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Questions and Answers
What happens to the size of a sparse matrix when additional zero elements are added?
What happens to the size of a sparse matrix when additional zero elements are added?
- It increases in size proportionally to the number of added zeros.
- It remains unchanged regardless of the number of added zeros. (correct)
- It changes based on the type of sparse matrix used.
- It becomes more efficient in storage.
Which of the following is NOT a type of sparse matrix mentioned?
Which of the following is NOT a type of sparse matrix mentioned?
- Dense Matrix (correct)
- Compressed Sparse Row (CSR)
- Compressed Sparse Column
- Dictionary of Keys
What is the index of the first element in a NumPy array?
What is the index of the first element in a NumPy array?
- Depends on the array length
- 1
- -1
- 0 (correct)
What represents a sparse matrix that was created from the larger matrix in the example?
What represents a sparse matrix that was created from the larger matrix in the example?
Which method of selecting elements in a NumPy array correctly references the second row, second column?
Which method of selecting elements in a NumPy array correctly references the second row, second column?
What advantage does a sparse matrix have in terms of storage?
What advantage does a sparse matrix have in terms of storage?
What is a primary purpose of the 'kernels' in a Google Colab notebook?
What is a primary purpose of the 'kernels' in a Google Colab notebook?
Which of the following operations can be performed easily with NumPy arrays?
Which of the following operations can be performed easily with NumPy arrays?
Which of the following statements about Python modules is correct?
Which of the following statements about Python modules is correct?
Which command correctly imports a module in Python using the recommended method?
Which command correctly imports a module in Python using the recommended method?
Why is it important to choose the right type of sparse matrix?
Why is it important to choose the right type of sparse matrix?
In NumPy, what is the outcome of executing 'np.array([1, 2, 3])'?
In NumPy, what is the outcome of executing 'np.array([1, 2, 3])'?
What would be the output of 'print(vector_row)' if vector_row is defined as 'np.array([1, 2, 3])'?
What would be the output of 'print(vector_row)' if vector_row is defined as 'np.array([1, 2, 3])'?
Which command is used to create a column vector in NumPy?
Which command is used to create a column vector in NumPy?
What does the combination 'Shift + Tab' perform in a code cell?
What does the combination 'Shift + Tab' perform in a code cell?
What is the primary data structure used in NumPy?
What is the primary data structure used in NumPy?
What will be the result of executing matrix[:,1:2] on the defined matrix?
What will be the result of executing matrix[:,1:2] on the defined matrix?
What value is returned by matrix.size for the given matrix?
What value is returned by matrix.size for the given matrix?
What does the ndim attribute of a NumPy array represent?
What does the ndim attribute of a NumPy array represent?
Using the vectorized_add_1000, what would be the output if applied to the array [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Using the vectorized_add_1000, what would be the output if applied to the array [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Which of the following correctly describes how to select all elements of a vector in NumPy?
Which of the following correctly describes how to select all elements of a vector in NumPy?
What will the output be for vector[-1] when vector is array([1, 2, 3, 4, 5, 6])?
What will the output be for vector[-1] when vector is array([1, 2, 3, 4, 5, 6])?
What is the shape of the matrix created by np.array([[1, 2, 3, 4],[5, 6, 7, 8],[9, 10, 11, 12]])?
What is the shape of the matrix created by np.array([[1, 2, 3, 4],[5, 6, 7, 8],[9, 10, 11, 12]])?
Which of the following statements about NumPy's vectorize is true?
Which of the following statements about NumPy's vectorize is true?
What does the argument -1 represent when using the reshape function in NumPy?
What does the argument -1 represent when using the reshape function in NumPy?
Which command correctly finds the inverse of a matrix A using NumPy?
Which command correctly finds the inverse of a matrix A using NumPy?
What will be the output of the command matrix.reshape(12) for a matrix of size 4x3?
What will be the output of the command matrix.reshape(12) for a matrix of size 4x3?
To calculate the eigenvalues of matrix A using NumPy, which of the following commands is correct?
To calculate the eigenvalues of matrix A using NumPy, which of the following commands is correct?
If you want to create a 2x2 matrix of ones with a border of zeros, which approach should you use?
If you want to create a 2x2 matrix of ones with a border of zeros, which approach should you use?
What will be the result of applying the operation matrix + 1000 to the following matrix: [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
What will be the result of applying the operation matrix + 1000 to the following matrix: [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
What is the output of np.max(matrix) for the given matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
What is the output of np.max(matrix) for the given matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
When using np.max(matrix, axis=0), what does the output represent?
When using np.max(matrix, axis=0), what does the output represent?
Which of the following functions would you use to calculate the variance of the elements in a matrix?
Which of the following functions would you use to calculate the variance of the elements in a matrix?
Which statement is true about reshaping a matrix using np.reshape()?
Which statement is true about reshaping a matrix using np.reshape()?
If you want to find the mean of the first row in the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]], which code should you use?
If you want to find the mean of the first row in the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]], which code should you use?
What is the result of np.max(matrix, axis=1) using the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
What is the result of np.max(matrix, axis=1) using the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Which operation would you use to find the standard deviation of a matrix in NumPy?
Which operation would you use to find the standard deviation of a matrix in NumPy?
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Study Notes
Introduction to Python with Google Colab
- Python is a high-level, interpreted programming language suitable for various applications.
- Google Colab is an online platform that allows users to write and execute Python code via Jupyter notebooks.
Google Colab Interface
- Kernels: The computational engine that executes code blocks.
- Cells: Containers for code or text, including markdown and code cells.
- Key Shortcuts:
- Shift + Enter: Execute the current cell and move to the next.
- Shift + Tab: View documentation for the selected function.
- Key Shortcuts:
Modules in Python
- A module is a file containing functions and definitions, similar to #include in C/C++.
- Import modules to access additional functions:
- Recommended method:
import module1 as mod1.
- Recommended method:
Basics of NumPy
- NumPy is essential for machine learning, enabling efficient operations with vectors, matrices, and arrays.
Creating Vectors
- Vectors can be created as one-dimensional arrays using NumPy:
- Row Vector:
vector_row = np.array([1, 2, 3]) - Column Vector:
vector_column = np.array([[1], [2], [3]])
- Row Vector:
Creating Matrices
- Use NumPy to create two-dimensional arrays (matrices).
- Larger matrices can illustrate advantages of sparse representations. For example, a sparse matrix minimizes storage of zero elements using
sparse.csr_matrix().
Selecting Elements in Arrays
- NumPy arrays are zero-indexed.
- Selection example:
- Third element of vector:
vector[2] - Element at second row, second column in a matrix:
matrix[1, 1]
- Third element of vector:
- Various slicing techniques allow selection of groups of elements.
Describing Matrix Properties
- Use attributes
shape,size, andndimto describe a matrix:- Shape:
matrix.shapeindicates rows and columns. - Size:
matrix.sizegives total elements. - Dimensions:
matrix.ndimreturns the number of matrix dimensions.
- Shape:
Applying Functions to Arrays
- Functions can be applied to multiple elements using
np.vectorize()or broadcasting techniques, e.g.,matrix + 1000.
Finding Maximum and Minimum Values
- Use
np.max()andnp.min()to find max/min values in arrays. - Operations can be specified along certain axes with parameters like
axis=0oraxis=1.
Descriptive Statistics
- Calculate mean, variance, and standard deviation using
np.mean(),np.var(), andnp.std(), respectively.
Reshaping Arrays
- Reshape matrices while maintaining data with
matrix.reshape(), ensuring the total number of elements remains unchanged. - Use -1 to auto-calculate dimensions.
Introduction to Linear Algebra with NumPy
- Calculate eigenvalues and eigenvectors using
np.linalg.eig(). - Compute matrix inverses with
np.linalg.inv().
Post Lab Exercises
- Implement programs to:
- Check if all elements in an array are non-zero.
- Create a 2x2 matrix of ones with a border of zeros.
- Multiply a randomly generated 4x3 matrix by a 3x5 matrix.
- Solve a system of equations using
np.linalg.solve().
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