{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "compose = lambda *fns: reduce(lambda f, g: lambda *args, **kwargs: f(g(*args, **kwargs)), fns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    return 3*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compose(f, g)(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.random.randint(10, size=(3, 6))\n",
    "b = np.random.randint(10, size=(3, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 3, 9, 8, 3, 3],\n",
       "       [1, 5, 8, 0, 1, 5],\n",
       "       [9, 9, 2, 4, 8, 8]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 9, 3, 6, 6, 4],\n",
       "       [0, 8, 8, 7, 2, 0],\n",
       "       [2, 0, 3, 4, 5, 2]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (3,6) and (3,6) not aligned: 6 (dim 1) != 3 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-19-579c274cec9b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: shapes (3,6) and (3,6) not aligned: 6 (dim 1) != 3 (dim 0)"
     ]
    }
   ],
   "source": [
    "np.dot(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "columnwise_dot = lambda a, b: np.sum(a*b, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 6, 0, 3, 3, 6],\n",
       "       [6, 6, 5, 3, 3, 3],\n",
       "       [0, 7, 2, 9, 1, 8],\n",
       "       [0, 8, 4, 5, 2, 4],\n",
       "       [1, 6, 1, 4, 8, 3],\n",
       "       [5, 6, 0, 3, 1, 8]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.random.randint(10, size=(6, 6))\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trace = lambda a: np.sum(np.diag(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.random.randint(10, size=(6, 6))\n",
    "b = np.random.randint(10, size=(6, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 1, 4, 6, 3, 2],\n",
       "       [6, 7, 6, 9, 1, 9],\n",
       "       [3, 4, 8, 3, 0, 0],\n",
       "       [8, 1, 9, 9, 8, 7],\n",
       "       [1, 4, 4, 2, 2, 3],\n",
       "       [3, 5, 0, 2, 4, 9]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9, 7, 9, 4, 4, 8],\n",
       "       [8, 7, 0, 3, 9, 9],\n",
       "       [1, 1, 9, 3, 5, 8],\n",
       "       [4, 0, 5, 1, 8, 7],\n",
       "       [6, 9, 0, 4, 1, 1],\n",
       "       [0, 0, 0, 4, 4, 7]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "672"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(columnwise_dot(a.T, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "672"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.trace(np.dot(a, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = ('a', 'b', 'c', 'd', 'e')\n",
    "y = ('b', 'g', 'd', 'g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Tree:\n",
    "\n",
    "    def __init__(self, *tups):\n",
    "        self.d = {}\n",
    "        for tup in tups:\n",
    "            self.add(tup, self.d)\n",
    "\n",
    "    def add(self, tup, d):\n",
    "        if len(tup) == 1:\n",
    "            return tup[0]\n",
    "            \n",
    "        if tup[0] in d:\n",
    "            self.add(tup[1:], d[tup[0]])\n",
    "        else:\n",
    "            d[tup[0]] = self.add(tup[1:], {})\n",
    "            \n",
    "        return d\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str(self.d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': {'b': {'c': {'d': 'e'}}}}"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': {'b': {'c': {'d': 'e'}, 'g': {'d': 'g'}}}}"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Tree(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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