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Merge pull request #158 from rpalo/numpy-tutorial
Add materials for Numpy Tutorial article.
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‎numpy-tutorial/README.md‎

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# Numpy Tutorial: First Steps in Data Science
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This folder contains the sample code for the [NumPy Tutorial](https://realpython.com/numpy-tutorial/) by @rpalo.
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## Installing
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First, you will need to have the dependencies installed:
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```shell
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$ python -m pip install -r requirements.txt
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```
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## Usage
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These examples all make use of the [Jupyter Notebook](https://jupyter-notebook.readthedocs.io/en/stable/). To run the examples, make sure the correct virtual environment is active (you may have to deactivate and reactivate after installing requirements), and run:
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```shell
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$ jupyter notebook
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```
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You should see listings for each of the example files. You can open them up and run them cell by cell to see how they perform. Feel free to make small changes to the code to see how those affect things.

‎numpy-tutorial/bad-gray.jpg‎

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‎numpy-tutorial/blue.jpg‎

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‎numpy-tutorial/curve_grades.ipynb‎

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{
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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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"# Curving Grades\n",
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"\n",
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"You'll be playing the part of a teacher, curving test grades to account for an unfortunately difficult test. The curving should improve the student's grade relative to where they ended up with respect to the group's average. It should also *not* hurt the student by reducing their grade, and it shouldn't give anyone anything over 100%."
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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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"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": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"CURVE_CENTER = 80"
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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": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"def curve(grades):\n",
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" \"\"\"Adjusts an array of grades so that the average is roughly shifted\n",
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" to the specified curve center.\n",
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"\n",
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" This will never cause a student's grade to decrease, and it will\n",
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" never cause the final grade to go over 100%.\n",
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"\n",
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" Parameters:\n",
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" grades (np.ndarray): The individual student grades, between 0\n",
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" and 100.\n",
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"\n",
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" Returns:\n",
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" (np.ndarray): A new array of grades, adjusted upwards, but in\n",
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" the same order.\n",
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" \"\"\"\n",
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" average = grades.mean()\n",
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" change = CURVE_CENTER - average\n",
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" new_grades = grades + change\n",
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" return np.clip(new_grades, grades, 100)"
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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": 4,
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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([[ 91.25, 54.25, 83.25, 100. , 70.25, 100. , 93.25, 31.25]])"
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]
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},
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"execution_count": 4,
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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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"grades = np.array([[72, 35, 64, 88, 51, 90, 74, 12]])\n",
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"curve(grades)"
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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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"Note how none of the grades are decreased or greater than 100%!"
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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": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

‎numpy-tutorial/durer.ipynb‎

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{
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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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"# Validating Dürer's Magic Square\n",
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"\n",
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"Albrecht Dürer was an artist and mathematician who created an engraving of a [magic square](https://mathworld.wolfram.com/DuerersMagicSquare.html), where lots of bits all add up to the same thing. Each row, column, quadrant, corners, etc. all add up to 34.\n",
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"\n",
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"At the bottom, you see 15 and 14, signifying the year it was engraved (1514) as well as 4 and 1, standing for D and A, the creator's initials.\n",
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"\n",
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"You're going to validate that everything does, in fact, add up."
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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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"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": "code",
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"execution_count": 2,
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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([[16, 3, 2, 13],\n",
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" [ 5, 10, 11, 8],\n",
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" [ 9, 6, 7, 12],\n",
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" [ 4, 15, 14, 1]])"
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]
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},
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"execution_count": 2,
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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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"square = np.array([\n",
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" [16, 3, 2, 13],\n",
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" [5, 10, 11, 8],\n",
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" [9, 6, 7, 12],\n",
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" [4, 15, 14, 1],\n",
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"])\n",
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"square"
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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": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"All assertions passed!\n"
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]
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}
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],
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"source": [
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"for i in range(4):\n",
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" assert square[i, :].sum() == 34\n",
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" assert square[:, i].sum() == 34\n",
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" \n",
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"assert square[:2, :2].sum() == 34\n",
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"assert square[2:, :2].sum() == 34\n",
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"assert square[:2, 2:].sum() == 34\n",
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"assert square[2:, 2:].sum() == 34\n",
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"\n",
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"print(\"All assertions passed!\")"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

‎numpy-tutorial/good-gray.jpg‎

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‎numpy-tutorial/image_mod.ipynb‎

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‎numpy-tutorial/kitty.jpg‎

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‎numpy-tutorial/maclaurin.ipynb‎

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{
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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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"# Using a Maclaurin Series to Estimate $e$\n",
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"\n",
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"A [Maclaurin series](https://mathworld.wolfram.com/MaclaurinSeries.html) is an infinite series of terms that can be used to approximate more complex functions quickly.\n",
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"\n",
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"You're going to approximate $e^x$ by using the first few terms of the series. The series equation for $e^x$ is this:\n",
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"\n",
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"$$\\sum_{n=0}^{\\infty} \\frac{x^n}{n!} = 1 + x + \\frac{x^2}{2} + \\frac{x^3}{6} \\ldots$$"
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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": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from math import e, factorial"
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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": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"fac = np.vectorize(factorial)"
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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": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"def e_x(x, terms=10):\n",
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" \"\"\"Approximates $e^x$ using a given number of terms of the Maclaurin series\"\"\"\n",
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" n = np.arange(terms)\n",
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" return np.sum((x ** n) / fac(n))"
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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": 6,
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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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"20.085536923187664"
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]
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},
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"execution_count": 6,
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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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"# Actual:\n",
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"e ** 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": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"N (terms)\tMaclaurin\tError\n",
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"1\t\t1.000\t\t19.086\n",
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"2\t\t4.000\t\t16.086\n",
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"3\t\t8.500\t\t11.586\n",
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"4\t\t13.000\t\t7.086\n",
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"5\t\t16.375\t\t3.711\n",
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"6\t\t18.400\t\t1.686\n",
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"7\t\t19.412\t\t0.673\n",
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"8\t\t19.846\t\t0.239\n",
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"9\t\t20.009\t\t0.076\n",
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"10\t\t20.063\t\t0.022\n",
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"11\t\t20.080\t\t0.006\n",
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"12\t\t20.084\t\t0.001\n",
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"13\t\t20.085\t\t0.000\n"
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]
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}
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],
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"source": [
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"print(\"N (terms)\\tMaclaurin\\tError\")\n",
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"\n",
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"for n in range(1, 14):\n",
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" maclaurin = e_x(3, terms=n)\n",
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" print(f\"{n}\\t\\t{maclaurin:.03f}\\t\\t{e**3 - maclaurin:.03f}\")"
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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": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

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