4_Typos_de_RNNs_Keras.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Typos de RNNs en Keras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://machinelearningmastery.com/timedistributed-layer-for-long-short-term-memory-networks-in-python/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](rnn_types.jpeg \"Title\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from numpy import array\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, RepeatVector, LSTM, SimpleRNN, Input, Masking"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One-to-One\n",
    "- No se usa el tiempo\n",
    "- es equivalente a usar MLP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X(5, 1, 1): [[[ 0. ]]\n",
      "\n",
      " [[ 0.2]]\n",
      "\n",
      " [[ 0.4]]\n",
      "\n",
      " [[ 0.6]]\n",
      "\n",
      " [[ 0.8]]]\n",
      "y(5, 1): [[ 0. ]\n",
      " [ 0.2]\n",
      " [ 0.4]\n",
      " [ 0.6]\n",
      " [ 0.8]]\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "simple_rnn_1 (SimpleRNN)     (None, 2)                 8         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 1)                 3         \n",
      "=================================================================\n",
      "Total params: 11\n",
      "Trainable params: 11\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "from numpy import array\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import LSTM, SimpleRNN\n",
    "# prepare sequence\n",
    "length = 5\n",
    "seq = array([i/float(length) for i in range(length)])\n",
    "X = seq.reshape(len(seq), 1, 1)\n",
    "y = seq.reshape(len(seq), 1)\n",
    "# define LSTM configuration\n",
    "print('X'+str(X.shape)+':',X)\n",
    "print('y'+str(y.shape)+':',y)\n",
    "n_neurons = 2\n",
    "# create LSTM\n",
    "model = Sequential()\n",
    "model.add(SimpleRNN(n_neurons, input_shape=(1, 1)))\n",
    "model.add(Dense(1))\n",
    "model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Epoch 1933/2000\n",
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      "Epoch 1959/2000\n",
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      "Epoch 1960/2000\n",
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      "Epoch 1961/2000\n",
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      "Epoch 1962/2000\n",
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      "Epoch 1963/2000\n",
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      "Epoch 1969/2000\n",
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      "Epoch 1970/2000\n",
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      "Epoch 1971/2000\n",
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      "Epoch 1972/2000\n",
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      "Epoch 1973/2000\n",
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      "Epoch 1974/2000\n",
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      "Epoch 1975/2000\n",
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      "Epoch 1976/2000\n",
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      "Epoch 1977/2000\n",
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      "Epoch 1978/2000\n",
      "0s - loss: 7.6119e-05\n",
      "Epoch 1979/2000\n",
      "0s - loss: 7.6117e-05\n",
      "Epoch 1980/2000\n",
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      "Epoch 1981/2000\n",
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      "Epoch 1982/2000\n",
      "0s - loss: 7.6106e-05\n",
      "Epoch 1983/2000\n",
      "0s - loss: 7.6103e-05\n",
      "Epoch 1984/2000\n",
      "0s - loss: 7.6100e-05\n",
      "Epoch 1985/2000\n",
      "0s - loss: 7.6096e-05\n",
      "Epoch 1986/2000\n",
      "0s - loss: 7.6093e-05\n",
      "Epoch 1987/2000\n",
      "0s - loss: 7.6089e-05\n",
      "Epoch 1988/2000\n",
      "0s - loss: 7.6086e-05\n",
      "Epoch 1989/2000\n",
      "0s - loss: 7.6083e-05\n",
      "Epoch 1990/2000\n",
      "0s - loss: 7.6080e-05\n",
      "Epoch 1991/2000\n",
      "0s - loss: 7.6076e-05\n",
      "Epoch 1992/2000\n",
      "0s - loss: 7.6073e-05\n",
      "Epoch 1993/2000\n",
      "0s - loss: 7.6069e-05\n",
      "Epoch 1994/2000\n",
      "0s - loss: 7.6066e-05\n",
      "Epoch 1995/2000\n",
      "0s - loss: 7.6063e-05\n",
      "Epoch 1996/2000\n",
      "0s - loss: 7.6059e-05\n",
      "Epoch 1997/2000\n",
      "0s - loss: 7.6056e-05\n",
      "Epoch 1998/2000\n",
      "0s - loss: 7.6053e-05\n",
      "Epoch 1999/2000\n",
      "0s - loss: 7.6050e-05\n",
      "Epoch 2000/2000\n",
      "0s - loss: 7.6046e-05\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1268909e8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train LSTM\n",
    "n_batch = length\n",
    "n_epoch = 2000\n",
    "model.fit(X, y, epochs=n_epoch, batch_size=n_batch, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 samples a la entrada (5, 1, 1)\n",
      "5 samples a la salida (5, 1)\n",
      "-0.0\n",
      "0.2\n",
      "0.4\n",
      "0.6\n",
      "0.8\n"
     ]
    }
   ],
   "source": [
    "# evaluate\n",
    "print('5 samples a la entrada', X.shape)\n",
    "result = model.predict(X, batch_size=n_batch, verbose=0)\n",
    "print('5 samples a la salida', result.shape)\n",
    "for value in result:\n",
    "    print('%.1f' % value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Son 5 muestras, no es una secuencia ya que T=1, cada muestra de 1 feature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Many-to-one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Otro ejemplo sería el de generación de texto como el de \"Bodas de Sangre\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 5, 1)\n",
      "(1, 5)\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "simple_rnn_2 (SimpleRNN)     (None, 2)                 8         \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 5)                 15        \n",
      "=================================================================\n",
      "Total params: 23\n",
      "Trainable params: 23\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "from numpy import array\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import LSTM\n",
    "# prepare sequence\n",
    "length = 5\n",
    "seq = array([i/float(length) for i in range(length)])\n",
    "X = seq.reshape(1, length, 1)\n",
    "y = seq.reshape(1, length)\n",
    "# define LSTM configuration\n",
    "print(X.shape)\n",
    "print(y.shape)\n",
    "n_neurons = 2\n",
    "# create LSTM\n",
    "model = Sequential()\n",
    "model.add(SimpleRNN(n_neurons, input_shape=(length, 1)))\n",
    "model.add(Dense(length))\n",
    "model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/1000\n",
      "0s - loss: 0.1232\n",
      "Epoch 2/1000\n",
      "0s - loss: 0.1218\n",
      "Epoch 3/1000\n",
      "0s - loss: 0.1200\n",
      "Epoch 4/1000\n",
      "0s - loss: 0.1181\n",
      "Epoch 5/1000\n",
      "0s - loss: 0.1164\n",
      "Epoch 6/1000\n",
      "0s - loss: 0.1147\n",
      "Epoch 7/1000\n",
      "0s - loss: 0.1129\n",
      "Epoch 8/1000\n",
      "0s - loss: 0.1112\n",
      "Epoch 9/1000\n",
      "0s - loss: 0.1094\n",
      "Epoch 10/1000\n",
      "0s - loss: 0.1077\n",
      "Epoch 11/1000\n",
      "0s - loss: 0.1060\n",
      "Epoch 12/1000\n",
      "0s - loss: 0.1043\n",
      "Epoch 13/1000\n",
      "0s - loss: 0.1026\n",
      "Epoch 14/1000\n",
      "0s - loss: 0.1010\n",
      "Epoch 15/1000\n",
      "0s - loss: 0.0993\n",
      "Epoch 16/1000\n",
      "0s - loss: 0.0977\n",
      "Epoch 17/1000\n",
      "0s - loss: 0.0961\n",
      "Epoch 18/1000\n",
      "0s - loss: 0.0945\n",
      "Epoch 19/1000\n",
      "0s - loss: 0.0929\n",
      "Epoch 20/1000\n",
      "0s - loss: 0.0914\n",
      "Epoch 21/1000\n",
      "0s - loss: 0.0898\n",
      "Epoch 22/1000\n",
      "0s - loss: 0.0883\n",
      "Epoch 23/1000\n",
      "0s - loss: 0.0868\n",
      "Epoch 24/1000\n",
      "0s - loss: 0.0854\n",
      "Epoch 25/1000\n",
      "0s - loss: 0.0839\n",
      "Epoch 26/1000\n",
      "0s - loss: 0.0825\n",
      "Epoch 27/1000\n",
      "0s - loss: 0.0811\n",
      "Epoch 28/1000\n",
      "0s - loss: 0.0797\n",
      "Epoch 29/1000\n",
      "0s - loss: 0.0783\n",
      "Epoch 30/1000\n",
      "0s - loss: 0.0770\n",
      "Epoch 31/1000\n",
      "0s - loss: 0.0757\n",
      "Epoch 32/1000\n",
      "0s - loss: 0.0743\n",
      "Epoch 33/1000\n",
      "0s - loss: 0.0730\n",
      "Epoch 34/1000\n",
      "0s - loss: 0.0718\n",
      "Epoch 35/1000\n",
      "0s - loss: 0.0705\n",
      "Epoch 36/1000\n",
      "0s - loss: 0.0693\n",
      "Epoch 37/1000\n",
      "0s - loss: 0.0681\n",
      "Epoch 38/1000\n",
      "0s - loss: 0.0669\n",
      "Epoch 39/1000\n",
      "0s - loss: 0.0657\n",
      "Epoch 40/1000\n",
      "0s - loss: 0.0646\n",
      "Epoch 41/1000\n",
      "0s - loss: 0.0634\n",
      "Epoch 42/1000\n",
      "0s - loss: 0.0623\n",
      "Epoch 43/1000\n",
      "0s - loss: 0.0612\n",
      "Epoch 44/1000\n",
      "0s - loss: 0.0601\n",
      "Epoch 45/1000\n",
      "0s - loss: 0.0590\n",
      "Epoch 46/1000\n",
      "0s - loss: 0.0580\n",
      "Epoch 47/1000\n",
      "0s - loss: 0.0570\n",
      "Epoch 48/1000\n",
      "0s - loss: 0.0559\n",
      "Epoch 49/1000\n",
      "0s - loss: 0.0549\n",
      "Epoch 50/1000\n",
      "0s - loss: 0.0539\n",
      "Epoch 51/1000\n",
      "0s - loss: 0.0530\n",
      "Epoch 52/1000\n",
      "0s - loss: 0.0520\n",
      "Epoch 53/1000\n",
      "0s - loss: 0.0511\n",
      "Epoch 54/1000\n",
      "0s - loss: 0.0502\n",
      "Epoch 55/1000\n",
      "0s - loss: 0.0493\n",
      "Epoch 56/1000\n",
      "0s - loss: 0.0484\n",
      "Epoch 57/1000\n",
      "0s - loss: 0.0475\n",
      "Epoch 58/1000\n",
      "0s - loss: 0.0466\n",
      "Epoch 59/1000\n",
      "0s - loss: 0.0457\n",
      "Epoch 60/1000\n",
      "0s - loss: 0.0449\n",
      "Epoch 61/1000\n",
      "0s - loss: 0.0441\n",
      "Epoch 62/1000\n",
      "0s - loss: 0.0433\n",
      "Epoch 63/1000\n",
      "0s - loss: 0.0425\n",
      "Epoch 64/1000\n",
      "0s - loss: 0.0417\n",
      "Epoch 65/1000\n",
      "0s - loss: 0.0409\n",
      "Epoch 66/1000\n",
      "0s - loss: 0.0402\n",
      "Epoch 67/1000\n",
      "0s - loss: 0.0394\n",
      "Epoch 68/1000\n",
      "0s - loss: 0.0387\n",
      "Epoch 69/1000\n",
      "0s - loss: 0.0380\n",
      "Epoch 70/1000\n",
      "0s - loss: 0.0373\n",
      "Epoch 71/1000\n",
      "0s - loss: 0.0366\n",
      "Epoch 72/1000\n",
      "0s - loss: 0.0359\n",
      "Epoch 73/1000\n",
      "0s - loss: 0.0352\n",
      "Epoch 74/1000\n",
      "0s - loss: 0.0346\n",
      "Epoch 75/1000\n",
      "0s - loss: 0.0339\n",
      "Epoch 76/1000\n",
      "0s - loss: 0.0333\n",
      "Epoch 77/1000\n",
      "0s - loss: 0.0326\n",
      "Epoch 78/1000\n",
      "0s - loss: 0.0320\n",
      "Epoch 79/1000\n",
      "0s - loss: 0.0314\n",
      "Epoch 80/1000\n",
      "0s - loss: 0.0308\n",
      "Epoch 81/1000\n",
      "0s - loss: 0.0302\n",
      "Epoch 82/1000\n",
      "0s - loss: 0.0296\n",
      "Epoch 83/1000\n",
      "0s - loss: 0.0291\n",
      "Epoch 84/1000\n",
      "0s - loss: 0.0285\n",
      "Epoch 85/1000\n",
      "0s - loss: 0.0280\n",
      "Epoch 86/1000\n",
      "0s - loss: 0.0274\n",
      "Epoch 87/1000\n",
      "0s - loss: 0.0269\n",
      "Epoch 88/1000\n",
      "0s - loss: 0.0264\n",
      "Epoch 89/1000\n",
      "0s - loss: 0.0259\n",
      "Epoch 90/1000\n",
      "0s - loss: 0.0254\n",
      "Epoch 91/1000\n",
      "0s - loss: 0.0249\n",
      "Epoch 92/1000\n",
      "0s - loss: 0.0244\n",
      "Epoch 93/1000\n",
      "0s - loss: 0.0239\n",
      "Epoch 94/1000\n",
      "0s - loss: 0.0234\n",
      "Epoch 95/1000\n",
      "0s - loss: 0.0230\n",
      "Epoch 96/1000\n",
      "0s - loss: 0.0225\n",
      "Epoch 97/1000\n",
      "0s - loss: 0.0221\n",
      "Epoch 98/1000\n",
      "0s - loss: 0.0216\n",
      "Epoch 99/1000\n",
      "0s - loss: 0.0212\n",
      "Epoch 100/1000\n",
      "0s - loss: 0.0208\n",
      "Epoch 101/1000\n",
      "0s - loss: 0.0204\n",
      "Epoch 102/1000\n",
      "0s - loss: 0.0200\n",
      "Epoch 103/1000\n",
      "0s - loss: 0.0196\n",
      "Epoch 104/1000\n",
      "0s - loss: 0.0192\n",
      "Epoch 105/1000\n",
      "0s - loss: 0.0188\n",
      "Epoch 106/1000\n",
      "0s - loss: 0.0184\n",
      "Epoch 107/1000\n",
      "0s - loss: 0.0181\n",
      "Epoch 108/1000\n",
      "0s - loss: 0.0177\n",
      "Epoch 109/1000\n",
      "0s - loss: 0.0173\n",
      "Epoch 110/1000\n",
      "0s - loss: 0.0170\n",
      "Epoch 111/1000\n",
      "0s - loss: 0.0167\n",
      "Epoch 112/1000\n",
      "0s - loss: 0.0163\n",
      "Epoch 113/1000\n",
      "0s - loss: 0.0160\n",
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      "Epoch 972/1000\n",
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      "Epoch 975/1000\n",
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      "Epoch 976/1000\n",
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      "Epoch 977/1000\n",
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      "Epoch 978/1000\n",
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      "Epoch 979/1000\n",
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      "Epoch 980/1000\n",
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      "Epoch 981/1000\n",
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      "Epoch 982/1000\n",
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      "Epoch 983/1000\n",
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      "Epoch 984/1000\n",
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      "Epoch 985/1000\n",
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      "Epoch 986/1000\n",
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      "Epoch 987/1000\n",
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      "Epoch 988/1000\n",
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      "Epoch 989/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 990/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 991/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 992/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 993/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 994/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 995/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 996/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 997/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 998/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 999/1000\n",
      "0s - loss: 6.8967e-14\n",
      "Epoch 1000/1000\n",
      "0s - loss: 6.8923e-14\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x126c7bf98>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train LSTM\n",
    "n_batch = 1\n",
    "n_epoch = 1000\n",
    "model.fit(X, y, epochs=n_epoch, batch_size=n_batch, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 5, 1)\n",
      "(1, 5)\n",
      "0.0\n",
      "0.2\n",
      "0.4\n",
      "0.6\n",
      "0.8\n"
     ]
    }
   ],
   "source": [
    "# evaluate\n",
    "print(X.shape)\n",
    "result = model.predict(X, batch_size=n_batch, verbose=0)\n",
    "print(result.shape)\n",
    "for value in result[0,:]:\n",
    "    print('%.1f' % value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En la entrada: Una sola muestra, T=5, 1 feature. \n",
    "\n",
    "A la salida de la RNN, solo toma las 2 neuronas de la ultima etapa temporal y las combina hacia una capa densa de 5 neuronas. \n",
    "\n",
    "La cantidad de pesos de la ultima capas es:\n",
    "\n",
    "2x5 + 5 = 15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Many-to-Many"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "simple_rnn_3 (SimpleRNN)     (None, 5, 2)              8         \n",
      "_________________________________________________________________\n",
      "time_distributed_1 (TimeDist (None, 5, 1)              3         \n",
      "=================================================================\n",
      "Total params: 11\n",
      "Trainable params: 11\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "from numpy import array\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import TimeDistributed\n",
    "from keras.layers import LSTM\n",
    "# prepare sequence\n",
    "length = 5\n",
    "seq = array([i/float(length) for i in range(length)])\n",
    "X = seq.reshape(1, length, 1)\n",
    "y = seq.reshape(1, length, 1)\n",
    "# define LSTM configuration\n",
    "n_neurons = 2\n",
    "# create LSTM\n",
    "model = Sequential()\n",
    "model.add(SimpleRNN(n_neurons, input_shape=(length, 1), return_sequences=True))\n",
    "# Probar de cambiar Dense(2), etc\n",
    "model.add(TimeDistributed(Dense(1)))\n",
    "#model.add(Dense(1))\n",
    "model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/2000\n",
      "0s - loss: 0.9409\n",
      "Epoch 2/2000\n",
      "0s - loss: 0.9345\n",
      "Epoch 3/2000\n",
      "0s - loss: 0.9290\n",
      "Epoch 4/2000\n",
      "0s - loss: 0.9232\n",
      "Epoch 5/2000\n",
      "0s - loss: 0.9173\n",
      "Epoch 6/2000\n",
      "0s - loss: 0.9112\n",
      "Epoch 7/2000\n",
      "0s - loss: 0.9052\n",
      "Epoch 8/2000\n",
      "0s - loss: 0.8991\n",
      "Epoch 9/2000\n",
      "0s - loss: 0.8930\n",
      "Epoch 10/2000\n",
      "0s - loss: 0.8868\n",
      "Epoch 11/2000\n",
      "0s - loss: 0.8807\n",
      "Epoch 12/2000\n",
      "0s - loss: 0.8746\n",
      "Epoch 13/2000\n",
      "0s - loss: 0.8686\n",
      "Epoch 14/2000\n",
      "0s - loss: 0.8625\n",
      "Epoch 15/2000\n",
      "0s - loss: 0.8565\n",
      "Epoch 16/2000\n",
      "0s - loss: 0.8506\n",
      "Epoch 17/2000\n",
      "0s - loss: 0.8446\n",
      "Epoch 18/2000\n",
      "0s - loss: 0.8387\n",
      "Epoch 19/2000\n",
      "0s - loss: 0.8329\n",
      "Epoch 20/2000\n",
      "0s - loss: 0.8270\n",
      "Epoch 21/2000\n",
      "0s - loss: 0.8212\n",
      "Epoch 22/2000\n",
      "0s - loss: 0.8155\n",
      "Epoch 23/2000\n",
      "0s - loss: 0.8097\n",
      "Epoch 24/2000\n",
      "0s - loss: 0.8041\n",
      "Epoch 25/2000\n",
      "0s - loss: 0.7985\n",
      "Epoch 26/2000\n",
      "0s - loss: 0.7929\n",
      "Epoch 27/2000\n",
      "0s - loss: 0.7873\n",
      "Epoch 28/2000\n",
      "0s - loss: 0.7818\n",
      "Epoch 29/2000\n",
      "0s - loss: 0.7764\n",
      "Epoch 30/2000\n",
      "0s - loss: 0.7710\n",
      "Epoch 31/2000\n",
      "0s - loss: 0.7657\n",
      "Epoch 32/2000\n",
      "0s - loss: 0.7604\n",
      "Epoch 33/2000\n",
      "0s - loss: 0.7550\n",
      "Epoch 34/2000\n",
      "0s - loss: 0.7498\n",
      "Epoch 35/2000\n",
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      "Epoch 36/2000\n",
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      "Epoch 37/2000\n",
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      "Epoch 38/2000\n",
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      "Epoch 39/2000\n",
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      "Epoch 40/2000\n",
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      "Epoch 41/2000\n",
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      "Epoch 42/2000\n",
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      "Epoch 43/2000\n",
      "0s - loss: 0.7042\n",
      "Epoch 44/2000\n",
      "0s - loss: 0.6993\n",
      "Epoch 45/2000\n",
      "0s - loss: 0.6944\n",
      "Epoch 46/2000\n",
      "0s - loss: 0.6897\n",
      "Epoch 47/2000\n",
      "0s - loss: 0.6849\n",
      "Epoch 48/2000\n",
      "0s - loss: 0.6803\n",
      "Epoch 49/2000\n",
      "0s - loss: 0.6756\n",
      "Epoch 50/2000\n",
      "0s - loss: 0.6710\n",
      "Epoch 51/2000\n",
      "0s - loss: 0.6664\n",
      "Epoch 52/2000\n",
      "0s - loss: 0.6619\n",
      "Epoch 53/2000\n",
      "0s - loss: 0.6574\n",
      "Epoch 54/2000\n",
      "0s - loss: 0.6529\n",
      "Epoch 55/2000\n",
      "0s - loss: 0.6485\n",
      "Epoch 56/2000\n",
      "0s - loss: 0.6441\n",
      "Epoch 57/2000\n",
      "0s - loss: 0.6397\n",
      "Epoch 58/2000\n",
      "0s - loss: 0.6354\n",
      "Epoch 59/2000\n",
      "0s - loss: 0.6311\n",
      "Epoch 60/2000\n",
      "0s - loss: 0.6268\n",
      "Epoch 61/2000\n",
      "0s - loss: 0.6226\n",
      "Epoch 62/2000\n",
      "0s - loss: 0.6184\n",
      "Epoch 63/2000\n",
      "0s - loss: 0.6143\n",
      "Epoch 64/2000\n",
      "0s - loss: 0.6102\n",
      "Epoch 65/2000\n",
      "0s - loss: 0.6061\n",
      "Epoch 66/2000\n",
      "0s - loss: 0.6020\n",
      "Epoch 67/2000\n",
      "0s - loss: 0.5980\n",
      "Epoch 68/2000\n",
      "0s - loss: 0.5940\n",
      "Epoch 69/2000\n",
      "0s - loss: 0.5901\n",
      "Epoch 70/2000\n",
      "0s - loss: 0.5862\n",
      "Epoch 71/2000\n",
      "0s - loss: 0.5823\n",
      "Epoch 72/2000\n",
      "0s - loss: 0.5785\n",
      "Epoch 73/2000\n",
      "0s - loss: 0.5747\n",
      "Epoch 74/2000\n",
      "0s - loss: 0.5709\n",
      "Epoch 75/2000\n",
      "0s - loss: 0.5672\n",
      "Epoch 76/2000\n",
      "0s - loss: 0.5634\n",
      "Epoch 77/2000\n",
      "0s - loss: 0.5598\n",
      "Epoch 78/2000\n",
      "0s - loss: 0.5561\n",
      "Epoch 79/2000\n",
      "0s - loss: 0.5525\n",
      "Epoch 80/2000\n",
      "0s - loss: 0.5489\n",
      "Epoch 81/2000\n",
      "0s - loss: 0.5454\n",
      "Epoch 82/2000\n",
      "0s - loss: 0.5418\n",
      "Epoch 83/2000\n",
      "0s - loss: 0.5383\n",
      "Epoch 84/2000\n",
      "0s - loss: 0.5349\n",
      "Epoch 85/2000\n",
      "0s - loss: 0.5314\n",
      "Epoch 86/2000\n",
      "0s - loss: 0.5280\n",
      "Epoch 87/2000\n",
      "0s - loss: 0.5247\n",
      "Epoch 88/2000\n",
      "0s - loss: 0.5213\n",
      "Epoch 89/2000\n",
      "0s - loss: 0.5180\n",
      "Epoch 90/2000\n",
      "0s - loss: 0.5147\n",
      "Epoch 91/2000\n",
      "0s - loss: 0.5115\n",
      "Epoch 92/2000\n",
      "0s - loss: 0.5083\n",
      "Epoch 93/2000\n",
      "0s - loss: 0.5051\n",
      "Epoch 94/2000\n",
      "0s - loss: 0.5019\n",
      "Epoch 95/2000\n",
      "0s - loss: 0.4987\n",
      "Epoch 96/2000\n",
      "0s - loss: 0.4956\n",
      "Epoch 97/2000\n",
      "0s - loss: 0.4925\n",
      "Epoch 98/2000\n",
      "0s - loss: 0.4895\n",
      "Epoch 99/2000\n",
      "0s - loss: 0.4865\n",
      "Epoch 100/2000\n",
      "0s - loss: 0.4835\n",
      "Epoch 101/2000\n",
      "0s - loss: 0.4805\n",
      "Epoch 102/2000\n",
      "0s - loss: 0.4775\n",
      "Epoch 103/2000\n",
      "0s - loss: 0.4746\n",
      "Epoch 104/2000\n",
      "0s - loss: 0.4717\n",
      "Epoch 105/2000\n",
      "0s - loss: 0.4688\n",
      "Epoch 106/2000\n",
      "0s - loss: 0.4660\n",
      "Epoch 107/2000\n",
      "0s - loss: 0.4632\n",
      "Epoch 108/2000\n",
      "0s - loss: 0.4604\n",
      "Epoch 109/2000\n",
      "0s - loss: 0.4576\n",
      "Epoch 110/2000\n",
      "0s - loss: 0.4548\n",
      "Epoch 111/2000\n",
      "0s - loss: 0.4521\n",
      "Epoch 112/2000\n",
      "0s - loss: 0.4494\n",
      "Epoch 113/2000\n",
      "0s - loss: 0.4467\n",
      "Epoch 114/2000\n",
      "0s - loss: 0.4440\n",
      "Epoch 115/2000\n",
      "0s - loss: 0.4414\n",
      "Epoch 116/2000\n",
      "0s - loss: 0.4388\n",
      "Epoch 117/2000\n",
      "0s - loss: 0.4362\n",
      "Epoch 118/2000\n",
      "0s - loss: 0.4336\n",
      "Epoch 119/2000\n",
      "0s - loss: 0.4311\n",
      "Epoch 120/2000\n",
      "0s - loss: 0.4286\n",
      "Epoch 121/2000\n",
      "0s - loss: 0.4261\n",
      "Epoch 122/2000\n",
      "0s - loss: 0.4236\n",
      "Epoch 123/2000\n",
      "0s - loss: 0.4211\n",
      "Epoch 124/2000\n",
      "0s - loss: 0.4187\n",
      "Epoch 125/2000\n",
      "0s - loss: 0.4163\n",
      "Epoch 126/2000\n",
      "0s - loss: 0.4139\n",
      "Epoch 127/2000\n",
      "0s - loss: 0.4115\n",
      "Epoch 128/2000\n",
      "0s - loss: 0.4092\n",
      "Epoch 129/2000\n",
      "0s - loss: 0.4068\n",
      "Epoch 130/2000\n",
      "0s - loss: 0.4045\n",
      "Epoch 131/2000\n",
      "0s - loss: 0.4022\n",
      "Epoch 132/2000\n",
      "0s - loss: 0.4000\n",
      "Epoch 133/2000\n",
      "0s - loss: 0.3977\n",
      "Epoch 134/2000\n",
      "0s - loss: 0.3955\n",
      "Epoch 135/2000\n",
      "0s - loss: 0.3933\n",
      "Epoch 136/2000\n",
      "0s - loss: 0.3911\n",
      "Epoch 137/2000\n",
      "0s - loss: 0.3889\n",
      "Epoch 138/2000\n",
      "0s - loss: 0.3867\n",
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      "0s - loss: 0.0052\n",
      "Epoch 1850/2000\n",
      "0s - loss: 0.0051\n",
      "Epoch 1851/2000\n",
      "0s - loss: 0.0051\n",
      "Epoch 1852/2000\n",
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      "Epoch 1856/2000\n",
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      "Epoch 1857/2000\n",
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      "Epoch 1865/2000\n",
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      "Epoch 1866/2000\n",
      "0s - loss: 0.0050\n",
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      "0s - loss: 0.0050\n",
      "Epoch 1868/2000\n",
      "0s - loss: 0.0050\n",
      "Epoch 1869/2000\n",
      "0s - loss: 0.0050\n",
      "Epoch 1870/2000\n",
      "0s - loss: 0.0050\n",
      "Epoch 1871/2000\n",
      "0s - loss: 0.0050\n",
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      "0s - loss: 0.0050\n",
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      "0s - loss: 0.0050\n",
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      "0s - loss: 0.0050\n",
      "Epoch 1882/2000\n",
      "0s - loss: 0.0050\n",
      "Epoch 1883/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1884/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1885/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1886/2000\n",
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      "Epoch 1887/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1888/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1889/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1890/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1891/2000\n",
      "0s - loss: 0.0049\n",
      "Epoch 1892/2000\n",
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      "Epoch 1895/2000\n",
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      "Epoch 1896/2000\n",
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      "Epoch 1898/2000\n",
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      "Epoch 1899/2000\n",
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      "Epoch 1900/2000\n",
      "0s - loss: 0.0048\n",
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      "Epoch 1902/2000\n",
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      "Epoch 1905/2000\n",
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      "Epoch 1907/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1908/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1909/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1910/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1911/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1912/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1913/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1914/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1915/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1916/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1917/2000\n",
      "0s - loss: 0.0048\n",
      "Epoch 1918/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1919/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1920/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1921/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1922/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1923/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1924/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1925/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1926/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1927/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1928/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1929/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1930/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1931/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1932/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1933/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1934/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1935/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1936/2000\n",
      "0s - loss: 0.0047\n",
      "Epoch 1937/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1938/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1939/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1940/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1941/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1942/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1943/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1944/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1945/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1946/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1947/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1948/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1949/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1950/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1951/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1952/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1953/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1954/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1955/2000\n",
      "0s - loss: 0.0046\n",
      "Epoch 1956/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1957/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1958/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1959/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1960/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1961/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1962/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1963/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1964/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1965/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1966/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1967/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1968/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1969/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1970/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1971/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1972/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1973/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1974/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1975/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1976/2000\n",
      "0s - loss: 0.0045\n",
      "Epoch 1977/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1978/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1979/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1980/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1981/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1982/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1983/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1984/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1985/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1986/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1987/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1988/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1989/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1990/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1991/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1992/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1993/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1994/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1995/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1996/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1997/2000\n",
      "0s - loss: 0.0044\n",
      "Epoch 1998/2000\n",
      "0s - loss: 0.0043\n",
      "Epoch 1999/2000\n",
      "0s - loss: 0.0043\n",
      "Epoch 2000/2000\n",
      "0s - loss: 0.0043\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1270d5780>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train LSTM\n",
    "n_batch = 1\n",
    "n_epoch = 2000\n",
    "model.fit(X, y, epochs=n_epoch, batch_size=n_batch, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 5, 1)\n",
      "(1, 5, 1)\n",
      "0.1\n",
      "0.1\n",
      "0.4\n",
      "0.6\n",
      "0.8\n"
     ]
    }
   ],
   "source": [
    "# evaluate\n",
    "result = model.predict(X, batch_size=n_batch, verbose=0)\n",
    "print(X.shape)\n",
    "print(result.shape)\n",
    "for value in result[0,:,0]:\n",
    "    print('%.1f' % value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La salida toma las 5 salidas temporales. Una neurona por cada T. Los pesos se comparten"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One-to-Many"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_4 (Dense)              (None, 1)                 2         \n",
      "_________________________________________________________________\n",
      "repeat_vector_1 (RepeatVecto (None, 10, 1)             0         \n",
      "_________________________________________________________________\n",
      "lstm_1 (LSTM)                (None, 10, 1)             12        \n",
      "=================================================================\n",
      "Total params: 14\n",
      "Trainable params: 14\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(1, input_shape=(1,)))\n",
    "model.add(RepeatVector(10))\n",
    "model.add(LSTM(1, return_sequences=True))\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Masking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "masking_1 (Masking)          (None, 10, 1)             0         \n",
      "=================================================================\n",
      "Total params: 0\n",
      "Trainable params: 0\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "#x[:, 3, :] = 0\n",
    "#x[:, 5, :] = 0\n",
    "timesteps = 10\n",
    "features = 1\n",
    "model = Sequential()\n",
    "model.add(Masking(mask_value=0., input_shape=(timesteps, features)))\n",
    "#model.add(LSTM(1, return_sequences=True))\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 10, 1)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = array([[[0.],[1],[2],[3],[4],[0.],[100],[25],[0],[1]]])\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[   0.]\n",
      "  [   1.]\n",
      "  [   2.]\n",
      "  [   3.]\n",
      "  [   4.]\n",
      "  [   0.]\n",
      "  [ 100.]\n",
      "  [  25.]\n",
      "  [   0.]\n",
      "  [   1.]]]\n"
     ]
    }
   ],
   "source": [
    "prediction = model.predict(x)\n",
    "print(prediction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "lstm_2 (LSTM)                (None, 5, 5)              140       \n",
      "_________________________________________________________________\n",
      "dense_5 (Dense)              (None, 5, 1)              6         \n",
      "=================================================================\n",
      "Total params: 146\n",
      "Trainable params: 146\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "from numpy import array\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import TimeDistributed\n",
    "from keras.layers import LSTM\n",
    "# prepare sequence\n",
    "length = 5\n",
    "seq = array([i/float(length) for i in range(length)])\n",
    "X = seq.reshape(1, length, 1)\n",
    "y = seq.reshape(1, length, 1)\n",
    "# define LSTM configuration\n",
    "n_neurons = length\n",
    "n_batch = 1\n",
    "n_epoch = 1000\n",
    "# create LSTM\n",
    "model = Sequential()\n",
    "model.add(LSTM(n_neurons, input_shape=(length, 1), return_sequences=True))\n",
    "#model.add(TimeDistributed(Dense(1)))\n",
    "model.add((Dense(1)))\n",
    "model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "print(model.summary())\n",
    "# train LSTM\n",
    "#model.fit(X, y, epochs=n_epoch, batch_size=n_batch, verbose=2)\n",
    "# evaluate\n",
    "#result = model.predict(X, batch_size=n_batch, verbose=0)\n",
    "#for value in result[0,:,0]:\n",
    "#    print('%.1f' % value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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