Deep-Learning-Course/LinearAlgebra.ipynb

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"\n",
"# Linear Algebra \n",
"\n",
"### Motivation\n",
"\n",
"Linear algebra deals with vectors, matrices and tensors. Before using machine learning to solve a problem, the first step is usually to represent the real-world input in the form of vectors/matrices of numbers. Following are the key reasons why linear algebra will be found everywhere throughout this course:\n",
"\n",
"**Compact Notation** Linear algebra provides a convenient language for compactly representing computations which may otherwise require more verbose expressions. Getting familiar with these notations will give you access to several books and literatures in the domain of machine learning and deep learning.\n",
"\n",
"**Standard Representation** In many important domains, data is naturally available in digital form. Speech, audio/video, images from social network to medical scans, etc. This kind of data can be readily be represented in vector or matrix forms, thus making vectors and matrices the most preferred input formats. Most machine learning libraries assume the input data structure to be matrices or tensors. \n",
"\n",
"**Fast Computation** Representing computations in the form of linear algebra equations enables underlying machine learning libraries to take advantage of fast matrix computation routines. Further more, frameworks like Tensorflow, can leverage distributed systems and GPUs to run matrix computations much faster. While what can be done with matrix operations can also be done using for loops, the speed difference between the two options is extremely significant.\n",
"\n",
"\n",
"```python\n",
"from sympy import *\n",
"import numpy as np\n",
"\n",
"r = r'$%s$'%latex(Matrix(np.arange(3).reshape(1,-1)))\n",
"c = r'$%s$'%latex(Matrix(np.arange(3).reshape(-1,1)))\n",
"m = r'$%s$'%latex(Matrix(np.arange(12).reshape(3,4)))\n",
"\n",
"```\n",
"\n",
"### Terms & Notations\n",
"\n",
"**Scalars** are 0 dimensional. They are just numbers. For example, height of a person, temperature, stock price etc. They are represented using lower case letters as $x,y,x_1,w_5$ etc.\n",
"\n",
"**Vectors** are 1 dimensional. Meaning, you can represent them as a collection of numbers. For example, to represent a color of pixel in an image, we will need three numbers, r, g and b. That is single color, $\\mathbf{c} = [r,g,b]$. Vectors are denoted by boldface, lower case letters, like $\\mathbf{x,y,z,w,v}$. While one dimensional array of numbers can be either row vector, {{r}} or column vector {{c}}, by convention, vector is taken to be a column vector.\n",
"\n",
"**Matrices** Matrices are 2 dimensional array of numbers. For example a matrix {{m}} is a $\\mathrm{3x4}$ array of numbers. That is, it has 3 rows and 4 columns. A gray scale image, for example, is represented as a matrix of size $\\mathrm{width\\ x\\ height}$. A collection of document vectors can be represented as a matrix.\n",
"\n",
"**Tensors** Higher dimensional arrays are called Tensors. They are generalisation of vectors and matrices. However, note that a whole lot of linear algebra computations like matrix multiplication, SVD, determinants etc. are not defined or are not used with Tensors. A color image is represented as $\\mathrm{w x h x c}$ array, which is a tensor. A training data may involve 1000s of such arrays in a single bigger tensor of dimensions $\\mathrm{N x w x h x c}$. In Tensorflow, the data is represented as generic tensors. We will see more of that soon.\n",
"\n",
"### Numpy\n",
"\n",
"Numpy is a python library for numerical computations, with rich support for linear algebra computations among lot of other things. It is essential to have a deep working expertise with numpy. Most numpy operations have equivalent operations in Tensorflow as well.\n",
"\n",
"\n",
"### Matrix operations in Action 1 - Slicing an Image to extract R,G,B channels\n",
"\n",
"Try the following code.\n",
"\n",
"```python\n",
"%matplotlib inline\n",
"import skimage.data as imgdata\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"astronaut = imgdata.astronaut()\n",
"\n",
"#Please take the opportunity to get familiar with matplotlib and numpy operations used in sample codes.\n",
"R = astronaut[:,:,0] #0th channel is R, 1st channel is G, and 2nd channel will be red\n",
"G = astronaut[:,:,1]\n",
"B = astronaut[:,:,2]\n",
"\n",
"plt.subplot(1,4,1) #We want to show the images as 1 row, 4 columns, the last number indicating that we are about to draw the first image\n",
"plt.imshow(astronaut)\n",
"plt.title('Color')\n",
"plt.axis('off') #When showing images, we don't need axes. They clutter the display with axis labels.\n",
"\n",
"plt.subplot(1,4,2) #Now we are setting the context to draw the R channel of the image\n",
"plt.imshow(R,'gray')\n",
"plt.title('Red Levels')\n",
"plt.axis('off')\n",
"\n",
"plt.subplot(1,4,3)\n",
"plt.imshow(G,'gray')\n",
"plt.title('Green Levels')\n",
"plt.axis('off')\n",
"\n",
"plt.subplot(1,4,4)\n",
"plt.imshow(B,'gray')\n",
"plt.title('Blue Levels')\n",
"plt.axis('off')\n",
"\n",
"plt.suptitle('Image and its Color Channels')\n",
"plt.show()\n",
"```\n",
"\n",
"### Matrix operations in Action 2 - Weighted average of pixels to convert a color image into grayscale\n",
"```python\n",
"%matplotlib inline\n",
"import skimage.data as imgdata\n",
"import matplotlib.pyplot as plt\n",
"\n",
"coffee_cup = imgdata.coffee()\n",
"\n",
"#Please take the opportunity to get familiar with matplotlib and numpy operations used in sample codes.\n",
"R = coffee_cup[:,:,0] #0th channel is R, 1st channel is G, and 2nd channel will be red\n",
"G = coffee_cup[:,:,1]\n",
"B = coffee_cup[:,:,2]\n",
"\n",
"I = 0.2125*R + 0.7154*G + 0.0721*B #Gray scale image is a weighted average of R, G and B values of the pixels. All pixels of I are simultaneously computed with this elementwise addition\n",
"\n",
"plt.subplot(1,2,1)\n",
"plt.imshow(coffee_cup)\n",
"plt.title('Color Image')\n",
"plt.axis('off')\n",
"\n",
"plt.subplot(1,2,2)\n",
"plt.imshow(I,'gray') #Even though I is a grayscale image, we have to set the colormap to \"gray\". Otherwise matplotlib will show the gray values using multicolor pallete, chosing color based on the intensity value\n",
"plt.title('Grayscale Image')\n",
"plt.axis('off')\n",
"\n",
"plt.show()\n",
"```\n",
"\n",
"### Matrix operations in Action 3 - Finding the mean of 1000 images in one numpy operation\n",
"Surprisingly, the mean face, which is an average of random faces appears to have very symmetric features. Try this code that averages 1000 different faces:\n",
"```python\n",
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import pickle\n",
"\n",
"faces = pickle.load(open('faces.pkl'))\n",
"\n",
"(num_of_images,height,width,clr_channels) = faces.shape #First dimension shows the number of face images we have.\n",
"\n",
"#Lets select 30 images randomly, and display them in 3x10 plot. You may want to understand this code\n",
"\n",
"idxList = np.random.randint(0,num_of_images,30) #Please check the documentation of np.random.randint for help. Type 'np.random.randint?' in iPython \n",
"\n",
"for i,idx in enumerate(idxList): #Check if sampled images change everytime you run the cell\n",
" plt.subplot(3,10,i+1)\n",
" plt.imshow(faces[idx])\n",
" plt.axis('off')\n",
"plt.suptitle('Sample Images from the Dataset')\n",
"plt.show()\n",
"\n",
"m = np.mean(faces,0)\n",
"m = m.astype(np.uint8) #Matplotlib expects the images to be of uint8 type, meaning RGB values should be integers in the range of 0 to 255. Else the image displayed looks like garbage\n",
"plt.imshow(m)\n",
"plt.axis('off')\n",
"plt.title('Mean of 1000 Faces - Surprising?')\n",
"plt.show()\n",
"```\n",
"\n",
"\n",
"### Matrix operations in Action 4 - Datatype checking, Casting, Counting etc.\n",
"```python\n",
"import numpy as np\n",
"\n",
"A = np.random.rand(3,6)\n",
"print \"Shape of A:\", A.shape #3x6\n",
"print\n",
"print \"Uniform Random Numbers\"\n",
"print A #array of 3 rows, 6 columns, uniform random numbers\n",
"print\n",
"print \"Sometimes it is clumsy to inspect arrays, with so many decimal places printed on the screen\"\n",
"print \"We can control the numpy printing options as below\"\n",
"np.set_printoptions(precision=2)\n",
"print A\n",
"print \"Pleas note! It doesn't round the numbers, but only printing is controlled!\"\n",
"print A.dtype #64 bit floating point number\n",
"\n",
"#How to generate an array of random integers between 5 to 20, of size 5x10?\n",
"\n",
"#Method 1. We can use uniform random numbers between 0 to 1 and scale them to the required range.\n",
"#Then we can convert the scaled array to integers\n",
"\n",
"A = np.random.rand(5,10) #Uniform random numbers between 0 to 1, of size 5x10\n",
"A = A*(20-5) + 5 #Scale and shift the values to fit in the range of 5 to 20\n",
"print\n",
"print \"Values are now between 5 to 20, but floating point.\"\n",
"print \"Note that A is still printed upto 2 decimal places. np.set_printoptions is a global setting.\"\n",
"print A #A is in the required range, but it is of type floating point\n",
"print \"Datatype of A is \", A.dtype\n",
"print \"Casting A to 16 bit integer values\"\n",
"A = A.astype(np.int16)\n",
"print A #Now A is the desired output\n",
"print A.dtype #This should be np.int16\n",
"print\n",
"print \"Are they really in 5 to 20 range?\"\n",
"print \"The unique values in A are:\", np.unique(A) #This will tell us what are the unique values present in the array\n",
"print \"Are they really unform? We can count how many times each number is appearing. That should be roughly equal.\"\n",
"counts = np.bincount(A.flatten()) #np.bincount takes only one dimension array. A.flatten() will flatten n-dimension array into a 1d array\n",
"print \"counts will be a 1d array of size np.max(A). counts[i] tells us how many times the number i has appeared in the input\"\n",
"print counts[5:] #We are interested in counts of numbers between 5 to 20 only.\n",
"print \"We can plot the counts and check. The numbers are not roughly equal! Why?\"\n",
"print \"Change the code to check if it helps if you generate much bigger sample.\"\n",
"```\n",
"\n",
"### Matrix operations in Action 5 - Zeros, Ones, Linspace,Elementwise computations\n",
"\n",
"```python\n",
"import numpy as np\n",
"\n",
"A = np.zeros(shape=(5,5))\n",
"print A\n",
"print\n",
"B = np.ones((3,5))\n",
"print B\n",
"print\n",
"x = np.linspace(-2*np.pi,2*np.pi,100) #x is a linearly spaced, 100 numbers between -2*pi to +2*pi\n",
"y = np.sin(x) #All scalar math functions in numpy apply to every element in the input, element wise. No need for for loop to call sin function on every value.\n",
"print 'x values:',x[:10] #Show only first 10 values.\n",
"print 'y values:',y[:10]\n",
"print 'You can zip x and y values together: '\n",
"points = zip(x,y) #Useful python function to combine corresponding elements in two 1d arrays into list of tuples.\n",
"print points[:10] #Note, the values are now printed beyond 2 decimals. Can you reason why?\n",
"print\n",
"print \"Plot:\"\n",
"plt.plot(x,y)\n",
"plt.show()\n",
"```\n",
"\n",
"\n",
"\n",
"### Matrix operations in Action 6- Broadcasting\n",
"\n",
"In math, two matrices can be added only if they both are of same dimension. Numpy does allow adding matrices of different dimensions under certain conditions. This is called broadcasting. It is important to understand how broadcasting in numpy works, one to avoid unintended effects causing bugs, two, to achieve computational efficiency. \n",
"\n",
"You can learn about broadcasting works on [this page](http://scipy.github.io/old-wiki/pages/EricsBroadcastingDoc)\n",
"\n",
"Run the following code to see the benefits of broadcasting.\n",
"\n",
"```python\n",
"import numpy as np\n",
"import time\n",
"\n",
"A = np.random.rand(10000,100) #10000x100 array of random numbers\n",
"B = np.ones((1,100))*10 #B is a a 1x100 array of 10s\n",
"\n",
"#Suppose we want to add B to every row of A.\n",
"#In matrix algebra, A+B is forbidden. We need to replicate B 10000 times and make an array of size compatible to A, and then add\n",
"\n",
"#Lets see how fast this code is. We will run this 1000 times and average the time.\n",
"start = time.time()\n",
"for i in range(1000):\n",
" B1 = np.repeat(B,10000,axis=0) #Repeat 10000 times along rows (axis=0)\n",
" S = A+B1 #desired output\n",
"stop = time.time()\n",
"\n",
"total_time1 = stop-start\n",
"print \"Average execution time to compute the desired output: \", total_time1/1000\n",
"\n",
"print \"With Numpy broadcasting, we save memory and time.\"\n",
"start = time.time()\n",
"for i in range(1000):\n",
" S = A+B #Numpy will automatically broadcast the values in a compatible way. Important to understand the rules to avoid unintended bugs\n",
"stop = time.time()\n",
"total_time2 = stop-start\n",
"print \"Total time taken for 1000 executions of A+B with broadcasting is: \",total_time2/100\n",
"\n",
"print \"Broadcasting is %s times faster for this case.\"%(total_time1/total_time2)\n",
"```\n",
"\n",
"### Matrix operations in Action 7 - Boolean Indexing \n",
"```python\n",
"%matplotlib inline\n",
"import skimage.data as imgdata\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"horse = imgdata.horse()\n",
"horse = horse[:,:,:3] #Drop the A channel\n",
"#This is a RGBA image. Convert it into Binary\n",
"horse = np.max(horse,2)\n",
"#Horse is a binary image, with values 0 an 1. You can inspect the values of the image\n",
"print 'Min and Max values in the horse image'\n",
"np.min(horse),np.max(horse)\n",
"#Let's make the horse red and background black, using boolean indexing to operate on the image\n",
"I,J = np.nonzero(horse==0) #Boolean indexing finds all (i,j)s in the image where the pixels are black(0), giving us the indices of horse pixels\n",
"#We will make R, G, and B panels separately and put them together to make color image\n",
"R = np.zeros_like(horse) #Make zeros of same type and shape as the horse array\n",
"R[I,J] = 255 #Red panel we have set\n",
"output = np.zeros((horse.shape[0],horse.shape[1],3),dtype=horse.dtype)\n",
"output[:,:,0] = R\n",
"#G and B channels are zeros. So we get a red horse and black background.\n",
"\n",
"plt.subplot(1,2,1)\n",
"plt.title('Input')\n",
"plt.axis('off')\n",
"plt.imshow(horse,'gray')\n",
"\n",
"\n",
"plt.subplot(1,2,2)\n",
"plt.title('output')\n",
"plt.axis('off')\n",
"plt.imshow(output,'gray')\n",
"\n",
"plt.show()\n",
"```\n",
"\n",
"### Matrix operations in Action 8 - Dot Product, Least Squares Error\n",
"```python\n",
"import numpy as np\n",
"from sklearn.datasets import load_digits\n",
"\n",
"digits = load_digits()\n",
"images = digits['images']\n",
"num_images = images.shape[0]\n",
"\n",
"print \"Shape of images array is: \", images.shape\n",
"\n",
"#The images array contains N number of 8x8 binary digit images, this is a 3 dimensional array\n",
"#We will flatten 8x8 images into 64 dimensional vector for each image, stacked as image vectors\n",
"image_vectors = images.reshape(-1,64)\n",
"#image_vectors will be of shape N x 64\n",
"\n",
"rand_idx = np.random.randint(0,num_images,1)[0]\n",
"sample = images[rand_idx,:].flatten() #Radomly select a sample image\n",
"\n",
"#Let's take a random digit image, and find top 30 digits from the images that are closest to this.\n",
"#To measure closeness, we will use euclidean distance.\n",
"images_diff = image_vectors - sample #Check the shapes of image_vectors and sample, and understand how broadcasting is at work here\n",
"distances = np.sum(images_diff**2,1) #Elementwise square all the differeneces and add them across columns to get distances\n",
"\n",
"#Find indices of smallest distances. We can use argsort, which gives you sorted indices.\n",
"sorted_idxes = np.argsort(distances)\n",
"#these indices can be used to select the corresponding images from the original images \n",
"\n",
"nearest_images = images[sorted_idxes,:,:][:20] #Last line truncates selects the nearest 20\n",
"\n",
"plt.subplot(5,5,1) #1 row for the input image, and 5 rows for 50 output images\n",
"plt.imshow(images[rand_idx],'gray',interpolation='nearest')\n",
"plt.axis('off')\n",
"plt.title('Input Sample')\n",
"\n",
"loc = 6 #Start from the second row\n",
"for i,img in enumerate(nearest_images):\n",
" plt.subplot(5,5,loc+i)\n",
" plt.imshow(img,'gray',interpolation='nearest')\n",
" plt.title('d = %0.0f'%distances[sorted_idxes[i]]) #Make sure you understand how we are reading the corresponding distance\n",
" plt.axis('off')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()\n",
"\n",
"```"
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"source": [
"from sympy import *\n",
"import numpy as np\n",
"\n",
"r = r'$%s$'%latex(Matrix(np.arange(3).reshape(1,-1)))\n",
"c = r'$%s$'%latex(Matrix(np.arange(3).reshape(-1,1)))\n",
"m = r'$%s$'%latex(Matrix(np.arange(12).reshape(3,4)))"
]
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yX3nllUycOJFly5aRTqfZsWMHixcvprW1FaUUqVQKz/P43e9+Rzab5ayzzqKh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uwYM2bM4Ac/+AEfffQRJpOJlStX8vDDD0uiZGVlJatWreK8885jy5YtbNy4kebmZhRFIT8/n+bm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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbec020110>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import skimage.data as imgdata\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"astronaut = imgdata.astronaut()\n",
"\n",
"#Please take the opportunity to get familiar with matplotlib and numpy operations used in sample codes.\n",
"R = astronaut[:,:,0] #0th channel is R, 1st channel is G, and 2nd channel will be red\n",
"G = astronaut[:,:,1]\n",
"B = astronaut[:,:,2]\n",
"\n",
"plt.subplot(1,4,1) #We want to show the images as 1 row, 4 columns, the last number indicating that we are about to draw the first image\n",
"plt.imshow(astronaut)\n",
"plt.title('Color')\n",
"plt.axis('off') #When showing images, we don't need axes. They clutter the display with axis labels.\n",
"\n",
"plt.subplot(1,4,2) #Now we are setting the context to draw the R channel of the image\n",
"plt.imshow(R,'gray')\n",
"plt.title('Red Levels')\n",
"plt.axis('off')\n",
"\n",
"plt.subplot(1,4,3)\n",
"plt.imshow(G,'gray')\n",
"plt.title('Green Levels')\n",
"plt.axis('off')\n",
"\n",
"plt.subplot(1,4,4)\n",
"plt.imshow(B,'gray')\n",
"plt.title('Blue Levels')\n",
"plt.axis('off')\n",
"\n",
"plt.suptitle('Image and its Color Channels')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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nlzSbTQ4ODhgOhzWGvrGxUUMtaZpyfHzMfffdx+HhIScnJ7V1WuH7KysrZFnG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05z7iTHvns/X/qLrzMjJA4SR0GIk1XzN7x2nMW1ZYw2hM0uH5nf4OFqlapKkFKlOwspiIMIz5Gp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\nCSHwhaCCoFZpU8xl8eoV5OZb8cuLnHjgj/nhH/4+t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DdPALxzhpIQkpKP/4e/IxKbYm6l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\nHsJlkCiR64EAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbf453b190>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import skimage.data as imgdata\n",
"import matplotlib.pyplot as plt\n",
"\n",
"coffee_cup = imgdata.coffee()\n",
"\n",
"#Please take the opportunity to get familiar with matplotlib and numpy operations used in sample codes.\n",
"R = coffee_cup[:,:,0] #0th channel is R, 1st channel is G, and 2nd channel will be red\n",
"G = coffee_cup[:,:,1]\n",
"B = coffee_cup[:,:,2]\n",
"\n",
"I = 0.2125*R + 0.7154*G + 0.0721*B #Gray scale image is a weighted average of R, G and B values of the pixels. All pixels of I are simultaneously computed with this elementwise addition\n",
"\n",
"plt.subplot(1,2,1)\n",
"plt.imshow(coffee_cup)\n",
"plt.title('Color Image')\n",
"plt.axis('off')\n",
"\n",
"plt.subplot(1,2,2)\n",
"plt.imshow(I,'gray') #Even though I is a grayscale image, we have to set the colormap to \"gray\". Otherwise matplotlib will show the gray values using multicolor pallete, chosing color based on the intensity value\n",
"plt.title('Grayscale Image')\n",
"plt.axis('off')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Y0Hms9vz580S9NpZJCDyXZJAPGBfXB8wvLNPrJ+zef4hD1x8mSmIuXVpkfX2N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\nESytre1peqRMTSJTXNfl1tIG8xsbnL/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eeeQRfN/HtASu63Lx4kWEEDz00EM7zUSWZWEI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0x2tyknhwibwVGknGUa30rIM3SZklcljnC4tLVcUm2THIoKW2kKbchKQ5pXZLleZMzCouRi2iNJ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\nzc/E0U9OxhiGXvsUxVM2NtfQNEmahigKpKCGU1QO1M6XSoHp6JDVdOWP7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Pjw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\nvx/sN8GaLmQiAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbec022710>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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ikxdUsuD32h5Pids+b1v/B9JrsoSJ+eXZNUnGvLK6n8ULQ198ITpEDV+IDjnf2Xn1KoZV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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbbe7b5f50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import pickle\n",
"\n",
"faces = pickle.load(open('faces.pkl'))\n",
"\n",
"(num_of_images,height,width,clr_channels) = faces.shape #First dimension shows the number of face images we have.\n",
"\n",
"#Lets select 30 images randomly, and display them in 3x10 plot. You may want to understand this code\n",
"\n",
"idxList = np.random.randint(0,num_of_images,30) #Please check the documentation of np.random.randint for help. Type 'np.random.randint?' in iPython \n",
"\n",
"for i,idx in enumerate(idxList): #Check if sampled images change everytime you run the cell\n",
" plt.subplot(3,10,i+1)\n",
" plt.imshow(faces[idx])\n",
" plt.axis('off')\n",
"plt.suptitle('Sample Images from the Dataset')\n",
"plt.show()\n",
"\n",
"m = np.mean(faces,0)\n",
"m = m.astype(np.uint8) #Matplotlib expects the images to be of uint8 type, meaning RGB values should be integers in the range of 0 to 255. Else the image displayed looks like garbage\n",
"plt.imshow(m)\n",
"plt.axis('off')\n",
"plt.title('Mean of 1000 Faces - Surprising?')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shape of A: (3, 6)\n",
"\n",
"Uniform Random Numbers\n",
"[[ 0.53026842 0.85568589 0.59917602 0.13160372 0.82012804 0.36597499]\n",
" [ 0.68449891 0.25387986 0.55686847 0.55368587 0.85834321 0.48071346]\n",
" [ 0.26787755 0.25289669 0.21857296 0.83156644 0.56501215 0.57388012]]\n",
"\n",
"Sometimes it is clumsy to inspect arrays, with so many decimal places printed on the screen\n",
"We can control the numpy printing options as below\n",
"[[ 0.53 0.86 0.6 0.13 0.82 0.37]\n",
" [ 0.68 0.25 0.56 0.55 0.86 0.48]\n",
" [ 0.27 0.25 0.22 0.83 0.57 0.57]]\n",
"Pleas note! It doesn't round the numbers, but only printing is controlled!\n",
"float64\n",
"\n",
"Values are now between 5 to 20, but floating point.\n",
"Note that A is still printed upto 2 decimal places. np.set_printoptions is a global setting.\n",
"[[ 7.81 18.93 6.21 ..., 19.72 17.44 18.95]\n",
" [ 11.42 18.6 14.93 ..., 7.79 8.07 10.11]\n",
" [ 16.4 17.86 14.55 ..., 18.49 15.98 14.67]\n",
" ..., \n",
" [ 18.67 6.67 8.71 ..., 10.98 10.91 13.49]\n",
" [ 15.5 8.98 18.79 ..., 8.52 10.42 16.95]\n",
" [ 17.4 10.77 16.5 ..., 9.47 10.77 18.58]]\n",
"Datatype of A is float64\n",
"Casting A to 16 bit integer values\n",
"[[ 7 18 6 ..., 19 17 18]\n",
" [11 18 14 ..., 7 8 10]\n",
" [16 17 14 ..., 18 15 14]\n",
" ..., \n",
" [18 6 8 ..., 10 10 13]\n",
" [15 8 18 ..., 8 10 16]\n",
" [17 10 16 ..., 9 10 18]]\n",
"int16\n",
"\n",
"Are they really in 5 to 20 range?\n",
"The unique values in A are: [ 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19]\n",
"Are they really unform? We can count how many times each number is appearing. That should be roughly equal.\n",
"counts will be a 1d array of size np.max(A). counts[i] tells us how many times the number i has appeared in the input\n",
"[33144 33358 33020 33266 33069 33198 33593 33313 33538 33421 33617 33221\n",
" 33235 33378 33629]\n",
"We can plot the counts and check. The numbers are not roughly equal! Why?\n",
"Change the code to check if it helps if you generate much bigger sample.\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"A = np.random.rand(3,6)\n",
"print \"Shape of A:\", A.shape #3x6\n",
"print\n",
"print \"Uniform Random Numbers\"\n",
"print A #array of 3 rows, 6 columns, uniform random numbers\n",
"print\n",
"print \"Sometimes it is clumsy to inspect arrays, with so many decimal places printed on the screen\"\n",
"print \"We can control the numpy printing options as below\"\n",
"np.set_printoptions(precision=2)\n",
"print A\n",
"print \"Pleas note! It doesn't round the numbers, but only printing is controlled!\"\n",
"print A.dtype #64 bit floating point number\n",
"\n",
"#How to generate an array of random integers between 5 to 20, of size 5x10?\n",
"\n",
"#Method 1. We can use uniform random numbers between 0 to 1 and scale them to the required range.\n",
"#Then we can convert the scaled array to integers\n",
"\n",
"A = np.random.rand(500,1000) #Uniform random numbers between 0 to 1, of size 5x10\n",
"A = A*(20-5) + 5 #Scale and shift the values to fit in the range of 5 to 20\n",
"print\n",
"print \"Values are now between 5 to 20, but floating point.\"\n",
"print \"Note that A is still printed upto 2 decimal places. np.set_printoptions is a global setting.\"\n",
"print A #A is in the required range, but it is of type floating point\n",
"print \"Datatype of A is \", A.dtype\n",
"print \"Casting A to 16 bit integer values\"\n",
"A = A.astype(np.int16)\n",
"print A #Now A is the desired output\n",
"print A.dtype #This should be np.int16\n",
"print\n",
"print \"Are they really in 5 to 20 range?\"\n",
"print \"The unique values in A are:\", np.unique(A) #This will tell us what are the unique values present in the array\n",
"print \"Are they really unform? We can count how many times each number is appearing. That should be roughly equal.\"\n",
"counts = np.bincount(A.flatten()) #np.bincount takes only one dimension array. A.flatten() will flatten n-dimension array into a 1d array\n",
"print \"counts will be a 1d array of size np.max(A). counts[i] tells us how many times the number i has appeared in the input\"\n",
"print counts[5:] #We are interested in counts of numbers between 5 to 20 only.\n",
"print \"We can plot the counts and check. The numbers are not roughly equal! Why?\"\n",
"print \"Change the code to check if it helps if you generate much bigger sample.\"\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 0.]]\n",
"\n",
"[[ 1. 1. 1. 1. 1.]\n",
" [ 1. 1. 1. 1. 1.]\n",
" [ 1. 1. 1. 1. 1.]]\n",
"\n",
"x values: [-6.28 -6.16 -6.03 -5.9 -5.78 -5.65 -5.52 -5.39 -5.27 -5.14]\n",
"y values: [ 2.45e-16 1.27e-01 2.51e-01 3.72e-01 4.86e-01 5.93e-01\n",
" 6.90e-01 7.76e-01 8.50e-01 9.10e-01]\n",
"You can zip x and y values together: \n",
"[(-6.2831853071795862, 2.4492935982947064e-16), (-6.1562522706709073, 0.12659245357374993), (-6.0293192341622293, 0.25114798718107939), (-5.9023861976535503, 0.37166245566032807), (-5.7754531611448723, 0.48619673610046882), (-5.6485201246361934, 0.59290792905464096), (-5.5215870881275153, 0.69007901148211204), (-5.3946540516188364, 0.77614646429175715), (-5.2677210151101583, 0.84972542994951439), (-5.1407879786014794, 0.90963199535451855)]\n",
"\n",
"Plot:\n"
]
},
{
"data": {
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+Xt74hWwE5ox4nOveNu4+IhIBJAPtUzwWAGPMk8aYMmNMWUZGxjUF+u0PLuGJ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\nBqWUUqP8/5G0Rxu3flqXAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbec08d750>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"\n",
"A = np.zeros(shape=(5,5))\n",
"print A\n",
"print\n",
"B = np.ones((3,5))\n",
"print B\n",
"print\n",
"x = np.linspace(-2*np.pi,2*np.pi,100) #x is a linearly spaced, 100 numbers between -2*pi to +2*pi\n",
"y = np.sin(x) #All scalar math functions in numpy apply to every element in the input, element wise. No need for for loop to call sin function on every value.\n",
"print 'x values:',x[:10] #Show only first 10 values.\n",
"print 'y values:',y[:10]\n",
"print 'You can zip x and y values together: '\n",
"points = zip(x,y) #Useful python function to combine corresponding elements in two 1d arrays into list of tuples.\n",
"print points[:10] #Note, the values are now printed beyond 2 decimals. Can you reason why?\n",
"print\n",
"print \"Plot:\"\n",
"plt.plot(x,y)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average execution time to compute the desired output: 0.0118508088589\n",
"With Numpy broadcasting, we save memory and time.\n",
"Total time taken for 1000 executions of A+B with broadcasting is: 0.00538574504852\n",
"Broadcasting is 2.20040286945 times faster for this case.\n"
]
}
],
"source": [
"import numpy as np\n",
"import time\n",
"\n",
"A = np.random.rand(10000,100) #10000x100 array of random numbers\n",
"B = np.ones((1,100))*10 #B is a a 1x100 array of 10s\n",
"\n",
"#Suppose we want to add B to every row of A.\n",
"#In matrix algebra, A+B is forbidden. We need to replicate B 10000 times and make an array of size compatible to A, and then add\n",
"\n",
"#Lets see how fast this code is. We will run this 1000 times and average the time.\n",
"start = time.time()\n",
"for i in range(1000):\n",
" B1 = np.repeat(B,10000,axis=0) #Repeat 10000 times along rows (axis=0)\n",
" S = A+B1 #desired output\n",
"stop = time.time()\n",
"\n",
"total_time1 = stop-start\n",
"print \"Average execution time to compute the desired output: \", total_time1/1000\n",
"\n",
"print \"With Numpy broadcasting, we save memory and time.\"\n",
"start = time.time()\n",
"for i in range(1000):\n",
" S = A+B #Numpy will automatically broadcast the values in a compatible way. Important to understand the rules to avoid unintended bugs\n",
"stop = time.time()\n",
"total_time2 = stop-start\n",
"print \"Total time taken for 1000 executions of A+B with broadcasting is: \",total_time2/1000\n",
"\n",
"print \"Broadcasting is %s times faster for this case.\"%(total_time1/total_time2)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min and Max values in the horse image\n",
"0 1\n"
]
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x7efbbe76d5d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import skimage.data as imgdata\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"horse = imgdata.horse().astype(np.uint8)\n",
"# horse = horse[:,:,:3] #Drop the A channel\n",
"#This is a RGBA image. Convert it into Binary\n",
"# horse = np.max(horse,2)\n",
"#Horse is a binary image, with values 0 an 1. You can inspect the values of the image\n",
"print 'Min and Max values in the horse image'\n",
"print np.min(horse),np.max(horse)\n",
"#Let's make the horse red and background black, using boolean indexing to operate on the image\n",
"I,J = np.nonzero(horse==0) #Boolean indexing finds all (i,j)s in the image where the pixels are black(0), giving us the indices of horse pixels\n",
"#We will make R, G, and B panels separately and put them together to make color image\n",
"# R = np.zeros_like(horse) #Make zeros of same type and shape as the horse array\n",
"# R[I,J] = 255#ed panel we have set\n",
"# R.shape\n",
"# B = np.zeros_like(horse) #Make zeros of same type and shape as the horse array\n",
"# B[I,J] = 128 #Red panel we have set\n",
"colored_horse = np.ones((horse.shape[0],horse.shape[1],3),dtype=horse.dtype)*255\n",
"colored_horse[I,J] = np.array([127,255,128])#ed panel we have set\n",
"output = colored_horse\n",
"# output[:,:,0] = R\n",
"#G and B channels are zeros. So we get a red horse and black background.\n",
"\n",
"plt.subplot(1,2,1)\n",
"plt.title('Input')\n",
"plt.axis('off')\n",
"plt.imshow(horse,'gray')\n",
"\n",
"\n",
"plt.subplot(1,2,2)\n",
"plt.title('output')\n",
"plt.axis('off')\n",
"plt.imshow(output,'gray')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shape of images array is: (1797, 8, 8)\n"
]
},
{
"data": {
"image/png": 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8JL1W0h2SpiU9JGlY0prS/KskPSDpUUl3Snpjw/pvlHSXpF2SviTpmPTvon0sIM9dDY+n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\nfMzMLDkXHzMzS87Fx8zMknPxMTOz5P4/4BYvIK6FtE8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbbe8673d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from sklearn.datasets import load_digits\n",
"\n",
"digits = load_digits()\n",
"images = digits['images']\n",
"num_images = images.shape[0]\n",
"\n",
"print \"Shape of images array is: \", images.shape\n",
"\n",
"#The images array contains N number of 8x8 binary digit images, this is a 3 dimensional array\n",
"#We will flatten 8x8 images into 64 dimensional vector for each image, stacked as image vectors\n",
"image_vectors = images.reshape(-1,64)\n",
"#image_vectors will be of shape N x 64\n",
"\n",
"rand_idx = np.random.randint(0,num_images,1)[0]\n",
"sample = images[rand_idx,:].flatten() #Radomly select a sample image\n",
"\n",
"#Let's take a random digit image, and find top 30 digits from the images that are closest to this.\n",
"#To measure closeness, we will use euclidean distance.\n",
"images_diff = image_vectors - sample #Check the shapes of image_vectors and sample, and understand how broadcasting is at work here\n",
"distances = np.sum(images_diff**2,1) #Elementwise square all the differeneces and add them across columns to get distances\n",
"\n",
"#Find indices of smallest distances. We can use argsort, which gives you sorted indices.\n",
"sorted_idxes = np.argsort(distances)\n",
"#these indices can be used to select the corresponding images from the original images \n",
"\n",
"nearest_images = images[sorted_idxes,:,:][:20] #Last line truncates selects the nearest 20\n",
"\n",
"plt.subplot(5,5,1) #1 row for the input image, and 5 rows for 50 output images\n",
"plt.imshow(images[rand_idx],'gray',interpolation='nearest')\n",
"plt.axis('off')\n",
"plt.title('Input Sample')\n",
"\n",
"loc = 6 #Start from the second row\n",
"for i,img in enumerate(nearest_images):\n",
" plt.subplot(5,5,loc+i)\n",
" plt.imshow(img,'gray',interpolation='nearest')\n",
" plt.title('d = %0.0f'%distances[sorted_idxes[i]]) #Make sure you understand how we are reading the corresponding distance\n",
" plt.axis('off')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1000, 60, 60)\n"
]
},
{
"data": {
"text/plain": [
"(-0.5, 59.5, 59.5, -0.5)"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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7lF1ToVJRhnZlZdsuK4m2eH0fx01P79j3kdWrHZ/PqGjId6tiybFq4JYaDvie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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbbc94a950>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import pickle\n",
"import matplotlib.pyplot as plt\n",
"\n",
"faces = pickle.load(open('faces.pkl'))\n",
"\n",
"(num_of_images,height,width,clr_channels) = faces.shape \n",
"\n",
"#grayscaler = lambda x : 0.2125*x[:,:,:,0] + 0.7154*x[:,:,:,1] + 0.0721*x[:,:,:,2]\n",
"# face_channels = faces.reshape(num_of_images*height*width,clr_channels)\n",
"#gray_faces = grayscaler(faces)#.reshape(num_of_images,height,width)\n",
"gray_faces = np.dot(faces,np.array([0.2125,0.7154,0.0721]))\n",
"print gray_faces.shape\n",
"plt.subplot(1,2,1)\n",
"plt.imshow(gray_faces[np.random.randint(num_of_images)],'gray')\n",
"plt.title('Grayscale Image')\n",
"plt.axis('off')"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shape of images array is: (1797, 8, 8)\n",
"[773]\n"
]
},
{
"data": {
"image/png": 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zE96xpWUDZFfy5WmgtPyD+bbb8v8f5zQ7t1bNE1iS5/cY2X2yYnp3vrxC1nPa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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbbc865f90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from sklearn.datasets import load_digits\n",
"\n",
"digits = load_digits()\n",
"images = digits['images']\n",
"num_images = images.shape[0]\n",
"\n",
"print \"Shape of images array is: \", images.shape\n",
"\n",
"#The images array contains N number of 8x8 binary digit images, this is a 3 dimensional array\n",
"#We will flatten 8x8 images into 64 dimensional vector for each image, stacked as image vectors\n",
"image_vectors = images.reshape(-1,64)\n",
"#image_vectors will be of shape N x 64\n",
"\n",
"rand_idx = np.random.randint(0,num_images,1)[0]\n",
"print(np.random.randint(0,num_images,1))\n",
"sample = images[rand_idx,:].flatten() #Radomly select a sample image\n",
"samples = images[np.random.choice(images.shape[0],5)].shape\n",
"\n",
"#Let's take a random digit image, and find top 30 digits from the images that are closest to this.\n",
"#To measure closeness, we will use euclidean distance.\n",
"images_diff = image_vectors - sample #Check the shapes of image_vectors and sample, and understand how broadcasting is at work here\n",
"distances = np.sum(images_diff**2,1) #Elementwise square all the differeneces and add them across columns to get distances\n",
"\n",
"#Find indices of smallest distances. We can use argsort, which gives you sorted indices.\n",
"sorted_idxes = np.argsort(distances)\n",
"#these indices can be used to select the corresponding images from the original images \n",
"\n",
"nearest_images = images[sorted_idxes,:,:][:20] #Last line truncates selects the nearest 20\n",
"\n",
"plt.subplot(5,5,1) #1 row for the input image, and 5 rows for 50 output images\n",
"plt.imshow(images[rand_idx],'gray',interpolation='nearest')\n",
"plt.axis('off')\n",
"plt.title('Input Sample')\n",
"\n",
"loc = 6 #Start from the second row\n",
"for i,img in enumerate(nearest_images):\n",
" plt.subplot(5,5,loc+i)\n",
" plt.imshow(img,'gray',interpolation='nearest')\n",
" plt.title('d = %0.0f'%distances[sorted_idxes[i]]) #Make sure you understand how we are reading the corresponding distance\n",
" plt.axis('off')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 133,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shape of images array is: (1797, 8, 8)\n"
]
},
{
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HQLVabVYKzVb/NPVwLPjVanWWp28vIIt4n6Ojo3WvyVINxu/k+YBEOXfffTeQp3/sRfjb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\nBSogQgghpUAFRAghpBSogAghhJTCfwCJq7NytzU3eQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7efbb5b7d850>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from sklearn.datasets import load_digits\n",
"\n",
"digits = load_digits()\n",
"images = digits['images']\n",
"num_images = images.shape[0]\n",
"\n",
"print \"Shape of images array is: \", images.shape\n",
"\n",
"#The images array contains N number of 8x8 binary digit images, this is a 3 dimensional array\n",
"#We will flatten 8x8 images into 64 dimensional vector for each image, stacked as image vectors\n",
"sample_idx = np.random.choice(images.shape[0],5)\n",
"samples = images[sample_idx].reshape(-1,1,64)\n",
"square_dist = np.sum((image_vectors - samples)**2,2)\n",
"ss = 20\n",
"image_nearest = zip(images[sample_idx],images[np.argsort(square_dist)[:,:ss]])\n",
"for i,(img,nearest) in enumerate(image_nearest):\n",
" plt.subplot(5,ss+1,(i*(ss+1))+1)\n",
" plt.imshow(img,'gray',interpolation='nearest')\n",
" plt.title('Input Image')\n",
" plt.axis('off')\n",
" for (j,nimg) in enumerate(nearest):\n",
" plt.subplot(5,ss+1,(i*(ss+1)+j+2))\n",
" plt.imshow(nimg,'gray',interpolation='nearest')\n",
" plt.title('Nearest Image')\n",
" plt.axis('off')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.14"
}
},
"nbformat": 4,
"nbformat_minor": 0
}