Numpy的Less基础.py.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0   1   4   9  16  25  36  49  64  81 100 121]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 1,  1,  9, 64, 25], dtype=int32)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.arange(12)**2\n",
    "print(a)\n",
    "i = np.array([1,1,3,8,5])\n",
    "a[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9, 16],\n",
       "       [81, 49]], dtype=int32)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "j = np.array([[3,4],[9,7]])\n",
    "a[j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  0,   0,   0],\n",
       "        [255,   0,   0],\n",
       "        [  0, 255,   0],\n",
       "        [  0,   0,   0]],\n",
       "\n",
       "       [[  0,   0,   0],\n",
       "        [  0,   0, 255],\n",
       "        [255, 255, 255],\n",
       "        [  0,   0,   0]]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "palette = np.array([[0,0,0],\n",
    "                   [255,0,0],\n",
    "                  [0,255,0],\n",
    "                  [0,0,255],\n",
    "                  [255,255,255]])\n",
    "image = np.array([[0,1,2,0],\n",
    "                 [0,3,4,0]])\n",
    "palette[image]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(12).reshape(3,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  5],\n",
       "       [ 7, 11]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 多维数组的索引形状必须相同\n",
    "i = np.array([[0,1],\n",
    "              [1,2]])\n",
    "j = np.array([[2,1],\n",
    "              [3,3]])\n",
    "a[i,j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  6],\n",
       "       [ 6, 10]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[i,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 2,  1],\n",
       "        [ 3,  3]],\n",
       "\n",
       "       [[ 6,  5],\n",
       "        [ 7,  7]],\n",
       "\n",
       "       [[10,  9],\n",
       "        [11, 11]]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:,j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  5],\n",
       "       [ 7, 11]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = [i,j]\n",
    "a[l]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = np.array([i,j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 1],\n",
       "        [1, 2]],\n",
       "\n",
       "       [[2, 1],\n",
       "        [3, 3]]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0, 1],\n",
       "        [1, 2]]), array([[2, 1],\n",
       "        [3, 3]]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuple(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "time = np.linspace(20,145,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.sin(np.arange(20)).reshape(5,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 20.  ,  51.25,  82.5 , 113.75, 145.  ])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.84147098,  0.90929743,  0.14112001],\n",
       "       [-0.7568025 , -0.95892427, -0.2794155 ,  0.6569866 ],\n",
       "       [ 0.98935825,  0.41211849, -0.54402111, -0.99999021],\n",
       "       [-0.53657292,  0.42016704,  0.99060736,  0.65028784],\n",
       "       [-0.28790332, -0.96139749, -0.75098725,  0.14987721]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "ind = data.argmax(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 0, 3, 1], dtype=int64)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_max = time[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 82.5 ,  20.  , 113.75,  51.25])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_max = data[ind,range(data.shape[1])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.98935825 0.84147098 0.99060736 0.6569866 ]\n"
     ]
    }
   ],
   "source": [
    "print(data_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.max(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(data_max == data.max(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function all in module numpy.core.fromnumeric:\n",
      "\n",
      "all(a, axis=None, out=None, keepdims=<class 'numpy._globals._NoValue'>)\n",
      "    Test whether all array elements along a given axis evaluate to True.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    a : array_like\n",
      "        Input array or object that can be converted to an array.\n",
      "    axis : None or int or tuple of ints, optional\n",
      "        Axis or axes along which a logical AND reduction is performed.\n",
      "        The default (`axis` = `None`) is to perform a logical AND over all\n",
      "        the dimensions of the input array. `axis` may be negative, in\n",
      "        which case it counts from the last to the first axis.\n",
      "    \n",
      "        .. versionadded:: 1.7.0\n",
      "    \n",
      "        If this is a tuple of ints, a reduction is performed on multiple\n",
      "        axes, instead of a single axis or all the axes as before.\n",
      "    out : ndarray, optional\n",
      "        Alternate output array in which to place the result.\n",
      "        It must have the same shape as the expected output and its\n",
      "        type is preserved (e.g., if ``dtype(out)`` is float, the result\n",
      "        will consist of 0.0's and 1.0's).  See `doc.ufuncs` (Section\n",
      "        \"Output arguments\") for more details.\n",
      "    \n",
      "    keepdims : bool, optional\n",
      "        If this is set to True, the axes which are reduced are left\n",
      "        in the result as dimensions with size one. With this option,\n",
      "        the result will broadcast correctly against the input array.\n",
      "    \n",
      "        If the default value is passed, then `keepdims` will not be\n",
      "        passed through to the `all` method of sub-classes of\n",
      "        `ndarray`, however any non-default value will be.  If the\n",
      "        sub-classes `sum` method does not implement `keepdims` any\n",
      "        exceptions will be raised.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    all : ndarray, bool\n",
      "        A new boolean or array is returned unless `out` is specified,\n",
      "        in which case a reference to `out` is returned.\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    ndarray.all : equivalent method\n",
      "    \n",
      "    any : Test whether any element along a given axis evaluates to True.\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    Not a Number (NaN), positive infinity and negative infinity\n",
      "    evaluate to `True` because these are not equal to zero.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> np.all([[True,False],[True,True]])\n",
      "    False\n",
      "    \n",
      "    >>> np.all([[True,False],[True,True]], axis=0)\n",
      "    array([ True, False])\n",
      "    \n",
      "    >>> np.all([-1, 4, 5])\n",
      "    True\n",
      "    \n",
      "    >>> np.all([1.0, np.nan])\n",
      "    True\n",
      "    \n",
      "    >>> o=np.array([False])\n",
      "    >>> z=np.all([-1, 4, 5], out=o)\n",
      "    >>> id(z), id(o), z                             # doctest: +SKIP\n",
      "    (28293632, 28293632, array([ True]))\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(np.all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "a[[1,3,4]]=0 # 使用数组索引作为目标来赋值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 2, 0, 0])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 3, 3, 4])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[0,0,2]]=[1,2,3] # 当使用索引列表包含重复时，赋值完成多次，留下最后一个值\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "a[[0,0,2]]+=1 # 在索引列表中出现两次，第0个元素只会增加一次"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 3, 3, 4])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "a =np.arange(12).reshape(3,4)\n",
    "b = a > 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [False,  True,  True,  True],\n",
       "       [ True,  True,  True,  True]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5,  6,  7,  8,  9, 10, 11])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[b]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "a[b]=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3],\n",
       "       [4, 0, 0, 0],\n",
       "       [0, 0, 0, 0]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PdDdwHDgGbAfuLXRgdlBCkZlcQctM5ONXW9dr9E/5uK/zN6xaOsilV79F719t4yOffI2p1oTpYsR012LNkXVJr9PuD7O/q48HL9md11iLxSoUW8ZWsKzjFPu7+mYJ1mDPo9kDoSk3a+m/LWMr2N/Vpz1Xj11Y8VJquKdXnVabWBQrEsX+8DIVpDH/D/t4Z6XU3JD2PWYMITX4aK03MRSP8LFf/ld8erUqX8s528Vr3ED/lI8Nz24kOOqfZSUZlsOSXZs4sW77TP6GHg8BTWg6+jZTP+IjMAmnr43RvMdP+OR0Ugp5qoXhScvCrVSbUBRLua5Ql179lpkktXeikxPvL5q1jzWfYdPAnfjDMRKh86ZQtIWcPxFKRabcDMAUQMMde2PjI0n7GAHaROg8U60Jzi62f2F2Y95F1S4k8xKF/jCcEoh8XI+Tv2qn4+BmQLMSVi0dzLr/01fsYg3reDscMs1xL7FlbAVNrWfYv06rsBUbrDcfM1yqBy/ZbXZqT3RM0RCeYjJST6PeGe2L1/+BTzS8zldfvwMOLKzUoRSNJ92QarIqChEKJ62IbEKRqTCN4ZNPt8RZ1nEqp0vRO9HKifcXsbX5kDODriBLdmmzNka5v9TZGSNomlr6b8muTYQGA4SGZ8r4pa5kTRfsdNIdKdYN8ZxlUS1Cka9IlMLNKDZJyB+O2Yo9aDGN4pOq3IC1aDAwaxrXiN8YQrFhaDUHxtrMmEY23FAEOBuejVl4lXwWgRU6o2GHQsrdpbL9hh84OiYvsL+rj1VLB20HaHe072FisImOvs0kOqYy5md4AU+JhdetinxFolQUalGkthHc8OxGJ4bjOeyugt0ytoIluzZRP+Jj/oCPhb/Q4h25WiZacVOg01Ni4WXsfOmVrhKdjmxt/nzROlbu6ynjaLzFS+9+EMi+BsVLeEYsvGpV2HE7yiUS+dSigMy1Jqw//slIPRuGVpvl+hUzPHjJbk6s284bGx+Z1Z8E0lt46X4HbrEuPBfg9Ap2LYlykW8h3VShMDIYU/MIjOlBxWyMIOdVD99LKP16Sk+hxMJh7FgR5aYQobBaEsGb3+W1rj6W7NqUlIl5Qu8UplF8Qd1qwlgn4xusZ97kzPbUgsB2cbJPaqF4Qiy84IJUg0jAzGKx9685S2J0Ln936894alibmm9qPcP4yHz84RgNyqLIyMp9PUwMNqVdSOdlPCEWbqUQV8N6AhfS8coOxVbbjnbEONG900ws2ti4i6F4hG9d+SO6uxKOFtCtNtYcWcf4yHyCWUTCal0Yy9W9gOsDnG61KvIVinTBxULLy2ejGKEw3I/QYICV+3qSMhDb/WHz/l2LnmdV44AzA64yPnzBn/CHY1lbDRRKpQOdyrLIk3xEwqhbCbnn1tOd5HavOPmKTTprInWKNNs6ju76BN311ZGR6TRbmw9pxXx2bWI6BPFwHYFJPVU+SzMjK27N5FRikYN81DzVkohcFDQDhUH9h5JPcMtJiyNr7cg0uRQdfZtnFalR2KN/ymeuRF25r4fpkQsI6kHOdILhFVfE1W5IpVwQIzeiGKEArfRarEGrYTC2Ok5kcZ2tMvnFkq0+5Kx9MyRd+SOCJbs20dm/vkSjrF6s7ptZ+CZDu4FC2wxUAteOtNxC4dQy8VRrQKvdGCDaEaP5r4cY+0k7kYuCrlgjkC070yC1dL4iPzr71+MLS7Ra1slBT6MQTjCPGdFKTqG62rIoJVbrodBl4nanQ0PDEl+0jrejM/vbOVGtGFei4Y8KIovrkqpNF0K651qTr+JhiT8cwx+OqdmPImgITzHdEue1+7+XVEX87GLt833vtinPtAkotH3h3wshTgohXtVvay2PPai3L3xDCLGmVAMvhkqUr/voTa+zKJQctLJ7sltrSXz+L55PqpJdjGBkwiiqu7TlHZa2vONY+8BaZFEoarYfMCppGbVABrp38sCHflnhEdrHjhuyE/gOkLoe+dtSyn+2bhBCLAfuBK4E2oBfCyGWSSnPOzDWonBq2imbUGS6OkTbBP0HLwcg1AAgzCrR2UrLpwpBrAGeePFGTtz/PT609V5br5HrNc3tulVhrb5d7gK61cjn2vax8YqZmaNEh5bM1r10kM7+9YT3ziNMxU8PW+QUCynlb/VWAHb4DPCklPJ94IQQ4hhwPVp1cNs4Fa+oZDl9g9PLIHTNu9zefpgnXrwRMPpnpCbtZLYQjBP5ok8N0Raa0ArAWl4jl2jksj7M1O6w5Lm//meM1G1roE5RGKnFjAe6d5rVtFaOtTHROZfwKe0xu7MilYpbFGPDfkXvlP59o4s6Lmlf6HSX8UKFYjrsY94pwfTzF9B3+Dq+eP0fZkrjW1r2xRo0UTm9jLSdvIz9nr5iFwfG2kiEzpuvAWnK06f0Fc04vjQNiTcN3FnQsSrsYwjIolCU+hHvhA0LHekjQAdwLXAK+J/69oq0L4TCpjvtYFcoMjXmCU5KLcCpF3pt7BhnuiXO+9ec5f1rznKmUxOPSz7yZ+JGfw1r3099Sbix2nN/Vx8n1m0n0THFRZ8a4vS1saS2e2cXy4yik3qzvofB0cHFs/p6KErDsYMXazU5C1hYVgkKmjqVUo4a/wshtgNGjbGi2xfm64K4oWFwJoKRhHllD0QEP/q3VSQ6psyuV9s7nwTg9lc30haaoO2mCfoPXk48XMdUq5brYBAPS7Nj1n2dv2FAX/G5MtpDdFSrGG203gP0eo+CgGXFYzqsQmHMgDx4ye5ZBWcVzrFhaDW/e+Yq5p8SBCPeiFdAgZaF3t/U4LOAMVPyc+BOIcQcIcQSoBN4sbghVgeBSU0wEqNzGR+Zz9HBxXx9+Dba/WHWth82Zxz84RiXXv0WvpbMvqvVD/7WlT9iuiVOPCzZcUsvW8ZW0Nm/fqZTeEOmV0n/2ED3Tj2dWwmF0wzFI6ZQzDslbLVCzEQl1onktCz09oXdwIVCiLeArwPdQohr0VyMN4EvA0gpXxdCPAUcBuLAfaWaCXGzRZEtK69+xEcsLIiHJd9o+wW9E5eaJfJ3tO9hy9zTbG0+xMpoD+MtWkKUPxwjEQngD8e4pjnZUOuuT9B99R/Ze7yDX09eqTXzffeDHI0sJhY2LJNkCyNVJGKW7lmK0rDmyDqODi4mNBhg3qS9nqluw3V9Q3K5IaVU1EKFIlO8wryfUkzGODkTHVNZW/mt3NfD2vbDnDy3wNyWLudhy9gKcx/r40axGl/LOXyD9WlrKxhjiYcll179lmfaCnoRo3dIQBcLY9bKGrPI1TA5lXxmRWqqb4gXhSIT8bAkEQnQtjTzl722/TBL5rydszlPpsetDYA6RjdnHQvA8dEL6b9ExSpKzczUuS9pmtvti8lcJRbZrAo3CkUqdoViuiVOU+sZIHtZ+WI7eFmTqhKh88TRSuIZgdN4Sj3Njy4dVEJRIvqnfPjDMWJh7Tcy1SqZP+Aj6KE6x56Y5PWCUGQiXZ6DL1rHNc3DfOvKH5X0va0nfvfVf6T3r7Zx6dVvmQFRg0ToPP5wTKV1l5Du+gQD3TsJXfMeiY4pev9qG69s+Z75uNutCvCIWLgVqwuSdRl4mnjF3uMdfPPNtfROtJZ2kDp3LXqe7voEH77gT4AmEMbNWLuwZWxFWcZSy6xtP8wq3YK76uF7Kz2cvHCVG5ION896GGQSCqtVkdpvIx4J8HY4xIn3F1GOPqCGlbG1+RC7W5czPjIfwBSKhvBUVTQudjvWzzhXDozbcK1lUYpsTAMnhMKwKnIJxellmFmaoMUJfC3n8IdjrG0/zN0L81o24wj7u/poaj1DU+sZGsJTNISnZq2IVZQGq/UWnCw+e7Oc+RautyycptRCYbUmom2CQATu+PRe+g5fRzwSMGcoNgyt5u6Fv5/VhbtcrG0/bLbXA2gLVbYnRbXTO9HK1j2fJjQY4Ges1tK8XVAAKR9cIxbWmZBKVzHOhDVGka08XmoD4R8+dzPP/fU/JwmDFkysXGOerc2H2AKcPLeAi+aeZsmctys2llpgY+MI/11v0JTqfnghuAkudEPcOPNhLdc/3ejnvcvnmAu1rKQu0IKZOMXHfvlfXVdx6u6Fv2dV4wBL5rxNR3Cs0sOpenwt59h93z8B9mqPuA3XiUWpKEQosvX0MMqkpVvFmYqR1+C2qcl2f5iO4BgdwTGWBs5UejhVT8/yl5OsS6+sNjVwjRtSSnIJRa76h6nt/YKTko6+zfg6pohF5pmPpa6/sAY1/eEYa46sY3vnkxWLU6RjJhfDPWOqVrY2H+Ky3ntY4MF1IeAysSiFC5Kr+nYusuVP9Cx/mSciNxIcNfYRxMJyVjcqX8s5Brp3MhSPuEooFOXDWBeyQA9ses2qgCp3Q3K1D8xGun4b1sK59SM+nnjxRrqv/qOZEWkIxWDPo/hazplJT6DVMFBCUZtsGVvBjlt6tQVkKbEKrwQ3wWWWhVNY2wfmSz5NX4KjfvYe7zALznT2r8eHJgwN4SnQ8xfejoa4a9HzeY9FUR143f0wcI1YpHNBMsUaMi3fLUYkwF6Lv3SBzA1Dq9nRvoee5S9z8twCdrTvYagtwvHYfJYGzvD14dsYnG5W/UFrkDVH1vHm7z6gFbvRq2J50QUBF4mFlVwByULK8efCjkWRTigawlPm/9ZU3nZ/mHZ/Aghr4hGPoIKItcfn2vbx7Ui7J4vdpOI6sShECKYb/UyHfZxeBs37089fZ1PzXEJhLV5jMNWqvc9kpJ4DtNG/KHsdCBWvqD0Mq2LBcPpCN05RrtYArhKLTEKRTSTM/xsE8XCCyOI6wqdmV/Kzs9hr1mOWMvxWjEY8K/f1sCgUVdWlFGkx3I8MBe49h50anB9A60bWCiSAbVLKh4UQC4E+4BK0Opyfk1KOCyEE8DCwFjgLrJdS7s/1PsUIBWh5Df6IdnJPT/qSKmvPeq7FSkg1D1NL5MfCktA17zEx2GQmVyVC51m5r4f9XX30T/nUlKgiCWOa1Ku1NjNhx7KIA38jpdwvhGgAXhZCPAOsB56VUj4khHgAeAD4GnAbWlXvTuAGtB4jN+R6E0MUrFNJ0fbkE9Aw4VLXZZxeBtMtMZpaz7C/q0/r2DVSl5QkFZyUSS36wBCXzJmXxlTo/q4+loxsYjqklao7PnqhWThXcz2UUCg0Ovo2ExrxJf/2PJjanQ477QtPoTUSQko5KYQ4gtZl7DNoVb8BHgf60cTiM8APpFYJ+A9CiAVCiMX662QlclEQLgoy3SDMk9tAu8prHb6ME9680ndMcULvowFaI58JmgjePE70wEKmW+JahexRTZAuvfotPte2j617Pk2iI0Y8EqCp9QyTkXrikQBbVv8bAN8d+JhZzWrHLb2AJg6qTqUiFaN6dzBNUeRqIa+kLL3n6YeAF4AWQwD0v836brZaGJayfaFCoXAe260AhBBh4DfAP0gpfyqEOC2lXGB5fFxK2SSE+Hfgm1LKvfr2Z4G/lVK+nOm154uF8rpb/hYoxg2Jp7ghPltuSLry+AbWjMwluzYBM27IqqWDrlsYpqg8qb89a8l/mD0bkimD024rAAM7syFlaQUghAgAPwGekFL+VN88argXeocyY41zQS0M031ooaFI2gBn+OR0UoCzeT+MLwsQHV3IVc/fy4XDkmDk/KwAZ3BSEpyEwKQvaZuV5ClS7f+V+3rwRevwRwRvjn6AeEucA2Nt0K5VbV4aOKMCnAoA88Ji9AcBffFhFcQt7MyGCKAXOCKl/JbloZ8DdwEP6X//1bL9K0KIJ9ECmxN24hV149G0MyKBiXNpBSM4EU8SjMCkVl5dy5TT57QzfEHW8uvpBGUGAWhd0OstW+PhOvZ39ampU0VaUvvNVsuMiB3L4mbgfwEOCSFe1bf9HZpIPCWE2AgMAXfoj+1GmzY9hjZ1usHuYLIJBsyeRjVMuulGP8FJiT8i0uZYWPedvT1zDkYwApyanZQVmPTR0ac17ZlsqWdltIdvXfkjFfRUJHHJR/7Mm7/7AEGPFebNhJ3ZkL0Y9vhsbkmzvwTuK3RAmQQDMvt3gQkIAU2HC0v3TrVSZj0eSQDJgqH1LJWEOqa4pnk4p1CoXIza4+krdtHb1sq3d/4nGNZzfxr9jmdxliN7E1y6RL1uPJo1wGM8nnqDwpf82vnlmprSAAAfDElEQVQC05mTk5EZB2XL2AqzdN5QPGImbG0YWs0z0UsLGpfC2zw13EUsLLNWUvMKrkn3luMTs1ae5hsRTt0/Xysjm4VhZISm5n/ATLm8vsPXAZrfdWCsDUAtUa9xnr5iF1yhxS+Ck6WzLsqBKy2LYjEsjcDEOfNml+BE3PYXOd0SZ9XSQZbs2qSV2RusJzE6lx3te5iM1DM+Mp+jg4uZjNTz+Ns3F3o4Co+zZWwFj33hMc9bF1UpFgZWS8MJ0TBnWSYlU60Jvnj9H+g/eDnBUb+Zs+GPCDr6NpMYnYsvWodPL/8+s0xdUWtsbT7Ehmc3auuWUmbfCi2pUAlc44ZAelekWFIDpukEI9sXls016Tt8HaHBwMxrT0JgUptuTSrYy1w6+9eztOUd1xXsVZQH63TqgqM+wHuuSFVbFga5Yh9WdyWd62JYGcGJuOZzNgitzuZgvS4QaRrHTGJmh/ojgngkwNNX7HKdUPRP+cxArKK0bBlbwRsbH/GsO1ITYgH5B0shu+ty1cP3aglgk9K8ZcKo9u22JkND8QiD080MTjdzPDa/0sOpevoOX5ckyvnUe3UDrhttKVwRg2w5HNmwJoUFJ+IsnIinbV9oCEZSAldEEA9LfnPrt11nVWx77yazfSGgaoSWmMToXNZ+928J4M0UcNdYFufHx83/y5Vkki9WSyN8clrr/5ByA2ZZGp//i+e5Ze9XWLJrE2uOrAM0K6OSpv+WsRW89O4HGY428tK7H2TvRGfFxlIL9E60mm0hUquveSXIaXvVaSmZLxbKG8QtZWuOXOpO6jAT9T69TO9Ipscv4mGJr0UTnJ7lL1esk/rKfT1J99Ual/KwZWyFWdj5hq/dQ/jkNDA78J6P22z34lqWVaeVwPgASiEahbojVowFbplmS4wkrgVHYbrBZ86O+COCOHNJhM6ze2g5kFwVvBys3NfD+IgWo/CHY2V971rH+l1PN4iiE7TKaYW7xg3JRKk+jFwp5fmQcZGaxSe1zo6AdpIuCkVZMudtR8aQi/4p7aveMrbCFAqAeESb+p2M1LNlbEVZxlLLWJcEpCsG7WZcLxZuJnV6NRNG/MIqGKuWDvLgJbvZ2FieoOLjb99M/5SPl979IICZMOaL1pmCUW4LpxbZPbScvcc76J/y8dr936v0cPLCtW6IFTfOkNglXZXxROg8B8ba+OrYHezv6ivZe/dPzdQK7T94Ob+NXqmPaSZ+AppwxJnprKZwnv4pH5te+BK+wXp8wMbRu5k/4COMHvRsnOv6vqeusiysMyKplNI3K7U7Mmu/UT8Tg02Mj8zPmnuxZWwFvROtBY/nm2+uNf83Kn35ra6Q5b4vWmde8RTO012fIB4JENCXBcwf8HmuKI4nLAsDN1oYqZW8ctXGMPBHBImWGMPRzMeze2g5a9sPs2FoZloz3ZV/y9gKTp5bMOvxo4OL6Ti4GV/LuYz1Rs2ga1iytOUdVcCnDAQmZ9fmBPdbF54SC3DnLEmm0n+QvHDIGtCKhyXPrfrOrDoXxtSaMWPxxMiN+MNauwJ/OMYGZgvGyXML2Hu8g57lWk1ksyz9qPb1BkbmJaWjW8cRiAhTMNTUaekw8musFJuYVe58JM/anHJ8oiQflhOzJNnckanWBNMtcRKh83x9+DY2No6YsxAbhlbTd/g61hxZx2SknuCon+CoX/Nz9UCkUSfDoH/KR//By0mMzuUTDa+zZWwFx0cvxBetM03etOtWLNuM/YxSgQrnefqKXfzm1m/z4c8e4uxibxbDySkWQogPCCGeE0IcEUK8LoS4X9/+90KIk0KIV/XbWstzHhRCHBNCvCGEWFPKA/AKRp6Fr+UcTa1nWNZxim+0/YKheITdQ8vN2EU8EuDYwYvNhkjpsMYxvvr6HeYS+Q3PbmRr8yEGuneasYhUobCS7rHO/vXm4jKFs7T7w+xo38NHPvla0YJRiSznnBmcepn/xdb2hcDtwOeAiJTyn1P2Xw78ELgeaAN+DSyTUqavpMtMBqeBNZPT9oGUKJZh1y1JdUOMzu4Gp5fBHZ/ey+6h5YyPzDeToRKjc/FHBJd85M8cO3ixGVswTmTrUvc3Nj5ivp6x5P3o4OKkZfLGvuksioxjb5h57nRLnGUdp5RLUgY6+jZz4X5hZnHCzHR8Luu2ELEoeQZnlvaFmfgM8KSU8n3ghBDiGJpw/L7QQdrB+uE5KRx24xhpA53hoNnYKNFxFoCJwSaCEUFAP8EDk9rJ+ubvPoCf2Se59v/MFciIZQRH/Zw80M6CWS6GUXo+d6TduLIZYwCUUJSRS69+i5Mj7QQj3qhtUUz7QtD6gxwUQnxfCGGYA7baF5YSp+MZhcYwgpEEZxdLgje/S8/yl3nixRu1blW6IBiiEJiEBUe1W2hYJi17D05Kc781R9ZxTfPwTDzC2vXKekuzuC3t+CwL3ozX2t75ZEHHqrCP4Ua+HQ2Z3fG8gG2x0NsX/gT4L1LKM2jd0TuAa9Esj/9p7Jrm6bMuc9l6nWbLt8gHQzScEI5CA58LjsL08xfwxIs3mtvMqbMsJ3hSy7tJSWhYcvJX7fQfvJzBnkeTXsPcL4M45BIOUzAigr/4yX8zt6vYRfGk5sl09q/noVduZcPQaiYj9cwfmPl87U6bVmpVtq1fQrr2hVLKUSnleSllAtiO5mqAzfaFUsptUsouKWVXgDnFHIMtnBKObIKR6csODUu6r/4jyzpOmSe5QdaTOOWxwCR88fo/cNXD99p+jVyvaW7XLZj6kZkGSt98c21SYpcif54a7qKzf7153zdYj2+wnv6DlzPQvZOv/G8/zfxkl2FnNiRt+0I98GnwWeA1/f+fA3cKIeYIIZYAncCLzg25eEopGJn47e+v5O1ocuwjnxMctBP6h8/dnNzwuQQFVAzBOD56IcdHL3RdhS8v8XY0ZK69uaz3HnOaOjjqN60Mr1BM+8LPCyGuRXMx3gS+DCClfF0I8RRwGIgD92WbCakUqYKRb1DUEAw7wc9omyARirMoFGWMC4D8T3Jj/7bfAhT/caZbs6JZK1pA1h8RTIe0H7laL1I4Rr7MVQ/fy7ykwLXgdEuA5j1+ghPTrs7cNCimfeHuLM/5B+AfihgX58fHC5pCLZRCZ1NSRSN1ViTaJoh2aNOkYz9pJzgpk6bKSoHd2o7pBCMVVe+iOAa6d3LVgXtnuZ+AJhR5XjQqWUXO1ene5RYMg0KEwzrFagjGdNinzXS8GtCDmOfLMkWW7j1ydVpLJR6WZvl6RX5YV/saFclSY0zm/x6YMjVwtVi4gXzcFauVEZg4R5iZk7SQH4Vd09RODUfr+6cKRzrBGOx51NZ7K2bTXZ9gya5NgLaad36GGJPxnXjBBQElFnljZyFbcic07W+uE7qYH4z1ufkIh1U0UgVj5b6ejLU2+qd8DE43l61wj5fYMraCvsPXmSUBrCt97VoUTpVMcBrXT6I7lXPhNHZ8x1ztEwvpxZqLfFs0Jt2PJAhOSqIdMfZ39SXlWBhd4UGruqWqgafnpXc/qK0QTlMOoFgqXfVeWRZFYCe2kS4AWmqsfU5yka7+RmgwQGf/ehKjc/m7W3/GU8NdPH3FLm5/9Q5zXUtDeAraSzJ8T/P0FbtYGe1hItqUUTCsIu0VFwQ8IhaVCnTmQy73JJ+pVqewKxpWtyQYScCwj8DkPAC+PfKfCN78LgDjI/PxRetIROuwuUatJtnf1cdKepiM1BMbrNf733ofV/UNyYbbxSIVO7Mo5RQOu41sDCvDGr8wFsPBzKpWgOmWOE2tZ7imeZhvtP3CdR3X3MJVD9+rrfmJJGa5fuksi3QxCydckGJXnbo+ZuFV7KSWO9mOIBd2zV3jx5y6NsVsAG0xrX3ROiYj9c4OtIowYjxeq+KdCU+4IeANVyQd+cyelNrSyMctMVwSw8IITmrFWowl84aF0RCe0jM8lVWRyjffXMsGvbzhvAaBdm32Z50yLZVV4QTKsigTdmdP3DZtli3DMBE6X9JWBl7nwxf8CSBtoWQv4imxcOs0ql3sXiFKLRqFRuBT05V33NLrxHA8h92FdVubD3Fi3XamWhOc6Uzw3m1TgP10fHCPVQEeE4tqIJ9l8oZolEI4cgmGNRCXybrY9MKXHB2TF1i5r4e9xzvSVutOx4ah1TR2jDPY8yi+wfqca3HcjOdG7nXrwiDf2hqlEI5i5/jjkYCtk6Z3orVq+qiOj8wnHglwfPRCQEtWs2IUuzGCmzva97C/q48luzbldEfc5oKm4jmxgOoRDCjMzHRSNLIJRjrrItagtTOIhyX+cIy2UO7xPzXcZXaM9xpbxlaYi8E6+9cntWdYsmsTmwbuNIVhzZF1PPTKrazc18OmF75kPm/L2Ap23NJL8OZ3Ob2MtNaFmwObBp6ZDalmCm2cZP2BFTOTkk/G50WfGjIL+m4YWs1Fc09n3X/NkXUcH72QeCRgViRvC014pkbG1uZDPPHijVzWew8+koOV8XBdUnHjp6/YxWW/u4co9STCknG96M0TL97ID6M3azVCWuJw1JunnSctC6gu68IJymXCHjt4sRngW9U4wJI5b8/ax7qmZHvnk8QjAS3zc3Qux0cvzNqy0W1YjyXVjUiEtCJExgpToxKWgS9aZ/6tH/Ex75T9WRG3WRXgoQzOdHgx78IOTrQyKNTSSGddWLM6o22CqdYEidB5dtzSO9OlXV+Juneik+FoIw9espvH376Z3/7+yqQ1Etn6kljrQJSbLWMreOndD2Zsg3DVw/fm1YfF6MHyxev/wNbmQ9zwtXsAzCxOq/tXLhek5H1D3IxXE7Vy4UQD6EJdlGx9W1Oxntjd9Qm++vrHmIzUkxidy8aDd+OPCOpTrsappjtoQcLbX93IolCU7jL2LOmdaDWX2W9tPsSSF29kZbSHRaFo0hg7+jabNSnsdT4XgGC6BbNvbQDSpnu7PahpxU7B3rlCiBeFEAf09oXf0LcvEUK8IIQYEEL0CSGC+vY5+v1j+uOXlPIAqtUdcbrvST4/ymxBz6nWBB+96XVOrNtO/5SP3olWc0Zkf1cfDeEpTSR0s9tME9dPNmv1cIN2f5jxkfkcHVycVDp/5b4eeida2TC0mi1jK+idaJ01+2CH/ikfW8ZWsGFoNWuOrDODlkax3KF4hI6+zQRH/YyPzOfpK3aZszdrjqyjfsSXse1CuvYNRnp8aDBgNoWabhC2CyC50QUBe+0LBRCSUkb0lgB7gfuBrwI/lVI+KYR4FDggpXxECHEvcLWUcrMQ4k7gs1LKnmzvUagbYlCN1oWVUrRmtGNtWC2M6UY/48vquP3ze+g7fB2J0bnUj/i46FNDHDt4MaBV1+qdaOWffvzZrO0Tz3QmGOx5lCW7NvHF6//A7qHlRA8sBLRyfgZGTKCp9QyLQlE+17av4II7G4ZWc2CszbR8DHwt5/AN1s+KR7x/zVl6lr/Mz364mtBw+pJ4mTBmO6YbBGc6NZeteY/frL2aq0VhKcTi/Pg4v5Y/LsoNyStmIYSYhyYW9wD/DrRKKeNCiJuAv5dSrhFCPK3//3shhB8YARbJLG9UrFiAEoxCyUc0Ihdp7RjFre8if3mBeaU1VqW+dv/32DK2IslHT4d1FWva99MFIx6WJELn8YdjDHTvtH9QGejsX28GW83G0RlE7UxngvoRn7la1EomC8GamTkd9pmfVeBHC2fFKsotFEDRYmErZiGEqENriHwp8F1gEDgtpTQ+NWuLQrN9oS4kE8AFwDuFDtIO1Rq/MCh0ejUXdmIbRhwjfHJaOyF2LCC5HYGP4KQ2GzDvlOCZyVVJz7eebNNhw6QnbRfxWEPK9CR1NLSecST4abSQzCQUVjfjwv2CYGTmGO24EMn7+AEfVFgonMTW1KneeexatO5i1wNXpNtN/1t0+0JFZbDTbS3dSWP46wuOzpxwmVompvr2dgKG+7v6HJkl2dp8KGNrA3uBS/sEJ+KET04TPjltSyhKhZMxvbxmQ6SUp4UQ/cCNwAIhhF+3LqwtCo32hW/pbkgj8F6a19oGbAPNDSn4CCxUu3UBzsyUZCPbcnnDwsh0lQ1aLoy5FksZgmFYGoC5BD6bi1IMmXImMpXph+JK9acGirMJhdutCrA3G7JICLFA/78e+ARwBHgO+M/6bncB/6r//3P9Pvrj/5EtXuE01To7YsXpLvHpyDSDYrfAcHAibt6y7pdSZAdIcg0SofOOtU/srk/wwId+yRsbHyEWlmn7ziaNLQ+hsBZfTvcZVWKK1OlzwY5lsRh4XI9b+ICnpJS7hBCHgSeFEFuBV9D6oaL//X+EEMfQLIo7HR2xDWrBwoDSWxmQ2dLItyiwQTqLI1ORndfuf8QMmDrFxsYRNgyt1mdd0pfpTx1zKvkuwMslFKUMajqJpzM4s1ELYmFQasGwkikIajeRCzK7KNYpR4CziyXP3PU/HKvt2TvRyncHPsbEoFZ5e94pkRRjMUgnFIWu0HWTUBQ7G+LZtSG5qAV3xKAcbolBph9/Pv1PcromhjsSEdz+6kbWHFlXUDJWKhsbR5iM1OfV/KfQvi6VqnpWyt991YoF1JZglBM7sya5sBsPmBhs4u1oiOOx+bb2z8Wzq77jyOtkw0sp3PlQ1WJRa5Qzop7tymm301rG5CZL/oU/IrQ1Iw4tMHsmeinTLXGiHTHOLk52we2U6c9FPkLh9PdV6otj1YvF+fHxmrIwyj0Fl+vkyCUa2cr3xcKSeFiyvfPJosZouDBbxlawsXGELav/jRPrtnPHp/dmHXe+VLNQgMdXneZDrcyQQOmyPTNRNx7NmTaebfYktYWiUY3LSPU2ApxGFme+2ZxfH76Nvcc7aAhPsbX5EA+9civ/fXQu8wd8BPV8wWI6mlfa7SjXxbBmxAJqSzCgPFOrBnZ7n2QSDatgfPizh/hG2y8AbUXqUDzC8dh8vvr6HUxG6lna8o6tpewbhlazqnGAvcc7SIzOZWJ0LhuaV/PAh37Jdwc+hhy4IGnZuNNTounwokVhUFNiAUowSo0dKwPSi4Z20vp59QcrWNugLRGfak3Q2DHOz67tZXxEC3IejSxmDdqy+Acv2Z3Ryjgw1mYKhbEe5Le/v5LfciW+lnPMaQBOFX6clabc7nXNiUUt4lbBgPTFdpIXmvmYbKnneGy+WaYO4OjgYppaz+R0R+KRAEHLVOm8U9qK11ik3nblq1QKFQonrYpKxOGqPsCZjloKeBq4LfBpxWr+ByfiM4vQ9CIyPctf5sv/75epH/FRP+LDHxFmn9VsqeD7u/o4sW67KRRGendoWLLgKIRPnc/LBXFLx7hK/X5rUiyg9mZJoLzJW1CcYACmYPz7ttXJVbf0k3+ge6dZJdy6SAxmuoZ19q8H0OpSpKyILdWxpMOpz72Sv9maFQuDWhMMKH8+hl0yCUb41HlzObthbVjL863c18NXX7/DLMm35sg6+g9eTkffZuKRQHLNihxp3enGr4RCo+bFAir/JVQCLwkGzF6dagjGZb33MDHYxPjIfD4ZOgZo7QeMalihwUDa18j0noWOOxPVIhSgxMLEDV9GuXHDmpJ0ZDp50wlGICLwRwTBUT+bBrQFzre/ulF7nSztAnNZFW4RCje5y0osFGWjkBMw9aTOFms4OrgYgMlIfV6vmYpbhMJtKLGw4CYVLydutDAyuSPZMErm9Sx/GV/LObPwbynGl41qcj2sqDyLNNRa4pZBudPEnSAwCVOtWhXwLR/6pVnB+8S67awMaz07jPaBDPtmWSa5OoPli1OuhxtRlkUG3PqFlYNylOyzgx3rItaA2Upx70QnvsF6QoMBLuvVWhHsuKWXwZ5HuehTQ2mriec7pmxUs1CAEous1KpbAu4RjEwYJ34sLPGHY/x68kruWvS8mY8x75RgbfthvrJtM5f13sPx0Qs505lgz3cfM1/DyYrbxX5eXvit2elINhf4LTAHzW35sZTy60KIncDHAONTWi+lfFXvYPYwsBY4q2/fn+09SlFWz2lq0S0xKKVbkistPDUV3FhsNrZSL8HXEqf76j9yYKyN6ecvSOoeZiXaJoiF9cxNm53B7OKEUJSDcjQZeh/4uLV9oRDiF/pj/7uU8scp+98GdOq3G4BH9L+eplbjGFDatSX5rCMxmA77CF3zHpOReprCU+w93gFoVzODWbMmwz7eu22K4H5tr1oTCifI6YZIDaMAYkC/ZTNHPgP8QH/eH9D6iywufqiVxwumYqkod6q4QWrOhRG7mH7+Arbf8AP2d/XhG6xnzoF5ZqvBdNOrwUhCW1TmYMOfWhIKsBmzEELUCSFeBcaAZ6SUL+gP/YMQ4qAQ4ttCCEPYzfaFOtbWhlWB175kJymFYORz0hpuSCws2fTCl8yUb1MoLP1KUm9Ln0wooSiCgtoXCiGuAh4ELgc+DCwEvqbvXhPtC5WV4aylUcjJm9CrXS04SlIRm3RYy/sVIxTFHreXfzd5zYZIKU8D/cCtUspTuqvxPrADrQcqzLQvNLC2NrS+1jYpZZeUsiuQ5G16Cy9/+U5QTsFI7Tfij2h9P9K5HZm6gxVTi6JWRcKg0PaFfzTiEPrsx+3Aa/pTfg58SWjcCExIKQusR+QdvP5DKAYnrQw7J3O0TfDYFx7jsS/MTINa61I4vTCs1kXCoJj2hf8hhFiE5na8CmzW99+NNm16DG3qdIPzw3YntTxjAs5lgGabIZkO+3j/mrN8ZdtmYmHJvAZBUA+/F9o1LBvVuMajUHKKhZTyIPChNNs/nmF/CdxX/NC8iXEVUaJRnGhYBcMovTe+rI5oR4zmX9QTjJwH9GnUoezdyspdWLdaLIlU1NqQEqFEo3jRsFYMD0yco+mon6ajPoIT0+Y+oaHM1kS+IlHt6drFosSixCjRmH0S5isexklvN3VLiURpUGJRJpRozGA9OfMRDqeK5VbrEvJSo8SizFh/YEo4irc6CnmPYqk1kTBQYlFBan32JB1OiUepZjFqVShAiUXFUe5JdtwwdVnLAmFFiYVLUO6J+1AikYwSCxeirI3KoQQiM0osXEzqD1eJR2lQAmEPJRYeQrkqzqDEoTBUDU6Pon7whaE+t8JRloWHSffDVxZHMkocnEOJRZVR63EOJQ6lQ4lFlZPp5PG6iChRKD9KLGqUbCebW4RECYK7UGKhmEWxJ6khNupkry6UWCgcR4lEdaKmThUKhS2UWCgUClvYFgu90dArQohd+v0lQogXhBADQog+IURQ3z5Hv39Mf/yS0gxdoVCUk3wsi/uBI5b7/wh8W0rZCYwDG/XtG4FxKeWlwLf1/RQKhcex277wYuAvgf9bvy+AjwNGU+TH0XqHgNbr9HH9/x8Dt+j7KxQKD2N3NuT/Av4WaNDvXwCcllIa/eKs/UzNXqdSyrgQYkLf/x3rCwoh7gbu1u++/2v549eoTi4k5dirhGo9LqjeY7usmCfnFAshxDpgTEr5shCi29icZldp47GZDVJuA7bp77FPStlla8Qeo1qPrVqPC6r32IQQ+4p5vh3L4mbgr4QQa4G5wHw0S2OBEMKvWxfWfqZGr9O3hBB+oBF4r5hBKhSKypMzZiGlfFBKebGU8hLgTuA/pJRfBJ4D/rO+213Av+r//1y/j/74f+hdyhQKhYcpJs/ia8BXhRDH0GISvfr2XuACfftXgQdsvNa2Isbhdqr12Kr1uKB6j62o4xLqoq9QKOygMjgVCoUtKi4WQohbhRBv6BmfdlwWVyGE+L4QYkwI8Zpl20IhxDN6duszQogmfbsQQvyLfqwHhRArKzfy7AghPiCEeE4IcUQI8boQ4n59u6ePTQgxVwjxohDigH5c39C3V0VGcikzrSsqFkKIOuC7wG3AcuDzQojllRxTAewEbk3Z9gDwrJ7d+iwzcZvbgE79djfwSJnGWAhx4G+klFcANwL36d+N14/tfeDjUsprgGuBW4UQN1I9Gcmly7SWUlbsBtwEPG25/yDwYCXHVOBxXAK8Zrn/BrBY/38x8Ib+/2PA59Pt5/Yb2mzXJ6vp2IB5wH7gBrQkLL++3fxdAk8DN+n/+/X9RKXHnuF4LkYT8I8Du9Bynhw7rkq7IWa2p441E9TLtEgpTwHof5v17Z48Xt1E/RDwAlVwbLqp/iowBjwDDGIzIxkwMpLdiJFpndDv2860xsZxVVosbGV7VhGeO14hRBj4CfBfpJRnsu2aZpsrj01KeV5KeS3alfh64Ip0u+l/PXFc1kxr6+Y0uxZ8XJUWCyPb08CaCeplRoUQiwH0v2P6dk8drxAigCYUT0gpf6pvropjA5BSngb60WIyC/SMY0ifkYzLM5KNTOs3gSfRXBEz01rfp6jjqrRYvAR06hHbIFqG6M8rPCYnsGaxpma3fkmfObgRmDBMerehrxTuBY5IKb9lecjTxyaEWCSEWKD/Xw98Ai0g6OmMZFmOTGsXBGXWAkfR/Mb/o9LjKWD8PwROATE0td6I5vs9Cwzofxfq+wq02Z9B4BDQVenxZzmuVWhm6UHgVf221uvHBlwNvKIf12vA/6lvXwq8CBwDfgTM0bfP1e8f0x9fWuljsHGM3cAup49LZXAqFApbVNoNUSgUHkGJhUKhsIUSC4VCYQslFgqFwhZKLBQKhS2UWCgUClsosVAoFLZQYqFQKGzx/wMX5Wsr3gS+AAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eba2019748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def mandelbrot(h,w,maxit = 20):\n",
    "    y,x = np.ogrid[-1.4:1.4:h*1j,-2:0.8:w*1j] # ogrid 函数用切片作为下标，返回十五是一组可用来计算的数组\n",
    "    c = x + y*1j\n",
    "    z = c\n",
    "    divtime = maxit + np.zeros(z.shape,dtype=int)\n",
    "    \n",
    "    for i in range(maxit):\n",
    "        z = z**2 + c\n",
    "        diverge = z*np.conj(z)>2**2\n",
    "        div_now = diverge & (divtime==maxit)\n",
    "        divtime[div_now] = i\n",
    "        z[diverge] = 2\n",
    "    return divtime\n",
    "plt.imshow(mandelbrot(400,400))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(12).reshape(3,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b1 = np.array([False,True,True])\n",
    "b2 = np.array([True,False,True,False])\n",
    "a[b1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[b1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2],\n",
       "       [ 4,  6],\n",
       "       [ 8, 10]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:,b2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, 10])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[b1,b2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ix_()函数是用来组合不同的向量以获得每个n-uplet的结果\n",
    "# 以下实现从向量a,b和c中的取得的所有三元组的所有a+b*c\n",
    "a = np.array([2,3,4,5])\n",
    "b = np.array([8,5,4])\n",
    "c = np.array([5,4,6,8,3])\n",
    "ax,bx,cx = np.ix_(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[2]],\n",
       "\n",
       "       [[3]],\n",
       "\n",
       "       [[4]],\n",
       "\n",
       "       [[5]]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[8],\n",
       "        [5],\n",
       "        [4]]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[5, 4, 6, 8, 3]]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1, 1)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 3, 1)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bx.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1, 5)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cx.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = ax + bx*cx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[42, 34, 50, 66, 26],\n",
       "        [27, 22, 32, 42, 17],\n",
       "        [22, 18, 26, 34, 14]],\n",
       "\n",
       "       [[43, 35, 51, 67, 27],\n",
       "        [28, 23, 33, 43, 18],\n",
       "        [23, 19, 27, 35, 15]],\n",
       "\n",
       "       [[44, 36, 52, 68, 28],\n",
       "        [29, 24, 34, 44, 19],\n",
       "        [24, 20, 28, 36, 16]],\n",
       "\n",
       "       [[45, 37, 53, 69, 29],\n",
       "        [30, 25, 35, 45, 20],\n",
       "        [25, 21, 29, 37, 17]]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result[3,2,4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[3] + b[2]*c[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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