Réseaux de neurones Auto-encodeur variationnel

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
from keras.layers import Input, Dense, Lambda
from keras.models import Model
from keras import backend as K
from keras import objectives
from keras.datasets import mnist
 
# Hyperparameters
batch_size = 100
original_dim = 784
latent_dim = 2
intermediate_dim = 256
nb_epoch = 10
epsilon_std = 1.0
 
#encoder
'''
The encoder's jo is to map inputs to our hidden distribution
parameters. We take the input and send it through a dense fully
connected layer with ReLU (classic non-linearity to squash
dimensionality). Next, we convert the input data into two
parameters in the hidden space. We predefine the size using
dense, fully connected layers — z mean and z log sigma.
'''
x = Input(batch_shape = (batch_size, original_dim))
h = Dense(intermediate_dim, activation = 'relu')(x)
z_mean = Dense(latent_dim)(h)
z_log_var = Dense(latent_dim)(h)
 
print(z_mean)
print(z_log_var)
 
'''
The decoder(in the next block) will take z as its input
and output the parameters to the probability distribution 
of the data.
Epsilon is a random normal tensor
'''
 
def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(batch_size, latent_dim), mean=0.)
    return z_mean + K.exp(z_log_var / 2) * epsilon
 
# note that "output_shape" isn't necessary with the TensorFlow backend
z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_var])
 
#latent hidden state
print(z)
 
'''
we first initialize it with two fully connected layers and
their own respective activation functions. Because the data
is extracted from a small dimensionality to a larger one, some
of it will be lost in the reconstruction process.
'''
 
#decoder
# we instantiate these layers separately so as to reuse them later
decoder_h = Dense(intermediate_dim, activation='relu')
decoder_mean = Dense(original_dim, activation='sigmoid')
h_decoded = decoder_h(z)
x_decoded_mean = decoder_mean(h_decoded)
 
print(x_decoded_mean)
 
'''
The first term below measures the reconstruction loss. If the
decoder output is bad at reconstructing data, the cost in terms
of loss will be considerable at this point. The next term is a
regularizer, meaning it keeps the representation of each digit as
diverse as possible. So for instance, if two different people were 
to write out the digit three, the representations might end up
looking very different because, of course, different people write
differently. This can be bad, and the regularizer comes to rescue!
We penalize bad behaviour (like the example here) and ensure similar
representations are close together. Our total loss function is
defined as the sum of our reconstruction term, and the KL divergence
regularization term.
'''
 
#loss
def vae_loss(x, x_decoded_mean):
    xent_loss = original_dim * objectives.binary_crossentropy(x, x_decoded_mean)
    kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
    return xent_loss + kl_loss
 
vae = Model(x, x_decoded_mean)
vae.compile(optimizer='rmsprop', loss=vae_loss)
 
# train the VAE on MNIST digits
(x_train, y_train), (x_test, y_test) = mnist.load_data()
 
x_train = x_train.astype('float32') / 255.
x_test = x_test.astype('float32') / 255.
x_train = x_train.reshape((len(x_train), np.prod(x_train.shape[1:])))
x_test = x_test.reshape((len(x_test), np.prod(x_test.shape[1:])))
 
vae.fit(x_train, x_train,
        shuffle=True,
        nb_epoch=nb_epoch,
        batch_size=batch_size,
        validation_data=(x_test, x_test),verbose=1)
 
#plot latent/hidden space
 
# build a model to project inputs on the latent space
encoder = Model(x, z_mean)
 
# display a 2D plot of the digit classes in the latent space
x_test_encoded = encoder.predict(x_test, batch_size=batch_size)
plt.figure(figsize=(6, 6))
plt.scatter(x_test_encoded[:, 0], x_test_encoded[:, 1], c=y_test)
plt.colorbar()
plt.show()
 
'''
Another way to represent this is to generate digits by scanning
the latent plan, sampling latent points at regular intervals and
generating the corresponding digit for each of these points like so:
'''
 
# build a digit generator that can sample from the learned distribution
decoder_input = Input(shape=(latent_dim,))
_h_decoded = decoder_h(decoder_input)
_x_decoded_mean = decoder_mean(_h_decoded)
generator = Model(decoder_input, _x_decoded_mean)
 
# display a 2D manifold of the digits
n = 15  # figure with 15x15 digits
digit_size = 28
figure = np.zeros((digit_size * n, digit_size * n))
# linearly spaced coordinates on the unit square were transformed through the inverse CDF (ppf) of the Gaussian
# to produce values of the latent variables z, since the prior of the latent space is Gaussian
grid_x = norm.ppf(np.linspace(0.05, 0.95, n))
grid_y = norm.ppf(np.linspace(0.05, 0.95, n))
 
for i, yi in enumerate(grid_x):
    for j, xi in enumerate(grid_y):
        z_sample = np.array([[xi, yi]])
        x_decoded = generator.predict(z_sample)
        digit = x_decoded[0].reshape(digit_size, digit_size)
        figure[i * digit_size: (i + 1) * digit_size,
               j * digit_size: (j + 1) * digit_size] = digit
 
plt.figure(figsize=(10, 10))
plt.imshow(figure, cmap='Greys_r')
plt.show()
 

import os
 
## GAN Variants
from GAN import GAN
from CGAN import CGAN
from infoGAN import infoGAN
from ACGAN import ACGAN
from EBGAN import EBGAN
from WGAN import WGAN
from WGAN_GP import WGAN_GP
from DRAGAN import DRAGAN
from LSGAN import LSGAN
from BEGAN import BEGAN
 
## VAE Variants
from VAE import VAE
from CVAE import CVAE
 
from utils import show_all_variables
from utils import check_folder
 
import tensorflow as tf
import argparse
 
"""parsing and configuration"""
def parse_args():
    desc = "Tensorflow implementation of GAN collections"
    parser = argparse.ArgumentParser(description=desc)
 
    parser.add_argument('--gan_type', type=str, default='GAN',
                        choices=['GAN', 'CGAN', 'infoGAN', 'ACGAN', 'EBGAN', 'BEGAN', 'WGAN', 'WGAN_GP', 'DRAGAN', 'LSGAN', 'VAE', 'CVAE'],
                        help='The type of GAN', required=True)
    parser.add_argument('--dataset', type=str, default='mnist', choices=['mnist', 'fashion-mnist', 'celebA'],
                        help='The name of dataset')
    parser.add_argument('--epoch', type=int, default=20, help='The number of epochs to run')
    parser.add_argument('--batch_size', type=int, default=64, help='The size of batch')
    parser.add_argument('--z_dim', type=int, default=62, help='Dimension of noise vector')
    parser.add_argument('--checkpoint_dir', type=str, default='checkpoint',
                        help='Directory name to save the checkpoints')
    parser.add_argument('--result_dir', type=str, default='results',
                        help='Directory name to save the generated images')
    parser.add_argument('--log_dir', type=str, default='logs',
                        help='Directory name to save training logs')
 
    return check_args(parser.parse_args())
 
"""checking arguments"""
def check_args(args):
    # --checkpoint_dir
    check_folder(args.checkpoint_dir)
 
    # --result_dir
    check_folder(args.result_dir)
 
    # --result_dir
    check_folder(args.log_dir)
 
    # --epoch
    assert args.epoch >= 1, 'number of epochs must be larger than or equal to one'
 
    # --batch_size
    assert args.batch_size >= 1, 'batch size must be larger than or equal to one'
 
    # --z_dim
    assert args.z_dim >= 1, 'dimension of noise vector must be larger than or equal to one'
 
    return args
 
"""main"""
def main():
    # parse arguments
    args = parse_args()
    if args is None:
      exit()
 
    # open session
    models = [GAN, CGAN, infoGAN, ACGAN, EBGAN, WGAN, WGAN_GP, DRAGAN,
              LSGAN, BEGAN, VAE, CVAE]
    with tf.Session(config=tf.ConfigProto(allow_soft_placement=True)) as sess:
        # declare instance for GAN
 
        gan = None
        for model in models:
            if args.gan_type == model.model_name:
                gan = model(sess,
                            epoch=args.epoch,
                            batch_size=args.batch_size,
                            z_dim=args.z_dim,
                            dataset_name=args.dataset,
                            checkpoint_dir=args.checkpoint_dir,
                            result_dir=args.result_dir,
                            log_dir=args.log_dir)
        if gan is None:
            raise Exception("[!] There is no option for " + args.gan_type)
 
        # build graph
        gan.build_model()
 
        # show network architecture
        show_all_variables()
 
        # launch the graph in a session
        gan.train()
        print(" [*] Training finished!")
 
        # visualize learned generator
        gan.visualize_results(args.epoch-1)
        print(" [*] Testing finished!")
 
if __name__ == '__main__':
    main()
 

#-*- coding: utf-8 -*-
from __future__ import division
import os
import time
import tensorflow as tf
import numpy as np
 
from ops import *
from utils import *
 
import prior_factory as prior
 
class VAE(object):
    model_name = "VAE"     # name for checkpoint
 
    def __init__(self, sess, epoch, batch_size, z_dim, dataset_name, checkpoint_dir, result_dir, log_dir):
        self.sess = sess
        self.dataset_name = dataset_name
        self.checkpoint_dir = checkpoint_dir
        self.result_dir = result_dir
        self.log_dir = log_dir
        self.epoch = epoch
        self.batch_size = batch_size
 
        if dataset_name == 'mnist' or dataset_name == 'fashion-mnist':
            # parameters
            self.input_height = 28
            self.input_width = 28
            self.output_height = 28
            self.output_width = 28
 
            self.z_dim = z_dim         # dimension of noise-vector
            self.c_dim = 1
 
            # train
            self.learning_rate = 0.0002
            self.beta1 = 0.5
 
            # test
            self.sample_num = 64  # number of generated images to be saved
 
            # load mnist
            self.data_X, self.data_y = load_mnist(self.dataset_name)
 
            # get number of batches for a single epoch
            self.num_batches = len(self.data_X) // self.batch_size
        else:
            raise NotImplementedError
 
    # Gaussian Encoder
    def encoder(self, x, is_training=True, reuse=False):
        # Network Architecture is exactly same as in infoGAN (https://arxiv.org/abs/1606.03657)
        # Architecture : (64)4c2s-(128)4c2s_BL-FC1024_BL-FC62*4
        with tf.variable_scope("encoder", reuse=reuse):
 
            net = lrelu(conv2d(x, 64, 4, 4, 2, 2, name='en_conv1'))
            net = lrelu(bn(conv2d(net, 128, 4, 4, 2, 2, name='en_conv2'), is_training=is_training, scope='en_bn2'))
            net = tf.reshape(net, [self.batch_size, -1])
            net = lrelu(bn(linear(net, 1024, scope='en_fc3'), is_training=is_training, scope='en_bn3'))
            gaussian_params = linear(net, 2 * self.z_dim, scope='en_fc4')
 
            # The mean parameter is unconstrained
            mean = gaussian_params[:, :self.z_dim]
            # The standard deviation must be positive. Parametrize with a softplus and
            # add a small epsilon for numerical stability
            stddev = 1e-6 + tf.nn.softplus(gaussian_params[:, self.z_dim:])
 
        return mean, stddev
 
    # Bernoulli decoder
    def decoder(self, z, is_training=True, reuse=False):
        # Network Architecture is exactly same as in infoGAN (https://arxiv.org/abs/1606.03657)
        # Architecture : FC1024_BR-FC7x7x128_BR-(64)4dc2s_BR-(1)4dc2s_S
        with tf.variable_scope("decoder", reuse=reuse):
            net = tf.nn.relu(bn(linear(z, 1024, scope='de_fc1'), is_training=is_training, scope='de_bn1'))
            net = tf.nn.relu(bn(linear(net, 128 * 7 * 7, scope='de_fc2'), is_training=is_training, scope='de_bn2'))
            net = tf.reshape(net, [self.batch_size, 7, 7, 128])
            net = tf.nn.relu(
                bn(deconv2d(net, [self.batch_size, 14, 14, 64], 4, 4, 2, 2, name='de_dc3'), is_training=is_training,
                   scope='de_bn3'))
 
            out = tf.nn.sigmoid(deconv2d(net, [self.batch_size, 28, 28, 1], 4, 4, 2, 2, name='de_dc4'))
            return out
 
    def build_model(self):
        # some parameters
        image_dims = [self.input_height, self.input_width, self.c_dim]
        bs = self.batch_size
 
        """ Graph Input """
        # images
        self.inputs = tf.placeholder(tf.float32, [bs] + image_dims, name='real_images')
 
        # noises
        self.z = tf.placeholder(tf.float32, [bs, self.z_dim], name='z')
 
        """ Loss Function """
        # encoding
        self.mu, sigma = self.encoder(self.inputs, is_training=True, reuse=False)        
 
        # sampling by re-parameterization technique
        z = self.mu + sigma * tf.random_normal(tf.shape(self.mu), 0, 1, dtype=tf.float32)
 
        # decoding
        out = self.decoder(z, is_training=True, reuse=False)
        self.out = tf.clip_by_value(out, 1e-8, 1 - 1e-8)
 
        # loss
        marginal_likelihood = tf.reduce_sum(self.inputs * tf.log(self.out) + (1 - self.inputs) * tf.log(1 - self.out),
                                            [1, 2])
        KL_divergence = 0.5 * tf.reduce_sum(tf.square(self.mu) + tf.square(sigma) - tf.log(1e-8 + tf.square(sigma)) - 1, [1])
 
        self.neg_loglikelihood = -tf.reduce_mean(marginal_likelihood)
        self.KL_divergence = tf.reduce_mean(KL_divergence)
 
        ELBO = -self.neg_loglikelihood - self.KL_divergence
 
        self.loss = -ELBO
 
        """ Training """
        # optimizers
        t_vars = tf.trainable_variables()
        with tf.control_dependencies(tf.get_collection(tf.GraphKeys.UPDATE_OPS)):
            self.optim = tf.train.AdamOptimizer(self.learning_rate*5, beta1=self.beta1) \
                      .minimize(self.loss, var_list=t_vars)
 
        """" Testing """
        # for test
        self.fake_images = self.decoder(self.z, is_training=False, reuse=True)
 
        """ Summary """
        nll_sum = tf.summary.scalar("nll", self.neg_loglikelihood)
        kl_sum = tf.summary.scalar("kl", self.KL_divergence)
        loss_sum = tf.summary.scalar("loss", self.loss)
 
        # final summary operations
        self.merged_summary_op = tf.summary.merge_all()
 
    def train(self):
 
        # initialize all variables
        tf.global_variables_initializer().run()
 
        # graph inputs for visualize training results
        self.sample_z = prior.gaussian(self.batch_size, self.z_dim)
 
        # saver to save model
        self.saver = tf.train.Saver()
 
        # summary writer
        self.writer = tf.summary.FileWriter(self.log_dir + '/' + self.model_name, self.sess.graph)
 
        # restore check-point if it exits
        could_load, checkpoint_counter = self.load(self.checkpoint_dir)
        if could_load:
            start_epoch = (int)(checkpoint_counter / self.num_batches)
            start_batch_id = checkpoint_counter - start_epoch * self.num_batches
            counter = checkpoint_counter
            print(" [*] Load SUCCESS")
        else:
            start_epoch = 0
            start_batch_id = 0
            counter = 1
            print(" [!] Load failed...")
 
        # loop for epoch
        start_time = time.time()
        for epoch in range(start_epoch, self.epoch):
 
            # get batch data
            for idx in range(start_batch_id, self.num_batches):
                batch_images = self.data_X[idx*self.batch_size:(idx+1)*self.batch_size]
                batch_z = prior.gaussian(self.batch_size, self.z_dim)
 
                # update autoencoder
                _, summary_str, loss, nll_loss, kl_loss = self.sess.run([self.optim, self.merged_summary_op, self.loss, self.neg_loglikelihood, self.KL_divergence],
                                               feed_dict={self.inputs: batch_images, self.z: batch_z})
                self.writer.add_summary(summary_str, counter)
 
                # display training status
                counter += 1
                print("Epoch: [%2d] [%4d/%4d] time: %4.4f, loss: %.8f, nll: %.8f, kl: %.8f" \
                      % (epoch, idx, self.num_batches, time.time() - start_time, loss, nll_loss, kl_loss))
 
                # save training results for every 300 steps
                if np.mod(counter, 300) == 0:
                    samples = self.sess.run(self.fake_images,
                                            feed_dict={self.z: self.sample_z})
 
                    tot_num_samples = min(self.sample_num, self.batch_size)
                    manifold_h = int(np.floor(np.sqrt(tot_num_samples)))
                    manifold_w = int(np.floor(np.sqrt(tot_num_samples)))
                    save_images(samples[:manifold_h * manifold_w, :, :, :], [manifold_h, manifold_w],
                                './' + check_folder(self.result_dir + '/' + self.model_dir) + '/' + self.model_name + '_train_{:02d}_{:04d}.png'.format(
                                    epoch, idx))
 
            # After an epoch, start_batch_id is set to zero
            # non-zero value is only for the first epoch after loading pre-trained model
            start_batch_id = 0
 
            # save model
            self.save(self.checkpoint_dir, counter)
 
            # show temporal results
            self.visualize_results(epoch)
 
        # save model for final step
        self.save(self.checkpoint_dir, counter)
 
    def visualize_results(self, epoch):
        tot_num_samples = min(self.sample_num, self.batch_size)
        image_frame_dim = int(np.floor(np.sqrt(tot_num_samples)))
 
        """ random condition, random noise """
 
        z_sample = prior.gaussian(self.batch_size, self.z_dim)
 
        samples = self.sess.run(self.fake_images, feed_dict={self.z: z_sample})
 
        save_images(samples[:image_frame_dim * image_frame_dim, :, :, :], [image_frame_dim, image_frame_dim],
                    check_folder(
                        self.result_dir + '/' + self.model_dir) + '/' + self.model_name + '_epoch%03d' % epoch + '_test_all_classes.png')
 
        """ learned manifold """
        if self.z_dim == 2:
            assert self.z_dim == 2
 
            z_tot = None
            id_tot = None
            for idx in range(0, 100):
                #randomly sampling
                id = np.random.randint(0,self.num_batches)
                batch_images = self.data_X[id * self.batch_size:(id + 1) * self.batch_size]
                batch_labels = self.data_y[id * self.batch_size:(id + 1) * self.batch_size]
 
                z = self.sess.run(self.mu, feed_dict={self.inputs: batch_images})
 
                if idx == 0:
                    z_tot = z
                    id_tot = batch_labels
                else:
                    z_tot = np.concatenate((z_tot, z), axis=0)
                    id_tot = np.concatenate((id_tot, batch_labels), axis=0)
 
            save_scattered_image(z_tot, id_tot, -4, 4, name=check_folder(
                self.result_dir + '/' + self.model_dir) + '/' + self.model_name + '_epoch%03d' % epoch + '_learned_manifold.png')
 
    @property
    def model_dir(self):
        return "{}_{}_{}_{}".format(
            self.model_name, self.dataset_name,
            self.batch_size, self.z_dim)
 
    def save(self, checkpoint_dir, step):
        checkpoint_dir = os.path.join(checkpoint_dir, self.model_dir, self.model_name)
 
        if not os.path.exists(checkpoint_dir):
            os.makedirs(checkpoint_dir)
 
        self.saver.save(self.sess,os.path.join(checkpoint_dir, self.model_name+'.model'), global_step=step)
 
    def load(self, checkpoint_dir):
        import re
        print(" [*] Reading checkpoints...")
        checkpoint_dir = os.path.join(checkpoint_dir, self.model_dir, self.model_name)
 
        ckpt = tf.train.get_checkpoint_state(checkpoint_dir)
        if ckpt and ckpt.model_checkpoint_path:
            ckpt_name = os.path.basename(ckpt.model_checkpoint_path)
            self.saver.restore(self.sess, os.path.join(checkpoint_dir, ckpt_name))
            counter = int(next(re.finditer("(\d+)(?!.*\d)",ckpt_name)).group(0))
            print(" [*] Success to read {}".format(ckpt_name))
            return True, counter
        else:
            print(" [*] Failed to find a checkpoint")
            return False, 0

"""
Most codes from https://github.com/carpedm20/DCGAN-tensorflow
"""
from __future__ import division
import math
import random
import pprint
import cv2
import imageio
import numpy as np
from time import gmtime, strftime
from six.moves import xrange
import matplotlib.pyplot as plt
import os, gzip
 
import tensorflow as tf
import tensorflow.contrib.slim as slim
 
def load_mnist(dataset_name):
    data_dir = os.path.join("./data", dataset_name)
 
    def extract_data(filename, num_data, head_size, data_size):
        with gzip.open(filename) as bytestream:
            bytestream.read(head_size)
            buf = bytestream.read(data_size * num_data)
            data = np.frombuffer(buf, dtype=np.uint8).astype(np.float)
        return data
 
    data = extract_data(data_dir + '/train-images-idx3-ubyte.gz', 60000, 16, 28 * 28)
    trX = data.reshape((60000, 28, 28, 1))
 
    data = extract_data(data_dir + '/train-labels-idx1-ubyte.gz', 60000, 8, 1)
    trY = data.reshape((60000))
 
    data = extract_data(data_dir + '/t10k-images-idx3-ubyte.gz', 10000, 16, 28 * 28)
    teX = data.reshape((10000, 28, 28, 1))
 
    data = extract_data(data_dir + '/t10k-labels-idx1-ubyte.gz', 10000, 8, 1)
    teY = data.reshape((10000))
 
    trY = np.asarray(trY)
    teY = np.asarray(teY)
 
    X = np.concatenate((trX, teX), axis=0)
    y = np.concatenate((trY, teY), axis=0).astype(np.int)
 
    seed = 547
    np.random.seed(seed)
    np.random.shuffle(X)
    np.random.seed(seed)
    np.random.shuffle(y)
 
    y_vec = np.zeros((len(y), 10), dtype=np.float)
    for i, label in enumerate(y):
        y_vec[i, y[i]] = 1.0
 
    return X / 255., y_vec
 
def check_folder(log_dir):
    if not os.path.exists(log_dir):
        os.makedirs(log_dir)
    return log_dir
 
def show_all_variables():
    model_vars = tf.trainable_variables()
    slim.model_analyzer.analyze_vars(model_vars, print_info=True)
 
def get_image(image_path, input_height, input_width, resize_height=64, resize_width=64, crop=True, grayscale=False):
    image = imread(image_path, grayscale)
    return transform(image, input_height, input_width, resize_height, resize_width, crop)
 
def save_images(images, size, image_path):
    return imsave(inverse_transform(images), size, image_path)
 
def imread(path, grayscale = False):
    if (grayscale):
        return imageio.imread(path, flatten = True).astype(np.float)
    else:
        return imageio.imread(path).astype(np.float)
 
def merge_images(images, size):
    return inverse_transform(images)
 
def merge(images, size):
    h, w = images.shape[1], images.shape[2]
    if (images.shape[3] in (3,4)):
        c = images.shape[3]
        img = np.zeros((h * size[0], w * size[1], c))
        for idx, image in enumerate(images):
            i = idx % size[1]
            j = idx // size[1]
            img[j * h:j * h + h, i * w:i * w + w, :] = image
        return img
    elif images.shape[3]==1:
        img = np.zeros((h * size[0], w * size[1]))
        for idx, image in enumerate(images):
            i = idx % size[1]
            j = idx // size[1]
            img[j * h:j * h + h, i * w:i * w + w] = image[:,:,0]
        return img
    else:
        raise ValueError('in merge(images,size) images parameter ''must have dimensions: HxW or HxWx3 or HxWx4')
 
def imsave(images, size, path):
    image = np.squeeze(merge(images, size))
    return imageio.imsave(path, image)
 
def center_crop(x, crop_h, crop_w, resize_h=64, resize_w=64):
    if crop_w is None:
        crop_w = crop_h
    h, w = x.shape[:2]
    j = int(round((h - crop_h)/2.))
    i = int(round((w - crop_w)/2.))
    return cv2.resize(x[j:j+crop_h, i:i+crop_w], [resize_h, resize_w])
 
def transform(image, input_height, input_width, resize_height=64, resize_width=64, crop=True):
    if crop:
        cropped_image = center_crop(image, input_height, input_width, resize_height, resize_width)
    else:
        cropped_image = cv2.resize(image, [resize_height, resize_width])
    return np.array(cropped_image)/127.5 - 1.
 
def inverse_transform(images):
    return (images+1.)/2.
 
""" Drawing Tools """
# borrowed from https://github.com/ykwon0407/variational_autoencoder/blob/master/variational_bayes.ipynb
def save_scattered_image(z, id, z_range_x, z_range_y, name='scattered_image.jpg'):
    N = 10
    plt.figure(figsize=(8, 6))
    plt.scatter(z[:, 0], z[:, 1], c=np.argmax(id, 1), marker='o', edgecolor='none', cmap=discrete_cmap(N, 'jet'))
    plt.colorbar(ticks=range(N))
    axes = plt.gca()
    axes.set_xlim([-z_range_x, z_range_x])
    axes.set_ylim([-z_range_y, z_range_y])
    plt.grid(True)
    plt.savefig(name)
 
# borrowed from https://gist.github.com/jakevdp/91077b0cae40f8f8244a
def discrete_cmap(N, base_cmap=None):
    """Create an N-bin discrete colormap from the specified input map"""
 
    # Note that if base_cmap is a string or None, you can simply do
    #    return plt.cm.get_cmap(base_cmap, N)
    # The following works for string, None, or a colormap instance:
 
    base = plt.cm.get_cmap(base_cmap)
    color_list = base(np.linspace(0, 1, N))
    cmap_name = base.name + str(N)
    return base.from_list(cmap_name, color_list, N)