{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lesson 3 - Shape Manipulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Original Tutorial may be found [here](http://wiki.scipy.org/Tentative_NumPy_Tutorial#head-62ef2d3c0a5b4b7d6fdc48e4a60fe48b1ffe5006)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Changing the shape of an array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Original Tutorial may be found [here](http://wiki.scipy.org/Tentative_NumPy_Tutorial#head-1ddf70136d56cfa02b4ce306264ed13398327f25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An array has a shape given by the number of elements along each axis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.floor(10*np.random.random((3,4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  6.,  5.,  5.],\n",
       "       [ 1.,  6.,  1.,  6.],\n",
       "       [ 0.,  5.,  2.,  2.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3L, 4L)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The shape of an array can be changed with various commands:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.,  6.,  5.,  5.,  1.,  6.,  1.,  6.,  0.,  5.,  2.,  2.])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ravel() # flatten the array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a.shape = (6, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  6.],\n",
       "       [ 5.,  5.],\n",
       "       [ 1.,  6.],\n",
       "       [ 1.,  6.],\n",
       "       [ 0.,  5.],\n",
       "       [ 2.,  2.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  5.,  1.,  1.,  0.,  2.],\n",
       "       [ 6.,  5.,  6.,  6.,  5.,  2.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `reshape` (non-mutative) method returns its argument with a modified shape, whereas the `resize` (mutative) method modifies the array itself:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  6.],\n",
       "       [ 5.,  5.],\n",
       "       [ 1.,  6.],\n",
       "       [ 1.,  6.],\n",
       "       [ 0.,  5.],\n",
       "       [ 2.,  2.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = a.resize((2,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  6.,  5.,  5.,  1.,  6.],\n",
       "       [ 1.,  6.,  0.,  5.,  2.,  2.]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the `resize` method has mutated `a`. It does not return anything. It just mutate (a side effect)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "b = a.reshape(3,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  6.,  5.,  5.,  1.,  6.],\n",
       "       [ 1.,  6.,  0.,  5.,  2.,  2.]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  6.,  5.,  5.],\n",
       "       [ 1.,  6.,  1.,  6.],\n",
       "       [ 0.,  5.,  2.,  2.]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the `reshape` method does not mutate `a`. It merely return the reshaped array."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stacking together different arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Original Tutorial may be found [here](http://wiki.scipy.org/Tentative_NumPy_Tutorial#head-2dbfc93288ea06a02f270f2f9e6930ffbdd78b87)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.floor(10*np.random.random((2,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  9.],\n",
       "       [ 7.,  7.]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "b = np.floor(10*np.random.random((2,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.,  5.],\n",
       "       [ 4.,  1.]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  9.],\n",
       "       [ 7.,  7.],\n",
       "       [ 9.,  5.],\n",
       "       [ 4.,  1.]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack((a, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  9.,  9.,  5.],\n",
       "       [ 7.,  7.,  4.,  1.]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack((a, b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `column_stack` stacks 1D arrays as columns into a 2D array. It is equivalent to `vstack` only for 1D arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  9.,  9.,  5.],\n",
       "       [ 7.,  7.,  4.,  1.]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.column_stack((a,b))   # With 2D arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create two 1D arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.array((4., 2.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.array((2., 8.))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is to quickly illustrate using the `newaxis` argument to increase a dimension for the array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.],\n",
       "       [ 2.]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.],\n",
       "       [ 8.]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's `column_stack` them!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  2.],\n",
       "       [ 2.,  8.]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.column_stack((a[:, np.newaxis], b[:, np.newaxis]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.],\n",
       "       [ 2.],\n",
       "       [ 2.],\n",
       "       [ 8.]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack((a[:, np.newaxis], b[:, np.newaxis]))   # The behavior of vstack is different"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let's try `concatenate`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.,  2.])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  8.])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.,  2.,  2.,  8.])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate((a, b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sort of similar to column stack."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let's try to create array using the `r_[]` and `c_[]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 0, 4])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.r_[1:4, 0, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [2, 3],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.c_[1:4, 2:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Splitting one array into serveral smaller ones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using `hsplit`, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.floor(10*np.random.random((2,12)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.,  9.,  4.,  3.,  4.,  5.,  3.,  8.,  0.,  6.,  6.,  8.],\n",
       "       [ 7.,  8.,  9.,  7.,  1.,  6.,  8.,  6.,  5.,  2.,  6.,  7.]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a_hsplit = np.hsplit(a, 3)    # Split a into 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.  9.  4.  3.]\n",
      " [ 7.  8.  9.  7.]]\n",
      "\n",
      "[[ 4.  5.  3.  8.]\n",
      " [ 1.  6.  8.  6.]]\n",
      "\n",
      "[[ 0.  6.  6.  8.]\n",
      " [ 5.  2.  6.  7.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in a_hsplit:\n",
    "    print i\n",
    "    print \"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a_vsplit = np.vsplit(a,2)   # Split a into 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.  9.  4.  3.  4.  5.  3.  8.  0.  6.  6.  8.]]\n",
      "\n",
      "[[ 7.  8.  9.  7.  1.  6.  8.  6.  5.  2.  6.  7.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in a_vsplit:\n",
    "    print i\n",
    "    print "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Recall axis 0 is out-most). Split along axis 1 (column)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a_as0 = np.array_split(a, 3, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.  9.  4.  3.]\n",
      " [ 7.  8.  9.  7.]]\n",
      "\n",
      "[[ 4.  5.  3.  8.]\n",
      " [ 1.  6.  8.  6.]]\n",
      "\n",
      "[[ 0.  6.  6.  8.]\n",
      " [ 5.  2.  6.  7.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in a_as0:\n",
    "    print i\n",
    "    print \"\" "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Recall axis 0 is out-most). Split along axis 0 (row)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a_as1 = np.array_split(a, 2, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.  9.  4.  3.  4.  5.  3.  8.  0.  6.  6.  8.]]\n",
      "\n",
      "[[ 7.  8.  9.  7.  1.  6.  8.  6.  5.  2.  6.  7.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in a_as1:\n",
    "    print i\n",
    "    print "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have now completed [Lesson 3 - Shape Manipulation](http://wiki.scipy.org/Tentative_NumPy_Tutorial#head-62ef2d3c0a5b4b7d6fdc48e4a60fe48b1ffe5006)."
   ]
  }
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