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Concatenating & Stacking Arrays (concatenate, vstack, hstack)0%
Concatenating & Stacking Arrays (concatenate, vstack, hstack)
Beginner12 min read•Updated: Jul 11, 2026
Stacking Arrays: np.vstack(), np.hstack(), & np.concatenate()
Combining multiple datasets, merging feature matrices with target labels, and assembling image tiles are fundamental tasks in numerical data pipelines.
NumPy provides specialized functions to combine arrays along existing or new axes:
np.concatenate(): The generalized foundational routine.np.vstack(): Vertical stacking (row-wise / along axis 0).np.hstack(): Horizontal stacking (column-wise / along axis 1).
Click to Zoom1. General Array Concatenation: np.concatenate()
np.concatenate((a1, a2, ...), axis=0) joins a sequence of arrays along an existing axis. All input arrays must have the exact same shape, except in the dimension corresponding to axis:
import numpy as np
A = np.array([[1, 2],
[3, 4]])
B = np.array([[5, 6],
[7, 8]])
# Concatenate vertically along axis 0 (rows)
concat_axis0 = np.concatenate((A, B), axis=0)
print("Concatenate axis 0 (Shape:", concat_axis0.shape, "):
", concat_axis0)
# Concatenate horizontally along axis 1 (columns)
concat_axis1 = np.concatenate((A, B), axis=1)
print("
Concatenate axis 1 (Shape:", concat_axis1.shape, "):
", concat_axis1)
Output:
Concatenate axis 0 (Shape: (4, 2) ):
[[1 2]
[3 4]
[5 6]
[7 8]]
Concatenate axis 1 (Shape: (2, 4) ):
[[1 2 5 6]
[3 4 7 8]]
2. Vertical Stacking: np.vstack()
np.vstack() stacks arrays vertically (row on top of row). For 2D arrays, this is equivalent to np.concatenate(..., axis=0).
Crucially, for 1D arrays, np.vstack() treats them as rows of shape (1, N) and stacks them into a 2D matrix:
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
# Stacking 1D arrays vertically creates a 2D array of shape (2, 3)
v_stacked = np.vstack((x, y))
print("vstack 1D arrays:
", v_stacked)
print("Shape:", v_stacked.shape)
Output:
vstack 1D arrays:
[[1 2 3]
[4 5 6]]
Shape: (2, 3)
3. Horizontal Stacking: np.hstack()
np.hstack() stacks arrays horizontally (column next to column).
- For 2D arrays, it stacks along columns (equivalent to
np.concatenate(..., axis=1)). - For 1D arrays, it concatenates them end-to-end into a longer 1D array:
# For 1D arrays: concatenates along the single axis
h_1d = np.hstack((x, y))
print("hstack 1D arrays:", h_1d) # [1 2 3 4 5 6]
print("Shape:", h_1d.shape) # (6,)
# For 2D arrays: stacks side-by-side
M1 = np.ones((2, 2))
M2 = np.zeros((2, 3))
h_2d = np.hstack((M1, M2))
print("
hstack 2D arrays:
", h_2d)
print("Shape:", h_2d.shape) # (2, 5)
4. Dimensional Alignment Rules and Common Pitfalls
When concatenating or stacking arrays, shape mismatches along non-concatenating axes raise ValueError:
A = np.ones((3, 4))
B = np.ones((2, 5))
# Attempting to vstack A (4 cols) and B (5 cols) will fail:
try:
np.vstack((A, B))
except ValueError as e:
print("Alignment Error:", e)
# Output: all the input array dimensions for the concatenation
# axis must match exactly, but along dimension 1,
# the array at index 0 has size 4 and the array at index 1 has size 5
Interactive Quiz
Multiple Choice Questions
Question 1
What is the required argument format for arrays passed to
np.concatenate()?Question 2
What is the resulting shape when executing
np.vstack((np.array([1, 2, 3]), np.array([4, 5, 6])))?Question 3
What is the resulting shape when executing
np.hstack((np.array([1, 2, 3]), np.array([4, 5, 6])))?Question 4
Given 2D arrays
A of shape (3, 4) and B of shape (3, 2), which function will successfully combine them?Question 5
How does
np.concatenate((a, b), axis=None) behave?Next Lesson
Depth & Column Stacking (dstack, column_stack, stack)
Continue learning with hands-on practice, examples, and exercises in the upcoming topic.
Related Lessons
Practice Quiz
Test your understanding of this lesson with 5 questions. Each question has one correct answer.