Operations on Numpy Arrays

 

the various transformations and computations you can perform:

1. Element-wise Arithmetic

• Basic Operations: NumPy supports addition (+), subtraction (-), multiplication (*), division (/), and more, directly on arrays.
  Python
  import numpy as np
  
  arr1 = np.array([2, 5, -1, 4])
  arr2 = np.array([1, 2, 5, -2])
  
  # Addition, Subtraction, Multiplication, Division
  result_add = arr1 + arr2
  result_sub = arr1 - arr2
  result_mul = arr1 * arr2
  result_div = arr1 / arr2
  
  

• Universal Functions: NumPy provides mathematical functions that operate on each element of an array.
  Python
  # Square root, exponent, trigonometric functions
  sqrt_array = np.sqrt(arr1)
  exp_array = np.exp(arr1)
  sin_array = np.sin(arr1)
  
  

2. Statistical Calculations

• Measures of Central Tendency:

• np.mean(): Mean (average)

• np.median(): Median

• np.std(): Standard deviation

• np.var(): Variance

• Other Statistics:

• np.min(), np.max(): Minimum and maximum values

• np.sum(): Sum of array elements

• np.correlate(): Correlation between arrays

3. Matrix Operations (Linear Algebra)

• Matrix Multiplication: Use np.dot() for the dot product of matrices.
  Python
  matrix1 = np.array([[1, 2], [3, 4]])
  matrix2 = np.array([[5, 6], [7, 8]])
  result_matrix = np.dot(matrix1, matrix2)
  
  

• Other Linear Algebra Functions:

• np.linalg.inv(): Matrix inverse

• np.linalg.eig(): Eigenvalues and eigenvectors

• np.linalg.det(): Determinant

4. Broadcasting

• Operations on Compatible Arrays: NumPy can perform operations between arrays with different but compatible shapes. It follows specific broadcasting rules.
  Python
  arr = np.array([1, 2, 3])
  # Add 5 to each element (broadcasting a scalar)
  result = arr + 5 
  
  

5. Array Manipulation

• Reshaping: Change the arrangement of elements using reshape().
  Python
  new_shape_array = arr.reshape(2, 6)
  
  

• Transposing: Swap rows and columns with transpose() or .T.
  Python
  transposed_array = matrix1.T
  
  

• Concatenation: Combine arrays with np.concatenate , np.vstack, np.hstack.

6. Comparison and Boolean Operations

• Element-wise Comparisons: NumPy supports >, <, >=, <=, == (equality), and != (not equal), resulting in boolean arrays.

• Logical Operators:

• np.all(): Check if all elements are True.

• np.any(): Check if at least one element is True.

comparison and boolean operations within the world of NumPy arrays.

1. Element-wise Comparisons

NumPy allows you to compare arrays element by element using familiar comparison operators:

• > (greater than)

• < (less than)

• >= (greater than or equal to)

• <= (less than or equal to)

• == (element-wise equality)

• != (element-wise inequality)

Result: Boolean Arrays: The outcome of these comparisons is a boolean NumPy array with the same shape as the original, containing True where the condition holds and False otherwise.

Example:

Python

import numpy as np

arr = np.array([5, 1, -2, 10, 5])

boolean_mask = arr > 3   # Find elements greater than 3
print(boolean_mask)       # Output: [ True False False  True  True]

values_less_than_5 = arr[arr < 5]  # Select elements less than 5
print(values_less_than_5)  # Output: [ 1 -2]

2. Logical Operators

• np.logical_and(arr1, arr2): Element-wise 'and' operation between two boolean arrays.

• np.logical_or(arr1, arr2): Element-wise 'or' operation.

• np.logical_not(arr): Element-wise negation ('not' operation).

Example: Combining Conditions

Python

condition1 = arr > 3
condition2 = arr < 8
combined_mask = np.logical_and(condition1, condition2)

elements_within_range = arr[combined_mask]

Applications of Boolean Arrays

1. Filtering/Indexing: Use boolean arrays to select elements meeting specific criteria (as shown in the examples).

2. Conditional Modification: Update array elements based on conditions.
   Python
   arr[arr < 0] = 0  # Replace negative values with 0
   
   

3. Counting: Count occurrences satisfying a condition.
   Python
   count_positive = np.count_nonzero(arr > 0)
   
   

Key Points

• Shape Matters: For comparisons or logical operations between arrays, they typically need to have the same shape or be broadcastable.

• Boolean Indexing: Is a powerful way to manipulate arrays based on conditions.

Practice Exercises

1. In an array representing student grades, find the indices of the students who passed (grade >= 60).

2. Given two arrays representing temperature measurements, create a boolean mask indicating where the measurements from the first array exceed those of the second array.

In an array representing student grades, find the indices of the students who passed (grade >= 60).

Steps

1. Create an Array of Student Grades:
   Python
   import numpy as np
   
   grades = np.array([75, 52, 86, 65, 93, 48])
   
   

2. Identify Passing Grades:
   Python
   passing_mask = grades >= 60  # Boolean mask indicating passing grades
   
   

3. Find Indices Using np.where():
   Python
   passing_indices = np.where(passing_mask)
   print(passing_indices)  # Output: (array([0, 2, 3, 4]),)
   
   

Explanation

• passing_mask = grades >= 60: Creates a boolean array with True for passing grades and False for failing grades.

• np.where(passing_mask): The np.where() function returns the indices of elements where the condition (in this case, passing_mask) is True.

Directly Accessing Passing Students

You can use the indices to directly access the passing grades:

Python

passing_grades = grades[passing_indices]
print(passing_grades)  # Output: [75 86 65 93]

Given two arrays representing temperature measurements, create a boolean mask indicating where the measurements from the first array exceed those of the second array.

Steps

1. Sample Temperature Arrays:
   Python
   import numpy as np
   
   temp_array1 = np.array([25, 18, 32, 21])
   temp_array2 = np.array([22, 19, 28, 20])
   
   

2. Comparison:
   Python
   comparison_mask = temp_array1 > temp_array2
   print(comparison_mask)  # Output: [ True False  True  True]
   
   

3. Using the Mask:
   Python
   higher_temps = temp_array1[comparison_mask] 
   print(higher_temps)   # Output:  [25 32 21]
   
   

Explanation

1. temp_array1 > temp_array2: NumPy performs this comparison element-wise, generating a boolean array where each element is True if the corresponding temperature in temp_array1 is greater than that in temp_array2.

2. Indexing with the Mask: We use this comparison_mask to select only the elements from temp_array1 where the condition held, giving us the higher temperatures.

Key Points

• Arrays of Equal Shape: For this direct comparison, the temperature arrays need to have the same shape.

• Boolean Masking: The boolean mask acts as a filter, allowing you to precisely extract the elements of interest.