{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using numpy backend.\n",
      "Using tensorflow backend.\n"
     ]
    }
   ],
   "source": [
    "import tensorly as tl\n",
    "tl.set_backend('tensorflow')\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "tfe = tf.contrib.eager\n",
    "\n",
    "from tensorly.tucker_tensor import tucker_to_tensor\n",
    "from tensorly.random import check_random_state\n",
    "from tensorly.metrics import RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs = 1000\n",
    "penalty = 0.0001\n",
    "lr = 0.01\n",
    "\n",
    "shape = [5, 5, 5]\n",
    "rank = [5, 5, 5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make the results reproducible by fixing the random seed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_state = 1234\n",
    "rng = check_random_state(random_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the tensor we want to decompose:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "tensor = tfe.Variable(tl.tensor(rng.random_sample(shape)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialise a random Tucker decomposition of that tensor (that is, the core tensor and the factors of the decomposition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "core = tfe.Variable(tl.tensor(rng.random_sample(rank)))\n",
    "factors = [tfe.Variable(tl.tensor(rng.random_sample((tensor.shape[i], rank[i])))) for i in range(len(tensor.get_shape()._dims))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define our optimiser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=lr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we just iterate through the training loop and backpropagate...\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 000: Loss: 118.707\n",
      "Epoch 100: Loss: 2.810\n",
      "Epoch 200: Loss: 2.653\n",
      "Epoch 300: Loss: 2.484\n",
      "Epoch 400: Loss: 2.326\n",
      "Epoch 500: Loss: 2.194\n",
      "Epoch 600: Loss: 2.057\n",
      "Epoch 700: Loss: 1.868\n",
      "Epoch 800: Loss: 1.633\n",
      "Epoch 900: Loss: 1.445\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(num_epochs):\n",
    "        \n",
    "    with tfe.GradientTape() as tape:\n",
    "        rec = tl.tucker_to_tensor(core, factors)\n",
    "        loss_value = tf.norm(rec - tensor, ord=2)\n",
    "        for f in factors: \n",
    "            loss_value = loss_value + penalty*tf.norm(f, 2)\n",
    "\n",
    "    grads = tape.gradient(loss_value, [core] + factors)\n",
    "    optimizer.apply_gradients(zip(grads, [core] + factors),\n",
    "                              global_step=tf.train.get_or_create_global_step())\n",
    "\n",
    "    rec_error = tl.norm(rec - tensor, 2)\n",
    "    if epoch % 100 == 0:\n",
    "        print(\"Epoch {:03d}: Loss: {:.3f}\".format(epoch, rec_error))"
   ]
  }
 ],
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