np.vstack() and np.hstack() in NumPy

Introduction

We use np.vstack() and np.hstack() to join arrays together easily. They help us combine data by stacking arrays vertically or horizontally.

When you have multiple lists of data and want to combine them into one bigger list by stacking rows.

When you want to add new data as new columns to an existing dataset.

When you want to merge small arrays into a bigger array for analysis or visualization.

Syntax

NumPy

import numpy as np

# Vertical stack: stacks arrays row-wise (one on top of another)
np.vstack((array1, array2, ...))

# Horizontal stack: stacks arrays column-wise (side by side)
np.hstack((array1, array2, ...))

Both functions take a tuple of arrays as input.

Arrays must have compatible shapes: for vstack, arrays must have the same number of columns; for hstack, arrays must have the same number of rows.

Examples

Stacks two 1D arrays as rows, creating a 2x3 array.

NumPy

import numpy as np

array1 = np.array([1, 2, 3])
array2 = np.array([4, 5, 6])

# Vertical stack
result_v = np.vstack((array1, array2))
print(result_v)

Stacks two 3x1 arrays side by side, creating a 3x2 array.

NumPy

import numpy as np

array1 = np.array([[1], [2], [3]])
array2 = np.array([[4], [5], [6]])

# Horizontal stack
result_h = np.hstack((array1, array2))
print(result_h)

Stacking empty arrays vertically results in an empty 2D array with shape (2, 0).

NumPy

import numpy as np

# Edge case: empty arrays
empty1 = np.array([])
empty2 = np.array([])

# Vertical stack of empty arrays
result_empty_v = np.vstack((empty1, empty2))
print(result_empty_v)

Stacks two single-element arrays side by side, resulting in a 1D array with two elements.

NumPy

import numpy as np

# Edge case: single element arrays
single1 = np.array([10])
single2 = np.array([20])

# Horizontal stack
result_single_h = np.hstack((single1, single2))
print(result_single_h)

Sample Program

This program shows how to stack two 1D arrays vertically and horizontally. For horizontal stacking, arrays are reshaped to columns first.

NumPy

import numpy as np

# Create two arrays
array_one = np.array([10, 20, 30])
array_two = np.array([40, 50, 60])

print("Original arrays:")
print("array_one:", array_one)
print("array_two:", array_two)

# Vertical stack: stack as rows
stacked_vertical = np.vstack((array_one, array_two))
print("\nAfter np.vstack():")
print(stacked_vertical)

# Horizontal stack: stack as columns
# First reshape to 2D column vectors
array_one_col = array_one.reshape(-1, 1)
array_two_col = array_two.reshape(-1, 1)

print("\nArrays reshaped to columns:")
print("array_one_col:\n", array_one_col)
print("array_two_col:\n", array_two_col)

stacked_horizontal = np.hstack((array_one_col, array_two_col))
print("\nAfter np.hstack():")
print(stacked_horizontal)

Important Notes

Time complexity: Both np.vstack() and np.hstack() run in O(n) time, where n is the total number of elements in the arrays.

Space complexity: They create a new array, so space is O(n) for the combined size.

Common mistake: Trying to stack arrays with incompatible shapes causes errors. Always check shapes before stacking.

Use vstack when you want to add rows (stack arrays vertically). Use hstack when you want to add columns (stack arrays horizontally).

Summary

np.vstack() stacks arrays vertically (row-wise).

np.hstack() stacks arrays horizontally (column-wise).

Arrays must have compatible shapes to stack without errors.