974 lines
20 KiB
Plaintext
974 lines
20 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"___\n",
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"\n",
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"<a href='http://www.pieriandata.com'> <img src='../Pierian_Data_Logo.png' /></a>\n",
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"___\n",
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"<center>*Copyright Pierian Data 2017*</center>\n",
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"<center>*For more information, visit us at www.pieriandata.com*</center>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# NumPy \n",
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"\n",
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"NumPy (or Numpy) is a Linear Algebra Library for Python, the reason it is so important for Finance with Python is that almost all of the libraries in the PyData Ecosystem rely on NumPy as one of their main building blocks. Plus we will use it to generate data for our analysis examples later on!\n",
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"\n",
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"Numpy is also incredibly fast, as it has bindings to C libraries. For more info on why you would want to use Arrays instead of lists, check out this great [StackOverflow post](http://stackoverflow.com/questions/993984/why-numpy-instead-of-python-lists).\n",
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"\n",
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"We will only learn the basics of NumPy, to get started we need to install it!"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Installation Instructions\n",
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"\n",
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"### NumPy is already included in your environment! You are good to go if you are using pyfinance env!\n",
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"\n",
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"_____\n",
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"##### For those not using the provided environment:\n",
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"\n",
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"**It is highly recommended you install Python using the Anaconda distribution to make sure all underlying dependencies (such as Linear Algebra libraries) all sync up with the use of a conda install. If you have Anaconda, install NumPy by going to your terminal or command prompt and typing:**\n",
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" \n",
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" conda install numpy\n",
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" \n",
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"**If you do not have Anaconda and can not install it, please refer to [Numpy's official documentation on various installation instructions.](http://docs.scipy.org/doc/numpy-1.10.1/user/install.html)**\n",
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"\n",
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"_____"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Using NumPy\n",
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"\n",
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"Once you've installed NumPy you can import it as a library:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"import numpy as np"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Numpy has many built-in functions and capabilities. We won't cover them all but instead we will focus on some of the most important aspects of Numpy: vectors,arrays,matrices, and number generation. Let's start by discussing arrays.\n",
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"\n",
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"# Numpy Arrays\n",
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"\n",
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"NumPy arrays are the main way we will use Numpy throughout the course. Numpy arrays essentially come in two flavors: vectors and matrices. Vectors are strictly 1-d arrays and matrices are 2-d (but you should note a matrix can still have only one row or one column).\n",
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"\n",
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"Let's begin our introduction by exploring how to create NumPy arrays.\n",
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"\n",
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"## Creating NumPy Arrays\n",
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"\n",
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"### From a Python List\n",
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"\n",
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"We can create an array by directly converting a list or list of lists:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[1, 2, 3]"
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]
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},
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"execution_count": 19,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"my_list = [1,2,3]\n",
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"my_list"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([1, 2, 3])"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.array(my_list)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[[1, 2, 3], [4, 5, 6], [7, 8, 9]]"
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]
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},
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"execution_count": 20,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"my_matrix = [[1,2,3],[4,5,6],[7,8,9]]\n",
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"my_matrix"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[1, 2, 3],\n",
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" [4, 5, 6],\n",
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" [7, 8, 9]])"
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.array(my_matrix)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Built-in Methods\n",
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"\n",
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"There are lots of built-in ways to generate Arrays"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### arange\n",
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"\n",
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"Return evenly spaced values within a given interval."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
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]
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},
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"execution_count": 22,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.arange(0,10)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([ 0, 2, 4, 6, 8, 10])"
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]
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},
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"execution_count": 23,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.arange(0,11,2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### zeros and ones\n",
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"\n",
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"Generate arrays of zeros or ones"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([ 0., 0., 0.])"
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]
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},
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"execution_count": 24,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.zeros(3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
|
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"array([[ 0., 0., 0., 0., 0.],\n",
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" [ 0., 0., 0., 0., 0.],\n",
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" [ 0., 0., 0., 0., 0.],\n",
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" [ 0., 0., 0., 0., 0.],\n",
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" [ 0., 0., 0., 0., 0.]])"
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]
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},
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"execution_count": 26,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.zeros((5,5))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([ 1., 1., 1.])"
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]
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},
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"execution_count": 27,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.ones(3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
|
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"array([[ 1., 1., 1.],\n",
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" [ 1., 1., 1.],\n",
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" [ 1., 1., 1.]])"
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]
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},
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"execution_count": 28,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.ones((3,3))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### linspace\n",
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"Return evenly spaced numbers over a specified interval."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 29,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
|
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"array([ 0., 5., 10.])"
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]
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},
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"execution_count": 29,
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"metadata": {},
|
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.linspace(0,10,3)"
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]
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},
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{
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"cell_type": "code",
|
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"execution_count": 31,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
|
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"array([ 0. , 0.20408163, 0.40816327, 0.6122449 ,\n",
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" 0.81632653, 1.02040816, 1.2244898 , 1.42857143,\n",
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" 1.63265306, 1.83673469, 2.04081633, 2.24489796,\n",
|
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" 2.44897959, 2.65306122, 2.85714286, 3.06122449,\n",
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" 3.26530612, 3.46938776, 3.67346939, 3.87755102,\n",
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" 4.08163265, 4.28571429, 4.48979592, 4.69387755,\n",
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" 4.89795918, 5.10204082, 5.30612245, 5.51020408,\n",
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" 5.71428571, 5.91836735, 6.12244898, 6.32653061,\n",
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" 6.53061224, 6.73469388, 6.93877551, 7.14285714,\n",
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" 7.34693878, 7.55102041, 7.75510204, 7.95918367,\n",
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" 8.16326531, 8.36734694, 8.57142857, 8.7755102 ,\n",
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" 8.97959184, 9.18367347, 9.3877551 , 9.59183673,\n",
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" 9.79591837, 10. ])"
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]
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},
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"execution_count": 31,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.linspace(0,10,50)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## eye\n",
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"\n",
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"Creates an identity matrix"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
|
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"array([[ 1., 0., 0., 0.],\n",
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" [ 0., 1., 0., 0.],\n",
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" [ 0., 0., 1., 0.],\n",
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" [ 0., 0., 0., 1.]])"
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]
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},
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"execution_count": 37,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"np.eye(4)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Random \n",
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"\n",
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"Numpy also has lots of ways to create random number arrays:\n",
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"\n",
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"### rand\n",
|
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"Create an array of the given shape and populate it with\n",
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"random samples from a uniform distribution\n",
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"over ``[0, 1)``."
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]
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},
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{
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"cell_type": "code",
|
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"execution_count": 47,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
|
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"array([ 0.11570539, 0.35279769])"
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]
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},
|
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"execution_count": 47,
|
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"metadata": {},
|
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"output_type": "execute_result"
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}
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],
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"source": [
|
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"np.random.rand(2)"
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]
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},
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{
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"cell_type": "code",
|
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"execution_count": 46,
|
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"metadata": {},
|
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"outputs": [
|
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{
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"data": {
|
|
"text/plain": [
|
|
"array([[ 0.66660768, 0.87589888, 0.12421056, 0.65074126, 0.60260888],\n",
|
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" [ 0.70027668, 0.85572434, 0.8464595 , 0.2735416 , 0.10955384],\n",
|
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" [ 0.0670566 , 0.83267738, 0.9082729 , 0.58249129, 0.12305748],\n",
|
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" [ 0.27948423, 0.66422017, 0.95639833, 0.34238788, 0.9578872 ],\n",
|
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" [ 0.72155386, 0.3035422 , 0.85249683, 0.30414307, 0.79718816]])"
|
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]
|
|
},
|
|
"execution_count": 46,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"np.random.rand(5,5)"
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]
|
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},
|
|
{
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|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
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"### randn\n",
|
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"\n",
|
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"Return a sample (or samples) from the \"standard normal\" distribution. Unlike rand which is uniform:"
|
|
]
|
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},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 48,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([-0.27954018, 0.90078368])"
|
|
]
|
|
},
|
|
"execution_count": 48,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"np.random.randn(2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 45,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([[ 0.70154515, 0.22441999, 1.33563186, 0.82872577, -0.28247509],\n",
|
|
" [ 0.64489788, 0.61815094, -0.81693168, -0.30102424, -0.29030574],\n",
|
|
" [ 0.8695976 , 0.413755 , 2.20047208, 0.17955692, -0.82159344],\n",
|
|
" [ 0.59264235, 1.29869894, -1.18870241, 0.11590888, -0.09181687],\n",
|
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" [-0.96924265, -1.62888685, -2.05787102, -0.29705576, 0.68915542]])"
|
|
]
|
|
},
|
|
"execution_count": 45,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"np.random.randn(5,5)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### randint\n",
|
|
"Return random integers from `low` (inclusive) to `high` (exclusive)."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 50,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
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"44"
|
|
]
|
|
},
|
|
"execution_count": 50,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"np.random.randint(1,100)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 51,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([13, 64, 27, 63, 46, 68, 92, 10, 58, 24])"
|
|
]
|
|
},
|
|
"execution_count": 51,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"np.random.randint(1,100,10)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Array Attributes and Methods\n",
|
|
"\n",
|
|
"Let's discuss some useful attributes and methods or an array:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 55,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"arr = np.arange(25)\n",
|
|
"ranarr = np.random.randint(0,50,10)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 56,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,\n",
|
|
" 17, 18, 19, 20, 21, 22, 23, 24])"
|
|
]
|
|
},
|
|
"execution_count": 56,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"arr"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 57,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([10, 12, 41, 17, 49, 2, 46, 3, 19, 39])"
|
|
]
|
|
},
|
|
"execution_count": 57,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"ranarr"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Reshape\n",
|
|
"Returns an array containing the same data with a new shape."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 54,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([[ 0, 1, 2, 3, 4],\n",
|
|
" [ 5, 6, 7, 8, 9],\n",
|
|
" [10, 11, 12, 13, 14],\n",
|
|
" [15, 16, 17, 18, 19],\n",
|
|
" [20, 21, 22, 23, 24]])"
|
|
]
|
|
},
|
|
"execution_count": 54,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"arr.reshape(5,5)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### max,min,argmax,argmin\n",
|
|
"\n",
|
|
"These are useful methods for finding max or min values. Or to find their index locations using argmin or argmax"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 64,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([10, 12, 41, 17, 49, 2, 46, 3, 19, 39])"
|
|
]
|
|
},
|
|
"execution_count": 64,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"ranarr"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 61,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"49"
|
|
]
|
|
},
|
|
"execution_count": 61,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"ranarr.max()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 62,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"4"
|
|
]
|
|
},
|
|
"execution_count": 62,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"ranarr.argmax()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 63,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"2"
|
|
]
|
|
},
|
|
"execution_count": 63,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"ranarr.min()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 60,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"5"
|
|
]
|
|
},
|
|
"execution_count": 60,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"ranarr.argmin()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Shape\n",
|
|
"\n",
|
|
"Shape is an attribute that arrays have (not a method):"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 65,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(25,)"
|
|
]
|
|
},
|
|
"execution_count": 65,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Vector\n",
|
|
"arr.shape"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 66,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,\n",
|
|
" 17, 18, 19, 20, 21, 22, 23, 24]])"
|
|
]
|
|
},
|
|
"execution_count": 66,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Notice the two sets of brackets\n",
|
|
"arr.reshape(1,25)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 69,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(1, 25)"
|
|
]
|
|
},
|
|
"execution_count": 69,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"arr.reshape(1,25).shape"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 70,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([[ 0],\n",
|
|
" [ 1],\n",
|
|
" [ 2],\n",
|
|
" [ 3],\n",
|
|
" [ 4],\n",
|
|
" [ 5],\n",
|
|
" [ 6],\n",
|
|
" [ 7],\n",
|
|
" [ 8],\n",
|
|
" [ 9],\n",
|
|
" [10],\n",
|
|
" [11],\n",
|
|
" [12],\n",
|
|
" [13],\n",
|
|
" [14],\n",
|
|
" [15],\n",
|
|
" [16],\n",
|
|
" [17],\n",
|
|
" [18],\n",
|
|
" [19],\n",
|
|
" [20],\n",
|
|
" [21],\n",
|
|
" [22],\n",
|
|
" [23],\n",
|
|
" [24]])"
|
|
]
|
|
},
|
|
"execution_count": 70,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"arr.reshape(25,1)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 76,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(25, 1)"
|
|
]
|
|
},
|
|
"execution_count": 76,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"arr.reshape(25,1).shape"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### dtype\n",
|
|
"\n",
|
|
"You can also grab the data type of the object in the array:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 75,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"dtype('int64')"
|
|
]
|
|
},
|
|
"execution_count": 75,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"arr.dtype"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Great Job!"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"anaconda-cloud": {},
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.7.5"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 1
|
|
}
|