吴恩达deeplearning.ai class 1 week 4_2 : Deep Neural Network - Application v3

秒速五厘米 2022-05-16 02:48 161阅读 0赞

# Deep Neural Network for Image Classification: Application #

When you finish this, you will have finished the last programming assignment of Week 4, and also the last programming assignment of this course!

You will use use the functions you’d implemented in the previous assignment to build a deep network, and apply it to cat vs non-cat classification. Hopefully, you will see an improvement in accuracy relative to your previous logistic regression implementation.

**After this assignment you will be able to:**  
\- Build and apply a deep neural network to supervised learning.

Let’s get started!

## 1 - Packages ##

Let’s first import all the packages that you will need during this assignment.  
\- numpy is the fundamental package for scientific computing with Python.  
\- [matplotlib][] is a library to plot graphs in Python.  
\- [h5py][] is a common package to interact with a dataset that is stored on an H5 file.  
\- [PIL][] and [scipy][] are used here to test your model with your own picture at the end.  
\- dnn\_app\_utils provides the functions implemented in the “Building your Deep Neural Network: Step by Step” assignment to this notebook.  
\- np.random.seed(1) is used to keep all the random function calls consistent. It will help us grade your work.

import time
    import numpy as np
    import h5py
    import matplotlib.pyplot as plt
    import scipy
    from PIL import Image
    from scipy import ndimage
    from dnn_app_utils_v2 import *
    
    %matplotlib inline
    plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots
    plt.rcParams['image.interpolation'] = 'nearest'
    plt.rcParams['image.cmap'] = 'gray'
    
    %load_ext autoreload
    %autoreload 2
    
    np.random.seed(1)

The autoreload extension is already loaded. To reload it, use:
      %reload_ext autoreload

## 2 - Dataset ##

You will use the same “Cat vs non-Cat” dataset as in “Logistic Regression as a Neural Network” (Assignment 2). The model you had built had 70% test accuracy on classifying cats vs non-cats images. Hopefully, your new model will perform a better!

**Problem Statement**: You are given a dataset (“data.h5”) containing:  
\- a training set of m\_train images labelled as cat (1) or non-cat (0)  
\- a test set of m\_test images labelled as cat and non-cat  
\- each image is of shape (num\_px, num\_px, 3) where 3 is for the 3 channels (RGB).

Let’s get more familiar with the dataset. Load the data by running the cell below.

train_x_orig, train_y, test_x_orig, test_y, classes = load_data()

The following code will show you an image in the dataset. Feel free to change the index and re-run the cell multiple times to see other images.

# Example of a picture
    index = 10
    plt.imshow(train_x_orig[index])
    print ("y = " + str(train_y[0,index]) + ". It's a " + classes[train_y[0,index]].decode("utf-8") +  " picture.")

y = 0. It's a non-cat picture.

![png][]

# Explore your dataset 
    m_train = train_x_orig.shape[0]
    num_px = train_x_orig.shape[1]
    m_test = test_x_orig.shape[0]
    
    print ("Number of training examples: " + str(m_train))
    print ("Number of testing examples: " + str(m_test))
    print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
    print ("train_x_orig shape: " + str(train_x_orig.shape))
    print ("train_y shape: " + str(train_y.shape))
    print ("test_x_orig shape: " + str(test_x_orig.shape))
    print ("test_y shape: " + str(test_y.shape))

Number of training examples: 209
    Number of testing examples: 50
    Each image is of size: (64, 64, 3)
    train_x_orig shape: (209, 64, 64, 3)
    train_y shape: (1, 209)
    test_x_orig shape: (50, 64, 64, 3)
    test_y shape: (1, 50)

As usual, you reshape and standardize the images before feeding them to the network. The code is given in the cell below.

![<img src="images/imvectorkiank.png" style="width:450px;height:300px;">][img src_images_imvectorkiank.png_ style_width_450px_height_300px]

Figure 1: Image to vector conversion.

# Reshape the training and test examples 
    train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0], -1).T   # The "-1" makes reshape flatten the remaining dimensions
    test_x_flatten = test_x_orig.reshape(test_x_orig.shape[0], -1).T
    # print(train_x_flatten.shape)
    # Standardize data to have feature values between 0 and 1.
    train_x = train_x_flatten/255.
    test_x = test_x_flatten/255.
    
    print ("train_x's shape: " + str(train_x.shape))
    print ("test_x's shape: " + str(test_x.shape))

train_x's shape: (12288, 209)
    test_x's shape: (12288, 50)

12,288  12 , 288  equals 64×64×3  64 × 64 × 3  which is the size of one reshaped image vector.

## 3 - Architecture of your model ##

Now that you are familiar with the dataset, it is time to build a deep neural network to distinguish cat images from non-cat images.

You will build two different models:  
\- A 2-layer neural network  
\- An L-layer deep neural network

You will then compare the performance of these models, and also try out different values for *L*  L .

Let’s look at the two architectures.

### 3.1 - 2-layer neural network ###

![这里写图片描述][70]

Figure 2: 2-layer neural network.  
The model can be summarized as: ***INPUT -> LINEAR -> RELU -> LINEAR -> SIGMOID -> OUTPUT***.

Detailed Architecture of figure 2:  
\- The input is a (64,64,3) image which is flattened to a vector of size (12288,1) ( 12288 , 1 ).  
\- The corresponding vector: \[*x*0,*x*1,...,*x*12287\]*T*  \[ x 0 , x 1 , . . . , x 12287 \] T  is then multiplied by the weight matrix *W*\[1\]  W \[ 1 \]  of size (*n*\[1\],12288)  ( n \[ 1 \] , 12288 ) .  
\- You then add a bias term and take its relu to get the following vector: \[*a*\[1\]0,*a*\[1\]1,...,*a*\[1\]*n*\[1\]−1\]*T*  \[ a 0 \[ 1 \] , a 1 \[ 1 \] , . . . , a n \[ 1 \] − 1 \[ 1 \] \] T .  
\- You then repeat the same process.  
\- You multiply the resulting vector by *W*\[2\]  W \[ 2 \]  and add your intercept (bias).  
\- Finally, you take the sigmoid of the result. If it is greater than 0.5, you classify it to be a cat.

### 3.2 - L-layer deep neural network ###

It is hard to represent an L-layer deep neural network with the above representation. However, here is a simplified network representation:  
![这里写图片描述][70 1]

Figure 3: L-layer neural network.  
The model can be summarized as: ***\[LINEAR -> RELU\] ×  ×  (L-1) -> LINEAR -> SIGMOID***

Detailed Architecture of figure 3:  
\- The input is a (64,64,3) image which is flattened to a vector of size (12288,1).  
\- The corresponding vector: \[*x*0,*x*1,...,*x*12287\]*T*  \[ x 0 , x 1 , . . . , x 12287 \] T  is then multiplied by the weight matrix *W*\[1\]  W \[ 1 \]  and then you add the intercept *b*\[1\]  b \[ 1 \] . The result is called the linear unit.  
\- Next, you take the relu of the linear unit. This process could be repeated several times for each (*W*\[*l*\],*b*\[*l*\])  ( W \[ l \] , b \[ l \] )  depending on the model architecture.  
\- Finally, you take the sigmoid of the final linear unit. If it is greater than 0.5, you classify it to be a cat.

### 3.3 - General methodology ###

As usual you will follow the Deep Learning methodology to build the model:  
1. Initialize parameters / Define hyperparameters  
2. Loop for num\_iterations:  
a. Forward propagation  
b. Compute cost function  
c. Backward propagation  
d. Update parameters (using parameters, and grads from backprop)  
4. Use trained parameters to predict labels

Let’s now implement those two models!

## 4 - Two-layer neural network ##

**Question**: Use the helper functions you have implemented in the previous assignment to build a 2-layer neural network with the following structure: *LINEAR -> RELU -> LINEAR -> SIGMOID*. The functions you may need and their inputs are:

def initialize_parameters(n_x, n_h, n_y):
        ...
        return parameters 
    def linear_activation_forward(A_prev, W, b, activation):
        ...
        return A, cache
    def compute_cost(AL, Y):
        ...
        return cost
    def linear_activation_backward(dA, cache, activation):
        ...
        return dA_prev, dW, db
    def update_parameters(parameters, grads, learning_rate):
        ...
        return parameters

### CONSTANTS DEFINING THE MODEL ####
    n_x = 12288     # num_px * num_px * 3
    n_h = 7
    n_y = 1
    layers_dims = (n_x, n_h, n_y)

# GRADED FUNCTION: two_layer_model
    
    def two_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
        """ Implements a two-layer neural network: LINEAR->RELU->LINEAR->SIGMOID. Arguments: X -- input data, of shape (n_x, number of examples) Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples) layers_dims -- dimensions of the layers (n_x, n_h, n_y) num_iterations -- number of iterations of the optimization loop learning_rate -- learning rate of the gradient descent update rule print_cost -- If set to True, this will print the cost every 100 iterations Returns: parameters -- a dictionary containing W1, W2, b1, and b2 """
    
        np.random.seed(1)
        grads = {}
        costs = []                              # to keep track of the cost
        m = X.shape[1]                           # number of examples
        (n_x, n_h, n_y) = layers_dims
    
        # Initialize parameters dictionary, by calling one of the functions you'd previously implemented
        ### START CODE HERE ### (≈ 1 line of code)
        parameters = initialize_parameters(n_x, n_h, n_y)
        ### END CODE HERE ###
    
        # Get W1, b1, W2 and b2 from the dictionary parameters.
        W1 = parameters["W1"]
        b1 = parameters["b1"]
        W2 = parameters["W2"]
        b2 = parameters["b2"]
    
        # Loop (gradient descent)
    
        for i in range(0, num_iterations):
    
            # Forward propagation: LINEAR -> RELU -> LINEAR -> SIGMOID. Inputs: "X, W1, b1". Output: "A1, cache1, A2, cache2".
            ### START CODE HERE ### (≈ 2 lines of code)
            A1, cache1 = linear_activation_forward(X, W1, b1, activation = "relu")
            A2, cache2 = linear_activation_forward(A1, W2, b2, activation = "sigmoid")
            ### END CODE HERE ###
    
            # Compute cost
            ### START CODE HERE ### (≈ 1 line of code)
            cost = compute_cost(A2, Y)
            ### END CODE HERE ###
    
            # Initializing backward propagation
            dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
    
            # Backward propagation. Inputs: "dA2, cache2, cache1". Outputs: "dA1, dW2, db2; also dA0 (not used), dW1, db1".
            ### START CODE HERE ### (≈ 2 lines of code)
            dA1, dW2, db2 = linear_activation_backward(dA2, cache2, activation = "sigmoid")
            dA0, dW1, db1 = linear_activation_backward(dA1, cache1, activation = "relu")
            ### END CODE HERE ###
    
            # Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2
            grads['dW1'] = dW1
            grads['db1'] = db1
            grads['dW2'] = dW2
            grads['db2'] = db2
    
            # Update parameters.
            ### START CODE HERE ### (approx. 1 line of code)
            parameters = update_parameters(parameters, grads, learning_rate)
            ### END CODE HERE ###
    
            # Retrieve W1, b1, W2, b2 from parameters
            W1 = parameters["W1"]
            b1 = parameters["b1"]
            W2 = parameters["W2"]
            b2 = parameters["b2"]
    
            # Print the cost every 100 training example
            if print_cost and i % 100 == 0:
                print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
            if print_cost and i % 100 == 0:
                costs.append(cost)
    
        # plot the cost
    
        plt.plot(np.squeeze(costs))
        plt.ylabel('cost')
        plt.xlabel('iterations (per tens)')
        plt.title("Learning rate =" + str(learning_rate))
        plt.show()
    
        return parameters

Run the cell below to train your parameters. See if your model runs. The cost should be decreasing. It may take up to 5 minutes to run 2500 iterations. Check if the “Cost after iteration 0” matches the expected output below, if not click on the square (⬛) on the upper bar of the notebook to stop the cell and try to find your error.

parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True)

Cost after iteration 0: 0.693049735659989
    Cost after iteration 100: 0.6464320953428849
    Cost after iteration 200: 0.6325140647912678
    Cost after iteration 300: 0.6015024920354664
    Cost after iteration 400: 0.5601966311605747
    Cost after iteration 500: 0.5158304772764729
    Cost after iteration 600: 0.4754901313943325
    Cost after iteration 700: 0.4339163151225749
    Cost after iteration 800: 0.4007977536203887
    Cost after iteration 900: 0.35807050113237976
    Cost after iteration 1000: 0.33942815383664127
    Cost after iteration 1100: 0.3052753636196265
    Cost after iteration 1200: 0.2749137728213015
    Cost after iteration 1300: 0.24681768210614827
    Cost after iteration 1400: 0.1985073503746609
    Cost after iteration 1500: 0.17448318112556654
    Cost after iteration 1600: 0.17080762978096686
    Cost after iteration 1700: 0.11306524562164708
    Cost after iteration 1800: 0.0962942684593714
    Cost after iteration 1900: 0.08342617959726858
    Cost after iteration 2000: 0.07439078704319078
    Cost after iteration 2100: 0.06630748132267927
    Cost after iteration 2200: 0.059193295010381675
    Cost after iteration 2300: 0.05336140348560557
    Cost after iteration 2400: 0.04855478562877014

![这里写图片描述][70 2]

**Expected Output**:

<table> 
 <tbody> 
  <tr> 
   <td> **Cost after iteration 0**</td> 
   <td> 0.6930497356599888 </td> 
  </tr> 
  <tr> 
   <td> **Cost after iteration 100**</td> 
   <td> 0.6464320953428849 </td> 
  </tr> 
  <tr> 
   <td> **…**</td> 
   <td> … </td> 
  </tr> 
  <tr> 
   <td> **Cost after iteration 2400**</td> 
   <td> 0.048554785628770206 </td> 
  </tr> 
 </tbody> 
</table>

Good thing you built a vectorized implementation! Otherwise it might have taken 10 times longer to train this.

Now, you can use the trained parameters to classify images from the dataset. To see your predictions on the training and test sets, run the cell below.

predictions_train = predict(train_x, train_y, parameters)

Accuracy: 0.9999999999999998

**Expected Output**:

<table> 
 <tbody> 
  <tr> 
   <td> **Accuracy**</td> 
   <td> 1.0 </td> 
  </tr> 
 </tbody> 
</table>

predictions_test = predict(test_x, test_y, parameters)

Accuracy: 0.72

**Expected Output**:

<table> 
 <tbody> 
  <tr> 
   <td> **Accuracy**</td> 
   <td> 0.72 </td> 
  </tr> 
 </tbody> 
</table>

**Note**: You may notice that running the model on fewer iterations (say 1500) gives better accuracy on the test set. This is called “early stopping” and we will talk about it in the next course. Early stopping is a way to prevent overfitting.

Congratulations! It seems that your 2-layer neural network has better performance (72%) than the logistic regression implementation (70%, assignment week 2). Let’s see if you can do even better with an *L*  L \-layer model.

## 5 - L-layer Neural Network ##

**Question**: Use the helper functions you have implemented previously to build an *L* L\-layer neural network with the following structure: *\[LINEAR -> RELU\]×  × (L-1) -> LINEAR -> SIGMOID*. The functions you may need and their inputs are:

def initialize_parameters_deep(layer_dims):
        ...
        return parameters 
    def L_model_forward(X, parameters):
        ...
        return AL, caches
    def compute_cost(AL, Y):
        ...
        return cost
    def L_model_backward(AL, Y, caches):
        ...
        return grads
    def update_parameters(parameters, grads, learning_rate):
        ...
        return parameters

### CONSTANTS ###
    layers_dims = [12288, 20, 7, 5, 1] # 5-layer model

# GRADED FUNCTION: L_layer_model
    
    def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):#lr was 0.009
        """ Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID. Arguments: X -- data, numpy array of shape (number of examples, num_px * num_px * 3) Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples) layers_dims -- list containing the input size and each layer size, of length (number of layers + 1). learning_rate -- learning rate of the gradient descent update rule num_iterations -- number of iterations of the optimization loop print_cost -- if True, it prints the cost every 100 steps Returns: parameters -- parameters learnt by the model. They can then be used to predict. """
    
        np.random.seed(1)
        costs = []                         # keep track of cost
    
        # Parameters initialization.
        ### START CODE HERE ###
        parameters = initialize_parameters(n_x, n_h, n_y)
        ### END CODE HERE ###
    
        # Loop (gradient descent)
        for i in range(0, num_iterations):
    
            # Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.
            ### START CODE HERE ### (≈ 1 line of code)
            AL, caches = L_model_forward(X, parameters)
            ### END CODE HERE ###
    
            # Compute cost.
            ### START CODE HERE ### (≈ 1 line of code)
            cost = compute_cost(AL, Y)
            ### END CODE HERE ###
    
            # Backward propagation.
            ### START CODE HERE ### (≈ 1 line of code)
            grads = L_model_backward(AL, Y, caches)
            ### END CODE HERE ###
    
            # Update parameters.
            ### START CODE HERE ### (≈ 1 line of code)
            parameters = update_parameters(parameters, grads, learning_rate)
            ### END CODE HERE ###
    
            # Print the cost every 100 training example
            if print_cost and i % 100 == 0:
                print ("Cost after iteration %i: %f" %(i, cost))
            if print_cost and i % 100 == 0:
                costs.append(cost)
    
        # plot the cost
        plt.plot(np.squeeze(costs))
        plt.ylabel('cost')
        plt.xlabel('iterations (per tens)')
        plt.title("Learning rate =" + str(learning_rate))
        plt.show()
    
        return parameters

You will now train the model as a 5-layer neural network.

Run the cell below to train your model. The cost should decrease on every iteration. It may take up to 5 minutes to run 2500 iterations. Check if the “Cost after iteration 0” matches the expected output below, if not click on the square (⬛) on the upper bar of the notebook to stop the cell and try to find your error.

parameters = L_layer_model(train_x, train_y, layers_dims, num_iterations = 2500, print_cost = True)

Cost after iteration 0: 0.693050
    Cost after iteration 100: 0.646432
    Cost after iteration 200: 0.632514
    Cost after iteration 300: 0.601502
    Cost after iteration 400: 0.560197
    Cost after iteration 500: 0.515830
    Cost after iteration 600: 0.475490
    Cost after iteration 700: 0.433916
    Cost after iteration 800: 0.400798
    Cost after iteration 900: 0.358071
    Cost after iteration 1000: 0.339428
    Cost after iteration 1100: 0.305275
    Cost after iteration 1200: 0.274914
    Cost after iteration 1300: 0.246818
    Cost after iteration 1400: 0.198507
    Cost after iteration 1500: 0.174483
    Cost after iteration 1600: 0.170808
    Cost after iteration 1700: 0.113065
    Cost after iteration 1800: 0.096294
    Cost after iteration 1900: 0.083426
    Cost after iteration 2000: 0.074391
    Cost after iteration 2100: 0.066307
    Cost after iteration 2200: 0.059193
    Cost after iteration 2300: 0.053361
    Cost after iteration 2400: 0.048555

![这里写图片描述][70 3]

**Expected Output**:

<table> 
 <tbody> 
  <tr> 
   <td> **Cost after iteration 0**</td> 
   <td> 0.771749 </td> 
  </tr> 
  <tr> 
   <td> **Cost after iteration 100**</td> 
   <td> 0.672053 </td> 
  </tr> 
  <tr> 
   <td> **…**</td> 
   <td> … </td> 
  </tr> 
  <tr> 
   <td> **Cost after iteration 2400**</td> 
   <td> 0.092878 </td> 
  </tr> 
 </tbody> 
</table>

pred_train = predict(train_x, train_y, parameters)

Accuracy: 0.9999999999999998

<table> 
 <tbody> 
  <tr> 
   <td> **Train Accuracy** </td> 
   <td> 0.985645933014 </td> 
  </tr> 
 </tbody> 
</table>

pred_test = predict(test_x, test_y, parameters)

Accuracy: 0.72

**Expected Output**:

<table> 
 <tbody> 
  <tr> 
   <td> **Test Accuracy**</td> 
   <td> 0.8 </td> 
  </tr> 
 </tbody> 
</table>

Congrats! It seems that your 5-layer neural network has better performance (80%) than your 2-layer neural network (72%) on the same test set.

This is good performance for this task. Nice job!

Though in the next course on “Improving deep neural networks” you will learn how to obtain even higher accuracy by systematically searching for better hyperparameters (learning\_rate, layers\_dims, num\_iterations, and others you’ll also learn in the next course).

## 6) Results Analysis ##

First, let’s take a look at some images the L-layer model labeled incorrectly. This will show a few mislabeled images.

print_mislabeled_images(classes, test_x, test_y, pred_test)

![这里写图片描述][70 4]

**A few type of images the model tends to do poorly on include:**  
\- Cat body in an unusual position  
\- Cat appears against a background of a similar color  
\- Unusual cat color and species  
\- Camera Angle  
\- Brightness of the picture  
\- Scale variation (cat is very large or small in image)

## 7) Test with your own image (optional/ungraded exercise) ##

Congratulations on finishing this assignment. You can use your own image and see the output of your model. To do that:  
1. Click on “File” in the upper bar of this notebook, then click “Open” to go on your Coursera Hub.  
2. Add your image to this Jupyter Notebook’s directory, in the “images” folder  
3. Change your image’s name in the following code  
4. Run the code and check if the algorithm is right (1 = cat, 0 = non-cat)!

## START CODE HERE ##
    my_image = "my_image.jpg" # change this to the name of your image file 
    my_label_y = [1] # the true class of your image (1 -> cat, 0 -> non-cat)
    ## END CODE HERE ##
    
    fname = "images/" + my_image
    image = np.array(ndimage.imread(fname, flatten=False))
    my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((num_px*num_px*3,1))
    my_predicted_image = predict(my_image, my_label_y, parameters)
    
    plt.imshow(image)
    print ("y = " + str(np.squeeze(my_predicted_image)) + ", your L-layer model predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") +  "\" picture.")

C:\Users\LRT\Anaconda3\lib\site-packages\ipykernel_launcher.py:7: DeprecationWarning: `imread` is deprecated!
    `imread` is deprecated in SciPy 1.0.0.
    Use ``matplotlib.pyplot.imread`` instead.
      import sys
    C:\Users\LRT\Anaconda3\lib\site-packages\ipykernel_launcher.py:8: DeprecationWarning: `imresize` is deprecated!
    `imresize` is deprecated in SciPy 1.0.0, and will be removed in 1.2.0.
    Use ``skimage.transform.resize`` instead.
    
    
    
    Accuracy: 1.0
    y = 1.0, your L-layer model predicts a "cat" picture.

![这里写图片描述][70 5]

**References**:

*  for auto-reloading external module: [http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython][http_stackoverflow.com_questions_1907993_autoreload-of-modules-in-ipython]

[matplotlib]: http://matplotlib.org
[h5py]: http://www.h5py.org
[PIL]: http://www.pythonware.com/products/pil/
[scipy]: https://www.scipy.org/
[png]: /images/20220516/76d58689b9d84c448c33a08a1fc6b3cb.png
[img src_images_imvectorkiank.png_ style_width_450px_height_300px]: /images/20220516/94fc594990104738b6516794a949a87e.png
[70]: /images/20220516/8f6eb7d329e54992bbc3fff35b6c6d7e.png
[70 1]: /images/20220516/a61fadf23e394cd79e173a8f5a498ad4.png
[70 2]: /images/20220516/ce52fa8c3bb14ad8a591b168a66e46c2.png
[70 3]: /images/20220516/455ae4605b484b228e65271dd8264de6.png
[70 4]: /images/20220516/bffb8e6ba5d94894866ad49dbdfa5e03.png
[70 5]: /images/20220516/b9a8bf93fafa431abec7d5bc65650e8c.png
[http_stackoverflow.com_questions_1907993_autoreload-of-modules-in-ipython]: http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython