{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate some data\n",
    "np.random.seed(42)\n",
    "lambda1 = np.random.normal(size=(c, c))\n",
    "lambda2 = np.random.normal(size=(c, c))\n",
    "lambda3 = np.random.normal(size=(c, c))\n",
    "G1 = np.random.normal(size=(c, c, c))\n",
    "G2 = np.random.normal(size=(c, c, c))\n",
    "U = np.random.normal(size=(c, c, c, c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Z_naive(lambda1, lambda2, lambda3, G1, G2, U):\n",
    "    c = lambda1.shape[0]\n",
    "    Z = np.zeros(shape=(c, c, c, c))\n",
    "    for a, b, c, d, e, f, g, h, i, j in itertools.product(*([range(c)]*10)):\n",
    "        Z[a, h, i, j] += lambda1[a, b]*lambda2[d, e]*lambda3[g, h]*G1[c, b, d]*G2[f, e, g]*U[i, j, c, f]\n",
    "    return Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "198 ms ± 30.6 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "Z = Z_naive(lambda1, lambda2, lambda3, G1, G2, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3, 3, 3)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = Z_naive(lambda1, lambda2, lambda3, G1, G2, U)\n",
    "Z.shape"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
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 },
 "nbformat": 4,
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}