2016-09-27 23:31:21 +02:00
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Chapter 9 –
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_This notebook contains all the sample code and solutions to the exercices in chapter 9._"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Setup"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# To support both python 2 and python 3\n",
"from __future__ import division, print_function, unicode_literals\n",
"\n",
"# Common imports\n",
"import numpy as np\n",
"import numpy.random as rnd\n",
"import os\n",
"\n",
"# to make this notebook's output stable across runs\n",
"rnd.seed(42)\n",
"\n",
"# To plot pretty figures\n",
"%matplotlib inline\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams['axes.labelsize'] = 14\n",
"plt.rcParams['xtick.labelsize'] = 12\n",
"plt.rcParams['ytick.labelsize'] = 12\n",
"\n",
"# Where to save the figures\n",
"PROJECT_ROOT_DIR = \".\"\n",
"CHAPTER_ID = \"tensorflow\"\n",
"\n",
"def save_fig(fig_id, tight_layout=True):\n",
" path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
" print(\"Saving figure\", fig_id)\n",
" if tight_layout:\n",
" plt.tight_layout()\n",
" plt.savefig(path, format='png', dpi=300)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Creating and running a graph"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import tensorflow as tf"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"x = tf.Variable(3, name=\"x\")\n",
"y = tf.Variable(4, name=\"y\")\n",
"f = x*x*y + y + 2\n",
"\n",
"f"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sess = tf.Session()\n",
"sess.run(x.initializer)\n",
"sess.run(y.initializer)\n",
"print(sess.run(f))\n",
"sess.close()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with tf.Session() as sess:\n",
" x.initializer.run()\n",
" y.initializer.run()\n",
" result = f.eval()\n",
"\n",
"result"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"init = tf.initialize_all_variables()\n",
"\n",
"with tf.Session():\n",
" init.run()\n",
" result = f.eval()\n",
"\n",
"result"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"init = tf.initialize_all_variables()\n",
"\n",
"sess = tf.InteractiveSession()\n",
"init.run()\n",
"result = f.eval()\n",
"sess.close()\n",
"\n",
"result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Managing graphs"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"x1 = tf.Variable(1)\n",
"x1.graph is tf.get_default_graph()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"graph = tf.Graph()\n",
"with graph.as_default():\n",
" x2 = tf.Variable(2)\n",
"\n",
"x2.graph is tf.get_default_graph()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"x2.graph is graph"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"w = tf.constant(3)\n",
"x = w + 2\n",
"y = x + 5\n",
"z = x * 3\n",
"\n",
"with tf.Session() as sess:\n",
" print(y.eval()) # 10\n",
" print(z.eval()) # 15"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with tf.Session() as sess:\n",
" y_val, z_val = sess.run([y, z])\n",
" print(y) # 10\n",
" print(z) # 15"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Linear Regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using the Normal Equation"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from sklearn.datasets import fetch_california_housing\n",
"\n",
"housing = fetch_california_housing()\n",
"m, n = housing.data.shape\n",
"housing_data_plus_bias = np.c_[np.ones((m, 1)), housing.data]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"X = tf.constant(housing_data_plus_bias, dtype=tf.float64, name=\"X\")\n",
"y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float64, name=\"y\")\n",
"XT = tf.transpose(X)\n",
"theta = tf.matmul(tf.matmul(tf.matrix_inverse(tf.matmul(XT, X)), XT), y)\n",
"\n",
"with tf.Session() as sess:\n",
" result = theta.eval()\n",
"\n",
"print(result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare with pure NumPy"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"X = housing_data_plus_bias\n",
"y = housing.target.reshape(-1, 1)\n",
"theta_numpy = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
"\n",
"print(theta_numpy)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare with Scikit-Learn"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression\n",
"lin_reg = LinearRegression()\n",
"lin_reg.fit(housing.data, housing.target.reshape(-1, 1))\n",
"\n",
"print(np.r_[lin_reg.intercept_.reshape(-1, 1), lin_reg.coef_.T])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using Batch Gradient Descent"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gradient Descent requires scaling the feature vectors first. We could do this using TF, but let's just use Scikit-Learn for now."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.preprocessing import StandardScaler\n",
"scaler = StandardScaler()\n",
"scaled_housing_data = scaler.fit_transform(housing.data)\n",
"scaled_housing_data_plus_bias = np.c_[np.ones((m, 1)), scaled_housing_data]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print(scaled_housing_data_plus_bias.mean(axis=0))\n",
"print(scaled_housing_data_plus_bias.mean(axis=1))\n",
"print(scaled_housing_data_plus_bias.mean())\n",
"print(scaled_housing_data_plus_bias.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Manually computing the gradients"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
"y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"error = y_pred - y\n",
"mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"gradients = 2/m * tf.matmul(tf.transpose(X), error)\n",
"training_op = tf.assign(theta, theta - learning_rate * gradients)\n",
"\n",
"init = tf.initialize_all_variables()\n",
"\n",
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" if epoch % 100 == 0:\n",
" print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
" sess.run(training_op)\n",
" \n",
" best_theta = theta.eval()\n",
"\n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Using autodiff\n",
"Same as above except for the `gradients = ...` line."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
"y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"error = y_pred - y\n",
"mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"gradients = tf.gradients(mse, [theta])[0]\n",
"training_op = tf.assign(theta, theta - learning_rate * gradients)\n",
"\n",
"init = tf.initialize_all_variables()\n",
"\n",
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" if epoch % 100 == 0:\n",
" print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
" sess.run(training_op)\n",
" \n",
" best_theta = theta.eval()\n",
"\n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Using a `GradientDescentOptimizer`"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
"y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"error = y_pred - y\n",
"mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
"training_op = optimizer.minimize(mse)\n",
"\n",
"init = tf.initialize_all_variables()\n",
"\n",
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" if epoch % 100 == 0:\n",
" print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
" sess.run(training_op)\n",
" \n",
" best_theta = theta.eval()\n",
"\n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Using a momentum optimizer"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
"y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"error = y_pred - y\n",
"mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate, momentum=0.25)\n",
"training_op = optimizer.minimize(mse)\n",
"\n",
"init = tf.initialize_all_variables()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" sess.run(training_op)\n",
" \n",
" best_theta = theta.eval()\n",
"\n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Feeding data to the training algorithm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Placeholder nodes"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
">>> tf.reset_default_graph()\n",
"\n",
">>> A = tf.placeholder(tf.float32, shape=(None, 3))\n",
">>> B = A + 5\n",
">>> with tf.Session() as sess:\n",
"... B_val_1 = B.eval(feed_dict={A: [[1, 2, 3]]})\n",
"... B_val_2 = B.eval(feed_dict={A: [[4, 5, 6], [7, 8, 9]]})\n",
"...\n",
">>> print(B_val_1)\n",
">>> print(B_val_2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mini-batch Gradient Descent"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
"y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"error = y_pred - y\n",
"mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
"training_op = optimizer.minimize(mse)\n",
"\n",
"init = tf.initialize_all_variables()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def fetch_batch(epoch, batch_index, batch_size):\n",
" rnd.seed(epoch * n_batches + batch_index)\n",
" indices = rnd.randint(m, size=batch_size)\n",
" X_batch = scaled_housing_data_plus_bias[indices]\n",
" y_batch = housing.target.reshape(-1, 1)[indices]\n",
" return X_batch, y_batch\n",
"\n",
"n_epochs = 10\n",
"batch_size = 100\n",
"n_batches = int(np.ceil(m / batch_size))\n",
"\n",
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" for batch_index in range(n_batches):\n",
" X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
" sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
"\n",
" best_theta = theta.eval()\n",
" \n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Saving and restoring a model"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
"y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"error = y_pred - y\n",
"mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
"training_op = optimizer.minimize(mse)\n",
"\n",
"init = tf.initialize_all_variables()\n",
"saver = tf.train.Saver()"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" if epoch % 100 == 0:\n",
" print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
" save_path = saver.save(sess, \"/tmp/my_model.ckpt\")\n",
" sess.run(training_op)\n",
" \n",
" best_theta = theta.eval()\n",
" save_path = saver.save(sess, \"my_model_final.ckpt\")\n",
"\n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Visualizing the graph\n",
"## inside Jupyter"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from IPython.display import clear_output, Image, display, HTML\n",
"\n",
"def strip_consts(graph_def, max_const_size=32):\n",
" \"\"\"Strip large constant values from graph_def.\"\"\"\n",
" strip_def = tf.GraphDef()\n",
" for n0 in graph_def.node:\n",
" n = strip_def.node.add() \n",
" n.MergeFrom(n0)\n",
" if n.op == 'Const':\n",
" tensor = n.attr['value'].tensor\n",
" size = len(tensor.tensor_content)\n",
" if size > max_const_size:\n",
" tensor.tensor_content = b\"<stripped %d bytes>\"%size\n",
" return strip_def\n",
"\n",
"def show_graph(graph_def, max_const_size=32):\n",
" \"\"\"Visualize TensorFlow graph.\"\"\"\n",
" if hasattr(graph_def, 'as_graph_def'):\n",
" graph_def = graph_def.as_graph_def()\n",
" strip_def = strip_consts(graph_def, max_const_size=max_const_size)\n",
" code = \"\"\"\n",
" <script>\n",
" function load() {{\n",
" document.getElementById(\"{id}\").pbtxt = {data};\n",
" }}\n",
" </script>\n",
" <link rel=\"import\" href=\"https://tensorboard.appspot.com/tf-graph-basic.build.html\" onload=load()>\n",
" <div style=\"height:600px\">\n",
" <tf-graph-basic id=\"{id}\"></tf-graph-basic>\n",
" </div>\n",
" \"\"\".format(data=repr(str(strip_def)), id='graph'+str(np.random.rand()))\n",
"\n",
" iframe = \"\"\"\n",
" <iframe seamless style=\"width:1200px;height:620px;border:0\" srcdoc=\"{}\"></iframe>\n",
" \"\"\".format(code.replace('\"', '"'))\n",
" display(HTML(iframe))"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"show_graph(tf.get_default_graph())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using TensorBoard"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"from datetime import datetime\n",
"\n",
"now = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
"root_logdir = \"tf_logs\"\n",
"logdir = \"{}/run-{}/\".format(root_logdir, now)\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
"y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"error = y_pred - y\n",
"mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
"training_op = optimizer.minimize(mse)\n",
"\n",
"init = tf.initialize_all_variables()\n",
"\n",
"mse_summary = tf.scalar_summary('MSE', mse)\n",
"summary_writer = tf.train.SummaryWriter(logdir, tf.get_default_graph())"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_epochs = 10\n",
"batch_size = 100\n",
"n_batches = int(np.ceil(m / batch_size))\n",
"\n",
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" for batch_index in range(n_batches):\n",
" X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
" if batch_index % 10 == 0:\n",
" summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})\n",
" step = epoch * n_batches + batch_index\n",
" summary_writer.add_summary(summary_str, step)\n",
" sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
"\n",
" best_theta = theta.eval()\n",
"\n",
"summary_writer.flush()\n",
"summary_writer.close()\n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Name scopes"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"now = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
"root_logdir = \"tf_logs\"\n",
"logdir = \"{}/run-{}/\".format(root_logdir, now)\n",
"\n",
"n_epochs = 1000\n",
"learning_rate = 0.01\n",
"\n",
"X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
"y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
"theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
"y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
"with tf.name_scope('loss') as scope:\n",
" error = y_pred - y\n",
" mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
"optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
"training_op = optimizer.minimize(mse)\n",
"\n",
"init = tf.initialize_all_variables()\n",
"\n",
"mse_summary = tf.scalar_summary('MSE', mse)\n",
"summary_writer = tf.train.SummaryWriter(logdir, tf.get_default_graph())"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_epochs = 10\n",
"batch_size = 100\n",
"n_batches = int(np.ceil(m / batch_size))\n",
"\n",
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" for epoch in range(n_epochs):\n",
" for batch_index in range(n_batches):\n",
" X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
" if batch_index % 10 == 0:\n",
" summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})\n",
" step = epoch * n_batches + batch_index\n",
" summary_writer.add_summary(summary_str, step)\n",
" sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
"\n",
" best_theta = theta.eval()\n",
"\n",
"summary_writer.flush()\n",
"summary_writer.close()\n",
"print(\"Best theta:\")\n",
"print(best_theta)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print(error.op.name)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print(mse.op.name)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"a1 = tf.Variable(0, name=\"a\") # name == \"a\"\n",
"a2 = tf.Variable(0, name=\"a\") # name == \"a_1\"\n",
"\n",
"with tf.name_scope(\"param\"): # name == \"param\"\n",
" a3 = tf.Variable(0, name=\"a\") # name == \"param/a\"\n",
"\n",
"with tf.name_scope(\"param\"): # name == \"param_1\"\n",
" a4 = tf.Variable(0, name=\"a\") # name == \"param_1/a\"\n",
"\n",
"for node in (a1, a2, a3, a4):\n",
" print(node.op.name)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Modularity"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An ugly flat code:"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"n_features = 3\n",
"X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
"\n",
"w1 = tf.Variable(tf.random_normal((n_features, 1)), name=\"weights1\")\n",
"w2 = tf.Variable(tf.random_normal((n_features, 1)), name=\"weights2\")\n",
"b1 = tf.Variable(0.0, name=\"bias1\")\n",
"b2 = tf.Variable(0.0, name=\"bias2\")\n",
"\n",
"linear1 = tf.add(tf.matmul(X, w1), b1, name=\"linear1\")\n",
"linear2 = tf.add(tf.matmul(X, w2), b2, name=\"linear2\")\n",
"\n",
"relu1 = tf.maximum(linear1, 0, name=\"relu1\")\n",
"relu2 = tf.maximum(linear1, 0, name=\"relu2\") # Oops, cut&paste error! Did you spot it?\n",
"\n",
"output = tf.add_n([relu1, relu2], name=\"output\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Much better, using a function to build the ReLUs:"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"def relu(X):\n",
" w_shape = int(X.get_shape()[1]), 1\n",
" w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
" b = tf.Variable(0.0, name=\"bias\")\n",
" linear = tf.add(tf.matmul(X, w), b, name=\"linear\")\n",
" return tf.maximum(linear, 0, name=\"relu\")\n",
"\n",
"n_features = 3\n",
"X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
"relus = [relu(X) for i in range(5)]\n",
"output = tf.add_n(relus, name=\"output\")\n",
"summary_writer = tf.train.SummaryWriter(\"logs/relu1\", tf.get_default_graph())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Even better using name scopes:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"def relu(X):\n",
" with tf.name_scope(\"relu\"):\n",
" w_shape = int(X.get_shape()[1]), 1\n",
" w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
" b = tf.Variable(0.0, name=\"bias\")\n",
" linear = tf.add(tf.matmul(X, w), b, name=\"linear\")\n",
" return tf.maximum(linear, 0, name=\"max\")\n",
"\n",
"n_features = 3\n",
"X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
"relus = [relu(X) for i in range(5)]\n",
"output = tf.add_n(relus, name=\"output\")\n",
"\n",
"summary_writer = tf.train.SummaryWriter(\"logs/relu2\", tf.get_default_graph())"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"summary_writer.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sharing a `threshold` variable the classic way, by defining it outside of the `relu()` function then passing it as a parameter:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"def relu(X, threshold):\n",
" with tf.name_scope(\"relu\"):\n",
" w_shape = int(X.get_shape()[1]), 1\n",
" w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
" b = tf.Variable(0.0, name=\"bias\")\n",
" linear = tf.add(tf.matmul(X, w), b, name=\"linear\")\n",
" return tf.maximum(linear, threshold, name=\"max\")\n",
"\n",
"threshold = tf.Variable(0.0, name=\"threshold\")\n",
"X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
"relus = [relu(X, threshold) for i in range(5)]\n",
"output = tf.add_n(relus, name=\"output\")"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"def relu(X):\n",
" with tf.name_scope(\"relu\"):\n",
" if not hasattr(relu, \"threshold\"):\n",
" relu.threshold = tf.Variable(0.0, name=\"threshold\")\n",
" w_shape = int(X.get_shape()[1]), 1\n",
" w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
" b = tf.Variable(0.0, name=\"bias\")\n",
" linear = tf.add(tf.matmul(X, w), b, name=\"linear\")\n",
" return tf.maximum(linear, relu.threshold, name=\"max\")\n",
"\n",
"X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
"relus = [relu(X) for i in range(5)]\n",
"output = tf.add_n(relus, name=\"output\")"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"def relu(X):\n",
" with tf.variable_scope(\"relu\", reuse=True):\n",
" threshold = tf.get_variable(\"threshold\", shape=(), initializer=tf.constant_initializer(0.0))\n",
" w_shape = int(X.get_shape()[1]), 1\n",
" w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
" b = tf.Variable(0.0, name=\"bias\")\n",
" linear = tf.add(tf.matmul(X, w), b, name=\"linear\")\n",
" return tf.maximum(linear, threshold, name=\"max\")\n",
"\n",
"X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
"with tf.variable_scope(\"relu\"):\n",
" threshold = tf.get_variable(\"threshold\", shape=(), initializer=tf.constant_initializer(0.0))\n",
"relus = [relu(X) for i in range(5)]\n",
"output = tf.add_n(relus, name=\"output\")\n",
"\n",
"summary_writer = tf.train.SummaryWriter(\"logs/relu6\", tf.get_default_graph())\n",
"summary_writer.close()"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"def relu(X):\n",
" with tf.variable_scope(\"relu\"):\n",
" threshold = tf.get_variable(\"threshold\", shape=(), initializer=tf.constant_initializer(0.0))\n",
" w_shape = int(X.get_shape()[1]), 1\n",
" w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
" b = tf.Variable(0.0, name=\"bias\")\n",
" linear = tf.add(tf.matmul(X, w), b, name=\"linear\")\n",
" return tf.maximum(linear, threshold, name=\"max\")\n",
"\n",
"X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
2016-11-23 09:26:19 +01:00
"with tf.variable_scope(\"\", default_name=\"\") as scope:\n",
2016-09-27 23:31:21 +02:00
" first_relu = relu(X) # create the shared variable\n",
" scope.reuse_variables() # then reuse it\n",
" relus = [first_relu] + [relu(X) for i in range(4)]\n",
"output = tf.add_n(relus, name=\"output\")\n",
"\n",
"summary_writer = tf.train.SummaryWriter(\"logs/relu8\", tf.get_default_graph())\n",
"summary_writer.close()"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"with tf.variable_scope(\"param\"):\n",
" x = tf.get_variable(\"x\", shape=(), initializer=tf.constant_initializer(0.))\n",
" #x = tf.Variable(0., name=\"x\")\n",
"with tf.variable_scope(\"param\", reuse=True):\n",
" y = tf.get_variable(\"x\")\n",
"\n",
2016-11-23 09:26:19 +01:00
"with tf.variable_scope(\"\", default_name=\"\", reuse=True):\n",
2016-09-27 23:31:21 +02:00
" z = tf.get_variable(\"param/x\", shape=(), initializer=tf.constant_initializer(0.))\n",
"\n",
"print(x is y)\n",
"print(x.op.name)\n",
"print(y.op.name)\n",
"print(z.op.name)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Extra material"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Strings"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"text = np.array(\"Do you want some café?\".split())\n",
"text_tensor = tf.constant(text)\n",
"\n",
"with tf.Session() as sess:\n",
" print(text_tensor.eval())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Distributed TensorFlow"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"server = tf.train.Server.create_local_server()"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = tf.constant(2) + tf.constant(3)\n",
"with tf.Session(server.target) as sess:\n",
" print(sess.run(x))"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"server.target"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class Const(object):\n",
" def __init__(self, value):\n",
" self.value = value\n",
" def evaluate(self, **variables):\n",
" return self.value\n",
" def __str__(self):\n",
" return str(self.value)\n",
"\n",
"class Var(object):\n",
" def __init__(self, name):\n",
" self.name = name\n",
" def evaluate(self, **variables):\n",
" return variables[self.name]\n",
" def __str__(self):\n",
" return self.name\n",
"\n",
"class BinaryOperator(object):\n",
" def __init__(self, a, b):\n",
" self.a = a\n",
" self.b = b\n",
"\n",
"class Add(BinaryOperator):\n",
" def evaluate(self, **variables):\n",
" return self.a.evaluate(**variables) + self.b.evaluate(**variables)\n",
" def __str__(self):\n",
" return \"{} + {}\".format(self.a, self.b)\n",
"\n",
"class Mul(BinaryOperator):\n",
" def evaluate(self, **variables):\n",
" return self.a.evaluate(**variables) * self.b.evaluate(**variables)\n",
" def __str__(self):\n",
" return \"({}) * ({})\".format(self.a, self.b)\n",
"\n",
"x = Var(\"x\")\n",
"y = Var(\"y\")\n",
"f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2\n",
"print(\"f(x,y) =\", f)\n",
"print(\"f(3,4) =\", f.evaluate(x=3, y=4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computing gradients\n",
"### Mathematical differentiation"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"df_dx = Mul(Const(2), Mul(Var(\"x\"), Var(\"y\"))) # df/dx = 2xy\n",
"df_dy = Add(Mul(Var(\"x\"), Var(\"x\")), Const(1)) # df/dy = x² + 1\n",
"print(\"df/dx(3,4) =\", df_dx.evaluate(x=3, y=4))\n",
"print(\"df/dy(3,4) =\", df_dy.evaluate(x=3, y=4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Numerical differentiation"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def derivative(f, x, y, x_eps, y_eps):\n",
" return (f.evaluate(x = x + x_eps, y = y + y_eps) - f.evaluate(x = x, y = y)) / (x_eps + y_eps)\n",
"\n",
"df_dx_34 = derivative(f, x=3, y=4, x_eps=0.0001, y_eps=0)\n",
"df_dy_34 = derivative(f, x=3, y=4, x_eps=0, y_eps=0.0001)\n",
"print(\"df/dx(3,4) =\", df_dx_34)\n",
"print(\"df/dy(3,4) =\", df_dy_34)"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def f(x, y):\n",
" return x**2*y + y + 2\n",
"\n",
"def derivative(f, x, y, x_eps, y_eps):\n",
" return (f(x + x_eps, y + y_eps) - f(x, y)) / (x_eps + y_eps)\n",
"\n",
"df_dx = derivative(f, 3, 4, 0.00001, 0)\n",
"df_dy = derivative(f, 3, 4, 0, 0.00001)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print(df_dx)\n",
"print(df_dy)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Symbolic differentiation"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Const.derive = lambda self, var: Const(0)\n",
"Var.derive = lambda self, var: Const(1) if self.name==var else Const(0)\n",
"Add.derive = lambda self, var: Add(self.a.derive(var), self.b.derive(var))\n",
"Mul.derive = lambda self, var: Add(Mul(self.a, self.b.derive(var)), Mul(self.a.derive(var), self.b))\n",
"\n",
"x = Var(\"x\")\n",
"y = Var(\"y\")\n",
"f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2\n",
"\n",
"df_dx = f.derive(\"x\") # 2xy\n",
"df_dy = f.derive(\"y\") # x² + 1\n",
"print(\"df/dx(3,4) =\", df_dx.evaluate(x=3, y=4))\n",
"print(\"df/dy(3,4) =\", df_dy.evaluate(x=3, y=4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Automatic differentiation (autodiff) –
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class Const(object):\n",
" def __init__(self, value):\n",
" self.value = value\n",
" def evaluate(self, derive, **variables):\n",
" return self.value, 0\n",
" def __str__(self):\n",
" return str(self.value)\n",
"\n",
"class Var(object):\n",
" def __init__(self, name):\n",
" self.name = name\n",
" def evaluate(self, derive, **variables):\n",
" return variables[self.name], (1 if derive == self.name else 0)\n",
" def __str__(self):\n",
" return self.name\n",
"\n",
"class BinaryOperator(object):\n",
" def __init__(self, a, b):\n",
" self.a = a\n",
" self.b = b\n",
"\n",
"class Add(BinaryOperator):\n",
" def evaluate(self, derive, **variables):\n",
" a, da = self.a.evaluate(derive, **variables)\n",
" b, db = self.b.evaluate(derive, **variables)\n",
" return a + b, da + db\n",
" def __str__(self):\n",
" return \"{} + {}\".format(self.a, self.b)\n",
"\n",
"class Mul(BinaryOperator):\n",
" def evaluate(self, derive, **variables):\n",
" a, da = self.a.evaluate(derive, **variables)\n",
" b, db = self.b.evaluate(derive, **variables)\n",
" return a * b, a * db + da * b\n",
" def __str__(self):\n",
" return \"({}) * ({})\".format(self.a, self.b)\n",
"\n",
"x = Var(\"x\")\n",
"y = Var(\"y\")\n",
"f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2\n",
"f34, df_dx_34 = f.evaluate(x=3, y=4, derive=\"x\")\n",
"f34, df_dy_34 = f.evaluate(x=3, y=4, derive=\"y\")\n",
"print(\"f(3,4) =\", f34)\n",
"print(\"df/dx(3,4) =\", df_dx_34)\n",
"print(\"df/dy(3,4) =\", df_dy_34)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Autodiff –
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class Const(object):\n",
" def __init__(self, value):\n",
" self.derivative = 0\n",
" self.value = value\n",
" def evaluate(self, **variables):\n",
" return self.value\n",
" def backpropagate(self, derivative):\n",
" pass\n",
" def __str__(self):\n",
" return str(self.value)\n",
"\n",
"class Var(object):\n",
" def __init__(self, name):\n",
" self.name = name\n",
" def evaluate(self, **variables):\n",
" self.derivative = 0\n",
" self.value = variables[self.name]\n",
" return self.value\n",
" def backpropagate(self, derivative):\n",
" self.derivative += derivative\n",
" def __str__(self):\n",
" return self.name\n",
"\n",
"class BinaryOperator(object):\n",
" def __init__(self, a, b):\n",
" self.a = a\n",
" self.b = b\n",
"\n",
"class Add(BinaryOperator):\n",
" def evaluate(self, **variables):\n",
" self.derivative = 0\n",
" self.value = self.a.evaluate(**variables) + self.b.evaluate(**variables)\n",
" return self.value\n",
" def backpropagate(self, derivative):\n",
" self.derivative += derivative\n",
" self.a.backpropagate(derivative)\n",
" self.b.backpropagate(derivative)\n",
" def __str__(self):\n",
" return \"{} + {}\".format(self.a, self.b)\n",
"\n",
"class Mul(BinaryOperator):\n",
" def evaluate(self, **variables):\n",
" self.derivative = 0\n",
" self.value = self.a.evaluate(**variables) * self.b.evaluate(**variables)\n",
" return self.value\n",
" def backpropagate(self, derivative):\n",
" self.derivative += derivative\n",
" self.a.backpropagate(derivative * self.b.value)\n",
" self.b.backpropagate(derivative * self.a.value)\n",
" def __str__(self):\n",
" return \"({}) * ({})\".format(self.a, self.b)"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = Var(\"x\")\n",
"y = Var(\"y\")\n",
"f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2\n",
"f34 = f.evaluate(x=3, y=4)\n",
"f.backpropagate(1)\n",
"print(\"f(3,4) =\", f34)\n",
"print(\"df/dx(3,4) =\", x.derivative)\n",
"print(\"df/dy(3,4) =\", y.derivative)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Autodiff –
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tf.reset_default_graph()\n",
"\n",
"x = tf.Variable(3., name=\"x\")\n",
"y = tf.Variable(4., name=\"x\")\n",
"f = x*x*y + y + 2\n",
"\n",
"gradients = tf.gradients(f, [x, y])\n",
"\n",
"init = tf.initialize_all_variables()\n",
"\n",
"with tf.Session() as sess:\n",
" init.run()\n",
" f_val, gradients_val = sess.run([f, gradients])\n",
"\n",
"f_val, gradients_val"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercise solutions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Coming soon**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
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"display_name": "Python 3",
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
2016-11-23 09:26:19 +01:00
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2016-09-27 23:31:21 +02:00
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"nav_menu": {
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"width": "616px"
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"toc": {
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
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"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": true
}
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