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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 CNTK 206  Part B
Step1:  Select the notebook runtime environment devices / settings
Set the device to cpu / gpu for the test environment. If you have both CPU and GPU on your machine, you can optionally switch the devices. By default, we choose the best available device.
Step2:  There are two run modes
Step3:  Data Reading
The input to the GAN will be a vector of random numbers. At the end of the traning, the GAN "learns" to generate images of hand written digits drawn from the MNIST database. We will be using the same MNIST data generated in tutorial 103A.  A more in-depth discussion of the data format and reading methods can be seen in previous tutorials.  For our purposes, just know that the following function returns an object that will be used to generate images from the MNIST dataset.  Since we are building an unsupervised model, we only need to read in features and ignore the labels.
Step4:  The random noise we will use to train the GAN is provided by the noise_sample function to generate random noise samples from a uniform distribution within the interval [-1, 1].
Step5:  Model Creation
First we provide a brief recap of the basics of GAN. You may skip this block if you are familiar with CNTK 206A. 
A GAN network is composed of two sub-networks, one called the Generator ($G$) and the other Discriminator ($D$). 
- The Generator takes random noise vector ($z$) as input and strives to output synthetic (fake) image ($x^$) that is indistinguishable from the real image ($x$) from the MNIST dataset. 
- The Discriminator strives to differentiate between the real image ($x$) and the fake ($x^$) image.
In each training iteration, the Generator produces more realistic fake images (in other words minimizes the difference between the real and generated counterpart) and the Discriminator maximizes the probability of assigning the correct label (real vs. fake) to both real examples (from training set) and the generated fake ones. The two conflicting objectives between the sub-networks ($G$ and $D$) leads to the GAN network (when trained) converge to an equilibrium, where the Generator produces realistic looking fake MNIST images and the Discriminator can at best randomly guess whether images are real or fake. The resulting Generator model once trained produces realistic MNIST image with the input being a random number. 
Model config
First, we establish some of the architectural and training hyper-parameters for our model.  
The generator network is fractional strided convolutional network.  The input is a 10-dimensional random vector and the output of the generator is a flattened version of a 28 x 28 fake image. The discriminator is strided-convolution network.  It takes as input the 784 dimensional output of the generator or a real MNIST image, reshapes into a 28 x 28 image format and outputs a single scalar - the estimated probability that the input image is a real MNIST image.
Model components
We build a computational graph for our model, one each for the generator and the discriminator. First, we establish some of the architectural parameters of our model.
Step6:  Generator
The generator takes a 100-dimensional random vector (for starters) as input ($z$) and the outputs a 784 dimensional vector, corresponding to a flattened version of a 28 x 28 fake (synthetic) image ($x^*$). In this tutorial, we use fractionally strided convolutions (a.k.a ConvolutionTranspose) with ReLU activations except for the last layer. We use a tanh activation on the last layer to make sure that the output of the generator function is confined to the interval [-1, 1]. The use of ReLU and tanh activation functions are key in addition to using the fractionally strided convolutions.
Step7:  Discriminator
The discriminator takes as input ($x^*$) the 784 dimensional output of the generator or a real MNIST image, re-shapes the input to a 28 x 28 image and outputs the estimated probability that the input image is a real MNIST image. The network is modeled using strided convolution with Leaky ReLU activation except for the last layer. We use a sigmoid activation on the last layer to ensure the discriminator output lies in the inteval of [0,1].
Step8:  We use a minibatch size of 128 and a fixed learning rate of 0.0002 for training. In the fast mode (isFast = True)  we verify only functional correctness with 5000 iterations. 
Note
Step9:  Build the graph
The rest of the computational graph is mostly responsible for coordinating the training algorithms and parameter updates, which is particularly tricky with GANs for couple reasons. The GANs are sensitive to the choice of learner and the parameters. Many of the parameters chosen here are based on many hard learnt lessons from the community. You may directly go to the code if you have read the basic GAN tutorial. 
First, the discriminator must be used on both the real MNIST images and fake images generated by the generator function.  One way to represent this in the computational graph is to create a clone of the output of the discriminator function, but with substituted inputs.  Setting method=share in the clone function ensures that  both paths through the discriminator model use the same set of parameters.
Second, we need to update the parameters for the generator and discriminator model separately using the gradients from different loss functions.  We can get the parameters for a Function in the graph with the parameters attribute.  However, when updating the model parameters, update only the parameters of the respective models while keeping the other parameters unchanged. In other words, when updating the generator we will update only the parameters of the $G$ function while keeping the parameters of the $D$ function fixed and vice versa.
Training the Model
The code for training the GAN very closely follows the algorithm as presented in the original NIPS 2014 paper. In this implementation, we train $D$ to maximize the probability of assigning the correct label (fake vs. real) to both training examples and the samples from $G$. In other words, $D$ and $G$ play the following two-player minimax game with the value function $V(G,D)$
Step10:  With the value functions defined we proceed to interatively train the GAN model. The training of the model can take significnantly long depending on the hardware especiallly if isFast flag is turned off.
Step11:  Generating Fake (Synthetic) Images
Now that we have trained the model, we can create fake images simply by feeding random noise into the generator and displaying the outputs.  Below are a few images generated from random samples.  To get a new set of samples, you can re-run the last cell.
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Python Code:
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
import os
import cntk as C
from cntk import Trainer
from cntk.layers import default_options
from cntk.device import set_default_device, gpu, cpu
from cntk.initializer import normal
from cntk.io import (MinibatchSource, CTFDeserializer, StreamDef, StreamDefs,
                     INFINITELY_REPEAT)
from cntk.layers import Dense, Convolution2D, ConvolutionTranspose2D, BatchNormalization
from cntk.learners import (adam, UnitType, learning_rate_schedule,
                          momentum_as_time_constant_schedule, momentum_schedule)
from cntk.logging import ProgressPrinter
%matplotlib inline
Explanation: CNTK 206  Part B: Deep Convolutional GAN with MNIST data
Prerequisites: We assume that you have successfully downloaded the MNIST data by completing the tutorial titled CNTK_103A_MNIST_DataLoader.ipynb.
Introduction
Generative models have gained a lot of attention in deep learning community which has traditionally leveraged discriminative models for (semi-supervised) and unsupervised learning. 
Overview
In the previous tutorial we introduce the original GAN implementation by Goodfellow et al at NIPS  2014. This pioneering work has since then been extended and many techniques have been published amongst which the Deep Convolutional Generative Adversarial Network a.k.a. DCGAN has become the recommended launch pad in the community.
In this tutorial, we introduce an implementation of the DCGAN with some well tested architectural constraints that improve stability in the GAN training: 
We use strided convolutions in the (discriminator) and fractional-strided convolutions in the generator.
We have used batch normalization in both the generator and the discriminator
We have removed fully connected hidden layers for deeper architectures.
We use ReLU activation in generator for all layers except for the output, which uses Tanh.
We use LeakyReLU activation in the discriminator for all layers.
End of explanation
# Select the right target device when this notebook is being tested:
if 'TEST_DEVICE' in os.environ:
    import cntk
    if os.environ['TEST_DEVICE'] == 'cpu':
        C.device.set_default_device(C.device.cpu())
    else:
        C.device.set_default_device(C.device.gpu(0))
C.device.set_default_device(C.device.gpu(0))
Explanation: Select the notebook runtime environment devices / settings
Set the device to cpu / gpu for the test environment. If you have both CPU and GPU on your machine, you can optionally switch the devices. By default, we choose the best available device.
End of explanation
isFast = True
Explanation: There are two run modes:
- Fast mode: isFast is set to True. This is the default mode for the notebooks, which means we train for fewer iterations or train / test on limited data. This ensures functional correctness of the notebook though the models produced are far from what a completed training would produce.
Slow mode: We recommend the user to set this flag to False once the user has gained familiarity with the notebook content and wants to gain insight from running the notebooks for a longer period with different parameters for training. 
Note
If the isFlag is set to False the notebook will take a few hours on a GPU enabled machine. You can try fewer iterations by setting the num_minibatches to a smaller number say 20,000 which comes at the expense of quality of the generated images.
End of explanation
# Ensure the training data is generated and available for this tutorial
# We search in two locations in the toolkit for the cached MNIST data set.
data_found = False
for data_dir in [os.path.join("..", "Examples", "Image", "DataSets", "MNIST"),
                 os.path.join("data", "MNIST")]:
    train_file = os.path.join(data_dir, "Train-28x28_cntk_text.txt")
    if os.path.isfile(train_file):
        data_found = True
        break
        
if not data_found:
    raise ValueError("Please generate the data by completing CNTK 103 Part A")
    
print("Data directory is {0}".format(data_dir))
def create_reader(path, is_training, input_dim, label_dim):
    deserializer = CTFDeserializer(
        filename = path,
        streams = StreamDefs(
            labels_unused = StreamDef(field = 'labels', shape = label_dim, is_sparse = False),
            features = StreamDef(field = 'features', shape = input_dim, is_sparse = False
            )
        )
    )
    return MinibatchSource(
        deserializers = deserializer,
        randomize = is_training,
        max_sweeps = INFINITELY_REPEAT if is_training else 1
    )
Explanation: Data Reading
The input to the GAN will be a vector of random numbers. At the end of the traning, the GAN "learns" to generate images of hand written digits drawn from the MNIST database. We will be using the same MNIST data generated in tutorial 103A.  A more in-depth discussion of the data format and reading methods can be seen in previous tutorials.  For our purposes, just know that the following function returns an object that will be used to generate images from the MNIST dataset.  Since we are building an unsupervised model, we only need to read in features and ignore the labels.
End of explanation
np.random.seed(123)
def noise_sample(num_samples):
    return np.random.uniform(
        low = -1.0,
        high = 1.0,
        size = [num_samples, g_input_dim]
    ).astype(np.float32)
Explanation: The random noise we will use to train the GAN is provided by the noise_sample function to generate random noise samples from a uniform distribution within the interval [-1, 1].
End of explanation
# architectural parameters
img_h, img_w = 28, 28
kernel_h, kernel_w = 5, 5 
stride_h, stride_w = 2, 2
# Input / Output parameter of Generator and Discriminator
g_input_dim = 100
g_output_dim = d_input_dim = img_h * img_w
# We expect the kernel shapes to be square in this tutorial and
# the strides to be of the same length along each data dimension
if kernel_h == kernel_w:
    gkernel = dkernel = kernel_h
else:
    raise ValueError('This tutorial needs square shaped kernel') 
            
if stride_h == stride_w:
    gstride = dstride = stride_h
else:
    raise ValueError('This tutorial needs same stride in all dims')
# Helper functions
def bn_with_relu(x, activation=C.relu):
    h = BatchNormalization(map_rank=1)(x)
    return C.relu(h)
# We use param-relu function to use a leak=0.2 since CNTK implementation 
# of Leaky ReLU is fixed to 0.01
def bn_with_leaky_relu(x, leak=0.2):
    h = BatchNormalization(map_rank=1)(x)
    r = C.param_relu(C.constant((np.ones(h.shape)*leak).astype(np.float32)), h)
    return r
Explanation: Model Creation
First we provide a brief recap of the basics of GAN. You may skip this block if you are familiar with CNTK 206A. 
A GAN network is composed of two sub-networks, one called the Generator ($G$) and the other Discriminator ($D$). 
- The Generator takes random noise vector ($z$) as input and strives to output synthetic (fake) image ($x^$) that is indistinguishable from the real image ($x$) from the MNIST dataset. 
- The Discriminator strives to differentiate between the real image ($x$) and the fake ($x^$) image.
In each training iteration, the Generator produces more realistic fake images (in other words minimizes the difference between the real and generated counterpart) and the Discriminator maximizes the probability of assigning the correct label (real vs. fake) to both real examples (from training set) and the generated fake ones. The two conflicting objectives between the sub-networks ($G$ and $D$) leads to the GAN network (when trained) converge to an equilibrium, where the Generator produces realistic looking fake MNIST images and the Discriminator can at best randomly guess whether images are real or fake. The resulting Generator model once trained produces realistic MNIST image with the input being a random number. 
Model config
First, we establish some of the architectural and training hyper-parameters for our model.  
The generator network is fractional strided convolutional network.  The input is a 10-dimensional random vector and the output of the generator is a flattened version of a 28 x 28 fake image. The discriminator is strided-convolution network.  It takes as input the 784 dimensional output of the generator or a real MNIST image, reshapes into a 28 x 28 image format and outputs a single scalar - the estimated probability that the input image is a real MNIST image.
Model components
We build a computational graph for our model, one each for the generator and the discriminator. First, we establish some of the architectural parameters of our model.
End of explanation
def convolutional_generator(z):
    with default_options(init=C.normal(scale=0.02)):
        print('Generator input shape: ', z.shape)
        s_h2, s_w2 = img_h//2, img_w//2 #Input shape (14,14)
        s_h4, s_w4 = img_h//4, img_w//4 # Input shape (7,7)
        gfc_dim = 1024
        gf_dim = 64
        h0 = Dense(gfc_dim, activation=None)(z)
        h0 = bn_with_relu(h0)
        print('h0 shape', h0.shape)
        h1 = Dense([gf_dim * 2, s_h4,  s_w4], activation=None)(h0)
        h1 = bn_with_relu(h1)
        print('h1 shape', h1.shape)
        h2 = ConvolutionTranspose2D(gkernel,
                                  num_filters=gf_dim*2,
                                  strides=gstride,
                                  pad=True,
                                  output_shape=(s_h2, s_w2),
                                  activation=None)(h1)
        h2 = bn_with_relu(h2)
        print('h2 shape', h2.shape)
        h3 = ConvolutionTranspose2D(gkernel,
                                  num_filters=1,
                                  strides=gstride,
                                  pad=True,
                                  output_shape=(img_h, img_w),
                                  activation=C.sigmoid)(h2)
        print('h3 shape :', h3.shape)
        return C.reshape(h3, img_h * img_w)
Explanation: Generator
The generator takes a 100-dimensional random vector (for starters) as input ($z$) and the outputs a 784 dimensional vector, corresponding to a flattened version of a 28 x 28 fake (synthetic) image ($x^*$). In this tutorial, we use fractionally strided convolutions (a.k.a ConvolutionTranspose) with ReLU activations except for the last layer. We use a tanh activation on the last layer to make sure that the output of the generator function is confined to the interval [-1, 1]. The use of ReLU and tanh activation functions are key in addition to using the fractionally strided convolutions.
End of explanation
def convolutional_discriminator(x):
    with default_options(init=C.normal(scale=0.02)):
        dfc_dim = 1024
        df_dim = 64
        print('Discriminator convolution input shape', x.shape)
        x = C.reshape(x, (1, img_h, img_w))
        h0 = Convolution2D(dkernel, 1, strides=dstride)(x)
        h0 = bn_with_leaky_relu(h0, leak=0.2)
        print('h0 shape :', h0.shape)
        h1 = Convolution2D(dkernel, df_dim, strides=dstride)(h0)
        h1 = bn_with_leaky_relu(h1, leak=0.2)
        print('h1 shape :', h1.shape)
        h2 = Dense(dfc_dim, activation=None)(h1)
        h2 = bn_with_leaky_relu(h2, leak=0.2)
        print('h2 shape :', h2.shape)
        h3 = Dense(1, activation=C.sigmoid)(h2)
        print('h3 shape :', h3.shape)
        return h3
Explanation: Discriminator
The discriminator takes as input ($x^*$) the 784 dimensional output of the generator or a real MNIST image, re-shapes the input to a 28 x 28 image and outputs the estimated probability that the input image is a real MNIST image. The network is modeled using strided convolution with Leaky ReLU activation except for the last layer. We use a sigmoid activation on the last layer to ensure the discriminator output lies in the inteval of [0,1].
End of explanation
# training config
minibatch_size = 128
num_minibatches = 5000 if isFast else 10000
lr = 0.0002
momentum = 0.5 #equivalent to beta1
Explanation: We use a minibatch size of 128 and a fixed learning rate of 0.0002 for training. In the fast mode (isFast = True)  we verify only functional correctness with 5000 iterations. 
Note: In the slow mode, the results look a lot better but it requires in the order of 10 minutes depending on your hardware. In general, the more number of minibatches one trains, the better is the fidelity of the generated images.
End of explanation
def build_graph(noise_shape, image_shape, generator, discriminator):
    input_dynamic_axes = [C.Axis.default_batch_axis()]
    Z = C.input(noise_shape, dynamic_axes=input_dynamic_axes)
    X_real = C.input(image_shape, dynamic_axes=input_dynamic_axes)
    X_real_scaled = X_real / 255.0
    # Create the model function for the generator and discriminator models
    X_fake = generator(Z)
    D_real = discriminator(X_real_scaled)
    D_fake = D_real.clone(
        method = 'share',
        substitutions = {X_real_scaled.output: X_fake.output}
    )
    # Create loss functions and configure optimazation algorithms
    G_loss = 1.0 - C.log(D_fake)
    D_loss = -(C.log(D_real) + C.log(1.0 - D_fake))
    G_learner = adam(
        parameters = X_fake.parameters,
        lr = learning_rate_schedule(lr, UnitType.sample),
        momentum = momentum_schedule(0.5)
    )
    D_learner = adam(
        parameters = D_real.parameters,
        lr = learning_rate_schedule(lr, UnitType.sample),
        momentum = momentum_schedule(0.5)
    )
    # Instantiate the trainers
    G_trainer = Trainer(
        X_fake,
        (G_loss, None),
        G_learner
    )
    D_trainer = Trainer(
        D_real,
        (D_loss, None),
        D_learner
    )
    return X_real, X_fake, Z, G_trainer, D_trainer
Explanation: Build the graph
The rest of the computational graph is mostly responsible for coordinating the training algorithms and parameter updates, which is particularly tricky with GANs for couple reasons. The GANs are sensitive to the choice of learner and the parameters. Many of the parameters chosen here are based on many hard learnt lessons from the community. You may directly go to the code if you have read the basic GAN tutorial. 
First, the discriminator must be used on both the real MNIST images and fake images generated by the generator function.  One way to represent this in the computational graph is to create a clone of the output of the discriminator function, but with substituted inputs.  Setting method=share in the clone function ensures that  both paths through the discriminator model use the same set of parameters.
Second, we need to update the parameters for the generator and discriminator model separately using the gradients from different loss functions.  We can get the parameters for a Function in the graph with the parameters attribute.  However, when updating the model parameters, update only the parameters of the respective models while keeping the other parameters unchanged. In other words, when updating the generator we will update only the parameters of the $G$ function while keeping the parameters of the $D$ function fixed and vice versa.
Training the Model
The code for training the GAN very closely follows the algorithm as presented in the original NIPS 2014 paper. In this implementation, we train $D$ to maximize the probability of assigning the correct label (fake vs. real) to both training examples and the samples from $G$. In other words, $D$ and $G$ play the following two-player minimax game with the value function $V(G,D)$:
$$
    \min_G \max_D V(D,G)= \mathbb{E}{x}[ log D(x) ] + \mathbb{E}{z}[ log(1 - D(G(z))) ]
$$
At the optimal point of this game the generator will produce realistic looking data while the discriminator will predict that the generated image is indeed fake with a probability of 0.5. The algorithm referred below is implemented in this tutorial.
End of explanation
def train(reader_train, generator, discriminator):
    X_real, X_fake, Z, G_trainer, D_trainer = \
        build_graph(g_input_dim, d_input_dim, generator, discriminator)
    # print out loss for each model for upto 25 times
    print_frequency_mbsize = num_minibatches // 25
   
    print("First row is Generator loss, second row is Discriminator loss")
    pp_G = ProgressPrinter(print_frequency_mbsize)
    pp_D = ProgressPrinter(print_frequency_mbsize)
    k = 2
    input_map = {X_real: reader_train.streams.features}
    for train_step in range(num_minibatches):
        # train the discriminator model for k steps
        for gen_train_step in range(k):
            Z_data = noise_sample(minibatch_size)
            X_data = reader_train.next_minibatch(minibatch_size, input_map)
            if X_data[X_real].num_samples == Z_data.shape[0]:
                batch_inputs = {X_real: X_data[X_real].data, Z: Z_data}
                D_trainer.train_minibatch(batch_inputs)
        # train the generator model for a single step
        Z_data = noise_sample(minibatch_size)
        batch_inputs = {Z: Z_data}
        G_trainer.train_minibatch(batch_inputs)
        G_trainer.train_minibatch(batch_inputs)
        pp_G.update_with_trainer(G_trainer)
        pp_D.update_with_trainer(D_trainer)
        G_trainer_loss = G_trainer.previous_minibatch_loss_average
    return Z, X_fake, G_trainer_loss
reader_train = create_reader(train_file, True, d_input_dim, label_dim=10)
# G_input, G_output, G_trainer_loss = train(reader_train, dense_generator, dense_discriminator)
G_input, G_output, G_trainer_loss = train(reader_train,
                                          convolutional_generator,
                                          convolutional_discriminator)
# Print the generator loss 
print("Training loss of the generator is: {0:.2f}".format(G_trainer_loss))
Explanation: With the value functions defined we proceed to interatively train the GAN model. The training of the model can take significnantly long depending on the hardware especiallly if isFast flag is turned off.
End of explanation
def plot_images(images, subplot_shape):
    plt.style.use('ggplot')
    fig, axes = plt.subplots(*subplot_shape)
    for image, ax in zip(images, axes.flatten()):
        ax.imshow(image.reshape(28, 28), vmin=0, vmax=1.0, cmap='gray')
        ax.axis('off')
    plt.show()
noise = noise_sample(36)
images = G_output.eval({G_input: noise})
plot_images(images, subplot_shape=[6, 6])
Explanation: Generating Fake (Synthetic) Images
Now that we have trained the model, we can create fake images simply by feeding random noise into the generator and displaying the outputs.  Below are a few images generated from random samples.  To get a new set of samples, you can re-run the last cell.
End of explanation
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