ch04.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy Basics: Arrays and Vectorized Computation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(12345)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('figure', figsize=(10, 6))\n",
    "np.set_printoptions(precision=4, suppress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "my_arr = np.arange(1000000)\n",
    "my_list = list(range(1000000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 17.8 ms\n",
      "Wall time: 1.05 s\n"
     ]
    }
   ],
   "source": [
    "%time for _ in range(10): my_arr2 = my_arr * 2\n",
    "%time for _ in range(10): my_list2 = [x * 2 for x in my_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The NumPy ndarray: A Multidimensional Array Object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.2047,  0.4789, -0.5194],\n",
       "       [-0.5557,  1.9658,  1.3934]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Generate some random data\n",
    "data = np.random.randn(2, 3)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.0471,  4.7894, -5.1944],\n",
       "       [-5.5573, 19.6578, 13.9341]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.4094,  0.9579, -1.0389],\n",
       "       [-1.1115,  3.9316,  2.7868]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data * 10\n",
    "data + data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape\n",
    "data.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating ndarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6. , 7.5, 8. , 0. , 1. ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1 = [6, 7.5, 8, 0, 1]\n",
    "arr1 = np.array(data1)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4],\n",
       "       [5, 6, 7, 8]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]\n",
    "arr2 = np.array(data2)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(2, 4)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.ndim\n",
    "arr2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1.dtype\n",
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[[1.2062e-311, 3.1620e-322],\n",
       "        [0.0000e+000, 0.0000e+000],\n",
       "        [0.0000e+000, 1.0061e-046]],\n",
       "\n",
       "       [[1.3131e-071, 3.4200e-032],\n",
       "        [8.0120e+165, 2.0397e+160],\n",
       "        [1.3695e-071, 1.3693e-071]]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(10)\n",
    "np.zeros((3, 6))\n",
    "np.empty((2, 3, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Types for ndarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array([1, 2, 3], dtype=np.float64)\n",
    "arr2 = np.array([1, 2, 3], dtype=np.int32)\n",
    "arr1.dtype\n",
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([1, 2, 3, 4, 5])\n",
    "arr.dtype\n",
    "float_arr = arr.astype(np.float64)\n",
    "float_arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.7, -1.2, -2.6,  0.5, 12.9, 10.1])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 3, -1, -2,  0, 12, 10])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([3.7, -1.2, -2.6, 0.5, 12.9, 10.1])\n",
    "arr\n",
    "arr.astype(np.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.25, -9.6 , 42.  ])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_strings = np.array(['1.25', '-9.6', '42'], dtype=np.string_)\n",
    "numeric_strings.astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_array = np.arange(10)\n",
    "calibers = np.array([.22, .270, .357, .380, .44, .50], dtype=np.float64)\n",
    "int_array.astype(calibers.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([         0, 1075314688,          0, 1075707904,          0,\n",
       "       1075838976,          0, 1072693248], dtype=uint32)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_uint32 = np.empty(8, dtype='u4')\n",
    "empty_uint32"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arithmetic with NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  4.,  9.],\n",
       "       [16., 25., 36.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "arr\n",
    "arr * arr\n",
    "arr - arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.    , 0.5   , 0.3333],\n",
       "       [0.25  , 0.2   , 0.1667]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[1.    , 1.4142, 1.7321],\n",
       "       [2.    , 2.2361, 2.4495]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / arr\n",
    "arr ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  4.,  1.],\n",
       "       [ 7.,  2., 12.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[False,  True, False],\n",
       "       [ True, False,  True]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])\n",
    "arr2\n",
    "arr2 > arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic Indexing and Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 12, 12, 12,  8,  9])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr\n",
    "arr[5]\n",
    "arr[5:8]\n",
    "arr[5:8] = 12\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 12, 12])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice = arr[5:8]\n",
    "arr_slice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0,     1,     2,     3,     4,    12, 12345,    12,     8,\n",
       "           9])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[1] = 12345\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 64, 64, 64,  8,  9])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[:] = 64\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "arr2d[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0][2]\n",
    "arr2d[0, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[42, 42, 42],\n",
       "        [42, 42, 42]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_values = arr3d[0].copy()\n",
    "arr3d[0] = 42\n",
    "arr3d\n",
    "arr3d[0] = old_values\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = arr3d[1]\n",
    "x\n",
    "x[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Indexing with slices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 64, 64, 64,  8,  9])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4, 64])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr\n",
    "arr[1:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d\n",
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[1, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [4],\n",
       "       [7]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:, :1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [4, 0, 0],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:] = 0\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boolean Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n",
       "       [ 1.0072, -1.2962,  0.275 ,  0.2289],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 1.669 , -0.4386, -0.5397,  0.477 ],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241],\n",
       "       [ 0.3026,  0.5238,  0.0009,  1.3438],\n",
       "       [-0.7135, -0.8312, -2.3702, -1.8608]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "data = np.random.randn(7, 4)\n",
    "names\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True, False, False, False])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names == 'Bob'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n",
       "       [ 1.669 , -0.4386, -0.5397,  0.477 ]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == 'Bob']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.769 ,  1.2464],\n",
       "       [-0.5397,  0.477 ]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([1.2464, 0.477 ])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == 'Bob', 2:]\n",
    "data[names == 'Bob', 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True,  True, False,  True,  True,  True])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.0072, -1.2962,  0.275 ,  0.2289],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241],\n",
       "       [ 0.3026,  0.5238,  0.0009,  1.3438],\n",
       "       [-0.7135, -0.8312, -2.3702, -1.8608]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names != 'Bob'\n",
    "data[~(names == 'Bob')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.0072, -1.2962,  0.275 ,  0.2289],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241],\n",
       "       [ 0.3026,  0.5238,  0.0009,  1.3438],\n",
       "       [-0.7135, -0.8312, -2.3702, -1.8608]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond = names == 'Bob'\n",
    "data[~cond]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True,  True,  True, False, False])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 1.669 , -0.4386, -0.5397,  0.477 ],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = (names == 'Bob') | (names == 'Will')\n",
    "mask\n",
    "data[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.0929, 0.2817, 0.769 , 1.2464],\n",
       "       [1.0072, 0.    , 0.275 , 0.2289],\n",
       "       [1.3529, 0.8864, 0.    , 0.    ],\n",
       "       [1.669 , 0.    , 0.    , 0.477 ],\n",
       "       [3.2489, 0.    , 0.    , 0.1241],\n",
       "       [0.3026, 0.5238, 0.0009, 1.3438],\n",
       "       [0.    , 0.    , 0.    , 0.    ]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data < 0] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.    , 7.    , 7.    , 7.    ],\n",
       "       [1.0072, 0.    , 0.275 , 0.2289],\n",
       "       [7.    , 7.    , 7.    , 7.    ],\n",
       "       [7.    , 7.    , 7.    , 7.    ],\n",
       "       [7.    , 7.    , 7.    , 7.    ],\n",
       "       [0.3026, 0.5238, 0.0009, 1.3438],\n",
       "       [0.    , 0.    , 0.    , 0.    ]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names != 'Joe'] = 7\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [2., 2., 2., 2.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [4., 4., 4., 4.],\n",
       "       [5., 5., 5., 5.],\n",
       "       [6., 6., 6., 6.],\n",
       "       [7., 7., 7., 7.]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.empty((8, 4))\n",
    "for i in range(8):\n",
    "    arr[i] = i\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4., 4., 4., 4.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [6., 6., 6., 6.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[4, 3, 0, 6]]###记住"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5., 5., 5., 5.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[-3, -5, -7]]###记住"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23],\n",
       "       [24, 25, 26, 27],\n",
       "       [28, 29, 30, 31]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 4, 23, 29, 10])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(32).reshape((8, 4))\n",
    "arr\n",
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]]###记住"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  7,  5,  6],\n",
       "       [20, 23, 21, 22],\n",
       "       [28, 31, 29, 30],\n",
       "       [ 8, 11,  9, 10]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transposing Arrays and Swapping Axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0,  5, 10],\n",
       "       [ 1,  6, 11],\n",
       "       [ 2,  7, 12],\n",
       "       [ 3,  8, 13],\n",
       "       [ 4,  9, 14]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(15).reshape((3, 5))\n",
    "arr\n",
    "arr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.8608,  0.5601, -1.2659],\n",
       "       [ 0.1198, -1.0635,  0.3329],\n",
       "       [-2.3594, -0.1995, -1.542 ],\n",
       "       [-0.9707, -1.307 ,  0.2863],\n",
       "       [ 0.378 , -0.7539,  0.3313],\n",
       "       [ 1.3497,  0.0699,  0.2467]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 9.2291,  0.9394,  4.948 ],\n",
       "       [ 0.9394,  3.7662, -1.3622],\n",
       "       [ 4.948 , -1.3622,  4.3437]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6, 3)\n",
    "arr\n",
    "np.dot(arr.T, arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7]],\n",
       "\n",
       "       [[ 8,  9, 10, 11],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 8,  9, 10, 11]],\n",
       "\n",
       "       [[ 4,  5,  6,  7],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(16).reshape((2, 2, 4))\n",
    "arr\n",
    "arr.transpose((1, 0, 2))###记住转置矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7]],\n",
       "\n",
       "       [[ 8,  9, 10, 11],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  4],\n",
       "        [ 1,  5],\n",
       "        [ 2,  6],\n",
       "        [ 3,  7]],\n",
       "\n",
       "       [[ 8, 12],\n",
       "        [ 9, 13],\n",
       "        [10, 14],\n",
       "        [11, 15]]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr\n",
    "arr.swapaxes(1, 2)###记住"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Universal Functions: Fast Element-Wise Array Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0.    , 1.    , 1.4142, 1.7321, 2.    , 2.2361, 2.4495, 2.6458,\n",
       "       2.8284, 3.    ])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([   1.    ,    2.7183,    7.3891,   20.0855,   54.5982,  148.4132,\n",
       "        403.4288, 1096.6332, 2980.958 , 8103.0839])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr\n",
    "np.sqrt(arr)\n",
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.0119,  1.0048,  1.3272, -0.9193, -1.5491,  0.0222,  0.7584,\n",
       "       -0.6605])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.8626, -0.01  ,  0.05  ,  0.6702,  0.853 , -0.9559, -0.0235,\n",
       "       -2.3042])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.8626,  1.0048,  1.3272,  0.6702,  0.853 ,  0.0222,  0.7584,\n",
       "       -0.6605])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randn(8)\n",
    "y = np.random.randn(8)\n",
    "x\n",
    "y\n",
    "np.maximum(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.2623, -6.0915, -6.663 ,  5.3731,  3.6182,  3.45  ,  5.0077])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([-0.2623, -0.0915, -0.663 ,  0.3731,  0.6182,  0.45  ,  0.0077])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([-3., -6., -6.,  5.,  3.,  3.,  5.])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(7) * 5\n",
    "arr\n",
    "remainder, whole_part = np.modf(arr)\n",
    "remainder\n",
    "whole_part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.2623, -6.0915, -6.663 ,  5.3731,  3.6182,  3.45  ,  5.0077])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-63-bcce5ef9aa78>:2: RuntimeWarning: invalid value encountered in sqrt\n",
      "  np.sqrt(arr)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-63-bcce5ef9aa78>:3: RuntimeWarning: invalid value encountered in sqrt\n",
      "  np.sqrt(arr, arr)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr\n",
    "np.sqrt(arr)\n",
    "np.sqrt(arr, arr)\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array-Oriented Programming with Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -5.  , -5.  , ..., -5.  , -5.  , -5.  ],\n",
       "       [-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],\n",
       "       [-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98],\n",
       "       ...,\n",
       "       [ 4.97,  4.97,  4.97, ...,  4.97,  4.97,  4.97],\n",
       "       [ 4.98,  4.98,  4.98, ...,  4.98,  4.98,  4.98],\n",
       "       [ 4.99,  4.99,  4.99, ...,  4.99,  4.99,  4.99]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points = np.arange(-5, 5, 0.01) # 1000 equally spaced points\n",
    "xs, ys = np.meshgrid(points, points)\n",
    "ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.0711, 7.064 , 7.0569, ..., 7.0499, 7.0569, 7.064 ],\n",
       "       [7.064 , 7.0569, 7.0499, ..., 7.0428, 7.0499, 7.0569],\n",
       "       [7.0569, 7.0499, 7.0428, ..., 7.0357, 7.0428, 7.0499],\n",
       "       ...,\n",
       "       [7.0499, 7.0428, 7.0357, ..., 7.0286, 7.0357, 7.0428],\n",
       "       [7.0569, 7.0499, 7.0428, ..., 7.0357, 7.0428, 7.0499],\n",
       "       [7.064 , 7.0569, 7.0499, ..., 7.0428, 7.0499, 7.0569]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x238794946d0>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x23879ca6100>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Image plot of $\\\\sqrt{x^2 + y^2}$ for a grid of values')"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.imshow(z, cmap=plt.cm.gray); plt.colorbar()\n",
    "plt.title(\"Image plot of $\\sqrt{x^2 + y^2}$ for a grid of values\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.close('all')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expressing Conditional Logic as Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])\n",
    "yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])\n",
    "cond = np.array([True, False, True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.1, 2.2, 1.3, 1.4, 2.5]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = [(x if c else y)\n",
    "          for x, y, c in zip(xarr, yarr, cond)]\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.1, 2.2, 1.3, 1.4, 2.5])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = np.where(cond, xarr, yarr)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5031, -0.6223, -0.9212, -0.7262],\n",
       "       [ 0.2229,  0.0513, -1.1577,  0.8167],\n",
       "       [ 0.4336,  1.0107,  1.8249, -0.9975],\n",
       "       [ 0.8506, -0.1316,  0.9124,  0.1882]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [ True,  True, False,  True],\n",
       "       [ True,  True,  True, False],\n",
       "       [ True, False,  True,  True]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-2, -2, -2, -2],\n",
       "       [ 2,  2, -2,  2],\n",
       "       [ 2,  2,  2, -2],\n",
       "       [ 2, -2,  2,  2]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(4, 4)\n",
    "arr\n",
    "arr > 0\n",
    "np.where(arr > 0, 2, -2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5031, -0.6223, -0.9212, -0.7262],\n",
       "       [ 2.    ,  2.    , -1.1577,  2.    ],\n",
       "       [ 2.    ,  2.    ,  2.    , -0.9975],\n",
       "       [ 2.    , -0.1316,  2.    ,  2.    ]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0, 2, arr) # set only positive values to 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mathematical and Statistical Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.1695, -0.1149,  2.0037,  0.0296],\n",
       "       [ 0.7953,  0.1181, -0.7485,  0.585 ],\n",
       "       [ 0.1527, -1.5657, -0.5625, -0.0327],\n",
       "       [-0.929 , -0.4826, -0.0363,  1.0954],\n",
       "       [ 0.9809, -0.5895,  1.5817, -0.5287]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.19607051119998253"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.19607051119998253"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3.9214102239996507"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5, 4)\n",
    "arr\n",
    "arr.mean()\n",
    "np.mean(arr)\n",
    "arr.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.022 ,  0.1875, -0.502 , -0.0881,  0.3611])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 3.1693, -2.6345,  2.2381,  1.1486])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean(axis=1)\n",
    "arr.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  3,  6, 10, 15, 21, 28], dtype=int32)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([0, 1, 2, 3, 4, 5, 6, 7])\n",
    "arr.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  5,  7],\n",
       "       [ 9, 12, 15]], dtype=int32)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0],\n",
       "       [  3,  12,  60],\n",
       "       [  6,  42, 336]], dtype=int32)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])\n",
    "arr\n",
    "arr.cumsum(axis=0)##记住 上下加\n",
    "arr.cumprod(axis=1) ##记住 左右乘"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Methods for Boolean Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(100)\n",
    "(arr > 0).sum() # Number of positive values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools = np.array([False, False, True, False])\n",
    "bools.any()\n",
    "bools.all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sorting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.6095, -0.4938,  1.24  , -0.1357,  1.43  , -0.8469])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([-0.8469, -0.4938, -0.1357,  0.6095,  1.24  ,  1.43  ])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6)\n",
    "arr\n",
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.6033,  1.2636, -0.2555],\n",
       "       [-0.4457,  0.4684, -0.9616],\n",
       "       [-1.8245,  0.6254,  1.0229],\n",
       "       [ 1.1074,  0.0909, -0.3501],\n",
       "       [ 0.218 , -0.8948, -1.7415]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.2555,  0.6033,  1.2636],\n",
       "       [-0.9616, -0.4457,  0.4684],\n",
       "       [-1.8245,  0.6254,  1.0229],\n",
       "       [-0.3501,  0.0909,  1.1074],\n",
       "       [-1.7415, -0.8948,  0.218 ]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5, 3)\n",
    "arr\n",
    "arr.sort(1)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.5311513550102103"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "large_arr = np.random.randn(1000)\n",
    "large_arr.sort()\n",
    "large_arr[int(0.05 * len(large_arr))] # 5% quantile"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unique and Other Set Logic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will'], dtype='<U4')"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "np.unique(names)\n",
    "ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])\n",
    "np.unique(ints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Bob', 'Joe', 'Will']"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(set(names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True,  True, False,  True])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values = np.array([6, 0, 0, 3, 2, 5, 6])\n",
    "np.in1d(values, [2, 3, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## File Input and Output with Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "np.save('some_array', arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.load('some_array.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez('array_archive.npz', a=arr, b=arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch = np.load('array_archive.npz')\n",
    "arch['b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez_compressed('arrays_compressed.npz', a=arr, b=arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'rm' 不是内部或外部命令，也不是可运行的程序\n",
      "或批处理文件。\n",
      "'rm' 不是内部或外部命令，也不是可运行的程序\n",
      "或批处理文件。\n",
      "'rm' 不是内部或外部命令，也不是可运行的程序\n",
      "或批处理文件。\n"
     ]
    }
   ],
   "source": [
    "!rm some_array.npy\n",
    "!rm array_archive.npz\n",
    "!rm arrays_compressed.npz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 6., 23.],\n",
       "       [-1.,  7.],\n",
       "       [ 8.,  9.]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 28.,  64.],\n",
       "       [ 67., 181.]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "y = np.array([[6., 23.], [-1, 7], [8, 9]])\n",
    "x\n",
    "y\n",
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 28.,  64.],\n",
       "       [ 67., 181.]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6., 15.])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, np.ones(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6., 15.])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x @ np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  933.1189,   871.8258, -1417.6902, -1460.4005,  1782.1391],\n",
       "       [  871.8258,   815.3929, -1325.9965, -1365.9242,  1666.9347],\n",
       "       [-1417.6902, -1325.9965,  2158.4424,  2222.0191, -2711.6822],\n",
       "       [-1460.4005, -1365.9242,  2222.0191,  2289.0575, -2793.422 ],\n",
       "       [ 1782.1391,  1666.9347, -2711.6822, -2793.422 ,  3409.5128]])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1., -0.,  0.,  0., -0.],\n",
       "       [ 0.,  1.,  0., -0., -0.],\n",
       "       [ 0.,  0.,  1., -0.,  0.],\n",
       "       [ 0., -0., -0.,  1.,  0.],\n",
       "       [ 0.,  0., -0., -0.,  1.]])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-1.6914,  4.38  ,  0.1757,  0.4075, -0.7838],\n",
       "       [ 0.    , -2.6436,  0.1939, -3.072 , -1.0702],\n",
       "       [ 0.    ,  0.    , -0.8138,  1.5414,  0.6155],\n",
       "       [ 0.    ,  0.    ,  0.    , -2.6445, -2.1669],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.0002]])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.linalg import inv, qr\n",
    "X = np.random.randn(5, 5)\n",
    "mat = X.T.dot(X)\n",
    "inv(mat)##记住\n",
    "mat.dot(inv(mat))\n",
    "q, r = qr(mat)\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pseudorandom Number Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5732,  0.1933,  0.4429,  1.2796],\n",
       "       [ 0.575 ,  0.4339, -0.7658, -1.237 ],\n",
       "       [-0.5367,  1.8545, -0.92  , -0.1082],\n",
       "       [ 0.1525,  0.9435, -1.0953, -0.144 ]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = np.random.normal(size=(4, 4))\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.06 s ± 29.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "32.5 ms ± 798 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "from random import normalvariate\n",
    "N = 1000000\n",
    "%timeit samples = [normalvariate(0, 1) for _ in range(N)]\n",
    "%timeit np.random.normal(size=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.4714, -1.191 ,  1.4327, -0.3127, -0.7206,  0.8872,  0.8596,\n",
       "       -0.6365,  0.0157, -2.2427])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1234)\n",
    "rng.randn(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Random Walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "position = 0\n",
    "walk = [position]\n",
    "steps = 1000\n",
    "for i in range(steps):\n",
    "    step = 1 if random.randint(0, 1) else -1\n",
    "    position += step\n",
    "    walk.append(position)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x432 with 0 Axes>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 720x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2387e0834f0>]"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bett3xyiEwPiof1+IsxrSa90fZbGC5t6ApGcZo6b68Xx1G1OhjaqPs1AMUkRERHtE4wncni6vFGbN/kxUqL8nEktgMssYx1QFofUIPnyRDHEBw8SrJ9vhb2uqyFhKoakKFtd2EEwFTd0w8dqpDvhaPfuOsx7NU8+Pi2GQIiIi2uPe3DI2I/GCnq+XTX+3F4M+b8UCwDtzy9iKxjPOMu1tdt+JxTE5E66b2SjL3l6u7Wgcdx4vZSw9Dvq86OtqqettEBikiIiI9tANE0IA14fLCx/jowpuTpmIJ+zv79GNEBwCuDFyeIz93V6cUbyYCJp4+/EydmIJjNdJo7llwOfFgK8FE8EQ3n68hEgskTG4Wn1SAcNEogJfRzswSBEREe2hGyGcPdWB7gNlpmKNqX6sbcfw4MmKTSPbpQdNnOvrRGeLO+Prmqrg1pSJb360CIcAro34bB9DubQRP25OmfhmMASnQ+DqUOYxjo8qWNqM4tHz1SqPsDC2BSkhhFMIcVcI8R/tOicREVE1bUXiePvxcnqJfjnGRirT37MZieHu3FLOct2Y6sfaTgz//vYszvd3oaM5c+CqJW1Uwep2DL91exYX+jvRnmWMYyPVfX5hseyckfpJAI9sPB8REVFVvfV4CZF4wpaeop72Jrxyot32jTnvzCwhGpc5y3VWiFvejGK8zvqjLNbXeDn1WJhsTnY2Y6SntWKN++WyJUgJIfoBfD+AX7HjfERERLWgGyG4HALXspSZijWmKpicCSMSS9hyPiA5w+V2ClwZ6s56jBXigNL2wqqG3vZmvNTbBiD/8wzHVT9uT4cRjdv3dbSLXTNSvwDg7wKov78hERFRgSYMExcHutDa5LLlfOOjfmxHE7g7u2TL+YBk2Ls00A2vJ/cYv/OVHrR6nDkDV61958s9aGty4fKZ3GPUVAUbkTjuzy9XZ2BFKDtICSE+BWBBSvlWnuM+K4S4I4S4s7i4WO5liYiIbLW6HcW788u2lsKuDfvgEPb1Sa1sRvHgyUpBj675qU+8hP/8k9+OZrfTlmtXwt/63pfxn/7Gt+Ud440RBULsPny5ntgxIzUO4AeEEDMAvgDgY0KI3zh4kJTyc1LKK1LKKz09PTZcloiIyD63psJIyGSjtl06W9w439dpW5/UzWkTCVlYuc7rceGM0mrLdSul0DF2t3pw9lRHXW7MWXaQklL+jJSyX0o5BOCHAPyhlPJHyh4ZERFRFelGCE0uBy6f6bL1vNqoH3dnl7EZiZV9roBhosXtxBsDXeUP7IjRVAVvzS5hOxqv9VD24T5SRERESIaUq0M+NLnsLYVpqoJYQmJypvw+Kd0I4eqwDx5X4719a6ofkVgCbz22r9/MDrbeCSnl16WUn7LznERERJUWWt/B+8/XKvIolStnfPA4HekH85ZqYW0bH75Yz7vC7bi6OuyDyyFs306iXI0XaYmIiA6wNnu0YyPOg1o8Tlwa7Cq7vyc9xjrdzqDS2ppcuDjQhYk6azhnkCIiooanGybam1w4d7qjIufXVD8ePF3Byma05HMEDBMdzS6crdAYjwJNVXB/fhmr26V/He3GIEVERA1PN0K4PqLA5azM26I2qkBKIDBV+mzKhBHCjREFToewcWRHi6b6kZDA7alwrYeSxiBFREQNbX5pE4/NzYr2Hl3s74LX40SgxP6eufAm5sJbFSk9HiWXBrvQ5HLU1TYIDFJERNTQrDflQja5LJXH5cDVIR8mSgwAVoN1ozaaW5rdyZ3a66nhnEGKiIgaWsAwobR60s+mqxRNVRBcWMfC6nbRn6sbJvxtTRhNPZuukWmqH+8/X0NofafWQwHAIEVERA1MSgndCGFMVSBEZXuPrN3Ii+2TSo7RhFaFMR4F1qzczTL6zezEIEVERA3LWNzAi9Wdgh65Uq6zpzvQ2eLGRJH7SQUX1rG4toPxCpYej5LzfZ1ob3LVTZ8UgxQRETUsq/m7GiHF6RC4MeIrOgCke7gadP+og1xOB66P+Mre4NQuDFJERNSwdMNEX1cLBn3eqlxPU/2YX9rCXHiz4M/RjRD6u1swUKUxHgVjqh8z5iaeLG/VeigMUkRE1JgSCYnAVHV7j6yZr0LLe/GERMAwG3Y382ysPql6mJVikCIioob08NkqljejFd324CC1pw097U0Fl/cePl3F6nasqmM8Cl450Q6l1ZN+bE4tMUgREVFD2t2bqXqzPUIIaKoC3TAhpcx7/ERqjGMjDFJ7ORwCN4r4OlZ0LDW9OhERUY3ohgm1pxUnOpqret1x1Y/Q+g4+WljPe6xumHiptw29VR7jUTCu+vF8dRtToY2ajoNBioiIGk40nsDt6TDGarBTuHXNfH1SkVgCkzUa41Fg9Undm1uu6TgYpIiIqOHcm1vGZiRekybuAZ8XA76WvH1S78wtYysa57YHWZxRvLj99z+OP3W5v6bjYJAiIqKGoxsmhABu1Kj3aFz14+aUiXgie3+PboQgBPujshFC1EXJk0GKiIgajm6EcPZUB7pbPTW5/piqYG07hveermQ9RjdMnDvdiU6vu4ojo2IxSBERUUPZisTx9uNljI/WrmRmlesmgpnLe5uRGO7OLnHbgyOAQYqIiBrKW4+XEIknatrE3dPehJdPtKW3YDjozswSonHJ/qgjgEGKiIgayoQRgsshcG3IV9NxaKofkzNhRGKJQ6/phgm3U+DqUHcNRkbFYJAiIqKGohsm3hjoQmuTq6bj0FQF29EE7s4uHXpNN0K4NNANr6e2Y6T8GKSIiKhhrG5H8e78cnoPolq6PqLAIXBoG4SVzSgePFnh/lFHBIMUERE1jFtTYSQkMFYHvUedLW6c6+s81Cd1c9pEQqIuwh7lxyBFREQNQzdCaHI5cPlMV62HAiDZJ3V3dhmbkVj6YwHDRLPbgUuD7I86ChikiIioYQQME1eHfGhyOWs9FADJWadYQmJyZrdPSjdCuDrkg8fFt+ijgHeJiIgaQmh9B+8/X6ur3qMrQ91wOwX01HP3Fta28eGLdW57cIQwSBERUUMIpJq6a7kR50FejwuXBrvTDee7Y6yfsEe5MUgREVFD0A0T7U0unDvdUeuh7KOpCh48XcHKZhQBw0RHswuvn+6s9bCoQAxSRETUEHQjhOsjClzO+nrrGx/1Q0ogMGViwgjhxogCp0PUelhUoPr6biIiIqqA+aVNPDY363JLgYv9XWhxO/Hbd+YwF96qyzFSdmUHKSHEgBDij4QQj4QQ7wkhftKOgREREdnF6kGqx4cAe1wOXB324Q/fXwAAaHXUw0X52TEjFQPwt6WUrwG4AeCvCSHO2nBeIiIiWwQME0qrB6+caK/1UDIaT81C+dua8FJvW41HQ8UoO0hJKZ9JKd9O/f81AI8A9JV7XiIiolxWNqP4+d95D2vb0ZzHSSmhGyGMqQqEqM/eI2u7A62Ox0iZ2dojJYQYAnAJwK0Mr31WCHFHCHFncXHRzssSEVED+o/vPsW/0Wfwew+e5zzOWNzAi9Wdut6b6ezpDvzAxdP44WuDtR4KFcm2ICWEaAPwHwD8lJRy9eDrUsrPSSmvSCmv9PT02HVZIiJqUAf3XsomkHqWXT3vzeR0CPziD1+qq81CqTC2BCkhhBvJEPWbUsov2XFOIiKibBIJiZupAKUbJqSUWY/VDRN9XS0Y9HmrNTxqIHas2hMAPg/gkZTyX5Q/JCIiotw+eLEGcyOCy4NdeL66janQRsbjEgmJwJTJ3iOqGDtmpMYB/CiAjwkh3kn998dtOC8REVFGVlnv73zvK/v+fNDDZ6tY3ozW5bYHdDy4yj2BlPJbABjziYioavRgCEOKF2OqgtOdzQgYIfzojTOHj0v1R9VzozkdbdzZnIiIjpRYPIFb02Foo34IIaCN+hEwTCQSh/ukdMOE2tOKEx3NNRgpNQIGKSIiOlLefbKC9Z1Y+lEqmqpgaTOKR8/3LxiPxhO4PR3mbBRVFIMUEREdKVY/1NiIFaSSQengNgj35paxGYnz2XVUUQxSRER0pOhGCK+ebIfS1gQAONnZjJGe1kMN57phQgjgxgiDFFUOgxQRER0Z29E47swsHSrXaaqCW1MmovFE+mO6EcLZUx3obvVUe5jUQBikiIjoyHh7dgk7scShXcrHVT82InHcn18BAGxF4nj78TLGR9kfRZXFIEVEREdGwDDhdAhcG/bt+7hVvrMeB/PW4yVE4gk+coUqjkGKiIiOjIlgCOf7OtHe7N738e5WD86e6sBE0HpsTAguh8C1IV+m0xDZhkGKiIiOhPWdGO7Nr2R9+PD4qIK3ZpewHY1jwjDxxkAXWpvK3neaKCcGKSIiOhImp8OIJ2TWfaE01Y9ILIGvf7CId+eXue0BVQWDFBERHQkTwRA8LgfePNOd8fWrwz64HAK/8AcfIiGBMW7ESVXAIEVEREeCbph4c7AbzW5nxtfbmly4ONCF95+vocnlwOUzXdUdIDUkBikiIqp7SxsRPHy2mrdcZ71+dciHJlfmwEVkJwYpIiKqe4Gp5Go8Lc++UFb/lJalIZ3IblzOQEREdU83Qmj1OHGhvzPncdeGffjp73sV/92VgSqNjBodgxQREdU9PWji2rAPbmfuQorTIfBXv1Ot0qiIWNojIqI692xlC1OhDT7uheoSgxQREdW1gJHsj+LjXqgeMUgREVFdmwia6Pa68drJjloPhegQBikiIqpbUkoEjBDGVAUOh6j1cIgOYZAiIqK69djcxNOVbe5STnWLQYqIiOrWhBECAD43j+oWgxQREdUt3TBxsqMZI/7WWg+FKCMGKSIiqkuJhETAMKGpCoRgfxTVJwYpIiKqSx+8WEN4I5L3sTBEtcQgRUREdUnn/lF0BDBIERFRXdKDIQwpXvR1tdR6KERZMUgREVHdicUTuDUdZlmP6h6DFBER1Z37T1awvhPjtgdU9xikiIio7qSfrzfCIEX1zZYgJYT4pBDiAyFEUAjx03ack4iIGpduhPDqyXYobU21HgpRTmUHKSGEE8AvAfg+AGcB/LAQ4my55yUiosa0HY3jzswSND4Who4AO2akrgEISimnpJQRAF8A8GkbzluyaDyB956uFHTs2nbU1mtHYglsR+N5j5NSYn0nZuu1NyMxxBMy73GFjpGIqBbenl3CTiyB8VGW9aj+2RGk+gDM7fnzfOpjNfPLXzfwqf/jW1jejOQ8Lriwhkv/6Kv41kch2679P37xHv77z9/Oe9wXJucw9k++hpUte4JcLJ7Ax//5N/CLX/so77F/+/+9hz//a/nHSERUCwHDhEMAV4d9tR4KUV52BKlM+/YfmhYRQnxWCHFHCHFncXHRhstmd0NVICVwc8rMedwfvb+IWELiDx69sOW6sXgCf/hoAZOPw1jayB3ifv+951jbieUdY6EePF3Fs5VtfPVh7r9LLJ7AH72/gFvTYaxs2jsbR0Rkh4lgCBf6u9DR7K71UIjysiNIzQMY2PPnfgBPDx4kpfyclPKKlPJKT0+PDZfN7mJ/F7weZ3pX3Gz01FPFrf8t14Onq1jbieUNcdF4ArenwwB2V6aUy/o7PHy2mjPEWUuKpQRuTttzbSIiu6zvxHBvfoVlPToy7AhSkwBeEkIMCyE8AH4IwO/YcN6SeVwOXB3yYSKYPSBZYabZ7cCHL9axuLZT9nWtMNPkcuQMcffnV7ARiaPZ7bAtxAUME83u5O3MFeKs4NbkctgW4oiI7DI5HUY8IdloTkdG2UFKShkD8D8A+K8AHgH4bSnle+Wet1zjowqMxQ28WN3O+Pr9+WVsROL489owAHtmpfSgiVdOtGNMVTCR43x6KuD92NgQPnyxjoW1zGMs1E4sjsmZMP70m/1o9ThzXnsimFxSfH1EyRk0iYhqYSIYgsflwJtnums9FKKC2LKPlJTyP0spX5ZSqlLKf2zHOctl/TaTbdZFDyY//pe/fRjtza6yZ2esMKONKhhX/Zha3MDzlcwBSTdMnD3Vge+/cCrnGAt1d3YZ29EEvvPlXlwb9mWdDduOxnHn8RLGR/0YVxV8tFB+iCMispNumHhzsBvNbmeth0JUkGO7s/lrpzrQ2eLOOusyYYRw9lQH/G1NuDGi5O2nyuftx8vYiSWgqf70k8oDU4evvR2N463ZJWiqgtdPd6Kj2ZUOdaXSUytcrg37oOUIcW8/XkIkloCmKnmDJhFRtS1tRPDw2SofC0NHyrENUk6HwFgqIEm5fxHhdjSOtx8vp5sZx1UFs+FNzIU3S75ewAjBIYDrIz6cPdWBLq87Y0B6KxVmxkf9cDpEMsRlCFzF0IMhnO/vQmeLG1rq75SpVKkbJpwOgWvDPpw93WFLiCMisksg1d/JBxXTUXJsgxQAaKMKnixvYS68te/jbz1eQiSeSM/KWP9oy5md0Q0T51PLdR05QpxuhOB0iPT+KJqqYC68VXKI29iJ4Z255fRvcK+dTIW4DH8X3QjhQn8n2pvdyaCplh/iiIjsohshtHqcuNDfWeuhEBXseAepVLg42Hw9EQzBtSfMvNTbBn9bU8kN5wfDjHXtJ8tbmD0QkCaCJi72d6KtyZU8LhXiSr325EwYsYRMXzsd4oKhfSFubTuKe/MrB8boLyvEERHZSTdMXBv2we081m9NdMwc6+9WtacNve1Nh2ZndMPExYGudJgRQkBTM88gFeJ2KsyM71muuxuQdq+9uh3F/flljO+Ztt4NcaXNhgUMEx6nA1fO7O4ArI368XRlG4/N3YA0OZNcUrxvjGr2MiARUTU9X9nG1OLGvp+PREfBsQ5SVkAKGLuzM1aYOdjMqKkKFtZ2YCyuF30dK8zsXa474m/FiY6mfc3uk9NhJCTSzeh7x1hqiJswQrg02IUWz+4Kl92AtBvO9KAJj8uBy3vGONrbhp4MQZOIqNqsX+jG2GhOR8yxDlJAsnwVWo/gwxfJgHR76nCYsY4DUFKomAgeDjPJgORHYE9AmgiaaHI5cHlw//4omqpgcW0HwYXiQtzyZgTvPV09tHFdOsTtmWmayLCkuNwQR0RkF90w0e1147WTHbUeClFRjn+QOrCKTTcyh5lBxYv+7paiV7FZy3UzTUdrqgJzYzfE6UYIV4YO748ynqEMWIibU2FIiUOPUhBCYFz146ZhIpGQCG9E8OjZasZHLpQa4oiI7CKlRMAwMaYqcDgyPb6VqH4d+yDV3+3FoM+bDinZwgyQDBWBKRPxROGzM7emTUiJjPueWH1SE8EQzPUdvP98LeNjDwZ8qRBXZK+SboTg9Thxob/r0GtjVohbWEs/MmYsw7XLmYkjIrLDY3MTT5a3Mv6MIqp3xz5IAckZm5tTJhZWt7OGmeRxfqxsRfHo2WrB554ImvB6nLg40HXotb6uFgwpyRCX3h8lS/1/PFUGLCbEWStcPK7Dt3E3xJmYCIbQ1uTCxQxLigd8Xgz4Wvi4GCKqGesXuXH2R9ER1BBBakz1Y207hl/51jSA7GFmbKT4VWy6Ecq5XHdM9ePWlIlvfpgMM+f7Mu+Poo0qWN2O4eHTwkLcwuo2ggvrWf8uVogLGCEEUoHLlWWM2ogfN4uciSMisotuhHCyoxnD/tZaD4WoaI0RpFIB6df1GbTnCDO9Hc0Y7W3DRIF9Us9XtmEsbuR8nIGmKljbieHL7zzB9RxhxhpjrgcO72X9BpfrCeljqh/f/CiEqVCeMaZC3HtPVwq6NhGRXRKJZH+UpioQgv1RdPQ0RJDqaW/CKyfasRNL4PpI9jADJKeWJ2fCiMQSec9rPUsvd5hJBpidWCLnYw96O5rxUm9bwb1KuhFCZ4sbZ09lX+EyPqpgJ/X3KGSM7JMiomr7cGEN5kaEj4WhI6shghSwGxbyNTOOqX5sRuK4P7+c95x60MwbZvxtTXj1ZDuA7CVFi6YqmJwuLMTphomxkdwrXG6kZrm6ve70GDLpbS8uxBFRsrxeSD9lJJawfdPbR89W8WL18IPJjyJrpTT3j6KjqmGC1Pe+fgIepwPf/UpPzuPGRhQIgbzlPSllQWEGAL737AkM+rx45UT2MAMkQ9xWNI535pZzHjdrbmJ+aSu9tUM2/rYmXDnTje85eyLvGIsJcUQE/PzvvofP/OubeXsLf+v2LD7zr28VtYgll3hC4s/9yi383Ffes+V8taYbIQwpXvR1tdR6KEQlaZggpal+3P/578VIT1vO4zq9bpw73Zn3N8jZcHK5bqa9mQ76yU+8jK/+re/IG2asEJfv2tbrucp1ln//V27gn/zJ83mP00YLC3FElAwzE0ETS5vRvAtEvvlR8t+rXStjHz1bRXgjAt0IHfkFIrF4Aremwizr0ZHWMEEKQMa9ozLRVAV3Z5exFYlnPcYqgxWy74nTIdDkyn/t3RCXezZMN0z0tjdB7cm/wsXjcuTsCbPcGFbgKCDEEVEyzKxsRQHk/jeTDArWHnb2lM6t6xWzyrdePXi6irWdWN62B6J61lBBqlBjqoJIPIE7j8NZj5kIhnCio7AwUwxtVMHd2SVsRmIZX7dKinavcOn0unGur7Pond2JGpE1u9Tb3oSJHAHJCgonOppwa8pENF5+6XwimPxFCih8lW+9sr6O1qploqOIQSqDa8M+uBwi62+Q1uMMNNVv+3JdTfUjGpe4M7OU8fWPFtYRWt+pyFT4mKrg7lz2EEdESbphYrS3Dd937mTO3kJr9uivffcoNiJx3J8vb4uRSCyByZkwPnnu5LFYIBIwTLx6sh1KW1Oth0JUMgapDLweFy4NdkHP0tPwwYvkct1KrDK5OtQNt1Nk/U3T+g2uElPhVoibzBLiiCgZZm5Ph6GpSnqByL0sq3z1oIlXTrTjUxdOp/5c3gzS/fllbEbi0FTlyC8Q2Y7GMTkTLqjXk6ieMUhlMab68e6TlXQfxF5W+asSYcbrceHSQDcCWX7T1A0Tgz4v+ru9tl/bCnHskyLK7t78MraicWiqf88q38P/ZnZiqaAwqsDX6sHZUx1lzyBNBE0Ikdza5KgvELk7u5zcX4/9UXTEMUhlMa4qSEjg9vThPindMHFGqUyYAZIltgdPVrCyuT/ExRMSN6fMglYKliJfiCOi5C9SyTDjy7lAZDcoJGdcNFXBW7NL2I5mX8SS99pGCK+f7kCX14Mbw4Wt8q1XASMEp0Pg+oiv1kMhKguDVBZvDHah2e049JumtQqnkr9FaakQd3N6/w/nB09WsLYdq+gT0sdUJTkTt3l4Jo6Ikg3eVpgBrFW+S4dW+erBEBwi2XMJJBeSRGIJvPW4tNL5ViSOu7PL6WCWDnFHdIHIhGHifF8n2pvdtR4KUVkYpLJocjlxdch3aHZmd7lu5cLMpcFuNLsdh66d3nKhgitcxkf9kBlCHBFZYWYJ43v+/WujqQUiB1b56oaJ8/1d6GxJBoVrwwqcjtJL53cehxGJ7y+FaaNHc4HI+k4M9+aWWdajY4FBKgdN9eODF2tYXNtJf8z6IXijgmHG43Lg6pDv0A9c3QjhlRPt6Gmv3AqXNwa6MoY4IkqGmWhc7ltokl4gsmdmaGMnhncOBIW2Jhcu9uffJy4b3TDhcghcHdotheVb5VuvJmfCiCUkxrkRJx0DDFI5WD8EA1O7P/isVTiVDDPJa/vx4Yt1LKwln6dlNa5W+nlUVoizaxdmouNkIpgMM1a5DtjbW7j7b+a2FRQOzFyPj/pxf34Fa9vFl851w8SlwS60NrnSH8u3yrde6cEQPE4H3jzTXeuhEJWNQSqHc32daG92pX9A7l2FU2lWQ7k1M/TO7DK2o9VZ4TI+6sdHC7shjoiSAkYIlwa74PW49n083VuYWuUbMMyMQWFMVRBPyIyLWHJZ2Yri3fnlQ/2RR3WBiG6YuHymq+CnTRDVMwapHJwOgRsjSnrK/u3H+1fhVNLrpzvR0exKN5JOGCYcArhehR2A0zNxR+yHM1ElrWxF8e6TlYyLPawFItbjYCaCycDV4tkfFC4PdqPJ5cj7UPSDbk+HkZCZt1w5agtEljYiePhs9dBsHdFRxSCVh6YqmA1vYi68iYARSoWZyi/XtUKcPpWcDQsYIZzv60w3rlbSwRBHRMmQlJDJrVEOshaI6Ia5GxQy9P80u524MtRddMO5boTQ7Hbg0mDXodeO2gKRm1MmpERVZvaJqoFBKg9r9ikwZaZX4XRUabmupiqYC2/hg+druDt7eFq/Ug6GOCJKlqOa3Q68kSHMWL2FAcPErelUUMhShtdUP95/vgZzfSfj6xmvHTRxdciX8eHnR22BiG6Y8HqcuNDfVeuhENmCQSqPl0+0wd/mwVcfvji0CqfSrOfp/eLXPkIsIat77VSImwtvVu2aRPVMN0JZwwywu8r3K+88zRkUxjIsYsllcW0HH7xYy7rQ5KgtEJkwQrg27IPbybcfOh7K+k4WQvxTIcT7Qoj7Qoj/TwjRZdO46oYQAmOqH199+CLjKpxKeqm3Df62Jvynd5/B7dy/7LnSrLLEUd01mchOi2s7+PDFes7+SGuByH958BzXhn3wuDL/eL3Q14m2JlfB2yDcTAWuXD97jsoCkecr25ha3GB/FB0r5f5K8FUA56SUFwB8COBnyh9S/bFmgqq9XFcIkb72pcHuQ42rlTSaCnFH/enyRHawZo9yzQq/fjq5yjffcS6nA9eHD2/2m41uhNDe7MLrpzuyHnNUFogEUu0Cld7GhaiaygpSUsrfl1JaW+reBNBf/pDqz26YObwKp1rXrvYOwFaImwiakFLadt7fuPkYD5+u2nY+yu3rHyzg9997Xuth1K1f12fw0Yu1vMfpwWSYOdfXmfUYq7cQQN6VvWOqgunQBp4ub+W/tmHi+rACV45SWDELRIILa/g3E9N5j6uEiaCJLq8bZ09lD4VER42dReq/COC/ZHtRCPFZIcQdIcSdxcVFGy9beYM+L77//Cl85vpg1a/98ddO4PJgFz514XTVrz0+qiC0voPgwrot5wut7+B/+vID/NLXg7acj/L7R7/7EP/gK+/ZGoaPi6fLW/i533kPv/yNqbzHWmHG6RA5j/uzVwbw3a/05A0Ku6Xz3MFnfmkTj83NvL9IFbNA5Je/MYWf/92HeFJAiLOTlBIBw8SNYQWOPF9HoqMkb5ASQvyBEOJBhv8+veeYnwUQA/Cb2c4jpfyclPKKlPJKT0+PPaOvEiEEfunPXcan3+ir+rV72pvwpZ8Yx2hvW9Wvbf1WbVcTq1V2CBgmEgm+sVfas5UtTIU28Hx1G1OhjVoPp+5YIUY3QjmD5lx4E7PhzXQPVC6fOHsCv/YXruUNCq+caIev1QM9z78ta4yFPEqlkAUiUsr0NfNd226PzU08Wd4q6OtIdJTkDVJSyk9IKc9l+O8rACCE+DEAnwLw5yR/7T1WBnxe9He32NYnZZ0nvBHBBwWUU6g8e8s87HU7zFpI8WxlGzNm9vBh/QJg50a8DofA2IgC3chdOg8YJvxtHrx8Iv8vUloBC0Qem5t4urKdPnc1pR+6zkZzOmbKXbX3SQB/D8APSCm5Tv4YGlf9uDllIm7DDFLACKUbZvnGXnm6YaLb68apzuZ9z4Gj3TLT7vdj9q+PboQKDjPF0EYVPF/dxnSW2UIpJXQjhDHVDyHyl8JeKmCBiPXa66c78oY4u+lGCCc6mqD2tFbtmkTVUG6P1P8JoB3AV4UQ7wghftmGMVEd0UYVrG7H8N7TlbLO82R5CzPmJv7U5X4MKd6qlxUaTTIohDCmKtBUP8upB0yHNvBsZRs/fG0QpzqbszZpSykxYZgFh5lipEvnWYKPsbiBF6s7BS80sRaI5ApIE0YIJzua8Znrg1Ut+SYSyeCqVeDrSFRr5a7aG5VSDkgp30j991ftGhjVB2uZcrkzSFZwGh9VoI36cWs6jFg8Ufb4KLOZVAlHU/0YH1WwtBnFo+dcLWnZ23ukqX4EpjIHTWNxHYtrOxkfC1OuIcWL0zlmC62PF7Nid3xUweJa5gUiiYTETcOENqqk93Gq1szwhwtrMDciVV99TFQN3FqWcuptb8ZLvW1l/8ANGCaUVg9e7m2HpipY34nh3SflzXJRdvqeN+GxI7LHUDUFDBOnOpsxpHihqUrWvj29Av1RFmuz32yzhbphoq+rBYM+b8Hn1HIEpN0w48eZPCHObtaMH/ePouOIQYry0lQFk9NhRGKlzSAlyyMh3FCVdJMtwD6pStINEyc7mjHsb8WpzhaM+FuPzCNEKi2RsHqPlGQ5LLWKLNPXZyIYQl9XCwZ8LRUZi6Zmni1MJCQCUya01BgLZS0Qyfx32d1UNF+Is5tuhHBG8aK/u/BQSHRUMEhRXtqoH1vRON6ZWy7p86dCyV4Pq5ygtDXh1ZPtfPxMhaT7UUZ334S1UQW3p8OIspyK95+vYWkzmv5+tILmwRm7eELi5lQY46PFhZliWCHu4LUfPlvF8mY0/Xoxsi0QCRghDPtbcborGQqrVfKNxRO4NRWuyKweUT1gkKK8bgwrEKL0/aSs/qi9/RGa6sedmSVsR+O2jJF2ffBiDeFUCceiqX5sROK4P79cu4HViXTZc09IGVOVQ317j56tYmUrWtEAYIW4g7Oz5Wy5YC0Q2fsEASvMjB34NwigoN3Qy/HukxWs7cTYH0XHFoMU5dXpdePc6c6Se2ysXo8zyu60/viogp1YAm/PLtk1TErZ7evZExSscmqF3zSPAt0wMZIqeVo01Y/1nRju7+nbs35xqHRfz5iq4NaUuW+2cMIIQe1pxYmO5uLPl7rXE3tmfK0ws/dhwSc7mzHS01rxmeHd/aMYpOh4YpCigmijCu7OLWEzEst/8B5Wr8fYgV6Pa8M+OB2CDdAVoAf3l3AAoLvVg7OnOhq+Ly0aT+BW6vtxrxsjPgD7S2y6YWK0t62kMFOM8VFrtnAlPcbb06WXwno7Di8Qsf6/9fe0aGrlS74Bw8SrJ9vhb2uq2DWIaolBigqiqX5E4xKTM8XNIKV7PQ68cbU3u3G+r5MN0DaLxRO4NR3O+Nu/pip4a7axy6n351ewEYkfCilKWxNeO9WR/n6MxKwwU/lZlBvp2cLkte/NLWMzEi/rUSoHF4joRgivnmyHciDMVLrkux2NY3Im8/cj0XHBIEUFuTrUDbdTFF0GyNXrMT6q4N78CtZ3ipvlouzefZL8eo5n/Hr7EYkl8Nbjxi2nWsv9swXNO4+TQfPe/DK2oocDVyX4DswW6oYJIYDrw2UEqT0LRLajcdyZWcr4vL5Kl3zvzi5jJ5bI+P1IdFwwSFFBvB4XLg10F12K040QRnpacbLzcHlEU/2IJyQmp8N2DbPhZSvhAMDVVDm1kVdL6oaJ1051wNfqOfSapiqIpPr29GAyzGT6OlbC3tlC3Qjh7KkOdGcYY6GsBSK6EUqHmUyza5Uu+QaMEBwCuFalryNRLTBIUcHGVAXvPlnByma0oON3ez0y/2b95plueFwOlvdslK2EAwBtTS5c7O9M7yfUaLajcdx5vJT1+9Hq29ODJiZSz4Xs8pYeZoqhjSZD3EQwhLcfL2ecPSqGtUBED5rQjRCcDoFrw5nDTCVLvhOGifP9Xehodtt+bqJ6wSBFBRsf9UNK4OZ0YW/E9+eXsRGJZ53Wb3Y78eZgd8M3QNslVwnHMj7qx/35ZaxuFxaGj5O3Hy8hEktk7T1qb3bjQn8nvvb+Au7OLlW1HHVtWIHTIfCLfxhEJJ6wpafIWiDytUcLuNDfifYsYaZSJd/1nRjuzS1X5PE6RPWEQYoK9sZAF1rczoLLe7vlkew/SDVVwcNnq1jaiNg1zIb19uxS1hKOZUxVkJBoyHKqbphwOgSuDmUvM2mqgkfPVhGNy6o2SFuzhffmluFyCFzLMcZCWQtEHj5bzfk9cXXYB1cFSr6TM2HEEpIbcdKxxyBFBfO4HLg67Cu4FDdRQK+Hlpo9CUxxVqpcgVRQyFbCAYDLg91ocjkasrw3YYRwMcfMDID0LJQrz9exEqyZxDcGutDa5Cr7fNYCEQA5Z9famly4ONBl+/eEHgzB43TgylC3reclqjcMUlQUTVXw0cI6Fla3cx63HY3j7cfLeZePX+jvRKvHWVA4+8o7T/AzX7pf1HgbiW6YOUs4QLKcemWou6DZhw+er+FHP38LazUoA/6Ht+bxP3/5gW3nW9uO4v78St7Zkcupvr1Lg13wesoPM8WwZsDs2nLBWiDicTlw+UzuMKOpiu0lX90wcflMF5rdTtvOSVSPGKSoKNYP+XwzSG89XkIknsj7xuV2OnBt2FfQjNS/DTzGb92eyxviGpHVj1LIm7Cm+vH+8zWE1ndyHvelu/P45kchfOuj6i8G+PXADP7dzce2lXxvT4cRT8i8X59mtxM//ydex0994mVbrluMq0M+/Ph3qfiha4O2nfOnvucl/PyfeD1vmLFKvren7Cn5Lm1EUiVFlvXo+GOQoqK8froTHc2uvPvOTARDcDkErhZQHhkf9WNqcQPPV7IHJCsoACwDZjI5nexHKaRB2goTN/N8HQN79jWqppXNKB6kHtVi173WDbOgmRkA+Mz1wbJXzZXC7XTg733y1X070pdLU/34zPX8wcwq+dp1r29OmZASZW0qSnRUMEhRUZwOgRsjCvSp3LMUumHi4kAX2gro9bBKGrnKTVbjKsDnxWWiG6GCg8L5vk60NblyvmnuDTPV3nfq1rSJ1K227dq6YeLKmW6WmbIopuRbCN0w4fU4caG/y5bzEdUzBikqmqYqmAtvYS68mfH11e0o7s8XVmYCgNdOdqDb6875xm41rn7nyz37HsZKSRNBE28OFhYUXE4Hrg/70o8kyeRmKsx8z9kTMPLMFtpNN0w0ux349pf8tsyQmOs7eJRn5RoVXvItxIQRwrVhH9xOvsXQ8cfvciqaVfbI9tvr7akwEjLzY2EycTgExlQFejAEKWXGY6zG1Y+92ov5pewhrhFZ/SjFlFG0UT9mzE08Wd7K+HrAMNHiduInvktN/jnPDKSddCOEq0M+fOfLPXlLvoW4mer70WpQrjtKCi355vN8ZRtTixt8LAw1DAYpKtpobxt62puyzhbohomm1MqnQo2pfjxd2cZj83BA2tu4qhVQBmw01hvfWBFvXOlFA1nvYQhXh3242N+FLq+7auXUxbUdfPhiHZrqL6jkWwjdCKGtyYULfZ12DPHYOt/XifY8Jd9CWKGbDyqmRsEgRUUTQkBTFeiGmXEGyZpRKKYfZTz9pnn4h/jexlUrxDXiPkjZTBghtHqcuNBfeFB45UQ7lFZPxvLewtp2KswoydnCkez32m5WaBofVQoq+RZ2ThPXh31wscyUk8vpwPWR3CXfQkwETXR53Th7qsOmkRHVN/5koZJoqoLFtR0EF9b3fTy0voP3n68V/dvosL8VJzuaM/Y/7W1czRfiGpFumLg+ohTVj+JwCNzI8nW0Zqms0oymKniyvIXZKpRTA4aJ9mYXXj/dWVDJN5+ny1uYDm1wdqRAY2rukm8+UkoEDBNjI8kQTtQIGKSoJFb/08GNNK0yU7GNvVZAummYSCT2v2kebFzVVAWh9R18dCDENSKrH6WURmpNVfB8dRtToY19H9eDJjqaXTh7OjmjMJa+15WfBZwwQrgxknzunHXtbCXfQlizWdzPqDDp0nmJs1KPUyGMjf3USBikqCQDPi8GfC2Hyi66YaK9yYXzJfSjaKN+mBsRfLiwlv5YpsZV602x3BLEcWCVwkqZcbG+pofu4dT+MKP2tOJER1PF+9LmwpuYC2/te8htrpJvIXQjBF+rB6+ebLdljMedVfIt9HmaB6WDKxv7qYEwSFHJtBE/bk6ZiO+ZQdKDIVwfKa0fxQoDe2c+MjWuZgtxjUg3THR73XjtZPH9KGcUL053NiOwJyClw8yeN8LkbKEfgQqXUwMZ3oRzlXzzYZmpeLlKvoXQjRBOdDRhxN9agdER1ScGKSqZNqpgdTuG954mN258sryFGXOzqNVje/V1tWBI8e57Y8/WuJopxDUaKSX0YAhjamlBQQiBsVRAssqp1qzTwdLMmKrA3Ijggxdrh85jlwkjBH9bE17qbds3xmwl33ymQxt4trLN/qgiZSv55pNIJIOrpvohBIMrNQ4GKSrZ2IGyS7pJuYzHQmijftyaCiMWT+ScUTgY4hrRY3MTT1e2Sw6uQPJeLW1G8ej5KoDkvexpb8LonjAD7O2dqcwsoJQSumFCU5VDb8KZSr6F0NPfjywzFSNbyTefDxfWYG5E2B9FDYdBikrW296Ml3rb0j9w9WAISqsHL/eW3o+iqQrWdmJ498kKZsPZG1cPhrhGlA4KZbxxWf1mVtkuW5jp7/bijOKt2NfbWFzH4tpOxnutZSj5FiJgmDjV2YwhxWvLGBtFppJvIayQzf4oajQMUlSW8VE/JqfD2InFoRtmyWUmy9jIbkCayPGDube9GS+faDu0arCRTBghnOxoxnAZ/SgnO5sx0tOKiWAIwYXsYQZIhq5bUyZi8UTJ18vGuteZZo9Od7Vg2N9a1Bt7IiGhGyGWmUoghIA2ur/kWwjdCGFI8aLPxocuEx0FDFJUljFVwVY0ji/ffYLnq9tlLzNX2prw6sl2BAwzb+OqpvoxORNGJGb/G3u9SyQkbmaZPSqWpiq4PR3GNz5cTP058z20ZgsfPF0t63qZ6EYI/d0tGPBlnj0aU5V0ybcQ7z9fw9JmlGWmEmnq/pJvPrF4AremwmWVmYmOKluClBDi7wghpBCC/4oazI1hBQ4B/OLXggCK3z8qEysg6XkaV8dUBdvRBO7OLpV9zaPmgxepfhQbyiia6sdGJI5fm5jBgC93mAEO7x1Wrni6STn7987ekm8h0k3zZfTrNbLdLUYKK6e++2QFazsxBldqSGUHKSHEAIDvATBb/nDoqOn0unGurxNPlrfQ19WCMzb0o4yPKtiJJRDO07h6YyQZ4hqxT8r6O9uxIs0qpz5Z3oI2kj2Y+ffMFtrp4dNVrG7HcjaF7y35FkI3TIz4W3Gqk2WmUlgl30L3DrPz+5HoqLFjRup/B/B3ATTuOvQGZ/3wHLOhzAQA14Z9e3a2zv6DubMlGeLsfmMvlJTS9n2VCu1JCdjYj9Ld6klvL5FvBmdMVTA5k+yJs0t6U9GR7NdWighx0XgCt6ZMvqmXySr5RgsopwYME6+ebIe/rakKIyOqL2UFKSHEDwB4IqW8Z9N46Aj6ttRMQjnbHuzV3uzGxf5ODCle9HfnnuEaUxXcnVvCZiRmy7WL8bd++x7+yr+9Y9v5Pnqxhtf+we/h3txyzuMq0Y/ybS/5IUTuMAMkSz47sQTefpx7jMWYMEyM9raht6M577UnZ8LYjuYOcffnV7ARifOxMGWySr7355dzHrcdjWNyJszgSg0rb5ASQvyBEOJBhv8+DeBnAfyDQi4khPisEOKOEOLO4uJiueOmOvJto3783z/6Jv7EhdO2nfOf/pmL+Fc/8mbe48ZVP6JxicmZ6vZJReMJ/P57z/H1DxZtC3F/8GgBO7EEvvrwRc7jrH4Uu4IrAPzEd6n4jb90PW+YuT7ig0Og6KXx2URiCUxOhwvawsEq+d6dXc55XKCMx+bQrnQ5NU+f1N3ZZezEEvse40TUSPIGKSnlJ6SU5w7+B2AKwDCAe0KIGQD9AN4WQpzMcp7PSSmvSCmv9PT02Pl3oBoTQuCPvX6ypMfCZKP2tOG1U/kfe3JlqBtup6j4c+AOevdJctYjlrAvxFl/h3x/l3Q/Sp7Zo2J0eT0FbVzZ0ezG+f4u2/rS7s0vYysaL2h2zSr55gtxumHitVMd8LV6bBljo7JKvvnudcAIwSGAayO+Ko2MqL6U/M4npXxXStkrpRySUg4BmAdwWUr53LbREeXh9bhwabC7YjtuZ2M9MNnlELY8PHknliyPeJwO3Jtfwdp2NPu1jRBePdkOpUb9KOOqgnfmlrGxU/5M3EQwVFBJEUiWfM/3dWIixxv7djSOO4+XytqklHaNjyp4a3YpZzl1wjBxob8LHc3uKo6MqH5wHyk68jRVwYOnK1jZzB4+7GbNelw+023L7Mw7s8vYjibwmeuDiCckJmfCGY/bjsZxZ2appv0/mupHLCFxO8sYi6EbJs6d7kSnt7A34fFRBffmlrGeJcS9/XgJkViC2x7YRFP9iMQSeOtx5lnX9Z0Y7s0tc9sDami2BanUzFTjbjNNNaOpfkgJBKaqMytlzXpoqpIOccubkbLOqRsmHAL4ie9W4XE5sj4O5e3ZJezEEjV943rzTDc8TkfZM3FbkTjuzi4V9XexQtzkdOYQN2GE4HQIXB1imckOV4d9cDlE1r3DJmfCiCUkG/upoXFGio68Nwa60OJ22tYAnY816zE+qmB8NBnibk6VNzujGyGc7+tEb3szruSY5QoYJpwOges17Edp8Thx+Uz5fVKTM2FE47KoTUXfPNMNj8uRtY9MN0xc7O9EO8tMtmhrcuHiQPZ7rQdD8DgduDLUXeWREdUPBik68jwuB64O+6q2MaeeCjNXh3y42F9+iNuMxHB3djndcK2pCh49W0V44/Asl26YON9X+6CgqX48fLaKpQxjLJRumHA5BK4W8Sbc7HbizcHMQXNtO4r78yucHbGZpiq4P7+M1Qx9e7ph4vKZLjS7nTUYGVF9YJCiY0FTFXy0sI6F1e2KX0s3QriQmvWwQlyuBuh8JmeWUuURa2PTZBA4uPlkPfWjaKqSmokr/e8dMEK4NNgFr8dV9LUzhbjb02HE93wdyR5jqoKEBG4fmHVd2ojg4bNVBldqeAxSdCxYe9hUuk9qbTuKe/Mr+/bMGVcVBMsIcXowBLdzt6/nYn8n2ppch8pXk9PJfpRCtimotIsDXfB6nCXPAq5sRfHuk9Jmj7TRzCFON0x4XA5cPsMyk50uD3ajyeU4dK9vTpmQ0r6NeImOKgYpOhbOnu5AR7PL9gfqHjQ5c3jWI/2A1xJDhW6YuDTYjRZPsjzicjpwbdh3aEZKN5L9KG/WQVBwp8Y4UWJJ89aUiYQs7SHXF/q70JohxOmGiStnullmslmz24krQ92Hgr1umPB6nLjQ31WbgRHVCQYpOhacDoEbI0rF+6T04OFZj7OnO9DZ4i5pU9CVzSgePF05tCu0piqYCm3g2cpW+mMTwfrqR9FUBVOLG3i+UvxMnG6YaHY78MZgV9GfmynEmes7ePRslWW9CtFUP95/vobQ+k76Y7oRwrVhH9w2bsRLdBTxXwAdG+OjfswvbWEuvFmxa0xkmPVIhrjSmt0DqfLIwX2P0rNcqW0QrH6UenoMh5YupxYfIHUjhKtDPjS5SguFmurfF+KsVZPFrACkwlkB1SqnvljdhrG4UVffj0S1wiBFx4b1w75S5b3wRiTrrIemJkPcrFlciAsYIbS4nbh4oDzy6sl2+Fo96VkXq/ernjaaPHuqA11ed9Y9r7JZXNvBhy/Wy2pStr4O1izghBFCW5MLF/o6Sz4nZXe+rxPtTa70vdb5PEOiNAYpOjZGe9vQ095UsfLezXSYORwAxg+8sRdKN0xcG/bB49r/T9HhEBgbURAwTEgpoRshtNZZP8rBMRbKCoXlNCm/djIZ4qx7HTBMXB/22fq8R9rlcjpwfcSX3uZDD5ro8rpxtoDnYRIdd/ypQ8eGEAKamuyTKuaNvVATweyzHmpP8SFuYXUbHy2sZ+3rGVMVPFvZxoy5mQ5c9daPoqkKnixvYbaIcqoeDKG92YXXT5c+e7Q3xD1d3sJ0aIOzIxU2pvoxY27iyfIWdMPE2IgCh0PUelhENVdfP5WJyqSpCkLrO/hoYd32cwdSYSbTrEcpIS5drstS4rIC1pfensfU4kZd7tdj7XlVTHlPN0zcGFHgLPNNWBv148nyFr5wezb55zr8+hwn1vfj/3N7Fk+Wt9jYT5TCIEXHym6Ttr19Us9WtjAV2sj55jGu+osKcXrQRGeLG2dPZy6PDPtbcaqzGb/6rWkA9dUfZVF7WnGio6ngkuZceBOz4U2M2/AmbN2Lz39rGr5WD1492V72OSm7V060Q2n14PPp70cGVyKAQYqOmQGfFwO+lrJ2Gs/EWj2Xa9ZjrMhm9wkjhBsjvqwzM0IIjKkKNiJxdHndeO1k/fWjJGfi/AgYJhKJ/DNx1t5YdrwJj/iTIW4jEmeZqQocDoEbqe/HEx1NGPG31npIRHWBQYqOHW3Ej5tTJuIFvLEXSjfMvLMeVogrpE9qLryJ+aWtvOUo6/V6DgpjqgJzI4IPF9byHqsbIfjbmvBSb1vZ17VCnDUGqjxrFlBT/RCiPr8fiaqNQYqOHW1Uwdp2DA+erNhyPiklAqnZo3xhZlwtLMRZpbB8fSbf/pIfHpcDH3u1t7hBV5H1yJp8fVLJ1YcmxlTFtjfhj7/WC7dT4Dte6rHlfJTbd7zUA7dT1PX3I1G1MUjRsWPNTti1DcKMuYmnK9sFNTOPqYWFuImgiZ72JozmmZk50dEM/ac/hj/9Zn9RY66mvq4WnFG86aXx2RiL61hY27GlP8ry/edPIfAzH8eg4rXtnJTdgM+LwM98HJ+6cKrWQyGqGwxSdOz0tjfj5RNtJT2yJZNCZ4+Sx+R/7p41M6MVODPjb2uq+zKKpvpxayqMWDyR9Rjra2Ln6johBPxtTbadj/I7Ct+PRNXEIEXHkqb6MTkTRiSW/Y29ULph4lRnM4YLaK7taW/KG+KCC+sIre8cq8draKqCtZ0YHjxdzXqMHjTR393C2SMiOlYYpOhYGlMVbEcTeGduuazzJBISgSL7eqwQtxOLZ3zdWtV3nBqk861YjCckAlMm9x4iomOHQYqOpRsjChyi/OfuffBiDeGNSFHlKM0KcbPLGV/XDRMDvhYM+I7PzIy/rQmvnmxPb29w0KNnq1jZinLTTCI6dhik6FjqbHHjXF9n1jf2Qu329RQ+k3I9FeIy9UnFExI3p8xjVdazjKlK1pm4YvrMiIiOEgYpOrbGVAV355awGYmVfA49GMKwvxWnu1oK/hwrxGXqk3rv6QpWt2PHqqxn0VQ/dmIJvP14+dBrE0ETo71t6O1orv7AiIgqiEGKjq1x1Y9oXGJyZqmkz4/FE7g1HS4p9GiqH3dnlw+FOGuW6jgGqesjPjgEDm2DEIklMDkT5mwUER1LDFJ0bF0Z6obbKUreBuH+kxWs78RKKsNpqoJY4nCI0w0TL59oQ2/78ZuZ6Wh243x/16GS5v35ZWxG4uyPIqJjiUGKji2vx4VLg90l90lZn3djxFf0514d8iVD3J5m90gsgcnp8LEOFOOqgnfmlrGxszsTNxE0IURpX0cionrHIEXHmqYqePfJClY2o0V/rm6E8OrJdiglbPjY4nHi0mD3vtmZd+aWsRWNH8uynkVT/YglJG7PhNMf040QXj/dgS6vp4YjIyKqDAYpOtY01Q8pgZvTxc1KbUfjuDOzlH6OXGnXVvDg6QqWNyMAklsxOERya4bj6s0z3fA4HemZuK1IHHdnl4/lKkUiIoBBio65Nwa60OJ2Fl3ee3t2CTuxRFkN0uOjqRA3lZydCRgmzvV1orPFXfI5612Lx4nLZ3b7pO48DiMSTxzrWTgiamwMUnSseVwOXB32Fb0xZ8Aw4XQIXBsuva/nYr8V4kLYjMRwd26pIQKFpvrx8NkqljYi0A0TLofA1SH2RxHR8cQgRceepir4aGEdC2vbBX/ORDCEC/2daG8uffYoHeIME5MzS4jGZUOUuDRVSc3EmdCDIVwa7EJrk6vWwyIiqggGKTr2rPBSaHlvfSeGe/Mrtux7NK4qCC6s4yt3n8DtFLgy1F32OevdxYEueD1O/N57z/HukxWMNUB4JKLGVXaQEkL8dSHEB0KI94QQ/5sdgyKy09nTHehodkEPFhakJqfDiCekLdsUWOf48jtPcGmgG17P8Z+ZcTsduDbsw+/ee4qE5GNhiOh4KytICSG+G8CnAVyQUr4O4J/ZMioiGzkdAmOqAn2qsD6piWAIHpcDb54pf/bo7OkOdLa4k4FitHECxbjqR0ICzW4HLg121Xo4REQVU+6M1I8D+F+llDsAIKVcKH9IRPbTVD/mwluYC2/mPVY3TLw52I1mt7Ps6zodIr0R5XHeiPMgq6n+6pAPTa7yv45ERPWq3CD1MoBvF0LcEkJ8QwhxNduBQojPCiHuCCHuLC4ulnlZouJY5aV8j4sJb0Tw8NmqreWoP3mpHxf6O/HGQJdt56x3Z0914MqZbvypy321HgoRUUXlbdgQQvwBgJMZXvrZ1Od3A7gB4CqA3xZCjEgp5cGDpZSfA/A5ALhy5cqh14kqabS3DT3tTdANE3/26mDW425OJfuotDI24jzok+dO4pPnMv0TOr4cDoEv/rhW62EQEVVc3iAlpfxEtteEED8O4Eup4HRbCJEA4AfAKSeqK0IIaKoC3TAhpYQQIuNxuhFCq8eJC/2dVR4hEREdReWW9r4M4GMAIIR4GYAHQHE7HxJViaYqWFzbQXBhPesxetDEtWEf3E7uDEJERPmV+27xqwBGhBAPAHwBwI9lKusR1QOr2VvPsp/Us5UtTIU2ynq+HhERNZaygpSUMiKl/BEp5Tkp5WUp5R/aNTAiuw34vBjwtWRtOLc27GyEx7gQEZE9WL+ghqKN+BEwTMQThydOJ4Imur1uvHayowYjIyKio4hBihqKNqpgdTuGh09X931cSomAEcKYqsDhyNyITkREdBCDFDUUq2w3caC8N2Nu4unKNp8LR0RERWGQoobS296Ml3rbDjWcW31T4+yPIiKiIjBIUcPRVAWT02FEYon0x3TDxMmOZgz7W2s4MiIiOmoYpKjhaKN+bEXjeGduGQCQSEgEDBOaqmTdqJOIiCgTBilqODeGFQixW8774MUawhsRWx8LQ0REjYFBihpOp9eNc6c7031SOvePIiKiEjFIUUPSRhXcnV3CZiQGPRjCkOJFX1dLrYdFRERHDIMUNSRN9SMal7g1Fcat6TDLekREVBIGKWpIV4e64XYK/PI3DKzvxKCxrEdERCVgkKKG5PW4cGmgG7emwwCAsREGKSIiKh6DFDUsq7n81ZPtUNqaajwaIiI6ihikqGFZ5TyNj4UhIqISMUhRw7p8phs/euMMPnN9sNZDISKiI8pV6wEQ1Yrb6cD/8oPnaj0MIiI6wjgjRURERFQiBikiIiKiEjFIEREREZWIQYqIiIioRAxSRERERCVikCIiIiIqEYMUERERUYkYpIiIiIhKxCBFREREVCIGKSIiIqISMUgRERERlYhBioiIiKhEDFJEREREJRJSyupfVIhFAI8rfBk/gFCFr0Gl4b2pT7wv9Yv3pj7xvtQvu+/NGSllT6YXahKkqkEIcUdKeaXW46DDeG/qE+9L/eK9qU+8L/WrmveGpT0iIiKiEjFIEREREZXoOAepz9V6AJQV70194n2pX7w39Yn3pX5V7d4c2x4pIiIioko7zjNSRERERBV1LIOUEOKTQogPhBBBIcRP13o8jUoIMSCE+CMhxCMhxHtCiJ9MfdwnhPiqEOKj1P9213qsjUgI4RRC3BVC/MfUn3lf6oAQoksI8UUhxPupfztjvDe1J4T4m6mfYw+EEL8lhGjmfakNIcSvCiEWhBAP9nws670QQvxMKg98IIT4Y3aP59gFKSGEE8AvAfg+AGcB/LAQ4mxtR9WwYgD+tpTyNQA3APy11L34aQBfk1K+BOBrqT9T9f0kgEd7/sz7Uh/+JYDfk1K+CuAikveI96aGhBB9AP4GgCtSynMAnAB+CLwvtfJvAHzywMcy3ovUe84PAXg99Tn/Vyon2ObYBSkA1wAEpZRTUsoIgC8A+HSNx9SQpJTPpJRvp/7/GpJvCH1I3o9fTx326wB+sCYDbGBCiH4A3w/gV/Z8mPelxoQQHQC+A8DnAUBKGZFSLoP3ph64ALQIIVwAvACegvelJqSU/w1A+MCHs92LTwP4gpRyR0o5DSCIZE6wzXEMUn0A5vb8eT71MaohIcQQgEsAbgE4IaV8BiTDFoDeGg6tUf0CgL8LILHnY7wvtTcCYBHAr6XKrr8ihGgF701NSSmfAPhnAGYBPAOwIqX8ffC+1JNs96LimeA4BimR4WNcmlhDQog2AP8BwE9JKVdrPZ5GJ4T4FIAFKeVbtR4LHeICcBnAv5JSXgKwAZaLai7Vb/NpAMMATgNoFUL8SG1HRQWqeCY4jkFqHsDAnj/3IzkFSzUghHAjGaJ+U0r5pdSHXwghTqVePwVgoVbja1DjAH5ACDGDZOn7Y0KI3wDvSz2YBzAvpbyV+vMXkQxWvDe19QkA01LKRSllFMCXAGjgfakn2e5FxTPBcQxSkwBeEkIMCyE8SDaZ/U6Nx9SQhBACyV6PR1LKf7Hnpd8B8GOp//9jAL5S7bE1Minlz0gp+6WUQ0j++/hDKeWPgPel5qSUzwHMCSFeSX3o4wAegvem1mYB3BBCeFM/1z6OZM8n70v9yHYvfgfADwkhmoQQwwBeAnDbzgsfyw05hRB/HMkeECeAX5VS/uPajqgxCSG+DcA3AbyL3V6cv49kn9RvAxhE8gfUn5FSHmwcpCoQQnwXgL8jpfyUEEIB70vNCSHeQHIRgAfAFIC/gOQvvbw3NSSE+IcA/iySq5HvAvjLANrA+1J1QojfAvBdAPwAXgD4OQBfRpZ7IYT4WQB/Ecl791NSyv9i63iOY5AiIiIiqobjWNojIiIiqgoGKSIiIqISMUgRERERlYhBioiIiKhEDFJEREREJWKQIiIiIioRgxQRERFRiRikiIiIiEr0/wN9WIrRcILAcwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(walk[:100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(12345)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=nsteps)\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walk = steps.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.min()\n",
    "walk.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating Many Random Walks at Once"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   0,   1, ...,   8,   7,   8],\n",
       "       [  1,   0,  -1, ...,  34,  33,  32],\n",
       "       [  1,   0,  -1, ...,   4,   5,   4],\n",
       "       ...,\n",
       "       [  1,   2,   1, ...,  24,  25,  26],\n",
       "       [  1,   2,   3, ...,  14,  13,  14],\n",
       "       [ -1,  -2,  -3, ..., -24, -23, -22]], dtype=int32)"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0 or 1\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walks = steps.cumsum(1)\n",
    "walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "138"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-133"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.max()\n",
    "walks.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False, ..., False,  True, False])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3410"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(1)\n",
    "hits30\n",
    "hits30.sum() # Number that hit 30 or -30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "498.8897360703812"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)\n",
    "crossing_times.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "steps = np.random.normal(loc=0, scale=0.25,\n",
    "                         size=(nwalks, nsteps))"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  }
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