PY0101EN-5-1-Numpy1D.ipynb

{"cells":[{"cell_type":"markdown","metadata":{},"source":["<center>\n","    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n","</center>\n","\n","# 1D Numpy in Python\n","\n","Estimated time needed: **30** minutes\n","\n","## Objectives\n","\n","After completing this lab you will be able to:\n","\n","*   Import and use the `numpy` library\n","*   Perform operations with `numpy`\n"]},{"cell_type":"markdown","metadata":{},"source":["<h2>Table of Contents</h2>\n","<div class=\"alert alert-block alert-info\" style=\"margin-thttps://op/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01: 20px\">\n","    <ul>\n","        <li><a href=\"https://pre/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Preparation</a></li>\n","        <li>\n","            <a href=\"https://numpy/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">What is Numpy?</a>\n","            <ul>\n","                <li><a href=\"https://type/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Type</a></li>\n","                <li><a href=\"https://val/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Assign Value</a></li>\n","                <li><a href=\"https://slice/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Slicing</a></li>\n","                <li><a href=\"https://list/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Assign Value with List</a></li>\n","                <li><a href=\"https://other/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Other Attributes</a></li>\n","            </ul>\n","        </li>\n","        <li>\n","            <a href=\"op\">Numpy Array Operations</a>\n","            <ul>\n","                <li><a href=\"https://add/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Array Addition</a></li>\n","                <li><a href=\"https://multi/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Array Multiplication</a></li>\n","                <li><a href=\"https://prod/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Product of Two Numpy Arrays</a></li>\n","                <li><a href=\"https://dot/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Dot Product</a></li>\n","                <li><a href=\"https://cons/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Adding Constant to a Numpy Array</a></li>\n","            </ul>\n","        </li>\n","        <li><a href=\"https://math/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Mathematical Functions</a></li>\n","        <li><a href=\"https://lin/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Linspace</a></li>\n","    </ul>\n","\n","</div>\n","\n","<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["<h2 id=\"pre\">Preparation</h2>\n"]},{"cell_type":"code","execution_count":null,"metadata":{"collapsed":true},"outputs":[],"source":["# Import the libraries\n","\n","import time \n","import sys\n","import numpy as np \n","\n","import matplotlib.pyplot as plt\n","%matplotlib inline  "]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Plotting functions\n","\n","def Plotvec1(u, z, v):\n","    \n","    ax = plt.axes()\n","    ax.arrow(0, 0, *u, head_width=0.05, color='r', head_length=0.1)\n","    plt.text(*(u + 0.1), 'u')\n","    \n","    ax.arrow(0, 0, *v, head_width=0.05, color='b', head_length=0.1)\n","    plt.text(*(v + 0.1), 'v')\n","    ax.arrow(0, 0, *z, head_width=0.05, head_length=0.1)\n","    plt.text(*(z + 0.1), 'z')\n","    plt.ylim(-2, 2)\n","    plt.xlim(-2, 2)\n","\n","def Plotvec2(a,b):\n","    ax = plt.axes()\n","    ax.arrow(0, 0, *a, head_width=0.05, color ='r', head_length=0.1)\n","    plt.text(*(a + 0.1), 'a')\n","    ax.arrow(0, 0, *b, head_width=0.05, color ='b', head_length=0.1)\n","    plt.text(*(b + 0.1), 'b')\n","    plt.ylim(-2, 2)\n","    plt.xlim(-2, 2)"]},{"cell_type":"markdown","metadata":{},"source":["Create a Python List as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a python list\n","\n","a = [\"0\", 1, \"two\", \"3\", 4]"]},{"cell_type":"markdown","metadata":{},"source":["We can access the data via an index:\n"]},{"cell_type":"markdown","metadata":{},"source":["<img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/labs/Module%205/images/NumOneList.png\" width=\"660\" />\n"]},{"cell_type":"markdown","metadata":{},"source":["We can access each element using a square bracket as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Print each element\n","\n","print(\"a[0]:\", a[0])\n","print(\"a[1]:\", a[1])\n","print(\"a[2]:\", a[2])\n","print(\"a[3]:\", a[3])\n","print(\"a[4]:\", a[4])"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["<h2 id=\"numpy\">What is Numpy?</h2>\n"]},{"cell_type":"markdown","metadata":{},"source":["A numpy array is similar to a list. It's usually fixed in size and each element is of the same type. We can cast a list to a numpy array by first importing `numpy`:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# import numpy library\n","\n","import numpy as np "]},{"cell_type":"markdown","metadata":{},"source":["We then cast the list as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a numpy array\n","\n","a = np.array([0, 1, 2, 3, 4])\n","a"]},{"cell_type":"markdown","metadata":{},"source":["Each element is of the same type, in this case integers:\n"]},{"cell_type":"markdown","metadata":{},"source":["<img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/labs/Module%205/images/NumOneNp.png\" width=\"500\" />\n"]},{"cell_type":"markdown","metadata":{},"source":["As with lists, we can access each element via a square bracket:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Print each element\n","\n","print(\"a[0]:\", a[0])\n","print(\"a[1]:\", a[1])\n","print(\"a[2]:\", a[2])\n","print(\"a[3]:\", a[3])\n","print(\"a[4]:\", a[4])"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"type\">Type</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["If we check the type of the array we get <b>numpy.ndarray</b>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Check the type of the array\n","\n","type(a)"]},{"cell_type":"markdown","metadata":{},"source":["As numpy arrays contain data of the same type, we can use the attribute \"dtype\" to obtain the data type of the array’s elements. In this case, it's a 64-bit integer:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Check the type of the values stored in numpy array\n","\n","a.dtype"]},{"cell_type":"markdown","metadata":{},"source":["We can create a numpy array with real numbers:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a numpy array\n","\n","b = np.array([3.1, 11.02, 6.2, 213.2, 5.2])"]},{"cell_type":"markdown","metadata":{},"source":["When we check the type of the array we get <b>numpy.ndarray</b>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Check the type of array\n","\n","type(b)"]},{"cell_type":"markdown","metadata":{},"source":["If we examine the attribute <code>dtype</code> we see float 64, as the elements are not integers:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Check the value type\n","\n","b.dtype"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"val\">Assign value</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["We can change the value of the array. Consider the array <code>c</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create numpy array\n","\n","c = np.array([20, 1, 2, 3, 4])\n","c"]},{"cell_type":"markdown","metadata":{},"source":["We can change the first element of the array to 100 as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Assign the first element to 100\n","\n","c[0] = 100\n","c"]},{"cell_type":"markdown","metadata":{},"source":["We can change the 5th element of the array to 0 as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Assign the 5th element to 0\n","\n","c[4] = 0\n","c"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"slice\">Slicing</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["Like lists, we can slice the numpy array. We can select the elements from 1 to 3 and assign it to a new numpy array <code>d</code> as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Slicing the numpy array\n","\n","d = c[1:4]\n","d"]},{"cell_type":"markdown","metadata":{},"source":["We can assign the corresponding indexes to new values as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Set the fourth element and fifth element to 300 and 400\n","\n","c[3:5] = 300, 400\n","c"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"list\">Assign Value with List</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["Similarly, we can use a list to select more than one specific index.\n","The list `select` contains several values:\n"]},{"cell_type":"code","execution_count":null,"metadata":{"collapsed":true},"outputs":[],"source":["# Create the index list\n","\n","select = [0, 2, 3]"]},{"cell_type":"markdown","metadata":{},"source":["We can use the list as an argument in the brackets. The output is the elements corresponding to the particular indexes:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Use List to select elements\n","\n","d = c[select]\n","d"]},{"cell_type":"markdown","metadata":{},"source":["We can assign the specified elements to a new value. For example, we can assign the values to 100 000 as follows:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Assign the specified elements to new value\n","\n","c[select] = 100000\n","c"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"other\">Other Attributes</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["Let's review some basic array attributes using the array <code>a</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a numpy array\n","\n","a = np.array([0, 1, 2, 3, 4])\n","a"]},{"cell_type":"markdown","metadata":{},"source":["The attribute <code>size</code> is the number of elements in the array:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Get the size of numpy array\n","\n","a.size"]},{"cell_type":"markdown","metadata":{},"source":["The next two attributes will make more sense when we get to higher dimensions but let's review them. The attribute <code>ndim</code> represents the number of array dimensions, or the rank of the array. In this case, one:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Get the number of dimensions of numpy array\n","\n","a.ndim"]},{"cell_type":"markdown","metadata":{},"source":["The attribute <code>shape</code> is a tuple of integers indicating the size of the array in each dimension:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Get the shape/size of numpy array\n","\n","a.shape"]},{"cell_type":"code","execution_count":null,"metadata":{"collapsed":true},"outputs":[],"source":["# Create a numpy array\n","\n","a = np.array([1, -1, 1, -1])"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Get the mean of numpy array\n","\n","mean = a.mean()\n","mean"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Get the standard deviation of numpy array\n","\n","standard_deviation=a.std()\n","standard_deviation"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a numpy array\n","\n","b = np.array([-1, 2, 3, 4, 5])\n","b"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Get the biggest value in the numpy array\n","\n","max_b = b.max()\n","max_b"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Get the smallest value in the numpy array\n","\n","min_b = b.min()\n","min_b"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["<h2 id=\"op\">Numpy Array Operations</h2>\n"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"add\">Array Addition</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["Consider the numpy array <code>u</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["u = np.array([1, 0])\n","u"]},{"cell_type":"markdown","metadata":{},"source":["Consider the numpy array <code>v</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["v = np.array([0, 1])\n","v"]},{"cell_type":"markdown","metadata":{},"source":["We can add the two arrays and assign it to z:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Numpy Array Addition\n","\n","z = u + v\n","z"]},{"cell_type":"markdown","metadata":{},"source":["The operation is equivalent to vector addition:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Plot numpy arrays\n","\n","Plotvec1(u, z, v)"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"multi\">Array Multiplication</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["Consider the vector numpy array <code>y</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a numpy array\n","\n","y = np.array([1, 2])\n","y"]},{"cell_type":"markdown","metadata":{},"source":["We can multiply every element in the array by 2:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Numpy Array Multiplication\n","\n","z = 2 * y\n","z"]},{"cell_type":"markdown","metadata":{},"source":["This is equivalent to multiplying a vector by a scaler:\n"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"prod\">Product of Two Numpy Arrays</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["Consider the following array <code>u</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a numpy array\n","\n","u = np.array([1, 2])\n","u"]},{"cell_type":"markdown","metadata":{},"source":["Consider the following array <code>v</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a numpy array\n","\n","v = np.array([3, 2])\n","v"]},{"cell_type":"markdown","metadata":{},"source":["The product of the two numpy arrays <code>u</code> and <code>v</code> is given by:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Calculate the production of two numpy arrays\n","\n","z = u * v\n","z"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"dot\">Dot Product</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["The dot product of the two numpy arrays <code>u</code> and <code>v</code> is given by:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Calculate the dot product\n","\n","np.dot(u, v)"]},{"cell_type":"markdown","metadata":{},"source":["<h3 id=\"cons\">Adding Constant to a Numpy Array</h3>\n"]},{"cell_type":"markdown","metadata":{},"source":["Consider the following array:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create a constant to numpy array\n","\n","u = np.array([1, 2, 3, -1]) \n","u"]},{"cell_type":"markdown","metadata":{},"source":["Adding the constant 1 to each element in the array:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Add the constant to array\n","\n","u + 1"]},{"cell_type":"markdown","metadata":{},"source":["The process is summarised in the following animation:\n"]},{"cell_type":"markdown","metadata":{},"source":["<img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/labs/Module%205/images/NumOneAdd.gif\" width=\"500\" />\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["<h2 id=\"math\">Mathematical Functions</h2>\n"]},{"cell_type":"markdown","metadata":{},"source":["We can access the value of <code>pi</code> in numpy as follows :\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# The value of pi\n","\n","np.pi"]},{"cell_type":"markdown","metadata":{},"source":["We can create the following numpy array in Radians:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Create the numpy array in radians\n","\n","x = np.array([0, np.pi/2 , np.pi])"]},{"cell_type":"markdown","metadata":{},"source":["We can apply the function <code>sin</code> to the array <code>x</code> and assign the values to the array <code>y</code>; this applies the sine function to each element in the array:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Calculate the sin of each elements\n","\n","y = np.sin(x)\n","y"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["<h2 id=\"lin\">Linspace</h2>\n"]},{"cell_type":"markdown","metadata":{},"source":["A useful function for plotting mathematical functions is <code>linspace</code>.   Linspace returns evenly spaced numbers over a specified interval. We specify the starting point of the sequence and the ending point of the sequence. The parameter \"num\" indicates the Number of samples to generate, in this case 5:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Makeup a numpy array within [-2, 2] and 5 elements\n","\n","np.linspace(-2, 2, num=5)"]},{"cell_type":"markdown","metadata":{},"source":["If we change the parameter <code>num</code> to 9, we get 9 evenly spaced numbers over the interval from -2 to 2:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Make a numpy array within [-2, 2] and 9 elements\n","\n","np.linspace(-2, 2, num=9)"]},{"cell_type":"markdown","metadata":{},"source":["We can use the function <code>linspace</code> to generate 100 evenly spaced samples from the interval 0 to 2π:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Make a numpy array within [0, 2π] and 100 elements \n","\n","x = np.linspace(0, 2*np.pi, num=100)"]},{"cell_type":"markdown","metadata":{},"source":["We can apply the sine function to each element in the array <code>x</code> and assign it to the array <code>y</code>:\n"]},{"cell_type":"code","execution_count":null,"metadata":{"collapsed":true},"outputs":[],"source":["# Calculate the sine of x list\n","\n","y = np.sin(x)"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Plot the result\n","\n","plt.plot(x, y)"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["<h2 id=\"quiz\">Quiz on 1D Numpy Array</h2>\n"]},{"cell_type":"markdown","metadata":{},"source":["Implement the following vector subtraction in numpy: u-v\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Write your code below and press Shift+Enter to execute\n","\n","u = np.array([1, 0])\n","v = np.array([0, 1])"]},{"cell_type":"markdown","metadata":{},"source":["<details><summary>Click here for the solution</summary>\n","\n","```python\n","u - v\n","```\n","\n","</details>\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["Multiply the numpy array z with -2:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Write your code below and press Shift+Enter to execute\n","\n","z = np.array([2, 4])"]},{"cell_type":"markdown","metadata":{},"source":["<details><summary>Click here for the solution</summary>\n","\n","```python\n","-2 * z\n","```\n","\n","</details>\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["Consider the list <code>\\[1, 2, 3, 4, 5]</code> and <code>\\[1, 0, 1, 0, 1]</code>. Cast both lists to a numpy array then multiply them together:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Write your code below and press Shift+Enter to execute\n"]},{"cell_type":"markdown","metadata":{},"source":["<details><summary>Click here for the solution</summary>\n","\n","```python\n","a = np.array([1, 2, 3, 4, 5])\n","b = np.array([1, 0, 1, 0, 1])\n","a * b\n","```\n","\n","</details>\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["Convert the list <code>\\[-1, 1]</code> and <code>\\[1, 1]</code> to numpy arrays <code>a</code> and <code>b</code>. Then, plot the arrays as vectors using the fuction <code>Plotvec2</code> and find their dot product:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Write your code below and press Shift+Enter to execute\n"]},{"cell_type":"markdown","metadata":{},"source":["<details><summary>Click here for the solution</summary>\n","\n","```python\n","a = np.array([-1, 1])\n","b = np.array([1, 1])\n","Plotvec2(a, b)\n","print(\"The dot product is\", np.dot(a,b))\n","\n","```\n","\n","</details>\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["Convert the list <code>\\[1, 0]</code> and <code>\\[0, 1]</code> to numpy arrays <code>a</code> and <code>b</code>. Then, plot the arrays as vectors using the function <code>Plotvec2</code> and find their dot product:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Write your code below and press Shift+Enter to execute\n"]},{"cell_type":"markdown","metadata":{},"source":["<details><summary>Click here for the solution</summary>\n","\n","```python\n","a = np.array([1, 0])\n","b = np.array([0, 1])\n","Plotvec2(a, b)\n","print(\"The dot product is\", np.dot(a, b))\n","\n","```\n","\n","</details>\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["Convert the list <code>\\[1, 1]</code> and <code>\\[0, 1]</code> to numpy arrays <code>a</code> and <code>b</code>. Then plot the arrays as vectors using the fuction <code>Plotvec2</code> and find their dot product:\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Write your code below and press Shift+Enter to execute\n"]},{"cell_type":"markdown","metadata":{},"source":["<details><summary>Click here for the solution</summary>\n","\n","```python\n","a = np.array([1, 1])\n","b = np.array([0, 1])\n","Plotvec2(a, b)\n","print(\"The dot product is\", np.dot(a, b))\n","\n","```\n","\n","</details>\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["Why are the results of the dot product for <code>\\[-1, 1]</code> and <code>\\[1, 1]</code> and the dot product for <code>\\[1, 0]</code> and <code>\\[0, 1]</code> zero, but not zero for the dot product for <code>\\[1, 1]</code> and <code>\\[0, 1]</code>? <p><i>Hint: Study the corresponding figures, pay attention to the direction the arrows are pointing to.</i></p>\n"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["# Write your code below and press Shift+Enter to execute\n"]},{"cell_type":"markdown","metadata":{},"source":["<details><summary>Click here for the solution</summary>\n","\n","```python\n","The vectors used for question 4 and 5 are perpendicular. As a result, the dot product is zero. \n","\n","```\n","\n","</details>\n"]},{"cell_type":"markdown","metadata":{},"source":["<hr>\n","<h2>The last exercise!</h2>\n","<p>Congratulations, you have completed your first lesson and hands-on lab in Python. \n","<hr>\n"]},{"cell_type":"markdown","metadata":{},"source":["## Author\n","\n","<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n","\n","## Other contributors\n","\n","<a href=\"https://www.linkedin.com/in/jiahui-mavis-zhou-a4537814a?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Mavis Zhou</a>\n","\n","## Change Log\n","\n","| Date (YYYY-MM-DD) | Version | Changed By | Change Description                 |\n","| ----------------- | ------- | ---------- | ---------------------------------- |\n","| 2022-01-10        | 2.1     | Malika     | Removed the readme for GitShare    |\n","| 2020-08-26        | 2.0     | Lavanya    | Moved lab to course repo in GitLab |\n","|                   |         |            |                                    |\n","|                   |         |            |                                    |\n","\n","<hr/>\n","\n","## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"]}],"metadata":{"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":"3.7.6"}},"nbformat":4,"nbformat_minor":2}