vectorize.ipynb

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   "source": [
    "import numpy as np"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the data"
   ]
  },
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   "source": [
    "nx = 2\n",
    "ny = 3\n",
    "nz = 4\n",
    "\n",
    "yvals = np.array([1, 3, 5, 7])\n",
    "\n",
    "Y = np.random.choice(yvals, size=(nx, ny, nz))\n",
    "\n",
    "X = np.zeros((len(yvals), 2))\n",
    "X[:, 0] = yvals\n",
    "X[:, 1] = np.array([val * 10 for val in yvals])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[7, 7, 5, 5],\n",
       "        [5, 3, 3, 3],\n",
       "        [1, 1, 1, 1]],\n",
       "\n",
       "       [[5, 1, 5, 5],\n",
       "        [3, 5, 7, 5],\n",
       "        [3, 1, 5, 1]]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,  10.],\n",
       "       [  3.,  30.],\n",
       "       [  5.,  50.],\n",
       "       [  7.,  70.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method one: Find the factors from X, go through Y, bring out the factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 490.,  490.,  250.,  250.],\n",
       "        [ 250.,   90.,   90.,   90.],\n",
       "        [  10.,   10.,   10.,   10.]],\n",
       "\n",
       "       [[ 250.,   10.,  250.,  250.],\n",
       "        [  90.,  250.,  490.,  250.],\n",
       "        [  90.,   10.,  250.,   10.]]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def find_factor(yval):\n",
    "    matches = X[X[:, 0] == yval, 1]\n",
    "    assert len(matches) == 1 # how can we be sure?\n",
    "    return matches[0]\n",
    "\n",
    "factors = np.zeros(Y.shape)\n",
    "\n",
    "for index, value in np.ndenumerate(Y):\n",
    "    factors[index] = find_factor(value)\n",
    "    \n",
    "Y * factors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method two: Use numpy's vectorize for convenience"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 490.,  490.,  250.,  250.],\n",
       "        [ 250.,   90.,   90.,   90.],\n",
       "        [  10.,   10.,   10.,   10.]],\n",
       "\n",
       "       [[ 250.,   10.,  250.,  250.],\n",
       "        [  90.,  250.,  490.,  250.],\n",
       "        [  90.,   10.,  250.,   10.]]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def multiply_factor(yval):\n",
    "    return find_factor(yval) * yval\n",
    "\n",
    "np.vectorize(multiply_factor)(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method three: Ensure that the factors actually map to one value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 490.,  490.,  250.,  250.],\n",
       "        [ 250.,   90.,   90.,   90.],\n",
       "        [  10.,   10.,   10.,   10.]],\n",
       "\n",
       "       [[ 250.,   10.,  250.,  250.],\n",
       "        [  90.,  250.,  490.,  250.],\n",
       "        [  90.,   10.,  250.,   10.]]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factors = {row[0]: row[1] for row in X}\n",
    "\n",
    "def multiply_factor(yval):\n",
    "    return factors[yval] * yval\n",
    "\n",
    "np.vectorize(multiply_factor)(Y)"
   ]
  }
 ],
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