DSS198Decal/copy_of_lecture2worksheet.py at main · pinkpanther108/DSS198Decal · GitHub

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# -*- coding: utf-8 -*-
"""Copy of Lecture2Worksheet.ipynb

Automatically generated by Colab.

Original file is located at
    https://colab.research.google.com/drive/1OCQsK6XZuccHskVgMLi2ozG-_sRDU_o1

#Week 2 Worksheet

###Please make a copy of this worksheet and work on it as we go through lecture.

*Author: Collin Duong* \
*Term: Fa2025*
"""

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

letters = pd.Series(['A', 'B', 'C', "D", "E"])
numbers = pd.Series([1, 2, 3, 4, 5])
details = pd.Series(["big", "big", "small", "small", "small"])
df = pd.DataFrame({"letters": letters, "numbers": numbers, "details": details})
df

"""###Problem 1
Access the column and index attribtues from the dataframe and save them to the following two variables.
"""

column_answer = df.columns
index_answer = df.index

"""### Problem 2


*   Use iloc to retreive the second row of the dataframe.
*   Use iloc to retrieve the 1st row and 3rd column of the dataframe.
*   Use iloc to retrieve the 3rd column of the dataframe.


"""

df.iloc[1]
df.iloc[0,2]
df.iloc[:,2]

"""###Problem 3

*   Extract the numbers column from the dataframe using regular column extraction.

*   Extract the numbers column from the dataframe using loc.


"""

df.numbers
df.loc[:,"numbers"]

"""###Problem 4
Extract all rows that have a number in the numbers column greater than 2.
"""

df.loc[df['numbers'] > 2]
#df.tail(3)

"""###Problem 5
Extract the row with the index "a" using loc. Also observe the following cell to see how to change the index in a DataFrame.
"""

# Do not modify this cell
df2 = df.copy()
df2.set_index("letters", inplace=True)
df2

df2.loc["A"]

"""### Problem 6
Compute the dot product between the following vectors using numpy.
$$\begin{bmatrix}1\\2\\3\end{bmatrix}, \begin{bmatrix}1\\2\\3\end{bmatrix}$$

Hint: You can create a vector with `np.array()`.
"""

v1 = np.array([1, 2, 3])
v2 = np.array([1, 2, 3])
dot_product = np.dot(v1, v2)
print(dot_product)

"""###Problem 7
Compute the cosine of the angle between the two vectors in the previous problem using numpy methods.

Hint: The formula is in the slides.
"""

np.dot(v1,v2)/(np.linalg.norm(v1)*np.linalg.norm(v2))

"""###Problem 8

Compute the projection (shadow) of the first vector described in problem six onto the second vector described in that problem. Use numpy methods.

Hint: This formula is also in the slides.
"""

np.dot(v2,v1)/np.dot(v1,v1) * v1

"""###Problem 9
You see the following function inputs and outputs. $$$$
$f(\begin{bmatrix}1\\0\\0\end{bmatrix})=\begin{bmatrix}1\\2\\3\end{bmatrix}\hspace{1cm}f(\begin{bmatrix}0\\1\\0\end{bmatrix})=\begin{bmatrix}7\\4\\2\end{bmatrix}\hspace{1cm}f(\begin{bmatrix}0\\0\\1\end{bmatrix})=\begin{bmatrix}3\\0\\1\end{bmatrix}$ $$$$

Use this information to find a matrix representation of f. Then compute $f(\begin{bmatrix}5\\6\\7\end{bmatrix})$ using numpy methods.

Hint: You can create a numpy matrix by doing the following:
`np.array(row1, row2, row3])`

"""

np.array([1, 0, 0])
np.array([1, 2, 3])
np.array([0, 1, 0])
np.array([7, 4, 2])