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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:
 Copyright 2019 The TensorFlow Authors.
Step1:  Post-training float16 quantization
<table class="tfo-notebook-buttons" align="left">
  <td>
    <a target="_blank" href="https
Step2:  Train and export the model
Step3:  For the example, you trained the model for just a single epoch, so it only trains to ~96% accuracy.
Convert to a TensorFlow Lite model
The savedmodel directory is named with a timestamp. Select the most recent one
Step4:  Using the Python TFLiteConverter, the saved model can be converted into a TensorFlow Lite model.
First load the model using the TFLiteConverter
Step5:  Write it out to a .tflite file
Step6:  To instead quantize the model to float16 on export, first set the optimizations flag to use default optimizations. Then specify that float16 is the supported type on the target platform
Step7:  Finally, convert the model like usual. Note, by default the converted model will still use float input and outputs for invocation convenience.
Step8:  Note how the resulting file is approximately 1/2 the size.
Step9:  Run the TensorFlow Lite models
Run the TensorFlow Lite model using the Python TensorFlow Lite Interpreter. 
Load the test data
First, let's load the MNIST test data to feed to the model
Step10:  Load the model into the interpreters
Step11:  Test the models on one image
Step12:  Evaluate the models
Step13:  Repeat the evaluation on the float16 quantized model to obtain
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Python Code:
#@title Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
Explanation: Copyright 2019 The TensorFlow Authors.
End of explanation
! pip uninstall -y tensorflow
! pip install -U tf-nightly
import tensorflow as tf
tf.enable_eager_execution()
import numpy as np
tf.logging.set_verbosity(tf.logging.DEBUG)
! git clone --depth 1 https://github.com/tensorflow/models
tf.lite.constants.FLOAT16
import sys
import os
if sys.version_info.major >= 3:
    import pathlib
else:
    import pathlib2 as pathlib
# Add `models` to the python path.
models_path = os.path.join(os.getcwd(), "models")
sys.path.append(models_path)
Explanation: Post-training float16 quantization
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  <td>
    <a target="_blank" href="https://www.tensorflow.org/lite/performance/post_training_float16_quant"><img src="https://www.tensorflow.org/images/tf_logo_32px.png" />View on TensorFlow.org</a>
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  <td>
    <a target="_blank" href="https://colab.research.google.com/github/tensorflow/tensorflow/blob/master/tensorflow/lite/g3doc/performance/post_training_float16_quant.ipynb"><img src="https://www.tensorflow.org/images/colab_logo_32px.png" />Run in Google Colab</a>
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  <td>
    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/master/tensorflow/lite/g3doc/performance/post_training_float16_quant.ipynb"><img src="https://www.tensorflow.org/images/GitHub-Mark-32px.png" />View source on GitHub</a>
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Overview
TensorFlow Lite now supports
converting weights to 16-bit floating point values during model conversion from TensorFlow to TensorFlow Lite's flat buffer format. This results in a 2x reduction in model size. Some harware, like GPUs, can compute natively in this reduced precision arithmetic, realizing a speedup over traditional floating point execution. The Tensorflow Lite GPU delegate can be configured to run in this way. However, a model converted to float16 weights can still run on the CPU without additional modification: the float16 weights are  upsampled to float32 prior to the first inference. This permits a significant reduction in model size in exchange for a minimal impacts to latency and accuracy.
In this tutorial, you train an MNIST model from scratch, check its accuracy in TensorFlow, and then convert the saved model into a Tensorflow Lite flatbuffer
with float16 quantization. Finally, check the
accuracy of the converted model and compare it to the original saved model. The training script, mnist.py, is available from the
TensorFlow official MNIST tutorial.
Build an MNIST model
Setup
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saved_models_root = "/tmp/mnist_saved_model"
# The above path addition is not visible to subprocesses, add the path for the subprocess as well.
!PYTHONPATH={models_path} python models/official/mnist/mnist.py --train_epochs=1 --export_dir {saved_models_root} --data_format=channels_last
Explanation: Train and export the model
End of explanation
saved_model_dir = str(sorted(pathlib.Path(saved_models_root).glob("*"))[-1])
saved_model_dir
Explanation: For the example, you trained the model for just a single epoch, so it only trains to ~96% accuracy.
Convert to a TensorFlow Lite model
The savedmodel directory is named with a timestamp. Select the most recent one:
End of explanation
converter = tf.lite.TFLiteConverter.from_saved_model(saved_model_dir)
tflite_model = converter.convert()
Explanation: Using the Python TFLiteConverter, the saved model can be converted into a TensorFlow Lite model.
First load the model using the TFLiteConverter:
End of explanation
tflite_models_dir = pathlib.Path("/tmp/mnist_tflite_models/")
tflite_models_dir.mkdir(exist_ok=True, parents=True)
tflite_model_file = tflite_models_dir/"mnist_model.tflite"
tflite_model_file.write_bytes(tflite_model)
Explanation: Write it out to a .tflite file:
End of explanation
tf.logging.set_verbosity(tf.logging.INFO)
converter.optimizations = [tf.lite.Optimize.DEFAULT]
converter.target_spec.supported_types = [tf.lite.constants.FLOAT16]
Explanation: To instead quantize the model to float16 on export, first set the optimizations flag to use default optimizations. Then specify that float16 is the supported type on the target platform:
End of explanation
tflite_fp16_model = converter.convert()
tflite_model_fp16_file = tflite_models_dir/"mnist_model_quant_f16.tflite"
tflite_model_fp16_file.write_bytes(tflite_fp16_model)
Explanation: Finally, convert the model like usual. Note, by default the converted model will still use float input and outputs for invocation convenience.
End of explanation
!ls -lh {tflite_models_dir}
Explanation: Note how the resulting file is approximately 1/2 the size.
End of explanation
_, mnist_test = tf.keras.datasets.mnist.load_data()
images, labels = tf.cast(mnist_test[0], tf.float32)/255.0, mnist_test[1]
mnist_ds = tf.data.Dataset.from_tensor_slices((images, labels)).batch(1)
Explanation: Run the TensorFlow Lite models
Run the TensorFlow Lite model using the Python TensorFlow Lite Interpreter. 
Load the test data
First, let's load the MNIST test data to feed to the model:
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interpreter = tf.lite.Interpreter(model_path=str(tflite_model_file))
interpreter.allocate_tensors()
interpreter_fp16 = tf.lite.Interpreter(model_path=str(tflite_model_fp16_file))
interpreter_fp16.allocate_tensors()
Explanation: Load the model into the interpreters
End of explanation
for img, label in mnist_ds:
  break
interpreter.set_tensor(interpreter.get_input_details()[0]["index"], img)
interpreter.invoke()
predictions = interpreter.get_tensor(
    interpreter.get_output_details()[0]["index"])
import matplotlib.pylab as plt
plt.imshow(img[0])
template = "True:{true}, predicted:{predict}"
_ = plt.title(template.format(true= str(label[0].numpy()),
                              predict=str(predictions[0])))
plt.grid(False)
interpreter_fp16.set_tensor(
    interpreter_fp16.get_input_details()[0]["index"], img)
interpreter_fp16.invoke()
predictions = interpreter_fp16.get_tensor(
    interpreter_fp16.get_output_details()[0]["index"])
plt.imshow(img[0])
template = "True:{true}, predicted:{predict}"
_ = plt.title(template.format(true= str(label[0].numpy()),
                              predict=str(predictions[0])))
plt.grid(False)
Explanation: Test the models on one image
End of explanation
def eval_model(interpreter, mnist_ds):
  total_seen = 0
  num_correct = 0
  input_index = interpreter.get_input_details()[0]["index"]
  output_index = interpreter.get_output_details()[0]["index"]
  for img, label in mnist_ds:
    total_seen += 1
    interpreter.set_tensor(input_index, img)
    interpreter.invoke()
    predictions = interpreter.get_tensor(output_index)
    if predictions == label.numpy():
      num_correct += 1
    if total_seen % 500 == 0:
      print("Accuracy after %i images: %f" %
            (total_seen, float(num_correct) / float(total_seen)))
  return float(num_correct) / float(total_seen)
# Create smaller dataset for demonstration purposes
mnist_ds_demo = mnist_ds.take(2000)
print(eval_model(interpreter, mnist_ds_demo))
Explanation: Evaluate the models
End of explanation
# NOTE: Colab runs on server CPUs. At the time of writing this, TensorFlow Lite
# doesn't have super optimized server CPU kernels. For this reason this may be
# slower than the above float interpreter. But for mobile CPUs, considerable
# speedup can be observed.
print(eval_model(interpreter_fp16, mnist_ds_demo))
Explanation: Repeat the evaluation on the float16 quantized model to obtain:
End of explanation
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