numpy tutorial

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7efc296b57b8>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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q/hJMgwZ+tE/WW//33QcXXxw6hWSNir8EVdH1U1YWOkkYr74KH33kb/aKFJKK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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efc2b996a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,3*np.pi,0.1)\n",
    "y = np.sin(x)\n",
    "#plot the points using matplotlib\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7efc290e1550>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A1665byPzgrcKhQpBWBhMn65aiXWZf3A+jco2orx3FomcXJDcuqkyaVK+CWky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\nnEvKfwE4bo/iU/5XKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efc2963f320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_cos = np.cos(x)\n",
    "y_sin = np.sin(x)\n",
    "# plot the points using matplotlib\n",
    "plt.plot(x, y_sin)\n",
    "plt.plot(x,y_cos)\n",
    "plt.xlabel('x axis label')\n",
    "plt.ylabel('y axis label')\n",
    "plt.title('Sine and Cosine')\n",
    "plt.legend(['Sine','Cosine'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6 7]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Create the following ranl 2 array with shape (3,4)\n",
    "# [[1 2 3 4]\n",
    "#  [5 6 7 8]\n",
    "#  [9 10 11 12]]\n",
    "a = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])\n",
    "# Use slicing to pull out the subsisdiary consisting of the first 2 rows\n",
    "# and columns 1 and 2; b is the following array of shape (2,2):\n",
    "# [[2,3]\n",
    "# [6,7]]\n",
    "b = a[1:2,1:3] # The slicing operation is a little bit weird for matlab user\n",
    "print(b)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'> (3,) 1 2 3\n",
      "[5 2 3]\n"
     ]
    }
   ],
   "source": [
    "# Arrays \n",
    "a= np.array([1,2,3])   # Create a rank 1 array\n",
    "print(type(a), a.shape,a[0],a[1],a[2])\n",
    "a[0] = 5\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "b = np.array([[1,2,3],[4,5,6]]) #Create a rank 2 array\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 3)\n",
      "1 2 4\n"
     ]
    }
   ],
   "source": [
    "print(b.shape)\n",
    "print(b[0,0],b[0,1],b[1,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.]\n",
      " [ 0.  0.]]\n",
      "[[ 1.  1.]]\n",
      "[[7 7]\n",
      " [7 7]]\n",
      "[[ 1.  0.]\n",
      " [ 0.  1.]]\n",
      "[[ 0.43047958  0.51013667]\n",
      " [ 0.3149202   0.27680466]]\n"
     ]
    }
   ],
   "source": [
    "# Numpy also provides many functions to create arrays\n",
    "a = np.zeros((2,2)) # Create an array of all zeros\n",
    "print(a)\n",
    "b = np.ones((1,2)) # Create an array of all ones\n",
    "print(b)\n",
    "c = np.full((2,2),7,int) # create a constant array\n",
    "print(c)\n",
    "d = np.eye(2)      # Create an array filled with random values\n",
    "print(d)\n",
    "e = np.random.random((2,2)) # Create an array filled with random values\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 3]\n",
      " [6 7]]\n"
     ]
    }
   ],
   "source": [
    "# Array indexing\n",
    "# Numpy offers several ways tp index into arrays\n",
    "# slicing: similar to python lists,numpy arrays can be sliced. Since arrays may be multidimensional,\n",
    "# You must specify a slice for each dimension of the array:\n",
    "import numpy as np\n",
    "# Create the following rank 2 array with shape(3,4)\n",
    "# [[1,2,3,4]\n",
    "#  [5,6,7,8]\n",
    "#  [9,10,11,12]]\n",
    "a = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])\n",
    "# Use slicing to pull out the subarray of shape(2,2):\n",
    "# [[2 3]\n",
    "#  [6 7]]\n",
    "b=a[:2,1:3]\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "77\n"
     ]
    }
   ],
   "source": [
    "# A slice of array is a view into the same data, so modifying it will modify the original array.\n",
    "print(a[0,1])\n",
    "b[0,0] = 77    # b[0,0] is the same piece of data as a[0,1]\n",
    "print(a[0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1 77  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]]\n",
      "[5 6 7 8] (4,)\n",
      "[[5 6 7 8]] (1, 4)\n",
      "[[5 6 7 8]] (1, 4)\n"
     ]
    }
   ],
   "source": [
    "print(a)\n",
    "row_r1 = a[1,:]    # Rank 1 view of the second row of a \n",
    "row_r2 = a[1:2,:]  # Rank 2 view of the second row of a \n",
    "row_r3 = a[[1],:]  # Rank 3 view of the third row of a\n",
    "print(row_r1, row_r1.shape)\n",
    "print(row_r2, row_r2.shape)\n",
    "print(row_r3, row_r3.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[77  6 10] (3,)\n",
      "[[77]\n",
      " [ 6]\n",
      " [10]] (3, 1)\n"
     ]
    }
   ],
   "source": [
    "# Two ways of accessing the data in the middle row of the array. Mixing integer indexing with slices yields an\n",
    "# array of lower rank, while using only slices yields an array of the same rank as the original array:\n",
    "col_r1 = a[:,1]\n",
    "col_r2 = a[:,1:2]\n",
    "print(col_r1, col_r1.shape)\n",
    "print(col_r2,col_r2.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 2]\n"
     ]
    }
   ],
   "source": [
    "# integer array indexing: when you index into numpy arrays using slicing, the resulting array view will always be \n",
    "# a subarray of the original array. In contrast, integer array indexing allows you to construct arbitrary arrays\n",
    "# using the data from another array.\n",
    "a = np.array([[1,2],[3,4],[5,6]])\n",
    "# An example of integer array indexing.\n",
    "# The returned array will have shape (3,) and\n",
    "#print([a[0,1,2],a[0,1,0]])\n",
    "\n",
    "# Equivalent to the previous integer array indexing example\n",
    "print(np.array([a[0,1],a[0,1]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "index 3 is out of bounds for axis 0 with size 3",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-39-14ff5fac6145>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;31m# Select one lement from each row of a using the indices in b\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# prints \"[1,6,7,11]\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m: index 3 is out of bounds for axis 0 with size 3"
     ]
    }
   ],
   "source": [
    "# Create an array of indices\n",
    "b = np.array([0, 2, 0, 1])\n",
    "\n",
    "# Select one lement from each row of a using the indices in b\n",
    "print(a[np.arange(4),b]) # prints \"[1,6,7,11]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[False False]\n",
      " [ True  True]\n",
      " [ True  True]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as no\n",
    "a = np.array([[1,2],[3,4],[5,6]])\n",
    "bool_idx = (a > 2)    # Find the elements of a that are bigger than 2;\n",
    "                      # This returns a numpy array of Booleans of the smae\n",
    "                      # shape as a, where each slot of bool_idx tells\n",
    "                      # Whether that element of a is > 2\n",
    "print(bool_idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4 5 6]\n",
      "[3 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "# We use boolean array indexing to construct a rank 1 array\n",
    "# consisting of the elements of a corresponding to the True values\n",
    "# of bool_idx\n",
    "print(a[bool_idx])\n",
    "# We can do all of the above in a single concise statement:\n",
    "print (a [a>2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int64 float64 int64\n"
     ]
    }
   ],
   "source": [
    "# Datatypes\n",
    "# Even numpy array is a grid of elements of the same type. Numpt provides a large set of numeric datatypes that \n",
    "# you can use to construct arrays. Numpy tries to guess a datatype when you create an array, but functions that \n",
    "# construct arrays. Numpy tries to guess a datatype when you can create an array\n",
    "x = np.array([1,2])   # Let numpy choose the datatype\n",
    "y = np.array([1.0,2.0]) # Let numy choose the dataype\n",
    "z = np.array([1,2],dtype = np.int64) # Force a particular datatype\n",
    "print(x.dtype,y.dtype,z.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  6.   8.]\n",
      " [ 10.  12.]]\n",
      "[[  6.   8.]\n",
      " [ 10.  12.]]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]],dtype = np.float64)\n",
    "y = np.array([[5,6],[7,8]],dtype = np.float64)\n",
    "# Elementwise sum; both produce the array\n",
    "print(x+y)\n",
    "print(np.add(x,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-4. -4.]\n",
      " [-4. -4.]]\n",
      "[[-4. -4.]\n",
      " [-4. -4.]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Elementwise difference; both produce the array\n",
    "print(x-y)\n",
    "print(np.subtract(x,y))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  5.  12.]\n",
      " [ 21.  32.]]\n",
      "[[  5.  12.]\n",
      " [ 21.  32.]]\n",
      "[[ 0.2         0.33333333]\n",
      " [ 0.42857143  0.5       ]]\n",
      "[[ 0.2         0.33333333]\n",
      " [ 0.42857143  0.5       ]]\n"
     ]
    }
   ],
   "source": [
    "# Element product; both produce the array\n",
    "print(x*y)\n",
    "print(np.multiply(x,y))\n",
    "# Element Division; both produce the array\n",
    "print(x/y)\n",
    "print(np.divide(x,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          1.41421356]\n",
      " [ 1.73205081  2.        ]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise squareroor; produces the array\n",
    "print(np.sqrt(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "219\n",
      "219\n",
      "[[19 22]\n",
      " [43 50]]\n",
      "[[19 22]\n",
      " [43 50]]\n",
      "[[19 22]\n",
      " [43 50]]\n",
      "[[19 22]\n",
      " [43 50]]\n",
      "10\n",
      "[4 6]\n",
      "[3 7]\n"
     ]
    }
   ],
   "source": [
    "# NOTE: unlike MATLAB, * is elementwise multiplication, not matrix multiplication. We instead use the dot\n",
    "# Function to compute inner products of vectors, to multiply a vector by a matrix, and to multiply matrices. \n",
    "x = np.array([[1,2],[3,4]])\n",
    "y = np.array([[5,6],[7,8]])\n",
    "\n",
    "v = np.array([9,10])\n",
    "w = np.array([11,12])\n",
    "\n",
    "#Inner product of vectors; \n",
    "print(v.dot(w))\n",
    "print(np.dot(v,w))\n",
    "\n",
    "#Matrix/vector product; Both produce the rank 1 array [29 67]\n",
    "print(x.dot(y))\n",
    "print(np.dot(x,y))\n",
    "\n",
    "# Matrix/matrix product; both produce the rank 2 array\n",
    "print(x.dot(y))\n",
    "print(np.dot(x,y))\n",
    "\n",
    "x = np.array([[1,2],[3,4]])\n",
    "print(np.sum(x))   # Compute sum of all elementsl prints \"10\"\n",
    "print(np.sum(x,axis = 0)) # compute sum of each column; prints \"[4 6]\"\n",
    "print(np.sum(x,axis = 1)) # compute sum of each row; prints \"[3,7]\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[[1 3]\n",
      " [2 4]]\n"
     ]
    }
   ],
   "source": [
    "v = np.array([1,2,3])\n",
    "print(v)\n",
    "print(x.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "# Broadcasting is a powerful mechanism that allows numpy to work with arrays of different shapes when performing\n",
    "# arithmetic operations. Frequently we have a smaller army and a larger array, and we want to use the smaller array \n",
    "# multiple times to perform some operation on the larger array\n",
    "# We will add the vector v to each row of the matrix with same shape as x\n",
    "# storing the result in the matrix y\n",
    "x = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])\n",
    "v = np.array([1,0,1])\n",
    "y = np.empty_like(x)   # Create an empty matrix with same shape as x\n",
    "\n",
    "# Add the vector v to each row of the matrix x with an explicit loop\n",
    "for i in range(4):\n",
    "    y[i,:] = x[i,:] + v\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]]\n",
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "# matrix x is very large, computing an explicit loop in python could be slow. Note that adding the vector v to each\n",
    "# row of the matrix x is equivalent to forming a matrix vv by stacking multiple copies of v vertically, then \n",
    "# performing elementwise summation of x and vv. We could implement this approach like this:\n",
    "vv = np.tile(v,(4,1))  # stack 4 copies of v on top of each other\n",
    "print(vv)              # Prints\"[ [1,0,1]\n",
    "#                                 [1,0,1]\n",
    "#                                 [1,0,1]\n",
    "#                                 [1,0,1]]\"\n",
    "y = x + vv # Add x and vv elementwise\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4  5]\n",
      " [ 8 10]\n",
      " [12 15]]\n"
     ]
    }
   ],
   "source": [
    "# Broadcasting two arrays together follows these rules:\n",
    "# 1. If the arrays do not have the same rank, prepend the shape of the lower rank array with 1s until both\n",
    "# shapes have the same length\n",
    "# 2. The two arrays are said to be compatible in a dimension if they have the same size in the dimension, or if one\n",
    "# of the arrays has size 1 in that dimension.\n",
    "# 3. The arrays can be broadcast together if they are compatible in all dimensions\n",
    "# 4. After broadcasting, each array behaves as if it had shape equal to the elementwise maximum of shapes of the two\n",
    "# input arrays\n",
    "# 5. In any dimension where one array had size 1 and the other array had size greater than 1, first array behaves as\n",
    "# if it were copied along that dimension \n",
    "# compute outer product of vectors\n",
    "v = np.array([1,2,3])   # v has shape (3,)\n",
    "w = np.array([4,5])     # w has shape (2,)\n",
    "# To compute an outer product, we first reshape v to be a column\n",
    "# vector of shape (3,1); we can then broadcast it against w to yield\n",
    "# an output of shape(3,2), which is the outer product of v and w:\n",
    "print(np.reshape(v,(3,1))*w)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 4 6]\n",
      " [5 7 9]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each row of a matrix\n",
    "x = np.array([[1,2,3],[4,5,6]])\n",
    "# X has shape(2,3) and v has shape (3,) so they broadcast to (2,3),\n",
    "# giving the following matrix:\n",
    "print(x+v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5  6  7]\n",
      " [ 9 10 11]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each column of a matrix\n",
    "# x has shape (2,3) and w has shape (2,).\n",
    "# If we transpose x then it has shape (3,2) and can be broadcast\n",
    "# against w to yield a result of shape (3,2); transposing this result\n",
    "# yields the final result of shape (2,3) which is the matrix x with\n",
    "# The vector w added to each column. Gives the following matrix:\n",
    "print((x.T + w).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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