Indexing and Slicing Arrays in Numpy¶

NumPy arrays (ndarray) are grid-like structures that can store data of the same type. They are similar to Python lists but offer faster computation and more efficient storage. Indexing and slicing are crucial for accessing and manipulating data within these arrays.

Importing NumPy¶

Before we begin, we need to import the NumPy library. It's a common practice to import NumPy using the alias np.

In [2]:

import numpy as np

import numpy as np

This line imports the NumPy library and allows you to access its functions using the np prefix.

1D Array Indexing and Slicing¶

One-dimensional (1D) arrays are the simplest form of NumPy arrays, similar to vectors. Indexing and slicing in 1D arrays work much like in standard Python lists.

Indexing Individual Elements¶

To access individual elements in a 1D array, you use square brackets [] with the index of the element. Remember that indexing starts at 0.

In [3]:

# Creating a 1D NumPy array
array_1d = np.array([10, 20, 30, 40, 50])

# Accessing the second element (index 1)
second_element = array_1d[1]

# Accessing the last element using negative indexing
last_element = array_1d[-1]

# Creating a 1D NumPy array array_1d = np.array([10, 20, 30, 40, 50]) # Accessing the second element (index 1) second_element = array_1d[1] # Accessing the last element using negative indexing last_element = array_1d[-1]

In the code above:

• array_1d[1] accesses the second element, which is 20.
• array_1d[-1] accesses the last element, which is 50.

Slicing Arrays¶

Slicing allows you to access a range of elements in an array. The syntax for slicing is array[start:stop:step].

In [15]:

# Slicing elements from index 1 to 3 (exclusive)
slice_1 = array_1d[1:3]
print(slice_1)
# Slicing elements from the beginning to index 3
slice_2 = array_1d[:3]

# Slicing elements from index 2 to the end
slice_3 = array_1d[2:]

# Slicing every other element in the array
slice_4 = array_1d[::2]
print(slice_4)

# Slicing elements from index 1 to 3 (exclusive) slice_1 = array_1d[1:3] print(slice_1) # Slicing elements from the beginning to index 3 slice_2 = array_1d[:3] # Slicing elements from index 2 to the end slice_3 = array_1d[2:] # Slicing every other element in the array slice_4 = array_1d[::2] print(slice_4)

[20 30]
[10 30 50]

In these examples:

• slice_1 contains elements at indices 1 and 2 (20 and 30).
• slice_2 contains elements at indices 0 to 2.
• slice_3 contains elements from index 2 to the end.
• slice_4 contains every second element (10, 30, 50).

2D Array Indexing and Slicing¶

Two-dimensional (2D) arrays are like matrices. Indexing and slicing in 2D arrays involve specifying row and column indices.

Indexing Individual Elements¶

To access an element in a 2D array, you provide two indices: one for the row and one for the column.

In [16]:

# Creating a 2D NumPy array
array_2d = np.array([
    [1, 2, 3],    # Row 0
    [4, 5, 6],    # Row 1
    [7, 8, 9]     # Row 2
])

# Accessing the element at row 1, column 2
element = array_2d[1][2]
print(element)
# Alternatively, using comma-separated indices
element_alt = array_2d[1, 2]

# Creating a 2D NumPy array array_2d = np.array([ [1, 2, 3], # Row 0 [4, 5, 6], # Row 1 [7, 8, 9] # Row 2 ]) # Accessing the element at row 1, column 2 element = array_2d[1][2] print(element) # Alternatively, using comma-separated indices element_alt = array_2d[1, 2]

6

Here:

• array_2d[1][2] and array_2d[1, 2] both access the element 6 at row 1, column 2.

Slicing Rows and Columns¶

You can slice subsets of a 2D array by specifying ranges for rows and columns.

In [6]:

# Selecting the first two rows
rows_slice = array_2d[:2, :]

# Selecting the first two columns
columns_slice = array_2d[:, :2]

# Selecting a subarray from rows 0-1 and columns 1-2
subarray = array_2d[0:2, 1:3]

# Selecting the first two rows rows_slice = array_2d[:2, :] # Selecting the first two columns columns_slice = array_2d[:, :2] # Selecting a subarray from rows 0-1 and columns 1-2 subarray = array_2d[0:2, 1:3]

In these examples:

• rows_slice contains all columns from rows 0 and 1.
• columns_slice contains all rows from columns 0 and 1.
• subarray is a 2x2 array containing elements from rows 0-1 and columns 1-2.

Explanation of the slicing syntax:

• array_2d[start_row:end_row, start_col:end_col]
• If start or end is omitted, it defaults to the beginning or end of that dimension.
• The : operator indicates the entire range in that dimension.

Examples:

• array_2d[1, :] selects all columns in row 1.
• array_2d[:, 2] selects all rows in column 2.
• array_2d[1:, 1:] selects rows 1 to the end and columns 1 to the end.

Higher-Dimensional Arrays¶

NumPy arrays can have more than two dimensions. The indexing and slicing principles extend naturally to higher dimensions.

In [18]:

# Creating a 3D NumPy array
array_3d = np.array([
    [  # Depth 0
        [1, 2, 3],   # Row 0
        [4, 5, 6]    # Row 1
    ],
    [  # Depth 1
        [7, 8, 9],   # Row 0
        [10, 11, 12] # Row 1
    ]
])
print(array_3d)
# Accessing an element at depth 1, row 0, column 2
element = array_3d[1][0][2]
print(element)
# Alternatively, using comma-separated indices
element_alt = array_3d[1, 0, 2]

# Creating a 3D NumPy array array_3d = np.array([ [ # Depth 0 [1, 2, 3], # Row 0 [4, 5, 6] # Row 1 ], [ # Depth 1 [7, 8, 9], # Row 0 [10, 11, 12] # Row 1 ] ]) print(array_3d) # Accessing an element at depth 1, row 0, column 2 element = array_3d[1][0][2] print(element) # Alternatively, using comma-separated indices element_alt = array_3d[1, 0, 2]

[[[ 1  2  3]
  [ 4  5  6]]

 [[ 7  8  9]
  [10 11 12]]]
9

Here, element and element_alt both access the value 9 at the specified indices.

Slicing in higher dimensions follows the same pattern:

In [8]:

# Slicing the first layer (depth 0)
layer = array_3d[0, :, :]

# Slicing all depths, row 1, columns 0-1
slice_3d = array_3d[:, 1, :2]

# Slicing the first layer (depth 0) layer = array_3d[0, :, :] # Slicing all depths, row 1, columns 0-1 slice_3d = array_3d[:, 1, :2]

Conditional Selection¶

Conditional selection allows you to select elements based on conditions rather than explicit indices. This is powerful for data analysis and preprocessing.

Using Comparison Operators¶

You can use comparison operators to create boolean arrays, which can then be used to index the array.

In [19]:

# Creating an array for demonstration
arr = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])

# Selecting elements less than 5
less_than_five = arr[arr < 5]
print(less_than_five)
# Selecting elements greater than or equal to 7
greater_or_equal_seven = arr[arr >= 7]

# Creating an array for demonstration arr = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9]) # Selecting elements less than 5 less_than_five = arr[arr < 5] print(less_than_five) # Selecting elements greater than or equal to 7 greater_or_equal_seven = arr[arr >= 7]

[1 2 3 4]

In these examples:

• arr < 5 produces a boolean array where elements less than 5 are True.
• less_than_five contains the elements where the condition is True.

Combining Conditions¶

You can combine multiple conditions using logical operators such as & (and), | (or), and ~ (not).

In [10]:

# Selecting even numbers
even_numbers = arr[arr % 2 == 0]

# Selecting odd numbers greater than 5
odd_numbers_gt_five = arr[(arr % 2 != 0) & (arr > 5)]

# Selecting numbers less than 3 or greater than 7
lt_three_or_gt_seven = arr[(arr < 3) | (arr > 7)]

# Selecting even numbers even_numbers = arr[arr % 2 == 0] # Selecting odd numbers greater than 5 odd_numbers_gt_five = arr[(arr % 2 != 0) & (arr > 5)] # Selecting numbers less than 3 or greater than 7 lt_three_or_gt_seven = arr[(arr < 3) | (arr > 7)]

Note: When combining conditions:

• Enclose each condition in parentheses.
• Use & for logical AND.
• Use | for logical OR.
• Use ~ to negate a condition.

Boolean Indexing¶

You can create a boolean array and use it to index your array.

In [11]:

# Creating a boolean array
bool_array = arr > 5

# Using the boolean array to index 'arr'
selected_elements = arr[bool_array]

# Creating a boolean array bool_array = arr > 5 # Using the boolean array to index 'arr' selected_elements = arr[bool_array]

In this example:

• bool_array is a boolean array where elements greater than 5 are True.
• selected_elements contains elements from arr where bool_array is True.

Advanced Indexing Techniques¶

NumPy offers advanced indexing methods for more complex data selection.

Integer Array Indexing¶

You can use lists or arrays of integers to select multiple elements.

In [20]:

# Creating an array
arr = np.array([10, 20, 30, 40, 50])

# Selecting elements at indices 1, 3, and 4
indices = [1, 3, 4]
selected_elements = arr[indices]
print(selected_elements)

# Creating an array arr = np.array([10, 20, 30, 40, 50]) # Selecting elements at indices 1, 3, and 4 indices = [1, 3, 4] selected_elements = arr[indices] print(selected_elements)

[20 40 50]

Here, selected_elements contains elements at indices 1, 3, and 4.

Fancy Indexing¶

Fancy indexing allows you to pass arrays of indices to select specific elements.

In [13]:

# Creating a 2D array
arr_2d = np.array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
])

# Selecting elements at (0,0), (1,1), and (2,2)
row_indices = np.array([0, 1, 2])
col_indices = np.array([0, 1, 2])
diagonal_elements = arr_2d[row_indices, col_indices]

# Creating a 2D array arr_2d = np.array([ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]) # Selecting elements at (0,0), (1,1), and (2,2) row_indices = np.array([0, 1, 2]) col_indices = np.array([0, 1, 2]) diagonal_elements = arr_2d[row_indices, col_indices]

In this example, diagonal_elements contains the elements 1, 5, and 9.

Ellipsis (...) in Indexing¶

The ellipsis ... is used to represent as many colons as needed to produce a complete indexing tuple.

In [22]:

# For a 3D array
array_3d = np.random.rand(2, 3, 4)

# Selecting all elements in the first dimension
slice_ellipsis = array_3d[0, ...]

# For a 3D array array_3d = np.random.rand(2, 3, 4) # Selecting all elements in the first dimension slice_ellipsis = array_3d[0, ...]

Out[22]:

array([[0.67422635, 0.83676805, 0.55202531, 0.60142282],
       [0.78950226, 0.5517025 , 0.35208583, 0.17114877],
       [0.94841662, 0.99977504, 0.60292442, 0.15129033]])

Here, slice_ellipsis selects all elements in depth 0 across all rows and columns.

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