcW8e7DCZifo1FPi2DCcs/ikhXIybyHkekRGTX0ljK4hRV/eYgl3SC5nfNuao66FpBVX0W2IvG8j2fHsHn/Q2L2rsIuB64Jx1/C/B14A4RuaJVXg2n8/iaxVEgIu/CfsC1ulUR+LSqfqc4q8aGiCwFXEbdE/ZfYKtURiTLTGCmiJyNvYg/k44fLiK3qWq/z8JtS2OB158WZYjjjJBDMcdOLRHB+sA/ROROrGDzeCyj3Qrp3+/H1rpkkyH0U8mfWZgDqxYBMT+wVlrfNwebRZtCPSHMK1j42qqZe/STeKpaex2nVmf0fOqlfV4AdlDVPzWd+ii2RvG3InIucAE2xt0UK12xX3csBnIcR4jIelh22BUyh7/DyITYaHiZRsF48nAXqOosEbkAS3oD9r5auZ3oO1X9EU1rPEXkDVg/91nsPbcDsIGIbKGq/22vGc5o8JnFESIiHwJ+R10ozgM+2M9CMfFFYKm0HYE9WwjF10kx8Udi3p8aXylBavYPZrZvVtXphVnSBUIIIbM9kiyLTo+RijdvSmOaebDoh52wjrU2wLgKm1lsTgzQN2JRVV8FFGguWj0Zez8vQl04PQPcycDMos37PUvV2jsY6T21ITZ77pSfXYDsGuyjWgjFBlT1N5iAqrFvKrfQLXIZR4jIttgsW1YofkFVj8hpnWKWbN/wIu3X07ymaf9tLc9qA1V9WFW/hP0eaiGoywAXtFHqrXBCCCsPf1Zv0vNfbi8hIl/B4s5rguhZLBPTL4uzauykh2zfzKHrVPXW4a5LL6esx2xZ4J0dNq9riMhi2KC6xtmDnVsGQggTgDMzhwZd4+b0B6o6W1V3whLX/AybUXwBm2Wagb2/NlPV7VX1MRoHHaRz+gZVfTUNxO4CnsC8369hDq+X0zFV1emqOo+BZSdGUgS6cKrW3mZCCJOxENsFGBgW55STrPB6kfZn6X7StL9nZ8wZmrzGESJyMLZGsbZ28BVsouLrnbh/G2SdVE+MQJw2z/gtPVZDVPVG4LjMoTfR+J33DCGEbJKjVQc9scfxMNQ2SPHnZ9AYxjADeI+q3lGMVR1lNerhp9C4KHk4/tm0vyGNmRn7iR1prEN2WVGG5E0IYX4stGfH2rEYY3MSDadPSZ73Ib3viTUz24+oal/+BlT1OdqbFc0m8JmbBFXfUbX2AoQQFsD6qgnYcoj7i7XI6RLZ4uu3tJvURFWni8iz1LN4bthxy1rT8XGEiHwVi/6q8QSwq6r+Zaz3HgHTgTXS9kjqtT7btN+pmou/wGo71tgW+E2H7j1mUtTWCWTKmsQYf1+cRWPDZxaHIQnFX9AoFG8G3l4SoQiNdYnAEtu0S/OAZfEx2lIk22W2Z6jqfUUZkichhMWw0JAdaUya4VSP7ABq2GiCEpCdjapCJr1StDeEsDA2UJ2AzXDMpAQhtU5bZMcnIxmbQOP4pFtjk46OI0TkGzQKxenY+LObQhEgWzt8cRFpVzA2i8PmMPpRoaoP0xgp0TOJblLU1umYUCzFe8pnFofn+1h20BpXAu9T1RcHOb8faR5EjKQwd3O9r+fHaEshpFDcrTKH/liULXkSQqiVe3kT8ACwNVAWp4czAlKGwGzYeB6FnHuG9Ixn31cdGbT0KmVpbwhhKpaFOwBPYkLxLUXa5HSVl6gv/RnJ2AQaf/+5j006PY4QkSOxMmY1bsaWPhURAXJzZnsClnDob4Ocm2Va0/5DtQ0RWRo4Hlt3uAzwS1U9pR1jUuKjrIbpiVrYKVT+XGyt7UvA+xiYR6Dv8JnFIRCRTwIfyxy6FNilZEIRTDRkGclC8DWb9gdNitPjrEOjB3Mkobh9QQhhDSz9+Juw5BcbxRjvLNYqp5OIyKIi0u5Aeh/qa9oicGE+VuWHiIxvVT5iEKbSWGewOblPz1O19oYQlqJeL/LRGON9Mca8E3k4vUV2TLF2EgnDkjJnZsVlN8YmHRtHiMguNIZZ/hV4V4FLBX5HYyme3dq8rjmPRbYO5LPAgdh6w7eSWRbTBqvSWCf44RFcmwshhEWw72kX7H27VYzximKt6gwuFgdBRNbFSkPUuBbLENq3az4GI718NHNo66EKejexS9P+dR0xqvus17RfqjTMIYQNsbqgK2HewE1jjL7mpySIyB4i8hAWpvVPEVlnmPOn0Oixvnqo7Me9hogslt7R62Pp2KcMc/44zHNd41lV7QlPdDtUrb3wehRELQHTgzHGvvl9Oh3l+sz2VGDLNq8rYmzSkXGEiCyL5cmoCePbsXIhhdXBVdXnaVx/eZCITB3qmvSeykbm3ZLCR2v3fAn4c+bftxSRVdo0aY+m/etbntUlQgjLYHkCNsNmTzeNMd5QpE2dxMViC1JH+wvqXvf7sBnFvs4kNwzZrJgL0EYNnVTc+72ZQ9eral9lU8zQPLgujVgMIWyJOTuWwEJQt4wxPlmsVU6H+TuNWea+Nlgq8eSZPxWodcqvYWVw+okXqIemASw3zPkr0piUod+ER2XaG4wVgTekQzNjjI8UaZNTKD9v2j9ZRIZMkpLCG7+cOfQscEmH7WpFp8YRP6aedHA2sL2q9kJ+geOor8FbDPjpMCUrTqTRafWDFuecntmeAJwxXAk2EVmDxj7rGWyJWCGEEFbFnPHrYRnIN44x3laUPXngYrE1e9PoIfqYqjZndCobpwD3ZPYPFJHzRWRa84kiMjGTxrn2G5oHfD53K/Nj7cz20z3yYh4zIYQ9sELFCwLnADvFGAvzTjr5kJIoZFO07wiclQZNryMiKwIXA/tnDp+sqv+Xt42dJM2SZR0ei4jIys2DDBGZT0RWpTG5xaPtZlTsFarS3pRBcGVgScyJcU+M8YlirXKKRFX/imXurrEucL2IbNTqfBHZCvgLjSLlq6o60uQ4o2HM4wgR2Rh4T+bQF1R11pgt6wApqWNW8O0KXC4iDSWYRGSqiJwOHJY5fBNwVovbnof9vWpsBvxZRN7afKKICMUC7AAAIABJREFUTBCR92PCbNHMP52gqoWE2YcQ1k/2rIJVB9gkxnhfEbbkSejn8P8QQgSIMbYVw94uInIn9bV4c7HB1Wg4vpMZU/Nqbw0REWwG6g2ZwxFLgDITi1dfAtiAxgxXrwKHqGq79Y/aIu/2ZhGRv1PPDHmvqrYbCtExOt3eEMJHgR9ioSzfA46IMb6W9+c6renC87s48A8aEwrMwbKcPow91xvQuM7jfGDvvAo659lmEZkArEVjLcHXsKQCc7GZuPlpXLf3dJ7RDyGEDQBijM0lhcZM2dsbQhiPrUNaCOtTpscYWyYlyfN7duqM9PkVkfOG+OdsncPbgcFmXgaMm9I63WuAjZvOfTDd6zlsfeK6DKzjd5aq7j+05cZY31edGEeIyFVYGYgalzC65C0/SiWUBmU07U0VAi4Cds4cfhWLbnkYWApbf5h1ZM3A1lvOHOSeS2IhnGs1/dMsbPz5AhaC/BYG1oP+FbBfO31YDmOszbFcJgtjJeN2jTEOKGlUhjGWZ0NtTTZpy0RGX8z1x/RRpklVVRFZHwtR2w0bdATMW7b2YJdhQvG6rhiZH9kXUF9mdK2RvPNfBo5Nh74AfMMTQ5QbVX1SRDYFfg28Ix2eTGOdshovA8cAJ+UlFPNGVeeJiGIe3Zrzahyt63hFbB3Jo10yr+OUub0hhIlYDcX5MeF7d4yxL2ZDnQbaHSsNNaYYMG5S1RdFZAssDPKT1EvCLMfgIdlPAseo6g/btKkTdGIc0SyYdh3lfX5He7V2R4SqvioiewBfwsYWEzAH5NsHueRy4CBVHfRdpKqPi8j/AN8CPkxdaK6Y/mvFs9g45/tF9GEhhF2xrKeTgAuAfWOMpV2q5mLRaUBVHwPeKyJrAXsBmwKrY/HpE7H4+YewkIKrgCv6dbDZRCnEYvLOfx/L4vsacHCMsaMzvkUjIusBC6pq24vHUzjmRqrajXUrhaGqD6Qwph2wgdv/AMtjs1GPYuuvLwfOVdW+T3CUwjP/mxJyTcUGkfNhTq65mEf+GeCpfkvw0ooytjeEMAnrYyZhToy7yzzockaHqs4FviAi3wY+AGyOrRFcHHOYPIsVq/8nNstzXgEJYUoxjhiO9Lc4RkTOwhLY7IAlo1oSa/eDWEKh89vtp9Pf6mMickK65+bAG7Gx5wLY7PHjwL+wkiTnpqQ7XSeE8GHgNMxZdyrwiRhjKeopDoaHofYR3t5yM9b2pkHXL7C6Pi8De8cYhxVH/fY9i8h+wE+A3VV12EXtIrIMFl59u6q+d7jz86LfvudOULU2Vy08cqztDSFMwYTiROBFLPR0bt6f67RHBZ9fb2+J6cAYK2C5Ob6WDh0LHD9c1FYZvmdPcOM4JSCEsBCWcOh9mId123aEYj+iqr/AQmAuEpEdhjo3IxTvB/btgnmO47RBCGFBQDCh+BxwVztC0XEcp9uEEMYB38GEYgQOjTEeV5XlPS4WHafPCSEsiYVlvBsLNdwsxnhdoUbljKqexDCCMYWe/hETijv3S0ZIxyk7IYRFsRnF8djShullD+NyHKc/CSHMB/wSWy87F9grxnhqsVZ1FxeLjtPHhBBWwtJOb4hlHNs4xnhLsVZ1h6EEYxKK12L15VwoOk6PEEJYHEvSMw5bYzajVZZmx3GcogkhLIBlPN0HW4+5fYzx18Va1X1cLDpOnxJCWBu4EVgD+A8mFO8Z+qpy0UowulB0nN4khLAMVtolAA/HGGdWJYzLcZz+Ijm2/oCVMnkC2CLG+PtirSoGz4bqOH1ICGEjbI3iYsCfgZ1ijM8Ua1UxqOpJViKUi0TkYOBIXCg6Tk8RQlieeg28+2OMjxVpT96IyBrYO3q+4c5tkxNV9UcdupfjOEMQQlgBuBorZTIT2DrGeFexVhWHi0XH6TNCCDtgdX2mAL/Bsp7OKdaqYkmCcVHg51hxYBeKjtMDpAyCK2ElDiJwX4zxqWKtyh9VvQuL+nAcp48IIawFXIOVnboNSxj4YLFWFYuHoTpOHxFC2A+Ln58C/AzYo+pCEUBElsUywd4JrAu8q1iLHMdJGQRXxYTia1gim9ILRcdx+pMQwtuwPBDLAzcA76y6UAQXi47TN4QQjgDOwjIIfh04KMY4r1iriicJxeuwgvNvAT5DG2U1HMfJjxDCeCzj6SLAPKw0xrPFWuU4jtOaEMI2WAb1qcCVWOjp08Va1Ru4WHScHicYJwInp0OHxxi/4IkhQESWw4TivcBOqjpHVU+hLhh3LNI+x6kiIYSJWA3FBYFXAI0xvlCsVY7jOK0JIeyNrTGeH3PK7xpjfLFYq3oHF4uO08OEECZg4aZHYt75D8QYv1usVb1Bk1DcWVVfD8fNCMYLXTA6TvcIIUwG1sRC5edgQrHyofKO4/QmIYRPAOdgeVxOAj4UY5xbrFW9hSe4cZweJYQwBTgP2Al4Cdg9xnhVsVb1BhmheA+wS1Yo1lDVU1KW1AtF5L2qekV3rXScahFCmB8LPZ0AvICtUaxkqLxnQ3Wc3iYl3zoeK78FcGSM8VsFmtSzuFh0nB4khLAocBmwKfA0sEOM8aZireoNRGR5rI7ioEKxRpNg3ENVL++SmY5TKUIIC2PJbMYBzwL3xBhfK9aq4vBsqI7Tu6Q11acCHwFexXJAnFmsVb2Lh6E6To8RQngD8CdMKD4AbOJCsYG9gDsYRijWSCGpnwY+lbdhjlNFQgiLAathY4qnsBnFygpFx3F6lxQq/2tMKM7B1ie6UByC0M85MkIIESDGGIq2pRt4e8tNrb1YVs9pgGLZuGZ143Or8j0XRRW/56q1OYSwAUCM8Z9F29INUnsXBWanQ4/FGO/v0udW5nsuigo+v97eEpMZY10HbA48A+wYY/xLNz63n79nn1l0nN5jGlZYfpO8haLjOM4YWAJYJm0/2A2h6DiOM0Y2Bx7GaijmKhTLQinWLGa8BZXA21t6rsGS2TxftCFO56ng7/n1maAKsBuA5U0oPROBbbDkW1fHGJ8o2B4nJ6r2zvL2lp67gW1ijPcWbUi/UAqx6Dgl4z0xxleKNsJxHGcI5mJhXLNdKDqO00dsEmN8rGgj+olSiMV+jgMeCWWIex4JFW6vC8USU5XfMzT8piuxtqw2o1i19jrlpirvrAqPOarWXheKI8TXLDqO4ziO4ziO4zgDcLHoOI7jOI7jOI7jDMDFouM4juM4juM4jjMAF4uO4ziO4ziO4zjOAFwsOo7jOI7jOI7jOANwseg4juM4juM4juMMwMWi4ziO4ziO4ziOMwAXi47jOI7jOI7jOM4AJhRtQD8gIosA+wHvBtYHFgcmArOBGcBNwNmqWqpCzCISgMOAE4HJ6fBxqnrs/7d353FyVOX+xz8nhLAFCFvY9+VxYVHhpyKLsggooAiyiCIgKohXwateAX/3iqgvr/4UUFFUUNCLAooimwgqi4CIy0URwYdIIBCibCEsYQkk5/fHqWGqa3pmume6u7q6vu/XK690Vap7njPprj7PqVPPKS2oDjGzjYB7JvMa7l6LhWylesxsM+BQYCfgZcCq2T8tAOaQzlk/cveby4mws8xsGVIbpwPLAUtl/7QYWAQsBOa7+8JyIuysurVXBp+ZLQ/sBxwMvBRYl3RB42Hgb8AVwLnu/lRpQXbQoJyjO9FPNLN7gQ0nEcYu7n7dJJ4v41CyOIbsQ/Bh4DPAik0OmZn9eS3wETO7AjjK3R/sXZTdYWZrAucCe5Ucioi0yMxmAKcCRwDNBjPWyv68BjjezG4AjnD32T0LsoPMbClgfdIAXjNTSAN7KwAzzewp4F53f65HIXZU3dor9WBmuwDn0DxhWD/7sxfwX2Z2hLv/vJfxddIgnaPVT6wPJYujyBLFc0lXFPPmALcDzwMbAVszPJ13b+BGM9vB3R/qTaSdZ2b7AN8F1ig7lh66Fqjs/5mIma0N/Jo0Kj9kMfBX0nlrCrABsBXD56ydgD+Y2Y7ufmcPw500M1sa2ILh0WyACDxDuroWgGmkK29DpgMvMTN392d7FWsn1K29Ug9mdihwHo2J0x3A3aT371bA6tn+NYBLzOytVUwYB+kc3cV+4t9Ifex2qO/WZUoWR3cSjYniHcAH3P03+YOy6YxfAd6S7doM+Bbwth7E2FFmthzwZeADud23Aq8sJ6KeOkXTGKSqzGwKcAGNnZDzgJPc/f7CsRsApwH7Z7tWBX5kZtu4+5JexNshm9CYOM0HHnD3RfmDzGwa6crEjGzX1Oy5d/QiyA6qW3tlwJnZjqQrikOJ4u+B97n7bbljppGuwn0VWIb0fj7HzF7i7o/1NuKJG5RzdA/6iRcNwq1Og0YFbpows3WA/8ztugvYsZgoArj7vaQP9DW53fuZ2VZdDbLDsukEf6LxBHAGsH05EYlIG/YDds5tn+HuhxU7IQDufh/wduDK3O4tgX26G2LnZFO5pud2PeTu9xQTJwB3X+TudwOP53Yvl71GJdStvTL4suTpG6Sr4QA3ADvlE0V48f38beCw3O6ZwHt7EmjnVP4crX5ifSlZbO5w0gjWkOPHGsFy98XAfxV2v6XZsX1sfYZHvB4D3ubuH9K9LiKVcGTu8WPAf4x1sLtH4JOF3Xt2OqguWj33eDHwQAvPmVfYXqlz4XRd3dorg+9dpOmWkKZSH9xs8GOIu/+YNGvry6RE8crRju1Tg3COVj+xpjQNtbk35B4/AlzVwnNuJp3whu4XeXmHY+qV3wLvyEa2RKQaNiDdtzYN+IW7PzPeE9z9VjN7kuHiXZOpRtdr00j36wXg8VamZrn702a2mOHKodPGOr7P1K29MviOyj0+y93/Od4T3P2YLsbTbYN0jlY/sWaULDZ3FGkEZW1gSYtfzEvMbAHDyeJo1er61RLgv4H/dPcXyg5GRFrn7tsAmNl02psxspDhjkhlloJx9zvgxals7cS9hOHkqTLq1l4ZbNl0xh1zu84vK5ZeGZBztPqJNaVksQl3nwvMbec52Zd4fqrQkx0Nqsvc/X+B/y07DhGZuHbWIMvWNZuZ23VX5yPqrnaKPWTn6KVzuyo3dapu7ZWB9UaGE6YFpMI2tVDlc7T6ifWlZLFzXknjF/NfygpERKQFR9I4wn1xWYH0SHG2R2UqKU5Q3dor1bF17vGd+UEQM9sO2I00u2s6aVmEW4Gr3H1+T6MsX93O0dKnlCx2zgcK2z8tJQqZsGwNpCNIX1RbAquQRuMfAm4BLgN+nBU0EqksM9sV+GJu16XNqj0PCjNbEVgvt2tBOyP8VVO39krlbJl7fBeAmW1PKmAzWiX5Z83sDOBkd1/Y5fhKV7dzdF52RfUQ0trl25Fm7U0BHiatwXgVcK67Pz7qi0hHKVnsADPbgcZKV5e6+9/Kikcm5N9JlcaKRSCmke4X2BQ4FDjFzI5095t6HJ/IhJnZCqR7sF9O+hI+iOER6yuBd5YUWlfkpmAuRxr0WTX3z48D95QRV7fUrb1SeRvnHi8wsyOAsxi7T7os8DFgNzN7k7s/2MX4eq5u5+gx7Ea6+DKzyb+tn/15E3CymX0iW1ZFukzJ4iSZ2frAhQx/qBcCx5cXkUzQvtnfS4DbSPesBtJi1vlFdDcHrjGzg939Z70NUaQ9ZnYvzSvoReB3wFfc/YJextRN2fq2o1X9XEhan3BgprLVrb0yMPLLuGwGHE3qj15OWnvx96S6D2sDewEnkaqJQrrl50Iz220QZvnU7Rzdgnzho7uB2aRz2TrAqxjOW2YA3zKzzdx9zGVIZPKULE6Cma1Duhy+bm73e9xdo7jV8xxwGunE/K/8P5jZ5qQKYPtnu6YB55nZdu7+996GKdIRlwK/AK4pO5AeWQA8kf2pg7q1V6plxdzjvbO/j3P3rxaOm0NKCM4nna+GFn9/PemWke90M8iS1e0cnXcR8Gl3vz2/08xWIV1d/gTDVZ4/bma3uft5PY6xVtop3ys5ZmbATTRedfq4u/+opJCkPU8DV2R/LgV2dPcTi4kigLvPcvcDgK/ldq8AfK4nkYpM3GWkmQ+XkEaph97fbwXOBOaa2almttwoz6+aBaRCLgtIo9HPZ/tnkK5MbG1m62XTNgdB3dorg2H5wvb5TRLFF7n7E6SpmU/ndn+0G4GVoG7n6GZ+zXB/7Ah3P7CYKAK4+2Pu/knSeyHm/ukLZrZMb0KtpxBjHP+oPhVCiAAxxp6uPZPdePwT0hcypDftR939tG7+3BLbm3+TfNrdT+7Fzy2rvaMxs6mkm6st2xWB9dx9Xidev6z29tvveVD1y+/ZzLYmTes6OLf7ZmB3d3+6+bMmph/anHWy1ibdyzdkIXBXO0tRtCKEsC1AjPFPnXzddtShvf3we66Dbn1+zWwhjQnjdu4+7v+lmZ0LHJ7btUknZ3L1w/kKeneO7mR7e91PNLOzSWuiDznU3cdcr1N9rInTaGObzOxI0tSAoUTxBeDwbieKUr5sEdqv53YFUlGcygohLJ17PMgjl5Jx99vc/RDgI7nd2wNfKimkrnL3Z9x9NnB/bvcKNFYLHRiD3t4QwrLAa2msqCnVkl+H+mlaX7vv6sL2azoTTn+p2zl6gr5S2N6rlCjaEEJ4WdkxTJSSxTaY2WeA7zK8nuITwD7u/j/lRSU9dl1he4syguiEEMLyNK7bpGSxRtz9dNLA15CjzKxZBbqB4O4P0XgP3+rZbIGBNIjtDSGsQJrZsQyjF/aR/pdf8uARd291iluxRsCaHYqnL9XtHN0Od/8rkC/e1Xd9sZB8Prdr1VEP7nNKFltgZkuZ2feA/5vbPRvY3t2vKiksKUexXHdx4etKCCGsAvyS4eICxBhVNbF+vp97PA3YtaxAeuTR3ONAY1XGQTQw7Q0hrETqEE4lVUm8tdyIZBL+kXvczr1mxYJNK3Qgln5Xt3N0O/L9sb7qi4UQpgJnAycM7Ysx3lheRJOjZHEcZrYU6cP67tzu3wOvdfc7yolKSlS8+la5ha5DCOsCvwFeR+NUNamfewvbzUq4D5LnCtuDfnVqINobQliVtMTCFFICPJfGAhdSLfl1qFdrozhJMTmsw6Ls9xa2B/0c3Y58f6xv+mLZLT0XAe8Bnik5nI6o9JSUHvkqaTH2IVcAB3W6EIRUxsaF7RHVU/tZCMFIy71sCNxJuufyvlKDkkkxsx2A9wJrZX/e7+5/aPHpSxe2F3Uytm4ws+nA6qTYpwL3ufvCFp9eLDDQ9wlH3dpbFEKYSVqIG+DBGOPcEEJfXUWQtv0+93gq8Arglhaet1FhuyPF5bqtbufoXsgGGNbO7eqLvlgIYQapsu3OpCrVe5NWTqg0JYtjMLPjgGNzuy4B3p4VOpGKypY9+SCptPyGpMpdP2vx6bsXtn/bydi6KYSwHXAlqeP5O2CfGOOjIVS2QJcky5PWHBuyG9BqR6R4n8c/OxFQl02hccrRiqRqn61YtrD9fNOj+kvd2vuiEMI6DHcI58YYi7cBSDX9AniW4ffn/rSWLO5c2P5dJ4Pqorqdo1uSJXyfIfXDNgCudfeTWnz6TjROYS69LxZCWJv03t6aNJCxZ4zx9kHoY2ka6iiy0sVfzO26FjhYieJAeBL4N9I6Rq+gcUBgVGa2Aml0cMgjtPYFV7oQwu6k9/DqpJPZ7jHGR8d+llTETTQmD+9po5DJgYXtGzoTUlc9BeSXgFjdzFr9Nl6lsP1k06P6S93aO1QYYkNSohiBe5UoDg53f4q0vvGQ95nZmMU/siVh8rO8/uzuVUmc6naObom7P0fqhx1EqnB8TNbPasXxhe0rOhlbu0IImwI3khLFu4DXxRhHrBVZVUoWm8gWMP4+w/d33Avsl72xpeKydRGvzO16o5kdNtZzsvfEt2msvnaqu/f9SH0I4SDg58B04AfAW2KMrV6ZkD6XTYn/QW7X5sAp4z3PzA4G9sjtut7dH+hweB2XrRWYL8a0DLDOeM8zs1VoLPDyZBU+v3VrbwhhCrAJaWBrCTBbA1sD6dPA4uzxKsDZ2ffsaL5AmsI55GvdCqzT6naObtPZucerMHJJjBHM7BhyxfmAq929tIJXIYRXkq5sbgL8EdgxxjinrHi6Qclic+8AtsltH+vuxSpcUm0n0Fj84Rwz+5yZzSgeaGZbkpLL/KjmrcDp3Q1x8kIIxwIXkO57OB14d4yx7zuM0raTaax8eaKZnWtm6xcPNLOVzexTwHm53YvJVW2rgHmkNW6HrGVmG5nZiAIuWTXrtWm83zgCVep01aK9IYSlSIVsZpDek7NijAvKjUq6ISsQmE/43gZcVjxnmdmqZnYW8KHc7puB73U/yo46mXqdo1v1DWBWbvsoM/upmW1WPNDMZprZ6cCZud1PAB/ucoyjCiG8AbgemAn8Ctg1xvhwWfF0S4ixcve7vyiEEAFijB2dEGxmdwIvyTafB346wZc6pZMVU7vVXgAzu2CMfz449/hvwGiX1ivTXnhx1O48Gu/dXURKBOeRrixvQRoFzHNgT3fv6MhRJ9sb0iT5T2V/AE4EvhCbfOC7/XuWpAfv59eRBjXyV5Mi6fM6h3QuWxt4FY1VMSNwjLt/u9MxdfmcNZ2UWCxV+KdnSJ/jSBokWZ6RhV7muPsjnY4phLAtQIzxT51+7UFvbwhhaVL7lie9V2fFGJtWEuzm71mG9eCctRTwE9JUxCGLSffz/ZPUAX81jUVeZgO7dvr7F+p3jm63vd3qJ5rZy0mJVv7KcSQV4ZtNGihbn3TbUP789wRwoLtf3Ur8nf7/DSHsD5xP+r+6EDg8xjhiBuIg9LGULDZhZp36pezi7td16LW63fHqRJsr094hWZWybwEvb+HwF4BzgY9240pzp9qbjc5/lXQv5hLg6Bjj2WMcX/kTWRX06P28Men9/MYWnzIbONrdf9WNeHrQ+VqGVBih1fUDnyNVE+3KTJFuJzGD2t4QwjKkQbllSDHPatbp6vTPlbH16Jy1NGkN65MYv+jiZcD73L0r96/W7Rw9gWSxa/3E7Arr14F9W3yda0iz/rzVH9zhAfn3Ad8kzdD8OnBcjHHxKMdWvo+lZLEJJYsTVpn25mXFIvYE9iONYq4PrEzqtDxKupJ4DXBBN0Yzh3SivVmn639IN8U/BxwSYxyz0usgnMiqoJe/ZzN7FXAAqXrgRsCqpNH5BaTpiL8nFQS4PLsnrit6+BlennS/y3TSKO9U0tW1xaSrbk8Dj7t7V6c09iqJGaT2ZmuSbU56fz5NShTHLCSnZLE3enzO2oR0q8fepO/gNUjFnR4ArgMudPeuLkFQt3N0PyWLuZ+xFfAuYHvSTINVSOe2R0nLfF0H/Mzd2y4u2KE+ViANbHw22/Up4DPNZm118ueWTclihai9g22y7Q0hrAhcTCrL/QSpkM313f650po6/p7r1ua6JTGTbW8IIT+19kng7tFG5zv5c6U1Nfz8qr0DrAN9rCnAaaR7JCNwbIzxm93+uf1A6yyKDIAQwhqkeyG2BR4E9oox/rncqEREmssWr96EdNXgMeCesUbnRUTKEkKYRroN6R2k2RvvjDFeVGpQPaRkUaTiQggbAVeTpnLdTVoI9u4yYxIRGU0IYXXSQtwADwP3K1EUkX6UzYC4iHS70lPAfjHGX5cbVW8pWRSpsBDCVsBVpApqfwbeFGP8V7lRiYg0F0JYC1g32/xnjHFemfGIiIwmG9i6glTP4mFSH6t209+VLIpUVAhhB+By0ppk1wNvjTE+Xm5UIiLNhRDWA9bMNu+PMT5UZjwiIqMJIWxAGox/CXAvsEeMcdaYTxpQU8oOQETaF0LYh7Qu0QxSUZu9lCiKSD8KyUakRDGS7k9UoigifSmE8FLgJlKieDuwQ10TRVCyKFI5IYTDgZ8BywJnAQfGGJ8tNyoRkZGyCoKbAquR1n39R4xxfrlRiYg0F0J4LXAjsF729851ny6vZFGkQkIIHyNV5FoK+BxwdCul5kVEei2EMBXYgrRu7QvAXTHGJ8qNSkSkuRDCXsCvSeteXkaaevpYuVGVT/csilRAthDsF4CPZ7uOjzF+pcSQRERGlZWa35w0A2IRMEszIESkX4UQDgW+R8qNzgXeF2N8odSg+oSSRZE+l43OnwUcQRqdPzzG+MNSgxIRGUUIYVlSojgNeIY09XRRuVGJiDQXQjgOOD3b/CJwgpbzGaZkUaSPhRCWBy4E9gGeBg6IMf6i3KhERJoLIawAbEbqXywkJYoanReRvpPN2voscFK26+Mxxi+VGFJfUrIo0qdCCKsAlwI7AvOBN8cYbyk3KhGR5kIIK5GK2UwBHgdmxxiXlBuViMhI2aytM4H3AouBo2KM3ys3qv6kZFGkD4UQ1iGt77MlMJd0k/Wd5UYlItJcCGFVYCMgAI8CczSNS0T6UTZV/nxgP9JU+YNijJeXG1X/UrIo0mdCCFsAVwMbAn8nJYr3lxuViEhzIYSZwPrZ5oMxxrllxiMiMpoQwsrAJcDrgQXAPjHGm8qNqr8pWRTpPzcCawC3AHvHGB8tOR4RkdGsnnv8QIzxX6VFIiIyvuuBbYB5wJ4xxttLjqfvaZ1Fkf6zBmkK6m5KFEWkj63FcLI4R4miiFTANsBdwA5KFFszEFcWQwi1ui9C7R14PwSOVKn5wVTD9zMhhG3LjqFH9gdIBfYG3jRgN1KV5itijAtKjke6pG7nLLV34P2RVDDw4bIDqYqBSBZFBsxhqiAoIn1uEfAY8JgSRRGpkF1jjE+WHUSVDESyGGOsxTDu0OiP2juYcu1VojjA6vJ+hob39J/KjqUXhq4o1q29Mtjqcs6qcZ+jbu1Votgm3bMoIiIiIiIiIyhZFBERERERkRGULIqIiIiIiMgIShZFRERERERkBCWLIiIiIiIiMoKSRRERERERERlByaKIiIiIiIiMoGRRRERERERERphadgBVZ2ZLA78HXpHbvYu7X1dORN01KO01s42AeybzGu5ei4VspXrMbAvgMGAHwIBVgKWAx4D7gFuAn7r7taUF2UFmtix3YSGcAAAX8klEQVSwKjAdWJbU1gC8ACwCFgIL3H0gFmOuW3ulesxsM+BQYCfgZaT3K8ACYA5wM/Ajd7+5jdecCuwP7A28FphJ+gw8Acwj9U1+Blzh7ks605KWY6tVe8cymX5i1uaDgDcBryG1eVngEWAW8EvgHHf/Z4fDljGEGGPZMUxYCCECxBhL67Sb2aeAkwu7u5I8qb2d04/JYln/v/3wvqqDXvyezWw14KvAO0jJw3huBY5y91u7EU+325x1LNZnuGM2nqeBOe7+dDfiCSFsCxBj/FM3Xr9u7e23n1s3E/n8mtkM4FTgCFo7B90AHOHus8d53d2Bs4CNWnjNvwOHufsfWzj2RWpvZ0y0n2hmOwDfIQ1wjuVp4LPu/vl24lIfa+KULE6CmW0N/BFYuvBPlUueWjFI7W2SLF4LPNTOa7j7IZ2MSSeywdaDxGlN4Hoav2hfAG4D5gKLgTWBVwLL5Y55FtjH3X/d6Zi6/BleGtiCNOo8JALPkK6uQZo9szyNt1wsAf7Rjatu3Uxi6tbefvy5ddPu59fM1gZ+Dbw0t3sx8FfS1bUpwAbAVjS+R+cDO7r7naO87vuAb9GYjM0H/pd0lW0msC2N57VngN3d/betxA5qbydMtJ9oZrsBl5LOX0PmAX8jJYcbA1sXnvYVdz++1djUx5o4TUOdoGyE9xxGfiAGUg3ae0rVptKKFHyXxkTxLOA/3f3B/EFmtgLwQeBzpO+AZYELzWxzd3+sV8F2wIY0Jk6PAPPc/fn8QWY2hdS5WofU+ZoCbGJmt7v74l4F2wF1a69USPa+u4DGxOk84CR3v79w7AbAaaQplpCulP/IzLYpTqc0s52AbzKcOC0APgKc5+4v5I5bCfgEcGJ27HLAj81sM3d/pjOtbIirVu1txUT7iWa2HnARw4niv4Cjgcvzv5/s9oqzSVN9AY7LzmtnTzZ2GZsK3EzcCcCrsse/KzOQHqlbe0Uqw8y2A96c2/VDd39/MVEEcPeF7v5F0md6yGqkL+dKMLPlgZVzu+a7+5xi4gTg7kvc/V/AA7ndU4E1uhxmx9StvVJJ+wE757bPcPfDiokTgLvfB7wduDK3e0tgnyavewbDfdXnSFfPzs0nTtlrPuHunwROye1eBziq7Za0pm7tbcVE+4mfBWZkj58CdnX3S4uJtLvfBewB/Dm3+7+zxFm6SMniBJjZlsB/ZpuLgE+WGE7X1a29IhX0psL2l1p4zjdInZEhe3QunK5bubA9Iilu4mHStM0hVepg1K29Uj1H5h4/BvzHWAe7e2RkX2LP/IaZbU/j1MOvuPt4U4+/AOSnXL91nOMnqm7tHdNE+4lmthapMNCQz482PRfA3Z8Fjs3tWg04vL1opV1KFttkZkuRLrNPy3adBox5o3KV1a29IhW1XmF71C/bIdlUpXtzu9bpZEBdNq2w/ex4T8hGqfPJcZWm1NetvVI9GzB87+wvWpkKmRXWyic6GxYOeUNh+7wWXvMZUuXRIS8f7zkTVLf2jmqS/cSDGD43PU+agjumrKJsPol+Z4s/SyZI9yy27z+A7bLHd5EqPq1VWjTdV7f2ilTRU4Xt6bSQUNBYIGFh58LpuuK9d1NIhVzGUyz8UhV1a69UjLtvA2Bm02nvQsRCYMXscbEAyLeAq4G1Sf2OO1p8zUdzj1drI5aW1a2945hMPzF/dfUP7j6/xeddRSryA/BqM1vN3R8d6wkycUoW22BmLwM+lW1GUsn5Z83Gq/JbTXVrr0iF/b6wvQ2pSt+oskI3+auJxdfoZ8XEdjkaR+xHyApS5K+uVSk5rlt7paLcvThwNarsXtyZuV13FV5rPqkKaLvWzD3u6lqjdWtvUQf6ia/NPb6xjR+dPzaQ1mT8eRvPlzZoGmqLcpfZl8l2fd3d23ljV0rd2itScZfQeB/biVmyMJajGR4wjKT1raricdKUpSFrt/CcNWgcyX+koxF1V93aK/VwJI390Isn+4JmNo00WDbkL5N9zQ4aqPZOtp+YLfeUXzN23Nsnxjj2pU2Pko7QlcXWfRR4dfb4XlK54kFWt/YOrZl0BLAbqVLZKqR7fh4CbgEuA36s8vPSb7KR3A8APyElCLsBF5vZh919Tv5YM1sOOB74TG736e0u6Fwmd19iZvcBm2a7VjSzTYH73X1R/tjCUhJDHuzWQvXdULf2yuAzs12BL+Z2Xeruv+nASx9E41TMn3TgNSdtQNs72X5i8Z7NB5oe1dy8wvbGbf5saYOSxRaY2UuAT+d2vb+dqQdVU7f2Zv6dNHe+WEhiGun+gk1JFbtOMbMj3f2mHscnMiZ3v9jM3kW672U68BZgXzO7DbifdGVqDRoXc14MfJkKDga5+wIzu4fU4ZhCKr0+w8yGFqmPjFykPpISp3Y6JX2hbu2VwZJNe1+bVIDlEFKSM/Q+vZIOFCkxs1WA/5fb9S/g3Mm+7gRjGej2dqifWFzOp+V7Dt19kZk9Rfqua/Za0kFKFseRjdJ+l+HFkL/r7r8sMaSuqlt7c/bN/l4C3AbMJV2h2YTG6Q2bA9eY2cHu/rPehigyNnf/oZn9EjiONACyHGmK0jaFQyPwA+AUd5/V2yg7x93nm9kTpCtpa5I6Y8vRWLhnyHzSIvbPNfm3Sqhbe6X6zOxeRl5BgnQO+h1peYgLOvBzlgZ+RGNhlQ/3+op6HdrbwX7i9MJ2u8lmPllccawDZXJ0z+L4PgJsnz2eR+qADbK6tXfIc8B/A+u6+yvdfV9338fdXwZsAfw0d+w04LxsZE2kb5jZesDpwCdonkAMCcC7gJ+Y2dt6EVs3ZPfrrE/qMI33fbYqsKmZzRjnuL5Vt/bKQLsU+B5wzWRfKPtcnA/sntt9prv/eLKv3UGD1N5O9ROLM7meb3rU6F4Y47Wkg5QsjsHMtqDxvp5j3P3xsuLptpq192ngiuzPpcCO7n6iu/+reKC7z3L3A4Cv5XavAHyuJ5GKtMDMXkO6Kn4oadbIY6QqdduQFmRfDtgIOIzhyqdbAT81s1N7He9kZdO8XkZKigJpSu08Urn5PwO3An8F7mG4EuhypASquC5l36tbe2VgXAZcSCrC9TvSVElIi8efCcw1s1Oze6nbZmYrkr7DD8jtvgT48IQjnpyBbm+X+4nt5iTFpUekSzQNdRS5y+xDH+jz3f2yEkPqqrq1190fAvZp82n/DuwBDNWEfpuZrePuxRutRXrKzGaSOhCrZLv+DrzR3ecWDp0DzDGzH5CKLXws2/8RM7vd3b/bk4AnycymApsBS2W7ngVmFYu9kO7lmw/MzxKmoRLza5rZs+5eiQqhdWuvDA53/1Bxn5ltDZwEHExa3uUjwGvNbPd2plGa2QbA5aRBryE/Ag5z9xeaP6u7Brm9XegnFs9f7SbQy4/xWtJBurI4ug8DO2SPH6a8UapeqVt725adjL+e2xVoXFC2ckIIy+cea85/dX2S4fW7InBwk0TxRe4eSQsp35Lb/ZnsPpgqWJvGwc7ZTRKnBtnvI7/W4DpmVpWR6bq1d1QhhBVIBcdU0KKi3P02dz+ElDQN2R74UquvYWbbkc5f+cTpTOAd4302em2A2tvpfmLximS7yWL++AWTjKUrQggh93jbMmOZDCWLTZjZZjROMfzQII/I1q29k3RdYXuLMoLohBDCqsDQTemL0JSOSspGew/L7brO3W8b73lZwnh2btc6wM4dDq9b8qXin3T3Z1p8Xv68tjQjCyz0q7q1t6kQwkqkc+5ztF8MQ/qMu58O/CK366hslsSYzOwtwPUMF3eJwEnufqy7L+l8pJ1R5fZ2qZ/4UGG75QEgM1uJ4QI7zV6rdCGEqQx/x8YyY5ksJYsF2cjrdxi+vP19d7+wxJC6qm7t7YAHC9urNT2qz4UQ1gV+A7yOtKzCNjHGJ8qNSiZoM4annwLc3MZz/1TY3m7y4XSXmS3L8HRMaLx6Np7ilK8VJh9Rd9WtvaPJBrc2I/Vb/gJo+aLB8P3c42nArmMdbGZHkxazH+qzPA283d0/353wOq5y7e1iP/GewnazKrKj2aSwffckY+moEMJypDUv3wM8A+wbYyx+31aG7lkcaQMaR9ffbWbvbvM1rjWzFzfcvZ+v2NStvZNVnCZRudHtEIIBV5P+7+8A9owxjjplUfre6oXtx9p47pOF7SoMfhS/t9q5V2fxOK/Vj+rW3hFCCDNJVWABHtT5aqDcW9geNWEws2OBMxieBfMQsI+7/6E7oXXFvYXtKrS3K/1Ed3/MzB4A1s12b97G61lh+69txtM1IYQZpBoCO5G+j/eJMf623Kgmp5JfHF02yIlOM3Vr72RtXNgeUT21n4UQ/g/wc1KCcTPpJDa/3KhkkopTEldq47nF+1SrMPhRnHa1VNOjmiseW0ym+lHd2tsghLAO6Z5NgLkxxuLsDimZme0AvJc0TXIt0gLtrSY0xfukm95/Z2YH05g4/QPYy917fkWpbu2lu/3EG0mFfwBe38bzdsk9XsRwhe9ShRDWJk013hp4gDQY/7dyo5o8JYsjPQ94m89ZmsZL4vczcvpPv6pbe7E0vPVB0mjZhsCn3f1nLT5998J2ZUaLQghvJE1nWQG4EjgwxtjOlDbpT8WrLFu28dziWqFVuGIzmQp6yxa2213Xqwx1ay/wYmGIDUgDWxGYE2N8tNyoZBTLA0fktncDWk2eivf9/7N4QLYs0Lk0Jk47NVvqqkfq1t5u9hMvZzhZfIWZrevuD4z1wma2FPDm3K5ftlNVtltCCJuRZm1tDNwF7BFjnFNuVJ2hZLEge5O2tdi6mW1E49zrd7v7dR0Mq2vq1t7Mk8C/MXwiPhYYN1nM1jl7b27XIzRWk+xbIYSDgPNIJ/DzgPfEGCvTcZTRufvDZuYMT8vZw8xWbnHtq/0K29d1NLgucPcXzOxZhhOhlcxsKXdv5apZcYH64jTcvlO39gKEEKaQOlwzSFdWZ8cYB3XN30FwE+le2qF7Yt9jZl9qcTmHAwvbN+Q3su/dHzD8/p8H7FFi4gQ1a2+X+4kXA0+QZsRMAT4EnDDOy7+d4WnpAOe0E1s3hBBeSbqiOJM0cLB3jPHhcqPqHBW4kdrJ1kW8MrfrjWZ22GjHw4sVJ7/N8LplAKe6e98nXCGEDwIXkBLF04DDlSgOnPyX5QrAl8d7gpm9gfSlO+QGd5/d4bi6JX+FaQow7qLz2WLW+UJAT7n7c50OrEtq094QwlKkQjYzSNNmZylR7G/ZVZ0f5HZtDpwy3vOyqZZ75HZd3+Sq0udJS6VAusL1FncvFkbpqbq1t5vcfSFpuu2Q481s1CUmzGwN4NTcrjtpYbC/m0IIu5Cq1c4kVZjfdZASRVCyKPV1Aqn8+pBzzOxzZlYcicfMtiQll4fmdt8KnN7dECcnJJ9m+L6HE4CPxhj7trS4TNgZNFaDO8rMLsxGdxuY2dJZhb3LGf4OeIHxR3P7yUM0fn5XN7NNzGxa8UAzC1kHY7Pc7ki6n6QqatHeEMLSpGl6K5JNfYsxVuE+WoGTaRzUONHMzjWz9YsHmtnKZvYp0iyXIYspnIOy89cxuV2nuXu/VJQ8mXq1t5s+DwwNVC4DXG1mB2SD9C/KpufeQFrmCdKsg2NbnGXRFSGE/UlXFFcELiRVPR24c1aIsbpLf4QQIkCMsdQiLU0ut+/SjWmZam9nZaN859E4HXsRKRGcRyprvQUjK3Q5sKe7d3Queifbm43Ofw34AOmE+v4Y43cm+7oycT14PxtwLcPFQCAlCXcAc4BnSfd/bUvjEgqLgWPcPb/mYkd0s83ZkhJbMLJgxDOkz3EkfbaXp3FgNAL3dWMt2aFFl7tRIn3Q2xtCWIZ0rl2GlBjPijH2/ZXQQdbu59fMXkcaWM0X2YrA7aRz0POk89OrSN+v+WOOcfdvF17vTBqTp6tpr9rzkIvc/aLxDlJ7O6fdfmL2/XUdw2tJQuqH/ZV0ftuCxgqoS4D3unvLU1A73d4QwvuBM0nn2zOA4wZ1MF73LEptufuFZjYX+Bbw8mz3NOA1ozzlBdJN5x91975dkzDrdJ1HmmL4HHBIjLHUaRrSfe7uZvYK4BvA/qSryYH03n75aE8jdVqu60mQHeTuz5rZHaQiKPnplssxehGYZ0mJUyXu3csb5PZma5JtTkqEnyYliu0sESJ9wN1/m52DvgW8MdsdgK2yP83MBo529181+beXFrb3aHJMK/4OjJs8tatu7e2m7PtrZ9J6jjtlu9dh+Cpi3lzgw+5+ca/iy8uKb30S+Ey267+Az8YqX30bh5JFqTV3v8nMtgL2JBX7eDXpxumVSYnWo6QO9TXABZ2+mthpIYQVSfP3dyXdNL5vjPE35UYlveLuDwFvN7OXAoeQvnQ3JyUXSwMLSKO1N5NGxC9398p+wWUFJWZnV91WBaaTrkxNJXXaFpNGpRcCj7dY9KdvDWJ7s3PWpqRlPp4E7o4xVm6JD0my++v2MLNXAQeQ1ufbiPR+HToHPUBa6uAK0jmosldj6tbebnL3WcDOZvZm0u9yB9KV2WnAg8BfSLdP/KCs6qdZ8a3TSYV4InBsjPGbZcTSS5qGWiFq72CbbHuzhat/Tppm+CBpfZ+/dC5CmYy6vZ+hfm3u5jTUfjTZ9maLV29CSnQfA+4Z5NH5qqnh51ftHWAd6GNNI80uewdpUO6dMcZKXcGdKF1ZFBkAIYSNSPc3bE4qdLJHjLEqlS1FpGZCCKuT1rkFeBi4X4miiPSjEMJ04CekqcFPAW+NMV5TblS9o2RRpOJCCFsBV5Gma/wZ2CvG+GC5UYmINBdCWAtYN9v8Z4xxXpnxiIiMJhvYuoJ0m9LDwJvqMntkiJJFkQoLIewIXEZak+w6YD+tSSYi/SqEsB7D69XeN2jrkYnI4AghbECatWXAvaRZW7NKDaoEWmdRpKJCCPuSFoCdAVxMGu1SoigifSdb93VjUqIYgdlKFEWkX4UQXgbcREoU/wrsUMdEEZQsilRSCOEIUoK4LHAWcGCM8dlSgxIRaSKrILgpqULkEuAfMcaJrB8nItJ1IYTtgRuA9YAbgZ3rPF1eyaJIxYQQPg6cQyo1/1ngaJWaF5F+FEKYSlpQe2XSWrV3xRj7dp1aEam3EMKbgF+RBrcuI009XVBuVOXSPYsiFZEtBPtF4GPZruNijF8tMSQRkVFlpeY3J82AWATM0gwIEelXIYR3kpbHmJr9/b4Y4wtlxtQPlCyKVEAIYWnSdNPDSaPzh8cYf1huVCIizYUQliUlitOAZ0iJ4vPlRiUi0lwI4XjgtGzzi8AJWs4nUbIo0udCCMsDFwL7AE8D+8cYryo3KhGR5kIIKwCbkfoYTwF3a3ReRPpRNmvrc8CJ2a6PxRi/XGJIfUfJokgfCyGsQpozvwMwH3hzjPGWcqMSEWkuhLASqZjNFOBxUtXTJeVGJSIyUnZP9TeBo4DFwHtijN8vN6r+o2RRpE+FENYBrgK2BO4H9owx3lluVCIizYUQVgU2AgLwKDBH07hEpB9lU+XPB/YjTZU/MMZ4RblR9ScliyJ9KISwBWkh2A2BO0mJ4v3lRiUi0lwIYSawfrb5YIxxbpnxiIiMJoSwMnAJ8HpgAbB3jPG35UbVv5QsivSZEMJ2wJXA6sAtpJPYo+VGJSLSXDYLYu1sc26M8cEy4xERGU0IYS3gF8A2wDzSYPzt5UbV35QsivSfa4HppCmoB8QYF5Ycj4jIaNbKPb5XA1si0uduAjYB7iKtoTin5Hj63kAkiyGEWt0TofYOvOnAD4EjY4yLyg5GOquG72dCCNuWHUOPvB4gFderhZ1IhWzmAffUfeHqQVW3c5baO/A2Af5IKhj4cNnBVMGUsgOYJP0nyyD6CnCYEsWBU9fz1eNlB9BDC7M/dTCN1Id4krSGohLFwVPXc5YMtl8BuypRbF1QoTKR/hBCeAlpxOtKVRAUkX4XQpgBPBNjfK7sWERExhJCWAPYBbhE56z2KFkUERERERGREao+DVVERERERES6QMmiiIiIiIiIjKBkUUREREREREZQsigiIiIiIiIjKFkUERERERGREZQsioiIiIiIyAhKFkVERERERGQEJYsiIiIiIiIygpJFERERERERGUHJooiIiIiIiIygZFFERERERERGULIoIiIiIiIiIyhZFBERERERkRGULIqIiIiIiMgIShZFRERERERkBCWLIiIiIiIiMoKSRRERERERERnh/wOZpti3usvv4wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1152x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jdgsLuRLMT6Z",
        "outputId": "b9f10f38-7862-4d04-9ace-4981acddbcca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "np.random.seed(11)\n",
        "\n",
        "m, n = 4, 3\n",
        "a = np.random.randint(0, 10, m).reshape(-1,1)\n",
        "b = np.random.randint(0, 10, n)\n",
        "\n",
        "a"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[9],\n",
              "       [0],\n",
              "       [1],\n",
              "       [7]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nAV8F__rMVS6",
        "outputId": "4e2ef4de-f9bd-442d-d15d-cf5a1de3279d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 7, 2])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P1k5OxBcMWwZ",
        "outputId": "6e529cb9-0768-4a4e-ca29-bf55950d8fcd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "a*b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 9, 63, 18],\n",
              "       [ 0,  0,  0],\n",
              "       [ 1,  7,  2],\n",
              "       [ 7, 49, 14]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WYeD69jDMYrB"
      },
      "source": [
        "## 그림 7-16"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y3iia2pQMXqR",
        "outputId": "6bfff49c-a949-494d-a6a0-8e9b230dcd35",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        }
      },
      "source": [
        "fig = plt.figure(figsize=(16,5))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "dy = 0.1\n",
        "dx = 0.0\n",
        "for j in range(m) :\n",
        "    for i in range(n) :\n",
        "        if i == 0 :\n",
        "            style = box_solid\n",
        "            la = 1.0\n",
        "        else :\n",
        "            style = box_gray\n",
        "            la = 0.2\n",
        "        \n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                if i == 0 :\n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, a[::-1][j,0], 40, la, hidden=('R+', 'U'), **style)\n",
        "                else :\n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, a[::-1][j,0], 40, la, hidden=('R', 'U'), **style)\n",
        "            else :\n",
        "                if i == 0 : \n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, a[::-1][j,0], 40, la, hidden=('R+',), **style)\n",
        "                else :\n",
        "                    cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, a[::-1][j,0], 40, la, hidden=('R',), **style)\n",
        "        else :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, a[::-1][j,0], 40, la, hidden=('U',), **style)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, a[::-1][j,0], 40, la, hidden=(None,), **style) \n",
        "ax.text(.43, .22, r'$\\times$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "dx = 0.5        \n",
        "for j in range(m) :\n",
        "    for i in range(n):\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 0.2, hidden=('R', 'U'), **box_gray)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 0.2, hidden=('U',), **box_gray)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, b[i], 40, 1.0, hidden=(None,), **box_solid) \n",
        "\n",
        "ax.text(.93, .22, r'$=$', ha='center', va='center', fontsize=30)\n",
        "\n",
        "C = a*b\n",
        "dx = 1.0       \n",
        "for j in range(m) :\n",
        "    for i in range(n):\n",
        "        if i < n-1 :\n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('R', 'U'), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx,   0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('R',), **box_solid)\n",
        "        else :    \n",
        "            if j < m-1 :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=('U',), **box_solid)\n",
        "            else :\n",
        "                cube2d2(ax, (0+dy*i+dx, 0+dy*j), 0.1, 0.1, 0.05, C[::-1,:][j,i], 40, 1.0, hidden=(None,), **box_solid)    \n",
        "\n",
        "ax.axis('off')\n",
        "\n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-16.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-16.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1152x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0j4j-OR7MckM"
      },
      "source": [
        "# 행렬 곱셈의 해석"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lr_JDYGlMd25"
      },
      "source": [
        "## 행렬곱을 열조합으로 계산"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q8JHJtkQMa0R"
      },
      "source": [
        "np.random.seed(10)\n",
        "\n",
        "A = np.random.randint(0, 9, 12).reshape(4,3)\n",
        "b = np.random.randint(0, 9, 3).reshape(3,1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nsON0LkUMe-h",
        "outputId": "b01d91e8-1cee-4a2b-b577-3a4ac444bb14",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "A"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4, 0, 1],\n",
              "       [0, 1, 8],\n",
              "       [0, 8, 6],\n",
              "       [4, 3, 0]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fsEggubQMgEp",
        "outputId": "5ce546fe-eae3-4daf-f92a-61b8ec7137de",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4],\n",
              "       [6],\n",
              "       [8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 87
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ph4GY7R6Mg0r",
        "outputId": "d0b16824-3c76-459c-f593-a7c9a67d532e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "C = np.dot(A,b)\n",
        "\n",
        "C"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[24],\n",
              "       [70],\n",
              "       [96],\n",
              "       [34]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a3SKfuW7MhxZ",
        "outputId": "bc6fc355-2f28-4d32-d897-8a15dc5a635b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "C_ = np.array([A[:,[i]]*b[i] for i in range(A.shape[1])])\n",
        "print(C_.shape)\n",
        "C_.sum(axis=0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(3, 4, 1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[24],\n",
              "       [70],\n",
              "       [96],\n",
              "       [34]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ly3PTXZQMkL7"
      },
      "source": [
        "### 이번엔 뒤가 행렬인 경우로 확장"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f5XLah1gMipp"
      },
      "source": [
        "B = np.random.randint(0, 9, 6).reshape(3,2)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H-bqgGboMl-6",
        "outputId": "77405bda-f78b-4ebd-f9a8-665cdda19613",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "B"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 8],\n",
              "       [4, 1],\n",
              "       [3, 6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ia8plVmzMnJi",
        "outputId": "c57edc42-bf37-42e7-a4a7-b249f61e10e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "C = np.dot(A,B)\n",
        "\n",
        "C"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 7, 38],\n",
              "       [28, 49],\n",
              "       [50, 44],\n",
              "       [16, 35]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6HzS67O_MoLC",
        "outputId": "dfaf8d83-6e4d-4c6d-f2ba-11cef3a12623",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "C_ = np.array([ [A[:,[i]]*B[i,j] for i in range(A.shape[1]) ] for j in range(B.shape[1]) ])\n",
        "\n",
        "print(C_.shape)\n",
        "C_ = C_.transpose(1, 2, 0, 3)\n",
        "print(C_.shape)\n",
        "C_ = C_.sum(axis=0)\n",
        "print(C_.shape)\n",
        "C_.squeeze()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(2, 3, 4, 1)\n",
            "(3, 4, 2, 1)\n",
            "(4, 2, 1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 7, 38],\n",
              "       [28, 49],\n",
              "       [50, 44],\n",
              "       [16, 35]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XiwuRjW3MrUX"
      },
      "source": [
        "## 행렬곱을 행조합으로 계산"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UDbS0RInMpBq"
      },
      "source": [
        "# 직접 확인해보세요."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bIZYpJhsMuii"
      },
      "source": [
        "## 행렬곱을 외적합으로 계산"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RYZBblw3MtHy"
      },
      "source": [
        "# 직접 확인해보세요."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dg1nrtB7Mx6q"
      },
      "source": [
        "# 행렬을 이용한 코딩\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZH8yZwM7MzYh"
      },
      "source": [
        "## 벡터화 실습 1 (기본 곱셈)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MKUmbfEUMv4a"
      },
      "source": [
        "A = np.eye(5)*np.array([1,3,0,5,4])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w9ICdtjMM0w5",
        "outputId": "c3b57b0e-0b51-4055-85a9-e663df1ca348",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0., 0., 0., 0.],\n",
              "       [0., 3., 0., 0., 0.],\n",
              "       [0., 0., 0., 0., 0.],\n",
              "       [0., 0., 0., 5., 0.],\n",
              "       [0., 0., 0., 0., 4.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PCZZydngM1ra",
        "outputId": "e596f589-5d1b-4e76-ded6-86db39eb1cac",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A = np.random.randint(0,10,12).reshape(4,3) #-----[1]\n",
        "x = np.random.randint(0,10,3)\n",
        "\n",
        "\n",
        "print(A)\n",
        "print(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[5 3 9]\n",
            " [6 9 1]\n",
            " [9 4 2]\n",
            " [6 7 8]]\n",
            "[8 9 2]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oRffjsC3M2tD"
      },
      "source": [
        "m = x.shape[0] #-----[2]\n",
        "y = [] #-----[3]\n",
        "temp = 0\n",
        "for i in range(A.shape[0]) : #-----[4]\n",
        "    for j in range(m) : #-----[5]\n",
        "        temp += A[i,j]*x[j] #-----[6]\n",
        "    y.append(temp) #-----[7]\n",
        "    temp = 0\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GG8nrQRoM4yi",
        "outputId": "a066edc0-6cd2-4495-e059-0ad017c642b4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[85, 131, 112, 127]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 100
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S0MeaO8CM6DS",
        "outputId": "f84862be-27e0-49f4-f50b-23f5028776ce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A.dot(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 85, 131, 112, 127])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 101
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "17mdU8WvM60y",
        "outputId": "db2608cb-00a0-4b27-dfc8-65c8bdc5c741",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A@x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 85, 131, 112, 127])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 102
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xZ3IQKeHM9h2"
      },
      "source": [
        "## 벡터화 실습 2 (전치 곱셈)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pfBE83H4M766"
      },
      "source": [
        "A = np.random.randint(0,10,12).reshape(3,4) \n",
        "x = np.random.randint(0,10,3)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1wP6sRyQM-4i"
      },
      "source": [
        "m = x.shape[0] \n",
        "y = [] \n",
        "temp = 0\n",
        "for i in range(A.shape[1]) : \n",
        "    for j in range(m) : \n",
        "        temp += A[j,i]*x[j] #-----[1]\n",
        "    y.append(temp) \n",
        "    temp = 0\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HCDy5ZhYM_iq",
        "outputId": "bf8a5d1a-0cbc-4e7d-dcf6-cc16dda51aaa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[8, 162, 97, 120]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jlIj9OF7NAfy",
        "outputId": "fcc265d1-82aa-4d06-8ede-95cff5d672d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "y = A.T.dot(x) \n",
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  8, 162,  97, 120])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 106
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w_nMCUSUNBiL",
        "outputId": "c2e075e1-bd49-4d18-c174-2f5c94e048c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "A.T@x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  8, 162,  97, 120])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 107
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P8aZPI2KNEDl"
      },
      "source": [
        "## 그림 7-17"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8pbAZvSjNCsq",
        "outputId": "289d8754-6c9c-4518-f05e-6702ce9bd2b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        }
      },
      "source": [
        "fig = plt.figure(figsize=(16,4))\n",
        "ax = [fig.add_subplot(1, 2, 1), fig.add_subplot(1, 2, 2)]\n",
        "\n",
        "plt.rcParams['text.usetex'] = True\n",
        "plt.rcParams['text.latex.preamble'] = r'\\usepackage{amsmath}'\n",
        "\n",
        "pdf_shift = 0.02\n",
        "\n",
        "y = [ r\"$\\begin{bmatrix}\" + \\\n",
        "r\"y_{1} \\\\\" + \\\n",
        "r\"y_{2} \\\\\" + \\\n",
        "r\"\\vdots \\\\\" + \\\n",
        "r\"y_{m} \" + \\\n",
        "r\"\\end{bmatrix}$\",\n",
        "    r\"$\\begin{bmatrix}\" + \\\n",
        "r\"y_{1} \\\\\" + \\\n",
        "r\"y_{2} \\\\\" + \\\n",
        "r\"\\vdots \\\\\" + \\\n",
        "r\"y_{n} \" + \\\n",
        "r\"\\end{bmatrix}$\" \n",
        "    ]\n",
        "\n",
        "A = [ r\"$\\begin{bmatrix}\" + \\\n",
        "r\"a_{11} & a_{12} & \\cdots & a_{1m} \\\\\" + \\\n",
        "r\"a_{21} & a_{22} & \\cdots & a_{2m} \\\\\" + \\\n",
        "r\"\\vdots & \\vdots & \\ddots & \\vdots \\\\\" + \\\n",
        "r\"a_{n1} & a_{n2} & \\cdots & a_{nm}\" + \\\n",
        "r\"\\end{bmatrix}$\", \n",
        "     r\"$\\begin{bmatrix}\" + \\\n",
        "r\"a_{11} & a_{12} & \\cdots & a_{1n} \\\\\" + \\\n",
        "r\"a_{21} & a_{22} & \\cdots & a_{2n} \\\\\" + \\\n",
        "r\"\\vdots & \\vdots & \\ddots & \\vdots \\\\\" + \\\n",
        "r\"a_{m1} & a_{m2} & \\cdots & a_{mn}\" + \\\n",
        "r\"\\end{bmatrix}$\" \n",
        "    ]\n",
        "\n",
        "x = r\"$\\begin{bmatrix}\" + \\\n",
        "r\"x_{1} \\\\\" + \\\n",
        "r\"x_{2} \\\\\" + \\\n",
        "r\"\\vdots \\\\\" + \\\n",
        "r\"x_{m} \" + \\\n",
        "r\"\\end{bmatrix}$\"\n",
        "\n",
        "for i in [0, 1]:\n",
        "    ax[i].text(0.08, 0.25, y[i], fontsize=30)\n",
        "    ax[i].text(0.21+pdf_shift, 0.24, r'$=$', fontsize=30)\n",
        "    ax[i].text(0.3, 0.24, A[i], fontsize=30)\n",
        "    if i == 0 :\n",
        "        ax[i].text(0.83, 0.24, x, fontsize=30)\n",
        "    else:\n",
        "        ax[i].text(0.86, 0.24, x, fontsize=30)\n",
        "        \n",
        "    if i == 0 :\n",
        "        a = FancyArrowPatch((0.32+pdf_shift, 0.38), (0.75+pdf_shift, 0.38) , lw=1, mutation_scale=70, alpha=0.2, color='gray')\n",
        "    else :\n",
        "        a = FancyArrowPatch((0.36+pdf_shift, 0.38), (0.36+pdf_shift, 0.1) , lw=1, mutation_scale=70, alpha=0.2, color='gray')\n",
        "    ax[i].add_patch(a)\n",
        "\n",
        "    b = FancyArrowPatch((0.88+pdf_shift, 0.4), (0.88+pdf_shift, 0.1) , lw=1, mutation_scale=70, alpha=0.2, color='gray')\n",
        "    ax[i].add_patch(b)\n",
        "\n",
        "    c = Circle((0.13+pdf_shift, 0.38), 0.04, alpha=0.2, color='gray')\n",
        "    ax[i].add_patch(c)\n",
        "\n",
        "    if i == 0 :\n",
        "        ax[i].set_title(r\"$y_i = \\sum_{j=1}^m a_{ij}x_j $\", fontsize=25)\n",
        "    else :\n",
        "        ax[i].set_title(r\"$y_i = \\sum_{j=1}^m a_{ji}x_j $\", fontsize=25)\n",
        "        \n",
        "    ax[i].axis('off')\n",
        "    \n",
        "    ax[i].set_xlim(0, 1)\n",
        "    ax[i].set_ylim(0, 0.5)\n",
        "    \n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-17.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-17.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1152x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gFzdTVe3P-P9"
      },
      "source": [
        "## 그림 7-18"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-QUfqxZWNFJ_",
        "outputId": "a6494bbe-597a-4af4-84d0-026fada4d60e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        }
      },
      "source": [
        "fig = plt.figure(figsize=(8,4))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "\n",
        "plt.rcParams['text.usetex'] = True\n",
        "plt.rcParams['text.latex.preamble'] = r'\\usepackage{amsmath}'\n",
        "\n",
        "pdf_shift = 0.02\n",
        "\n",
        "y = r\"$\\begin{bmatrix}\" + \\\n",
        "r\"y_{1} \\\\\" + \\\n",
        "r\"y_{2} \\\\\" + \\\n",
        "r\"\\vdots \\\\\" + \\\n",
        "r\"y_{n} \" + \\\n",
        "r\"\\end{bmatrix}$\"\n",
        "\n",
        "A = r\"$\\begin{bmatrix}\" + \\\n",
        "r\"a_{11} & a_{21} & \\cdots & a_{m1} \\\\\" + \\\n",
        "r\"a_{12} & a_{22} & \\cdots & a_{m2} \\\\\" + \\\n",
        "r\"\\vdots & \\vdots & \\ddots & \\vdots \\\\\" + \\\n",
        "r\"a_{1n} & a_{2n} & \\cdots & a_{mn}\" + \\\n",
        "r\"\\end{bmatrix}$\"\n",
        "\n",
        "x = r\"$\\begin{bmatrix}\" + \\\n",
        "r\"x_{1} \\\\\" + \\\n",
        "r\"x_{2} \\\\\" + \\\n",
        "r\"\\vdots \\\\\" + \\\n",
        "r\"x_{m} \" + \\\n",
        "r\"\\end{bmatrix}$\"\n",
        "\n",
        "ax.text(0.08, 0.24, y, fontsize=30)\n",
        "ax.text(0.2+pdf_shift, 0.25, r'$=$', fontsize=30)\n",
        "ax.text(0.3, 0.24, A, fontsize=30)\n",
        "ax.text(0.83, 0.24, x, fontsize=30)\n",
        "\n",
        "a = FancyArrowPatch((0.32+pdf_shift, 0.38), (0.75+pdf_shift, 0.38) , lw=1, mutation_scale=70, alpha=0.2, color='gray')\n",
        "ax.add_patch(a)\n",
        "\n",
        "b = FancyArrowPatch((0.88+pdf_shift, 0.4), (0.88+pdf_shift, 0.1) , lw=1, mutation_scale=70, alpha=0.2, color='gray')\n",
        "ax.add_patch(b)\n",
        "\n",
        "c = Circle((0.13+pdf_shift, 0.38), 0.04, alpha=0.2, color='gray')\n",
        "ax.add_patch(c)\n",
        "\n",
        "ax.axis('off')\n",
        "\n",
        "ax.set_title(r\"$\\mathbf{y} = \\mathbf{A}^\\text{T}\\mathbf{x} $\", fontsize=25)\n",
        "\n",
        "ax.set_xlim(0, 1)\n",
        "ax.set_ylim(0, 0.5)\n",
        "    \n",
        "if file_print == True :\n",
        "    fig.savefig(\"imgs/chap7/fig7-18.png\", dpi=300, bbox_inches='tight')\n",
        "    fig.savefig(\"imgs/chap7/fig7-18.pdf\", format='pdf', bbox_inches='tight')\n",
        "    \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CkVQMzFjQQ5-"
      },
      "source": [
        "## 벡터화 실습 3 (선형회귀 식)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z97Sq674QAI0"
      },
      "source": [
        "np.random.seed(10)\n",
        "\n",
        "n, m = 5, 2\n",
        "\n",
        "X = np.random.rand(n, m)\n",
        "w = np.random.rand(m)\n",
        "y = np.random.rand(n)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tmRwPe0tQSTU",
        "outputId": "4a5a04ac-aaca-4919-a456-91da6a5caebc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.7713, 0.0208],\n",
              "       [0.6336, 0.7488],\n",
              "       [0.4985, 0.2248],\n",
              "       [0.1981, 0.7605],\n",
              "       [0.1691, 0.0883]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 111
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dyqyGAnGQTQ1",
        "outputId": "756eac99-f234-49d8-d966-2171b69219e6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "w"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.6854, 0.9534])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 112
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G5Wiww9fQULc",
        "outputId": "db09f7db-3c52-4008-daf1-af2039ac553c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.0039, 0.5122, 0.8126, 0.6125, 0.7218])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 113
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VDjImUvWQU7U"
      },
      "source": [
        "g = np.zeros_like(w)\n",
        "\n",
        "# X:(5,2), y:(5,), w:(2,)\n",
        "for j in range(m):\n",
        "    for i in range(n):\n",
        "        g[j] += (np.dot(X[i,:], w) - y[i]) * X[i,j]\n",
        "        "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NOGBzQDNQVt1",
        "outputId": "89917f4b-d089-4b1b-be74-e2326df45650",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "g"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.656 , 0.5726])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 115
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tDrtkibRQW7d"
      },
      "source": [
        "g = np.dot(X.T, np.dot(X,w)-y)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vnSbJoizQX_s",
        "outputId": "fcd5c52c-b65c-4a92-dfb8-c20e1a72bf78",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "g"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.656 , 0.5726])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 117
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yLBvZKZMQZH0",
        "outputId": "3b5e4f68-bef0-43c3-a540-3c8439916222",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "%%timeit\n",
        "# X:(5,2), y:(5,), w:(2,)\n",
        "for j in range(m):\n",
        "    for i in range(n):\n",
        "        g[j] += (np.dot(X[i,:], w) - y[i]) * X[i,j]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "10000 loops, best of 3: 23.7 µs per loop\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DEtyBKllQauE",
        "outputId": "c7078939-6927-4ea9-cd72-eeb89634c483",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "%%timeit\n",
        "g = np.dot(X.T, np.dot(X,w)-y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The slowest run took 16.86 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 3: 3.05 µs per loop\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M95MnFYCQhAx"
      },
      "source": [
        "### 참고 einsum"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "owbz8BcqQbv0",
        "outputId": "b8384ef2-a8ca-4011-951a-2ca2f3bcac25",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.einsum('i,ij->j', np.einsum('ij,j->i', X, w) - y, X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.656 , 0.5726])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 120
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Haz7ECiIQic5",
        "outputId": "1692e2d4-ff95-4dc4-a85e-59d833bc373b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "%%timeit\n",
        "np.einsum('i,ij->j', np.einsum('ij,j->i', X, w) - y, X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The slowest run took 8.56 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "100000 loops, best of 3: 6.29 µs per loop\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qDOdGyxGQjec"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}