numpy/SciPy Numpy Extended Lectures Part 3 - Broadcasting, Shape Manipulation and Sorting Data.ipynb

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    "# Numerical operations with Numpy\n",
    "\n",
    "## 3.1 **Broadcasting**\n",
    "## 3.2 **Array shape manipulation**\n",
    "##  3.3 **Sorting data**\n",
    "##  **Summary**\n",
    "## **Exercises**\n"
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
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    "## 3.1 Broadcasting Operations\n",
    "\n",
    "-  We just covered basic operations (add, multiple, square etc) such are element-wise but that works on arrays of same size\n",
    "- **Broadcasting** comes handy when we are dealing with different shapes. This time, we'll explore a more advanced concept in numpy called broadcasting. \n",
    "\n",
    "- The term broadcasting describes how numpy treats arrays with different shapes during arithmetic operations. Subject to certain constraints, *the smaller array is \"broadcast\" across the larger array so that they have compatible shapes*. \n",
    "- Broadcasting provides a means of **vectorizing array operations** so that looping occurs in C instead of Python. It does this without making needless copies of data and usually leads to efficient algorithm implementations. There are also cases where broadcasting is a bad idea because it leads to inefficient use of memory that slows computation.\n",
    "- In this little tutorial we will provide a gentle introduction to broadcasting with numerous examples ranging from simple to involved. \n",
    "- We will also go through a few examples of when to and when not to use boradcasting.\n",
    "\n",
    "\n",
    "\n",
    "#### This example below shows how broadcasting works\n",
    "\n",
    "<img src=\"figures/numpy_broadcasting.png\">"
   ]
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   "source": [
    "### So, lets start taking baby steps...\n",
    "\n",
    "Here an element-wise multiplication occurs since the two arrays are of same shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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    {
     "data": {
      "text/plain": [
       "array([ 2.,  4.,  6.])"
      ]
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     "execution_count": 4,
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   "source": [
    "e = np.array([1.0, 2.0, 3.0])\n",
    "f = np.array([2.0, 2.0, 2.0])\n",
    "e*f"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "##### Hint / Try it?\n",
    "\n",
    "What would have happened if `f = np.array([2.0, 2.0])`. would it still multiply?"
   ]
  },
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     "data": {
      "text/plain": [
       "array([ 2.,  4.,  6.])"
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     "execution_count": 5,
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   "source": [
    "# But if it was like this\n",
    "\n",
    "e = np.array([1.0, 2.0, 3.0])\n",
    "f = 2.0\n",
    "e*f"
   ]
  },
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   "source": [
    "##### What happened here\n",
    "\n",
    "This is the most simplest example on numpy broadcasting where an array and a scalar values were combined in an operation.\n",
    "\n",
    "so it kind of *stechted in the row direction*! The scalar **f** is stretched to become an array of with the same shape as **e** so the shapes are compatible for element-by-element multiplication.\n",
    "\n",
    "<img src=\"figures/broadcast_stretch.gif\">\n",
    "\n",
    "** So what are the rules then?**\n",
    "- They must either be equal / same shape\n",
    "OR\n",
    "- One of them must be 1, like f was above"
   ]
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   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "array([[  0.,   0.,   0.],\n",
       "       [ 10.,  10.,  10.],\n",
       "       [ 20.,  20.,  20.],\n",
       "       [ 30.,  30.,  30.]])"
      ]
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     "execution_count": 6,
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   "source": [
    "# Typical broadcasting in practice\n",
    "g = np.array([[ 0.0, 0.0, 0.0], [10.0,10.0,10.0],[20.0,20.0,20.0],[30.0,30.0,30.0]])\n",
    "g       "
   ]
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   "cell_type": "code",
   "execution_count": 7,
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    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.])"
      ]
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "h = np.array([1.0, 2.0, 3.0])\n",
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "array([[  1.,   2.,   3.],\n",
       "       [ 11.,  12.,  13.],\n",
       "       [ 21.,  22.,  23.],\n",
       "       [ 31.,  32.,  33.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "g + h"
   ]
  },
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   "source": [
    "### What happened above?\n",
    "\n",
    "A 2-D (two-dimensional) array multiplied by 1-D (one-dimensional) array. It got stretched in the column direction so as to match the elements of the 2D array columns.\n",
    "<img src=\"figures/broadcast_strectch2.gif\">\n",
    "\n",
    "Would the same be possible for different shapes? Does broadcasting magically understands and fixes our assumptions?\n",
    "\n",
    "Let's take a look...\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
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   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (4,3) (4,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-baf25e1d8c2c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m10.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m20.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m20.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m20.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m30.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m30.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m30.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mg\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,3) (4,) "
     ]
    }
   ],
   "source": [
    "g = np.array([[ 0.0, 0.0, 0.0], [10.0,10.0,10.0],[20.0,20.0,20.0],[30.0,30.0,30.0]])\n",
    "i = np.array([0.0, 1.0, 2.0, 3.0])\n",
    "g+i       "
   ]
  },
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   "source": [
    "### We had a mismatch...\n",
    "\n",
    "<img src=\"figures/broadcast_strectch3.gif\">\n",
    "\n",
    "Explanation: When the trainling dimensions of the arrays are different as you saw above, then broadcasting will fail making it impossible to align the values in the rows of the first array with the elements of the second array for an **element-by-element** addition or multiplication.\n",
    "\n",
    "### Also, is there a way to do this in one line of code\n",
    "\n",
    "Tip: look up more into np.tile and np.arange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hideCode": false,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0],\n",
       "       [10, 10, 10],\n",
       "       [20, 20, 20],\n",
       "       [30, 30, 30]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.tile(np.arange(0, 40, 10), (3, 1))\n",
    "a = a.T # transpose this\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([0, 1, 2])\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
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   "source": [
    "##### Now, we add these two"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [10, 11, 12],\n",
       "       [20, 21, 22],\n",
       "       [30, 31, 32]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "##### So you see that broadcasting was applied magically...\n",
    "\n",
    "Ask yourself, why couldn't we add original `a` and `b` ?\n",
    "\n",
    "Note, original a was:\n",
    "```python\n",
    "array([[ 0, 10, 20, 30],\n",
    "       [ 0, 10, 20, 30],\n",
    "       [ 0, 10, 20, 30]])\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.ones((5, 6))\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "##### Let's assign an array of dimension 0 to an array of dimension 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  2.,  2.,  2.,  2.,  2.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.,  1.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[0] = 2\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 10, 20])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.arange(0, 30, 10)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = d[:, np.newaxis] # Here we add a new axis and make it a 2D array\n",
    "d.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (4,3) (3,1) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-18-a7e39af9a194>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,3) (3,1) "
     ]
    }
   ],
   "source": [
    "a + d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Another example on broadcasting\n",
    "\n",
    "Let’s construct an array of distances (in miles) between cities of Route 66: Chicago, Springfield, Saint-Louis, Tulsa, Oklahoma City, Amarillo, Santa Fe, Albuquerque, Flagstaff and Los Angeles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0,  198,  303,  736,  871, 1175, 1475, 1544, 1913, 2448],\n",
       "       [ 198,    0,  105,  538,  673,  977, 1277, 1346, 1715, 2250],\n",
       "       [ 303,  105,    0,  433,  568,  872, 1172, 1241, 1610, 2145],\n",
       "       [ 736,  538,  433,    0,  135,  439,  739,  808, 1177, 1712],\n",
       "       [ 871,  673,  568,  135,    0,  304,  604,  673, 1042, 1577],\n",
       "       [1175,  977,  872,  439,  304,    0,  300,  369,  738, 1273],\n",
       "       [1475, 1277, 1172,  739,  604,  300,    0,   69,  438,  973],\n",
       "       [1544, 1346, 1241,  808,  673,  369,   69,    0,  369,  904],\n",
       "       [1913, 1715, 1610, 1177, 1042,  738,  438,  369,    0,  535],\n",
       "       [2448, 2250, 2145, 1712, 1577, 1273,  973,  904,  535,    0]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mileposts = np.array([0, 198, 303, 736, 871, 1175, 1475, 1544, 1913, 2448])\n",
    "distance_array = np.abs(mileposts - mileposts[:, np.newaxis])\n",
    "distance_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Another example\n",
    "\n",
    "A lot of grid-based or network-based problems can also use broadcasting. For instance, if we want to compute the distance from the origin of points on a 10x10 grid, we can do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.        ,  2.        ,  3.        ,  4.        ],\n",
       "       [ 1.        ,  1.41421356,  2.23606798,  3.16227766,  4.12310563],\n",
       "       [ 2.        ,  2.23606798,  2.82842712,  3.60555128,  4.47213595],\n",
       "       [ 3.        ,  3.16227766,  3.60555128,  4.24264069,  5.        ],\n",
       "       [ 4.        ,  4.12310563,  4.47213595,  5.        ,  5.65685425]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, y = np.arange(5), np.arange(5)[:, np.newaxis]\n",
    "distance = np.sqrt(x**2 + y**2)\n",
    "distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Or in color... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.colorbar>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAMP8Dw6TQTvpFm1KAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108327630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolor(distance)\n",
    "plt.colorbar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0],\n",
       "        [1],\n",
       "        [2],\n",
       "        [3],\n",
       "        [4]]), array([[0, 1, 2, 3, 4]]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Note : The numpy.ogrid function allows to directly create vectors\n",
    "# x and y of the previous example\n",
    "x, y = np.ogrid[0:5, 0:5]\n",
    "x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5, 1), (1, 5))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape, y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " `np.ogrid` is quite useful as soon as we have to handle computations on a grid. While on other hand, `np.mgrid`\n",
    " directly provides matrices full of indices for cases where we can't or maybe don't want to benefit from broadcasting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, y = np.mgrid[0:4, 0:4]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3],\n",
       "       [0, 1, 2, 3],\n",
       "       [0, 1, 2, 3],\n",
       "       [0, 1, 2, 3]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A bit on Vector quantization or VQ\n",
    "\n",
    "A simple way to understand bradcasting is with this real world situation. The basic operatio in VQ finds the closest point in a set of points, called $codes$ in VQ speak, to a given point, called the `observation`.\n",
    "\n",
    "In the 2D example below, the value in an $observation$ describe the weight and height of an athlete to be classified. The $codes$ represent different classes of athletes such as dancer, runner, swimmer an so on.\n",
    "\n",
    "Finding the closest point requires calculating the distance between `observation` and each of the `codes`.\n",
    "\n",
    "The shortest distance provides the best match. Here in this example, `codes[0]` is the closest class indicating that the athlete is likely a basketball player.\n",
    "\n",
    "<img src=\"figures/VQ.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import array, argmin, sqrt, sum\n",
    "observation = array([111.0, 188.0])\n",
    "codes = array([[102.0, 203.0],\n",
    "               [132.0, 193.0],\n",
    "                [45.0, 155.0],\n",
    "                [57.0, 173.0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is how broadcast happens\n",
    "difference = codes - observation\n",
    "distance = sqrt(sum(difference**2, axis=-1))\n",
    "nearest = argmin(distance)\n",
    "nearest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The basic operation of vector quantization calculates the distance between an object to be classified, the black square, and multiple known codes, the gray circles. In the very basic case, the codes represent classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A more advanced example  \n",
    "\n",
    "`@article{scikit-learn,\n",
    " title={Scikit-learn: Machine Learning in {P}ython},\n",
    " author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.\n",
    "         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.\n",
    "         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and\n",
    "         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},\n",
    " journal={Journal of Machine Learning Research},\n",
    " volume={12},\n",
    " pages={2825--2830},\n",
    " year={2011}\n",
    "}`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nZrOZl19+GY1GwwsvvEBDQwO7du3C4/EI8GB6epp9+/YxOztLb2+vQGakC6xY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1085a28d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4JFGLA4UQfhCjLUx+GcAHAPxDAP8HwEtjjH8dQvhJAB+OMb45hPCH499/EkK4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\nFebAioBWWGEO/H9RuO832VvivQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f125f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0JGijmlmL5AbfC1N70S7btsfItl2+lpmUfQmbn2GHXtvhYAYzlOds22ibR7dd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2c9828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MMTuttSL7/iW7gWw/yW4gy087jhRFOBqkiiKcegjSB1wLlECyG8j2k+wGgvzEt0kVxXfq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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2bc400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A more complex example\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn import cluster\n",
    "\n",
    "\n",
    "try:  # SciPy >= 0.16 have face in misc\n",
    "    from scipy.misc import face\n",
    "    face = face(gray=True)\n",
    "except ImportError:\n",
    "    face = sp.face(gray=True)\n",
    "\n",
    "n_clusters = 5\n",
    "np.random.seed(0)\n",
    "\n",
    "X = face.reshape((-1, 1))  # We need an (n_sample, n_feature) array\n",
    "k_means = cluster.KMeans(n_clusters=n_clusters, n_init=4)\n",
    "k_means.fit(X)\n",
    "values = k_means.cluster_centers_.squeeze()\n",
    "labels = k_means.labels_\n",
    "\n",
    "# create an array from labels and values\n",
    "face_compressed = np.choose(labels, values)\n",
    "face_compressed.shape = face.shape\n",
    "\n",
    "vmin = face.min()\n",
    "vmax = face.max()\n",
    "\n",
    "# original face\n",
    "plt.figure(1, figsize=(3, 2.2))\n",
    "plt.imshow(face, cmap=plt.cm.gray, vmin=vmin, vmax=256)\n",
    "\n",
    "# compressed face\n",
    "plt.figure(2, figsize=(3, 2.2))\n",
    "plt.imshow(face_compressed, cmap=plt.cm.gray, vmin=vmin, vmax=vmax)\n",
    "\n",
    "# equal bins face\n",
    "regular_values = np.linspace(0, 256, n_clusters + 1)\n",
    "regular_labels = np.searchsorted(regular_values, face) - 1\n",
    "regular_values = .5 * (regular_values[1:] + regular_values[:-1])  # mean\n",
    "regular_face = np.choose(regular_labels.ravel(), regular_values, mode=\"clip\")\n",
    "regular_face.shape = face.shape\n",
    "plt.figure(3, figsize=(3, 2.2))\n",
    "plt.imshow(regular_face, cmap=plt.cm.gray, vmin=vmin, vmax=vmax)\n",
    "\n",
    "# histogram\n",
    "plt.figure(4, figsize=(3, 2.2))\n",
    "plt.clf()\n",
    "plt.axes([.01, .01, .98, .98])\n",
    "plt.hist(X, bins=256, color='.5', edgecolor='.5')\n",
    "plt.yticks(())\n",
    "plt.xticks(regular_values)\n",
    "values = np.sort(values)\n",
    "for center_1, center_2 in zip(values[:-1], values[1:]):\n",
    "    plt.axvline(.5 * (center_1 + center_2), color='b')\n",
    "\n",
    "for center_1, center_2 in zip(regular_values[:-1], regular_values[1:]):\n",
    "    plt.axvline(.5 * (center_1 + center_2), color='b', linestyle='--')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## 3.2 Array Shape Manipulation\n",
    "\n",
    "### Flattening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nA 1-D array, containing the elements of the input, is returned.  A copy is\\n    made only if needed.\\n    Do help(np.ravel) to learn more\\n'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "a.ravel() \n",
    "\"\"\"\n",
    "A 1-D array, containing the elements of the input, is returned.  A copy is\n",
    "    made only if needed.\n",
    "    Do help(np.ravel) to learn more\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4],\n",
       "       [2, 5],\n",
       "       [3, 6]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "###  Reshaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.reshape(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a.ravel()\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = b.reshape((2, 3))\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Which is same as ...\n",
    "a.reshape(2, -1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[99,  2,  3],\n",
       "       [ 4,  5,  6]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Note:  ndarray.reshape may return a view (cf help(np.reshape))), or copy\n",
    "b[0, 0] = 99\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.],\n",
       "       [ 0.,  0.],\n",
       "       [ 0.,  0.]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reshape also returns a copy, take a look\n",
    "a = np.zeros((3, 2))\n",
    "b = a.T.reshape(3 * 2)\n",
    "b [0] = 9\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Memory layout of a numpy array\n",
    "\n",
    "- [Here's a good example of how it works](https://eli.thegreenplace.net/2015/memory-layout-of-multi-dimensional-arrays/)\n",
    "- "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<memory at 0x10f128120>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.rand(2, 2)\n",
    "x.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140329574190480, False)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.__array_interface__['data']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140329574190480, False)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0].__array_interface__['data']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140329574190480, False)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0,:].__array_interface__['data']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140329574190496, False)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[1,:].__array_interface__['data']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140329652477104, False)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0,0].__array_interface__['data']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## 3.3 Sorting Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Function*\n",
    "\n",
    "`sort (arr, axis=-1, kind='quick', order=None)`\n",
    "\n",
    "*Method*\n",
    "\n",
    "`arr.sort (axis=-1, kind='quick', order=None)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 3 4]\n",
      " [1 3 3]]\n"
     ]
    }
   ],
   "source": [
    "# Sorting along an axis. see what happens?\n",
    "a = np.array([[1, 4, 3], [3, 1, 3]])\n",
    "b = np.sort(a, axis=1)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 3 4]\n",
      " [1 3 3]]\n"
     ]
    }
   ],
   "source": [
    "# In-place sort\n",
    "a.sort(axis=1)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1, 0, 2])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sorting with fancy indexing\n",
    "a = np.array([5, 4, 6, 1])\n",
    "x = np.argsort(a)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "# Finding minima and maxima\n",
    "b = np.array([3,5,2,6])\n",
    "b_max = np.argmax(b)\n",
    "b_min = np.argmin(b)\n",
    "print(b_max)\n",
    "print(b_min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some Exercises  😅\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Array manipulations\n",
    "\n",
    "Create this 2D array (without typing manually)\n",
    "\n",
    "`\n",
    "[[1,  7, 12],\n",
    " [2,  8, 13],\n",
    " [3,  9, 14],\n",
    " [4, 10, 15],\n",
    " [5, 11, 16]]\n",
    "`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Fun Exercises: Challenge questions\n",
    "\n",
    "1. Try in-place, out_of_place sorting\n",
    "2. Create arrays with different dtypes and sort them.\n",
    "3. Use all or array_equal to see what it returns\n",
    "4. Use np.random.shuffle to create a more sortable input\n",
    "5. Combine ravel, sort and reshape in one\n",
    "6. Look at the `axis` keyword for `sort` and rewrite the previous exercise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14],\n",
       "       [15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(25).reshape(5, 5)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function sum in module numpy.core.fromnumeric:\n",
      "\n",
      "sum(a, axis=None, dtype=None, out=None, keepdims=<class 'numpy._globals._NoValue'>)\n",
      "    Sum of array elements over a given axis.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    a : array_like\n",
      "        Elements to sum.\n",
      "    axis : None or int or tuple of ints, optional\n",
      "        Axis or axes along which a sum is performed.  The default,\n",
      "        axis=None, will sum all of the elements of the input array.  If\n",
      "        axis is negative it counts from the last to the first axis.\n",
      "    \n",
      "        .. versionadded:: 1.7.0\n",
      "    \n",
      "        If axis is a tuple of ints, a sum is performed on all of the axes\n",
      "        specified in the tuple instead of a single axis or all the axes as\n",
      "        before.\n",
      "    dtype : dtype, optional\n",
      "        The type of the returned array and of the accumulator in which the\n",
      "        elements are summed.  The dtype of `a` is used by default unless `a`\n",
      "        has an integer dtype of less precision than the default platform\n",
      "        integer.  In that case, if `a` is signed then the platform integer\n",
      "        is used while if `a` is unsigned then an unsigned integer of the\n",
      "        same precision as the platform integer is used.\n",
      "    out : ndarray, optional\n",
      "        Alternative output array in which to place the result. It must have\n",
      "        the same shape as the expected output, but the type of the output\n",
      "        values will be cast if necessary.\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 `sum` 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",
      "    sum_along_axis : ndarray\n",
      "        An array with the same shape as `a`, with the specified\n",
      "        axis removed.   If `a` is a 0-d array, or if `axis` is None, a scalar\n",
      "        is returned.  If an output array is specified, a reference to\n",
      "        `out` is returned.\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    ndarray.sum : Equivalent method.\n",
      "    \n",
      "    cumsum : Cumulative sum of array elements.\n",
      "    \n",
      "    trapz : Integration of array values using the composite trapezoidal rule.\n",
      "    \n",
      "    mean, average\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    Arithmetic is modular when using integer types, and no error is\n",
      "    raised on overflow.\n",
      "    \n",
      "    The sum of an empty array is the neutral element 0:\n",
      "    \n",
      "    >>> np.sum([])\n",
      "    0.0\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> np.sum([0.5, 1.5])\n",
      "    2.0\n",
      "    >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)\n",
      "    1\n",
      "    >>> np.sum([[0, 1], [0, 5]])\n",
      "    6\n",
      "    >>> np.sum([[0, 1], [0, 5]], axis=0)\n",
      "    array([0, 6])\n",
      "    >>> np.sum([[0, 1], [0, 5]], axis=1)\n",
      "    array([1, 5])\n",
      "    \n",
      "    If the accumulator is too small, overflow occurs:\n",
      "    \n",
      "    >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)\n",
      "    -128\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(np.sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function sum in module numpy.matrixlib.defmatrix:\n",
      "\n",
      "sum(self, axis=None, dtype=None, out=None)\n",
      "    Returns the sum of the matrix elements, along the given axis.\n",
      "    \n",
      "    Refer to `numpy.sum` for full documentation.\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    numpy.sum\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    This is the same as `ndarray.sum`, except that where an `ndarray` would\n",
      "    be returned, a `matrix` object is returned instead.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> x = np.matrix([[1, 2], [4, 3]])\n",
      "    >>> x.sum()\n",
      "    10\n",
      "    >>> x.sum(axis=1)\n",
      "    matrix([[3],\n",
      "            [7]])\n",
      "    >>> x.sum(axis=1, dtype='float')\n",
      "    matrix([[ 3.],\n",
      "            [ 7.]])\n",
      "    >>> out = np.zeros((1, 2), dtype='float')\n",
      "    >>> x.sum(axis=1, dtype='float', out=out)\n",
      "    matrix([[ 3.],\n",
      "            [ 7.]])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(np.matrix.sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum([1.0, 1.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum([1.0, 0.4, 0.5, 0.6], dtype=np.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum([[0, 2], [0, 6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 8])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum([[0, 2], [0, 6]], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 6])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum([[0, 2], [0, 6]], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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