NumPy Arrays and Linear Algebra

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Questions and Answers

What will the output of `a.sum(axis=0)` be for the array `a = [[1, 2, 3, 4], [5, 6, 7, 8]]`?

[3, 7, 11]

[36]

[10, 26]

[ 6, 8, 10, 12] (correct)

Which function would you use to find the maximum element in a NumPy array along a specific axis?

max() (correct)

argmax()

mean()

sum()

Which of the following methods would return the standard deviation of an entire NumPy array if no axis is specified?

sort()

mean()

std() (correct)

prod()

What does the `lstsq()` function in NumPy's linalg submodule return?

The answer that minimizes the square error. Signup and view all the answers

What will the output of `np.linalg.solve(A, b)` be for the given matrices if `A` is invertible?

The solution vector x of the equation Ax = b. Signup and view all the answers

Which function is used to compute the dot product of two matrices in NumPy?

dot() Signup and view all the answers

What is the purpose of the `inv()` function in the linalg submodule?

To return the inverse of a matrix. Signup and view all the answers

Which function would you use to compute the eigenvalues and eigenvectors of a given matrix in NumPy?

eig() Signup and view all the answers

If `A` is a square matrix, what does the `det()` function compute?

The determinant of the matrix. Signup and view all the answers

What will happen if `argmax()` is called on a NumPy array?

It will return the index of the maximum element in the array. Signup and view all the answers

What happens when a value in a view array is modified?

Both the view and original array are affected. Signup and view all the answers

How can you determine if an array is a view?

Check if the base attribute is None. Signup and view all the answers

Which method can be used to create a copy of a view array?

copy() Signup and view all the answers

Which of the following operations does not create a view?

Using the copy method Signup and view all the answers

What will the line 'v = M[0,:]' return?

The first row of the array M. Signup and view all the answers

What does the expression 'M.base' return if M is an original array?

None. Signup and view all the answers

Which of the following correctly demonstrates changing a view without altering the original array?

Use v = M.copy() and then modify v. Signup and view all the answers

When comparing arrays with '==' operator, what is a requirement for the arrays?

They must be of the same shape or broadcastable. Signup and view all the answers

Which of the following best describes an array view?

An array that shares data with another array. Signup and view all the answers

What are functions that act element-wise on NumPy arrays called?

Universal functions Signup and view all the answers

Which function would give you the ceiling values of a NumPy array?

np.ceil Signup and view all the answers

Using the vectorize decorator in NumPy allows you to convert which type of function?

A function that acts on a single value Signup and view all the answers

What does the np.tan function do when applied to an array?

Computes the tangent of each element in radians Signup and view all the answers

What would be the result of using np.exp on the array [1, 2, 3]?

[2.71828183, 7.3890561, 20.08553692] Signup and view all the answers

Which of the following functions will convert an array to its floor values?

np.floor Signup and view all the answers

The output of `np.round([1.5, 2.5, 3.5])` will be?

[2.0, 3.0, 4.0] Signup and view all the answers

Which of the following is an example of a universal function in NumPy?

np.sqrt Signup and view all the answers

Study Notes

NumPy Arrays

NumPy arrays (ndarrays) offer various methods for operations on arrays, including mathematical functions.
Universal functions (ufuncs) operate element-wise on arrays; many are already defined in NumPy (e.g., cos, tan, exp, log, ceil, floor, round).

Creating Universal Functions

Python functions can be converted into universal functions using np.vectorize.
Alternatively, a decorator @np.vectorize can be applied directly above the function definition.

Array Methods

NumPy arrays (ndarray) have methods for specific operations (e.g., sum, min, max, mean, std, prod).
These methods often operate along a specified axis.
Function equivalents with the same name typically exist within the NumPy module. For instance, the sum function can also calculated by ndarray.sum()

Linear Algebra Functions

NumPy's linalg submodule provides linear algebra operations.
The solve function can solve systems of equations with invertible matrices ($Ax = b$).
For non-invertible matrices, lstsq (least squares) minimizes the square error.

Array Views

Array views share data with the original array.
Changes in a view affect the original array.
The base attribute of an array can distinguish between original arrays and views.
Operations like reshaping and transposing make views of the original array.

Boolean Operations

Boolean operations on arrays yield boolean arrays (e.g., comparisons using operators like ==, !=, <, >).
The all function checks if all elements are True; any checks if at least one element is True.

Integer Array Indexing

Integer arrays select elements from arrays;
Colons (:) in indices access all elements in the corresponding dimension.

Boolean Array Indexing

Boolean array indexing selects elements based on a boolean condition.
Boolean selection can be applied on multiple dimensions using boolean arrays with dimensions that correspond to the array shape.

Assignment by Array Indexing

The selected elements in arrays using indexing can be updated with new values (broadcastable).

The `where` Function

np.where(condition, x, y) can choose elements based on a condition.
If x and y are not given, the function returns indices where a condition is True.
If both x and y are given, the output returns values from x where a condition is True and y otherwise.

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Description

This quiz covers essential concepts related to NumPy arrays, including their creation, universal functions, array methods, and linear algebra functions. Test your understanding of how to perform various mathematical operations using NumPy and its capabilities for handling array data effectively.