NumPy: Concatenation and Splitting

Last updated: 2026-08-26

Concatenation and Splitting

1. What You'll Learn

❶ concatenate — joining along an axis
❷ vstack / hstack — convenience functions
❸ stack — joining with a new dimension
❹ split / vsplit / hsplit — splitting arrays
❺ repeat / tile — repeating and expanding

2. A Developer's True Story

(1) The Problem

Alice has 3 months of sales data, each month as a 4×3 array (4 products × 3 regions). She wants to merge them into one big table but keeps mixing up which axis to use with concatenate.

(2) The Solution

Bob draws a diagram: "Along axis 0, rows increase; along axis 1, columns increase." concatenate(axis=0) stacks vertically, concatenate(axis=1) stacks horizontally.

(3) The Payoff

After mastering concatenation and splitting, Alice can merge monthly data with one command, split by quarter, and use tile to expand prediction templates — 10x improvement in data assembly efficiency.

3. Key Concepts

(1) np.concatenate — Join Along an Axis

np.concatenate is the most general joining function, with the axis parameter controlling the direction.

PYTHON

import numpy as np

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

b = np.array([[7, 8, 9],
              [10, 11, 12]])

# Along axis 0: stack vertically (rows increase)
c0 = np.concatenate([a, b], axis=0)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]]

# Along axis 1: stack horizontally (columns increase)
c1 = np.concatenate([a, b], axis=1)
# [[ 1  2  3  7  8  9]
#  [ 4  5  6 10 11 12]]

TEXT 📖 Display only

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

⚠️ Note: The code below needs to run in a local Python environment.

(2) vstack and hstack

PYTHON

import numpy as np

a = np.array([[1, 2],
              [3, 4]])
b = np.array([[5, 6],
              [7, 8]])

# vstack: same as concatenate(axis=0)
v = np.vstack([a, b])
print(v.shape)  # (4, 2)

# hstack: same as concatenate(axis=1)
h = np.hstack([a, b])
print(h.shape)  # (2, 4)

TEXT 📖 Display only

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

⚠️ Note: The code below needs to run in a local Python environment.

(3) stack — Join with a New Dimension

stack creates a new axis and joins along it:

PYTHON

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
c = np.array([7, 8, 9])

s = np.stack([a, b, c])
print(s.shape)  # (3, 3)
print(s)
# [[1 2 3]
#  [4 5 6]
#  [7 8 9]]

TEXT 📖 Display only

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

⚠️ Note: The code below needs to run in a local Python environment.

(4) split — Splitting Arrays

PYTHON

import numpy as np

a = np.arange(12).reshape(6, 2)

# Split into 3 equal parts
parts = np.split(a, 3)
print(len(parts))  # 3
print(parts[0].shape)  # (2, 2)
print(parts[1].shape)  # (2, 2)
print(parts[2].shape)  # (2, 2)

# Split at specific indices
parts2 = np.split(a, [2, 4])
print([p.shape for p in parts2])  # [(2,2), (2,2), (2,2)]

# vsplit: split along axis 0 (vertical)
# hsplit: split along axis 1 (horizontal)
v = np.vsplit(a, 3)  # same as split(a, 3, axis=0)
h = np.hsplit(a, 2)  # split columns

TEXT 📖 Display only

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

⚠️ Note: The code below needs to run in a local Python environment.

(5) repeat and tile

PYTHON

import numpy as np

a = np.array([1, 2, 3])

# repeat: repeat each element
print(np.repeat(a, 3))  # [1 1 1 2 2 2 3 3 3]

# tile: repeat the entire array
print(np.tile(a, 3))  # [1 2 3 1 2 3 1 2 3]

# 2D tile
b = np.array([[1, 2], [3, 4]])
print(np.tile(b, (2, 3)).shape)  # (4, 6)

TEXT 📖 Display only

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

⚠️ Note: The code below needs to run in a local Python environment.

▶ Example

TEXT 📖 Display only

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

: Concatenation vs stacking (Difficulty ⭐)

PYTHON

import numpy as np

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

print("concatenate:", np.concatenate([a, b]))
# [1 2 3 4 5 6]

print("stack:", np.stack([a, b]))
# [[1 2 3]
#  [4 5 6]]

print("vstack:", np.vstack([a, b]))
# [[1 2 3]
#  [4 5 6]]

print("hstack:", np.hstack([a, b]))
# [1 2 3 4 5 6]

TEXT 📖 Display only

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

⚠️ Note: The code below needs to run in a local Python environment.

4. Comparison Tables

(1) Concatenation Methods

Function	axis	Shape Requirement	Result Shape Change
`concatenate`	specified	Same except join axis	Join axis sums
`vstack`	0	Same # of columns	Rows increase
`hstack`	1	Same # of rows	Columns increase
`stack`	new axis	Same shape entirely	New dimension added

(2) repeat vs tile

Function	Behavior	Example
`repeat(3)`	Repeat each element 3x	`[1,2]` → `[1,1,1,2,2,2]`
`tile(3)`	Repeat the whole array 3x	`[1,2]` → `[1,2,1,2,1,2]`

▶ Example: Using array_split for uneven splits (Difficulty ⭐⭐)

PYTHON

import numpy as np

a = np.arange(10)

# split requires equal parts — raises error for 3 parts
# array_split handles uneven splits gracefully
parts = np.array_split(a, 3)
for i, p in enumerate(parts):
    print(f"Part {i}: shape={p.shape}, values={p}")

# 2D array_split
b = np.arange(20).reshape(5, 4)
parts_2d = np.array_split(b, 3)
for i, p in enumerate(parts_2d):
    print(f"2D Part {i}: shape={p.shape}")

Output:

TEXT 📖 Display only

Part 0: shape=(4,), values=[0 1 2 3]
Part 1: shape=(3,), values=[4 5 6]
Part 2: shape=(3,), values=[7 8 9]
2D Part 0: shape=(2, 4)
2D Part 1: shape=(2, 4)
2D Part 2: shape=(1, 4)

▶ Example: repeat and tile for data expansion (Difficulty ⭐)

PYTHON

import numpy as np

a = np.array([1, 2, 3])

# repeat: repeat each element individually
print("repeat:", np.repeat(a, 3))

# tile: repeat the entire array
print("tile:", np.tile(a, 3))

# Practical: expand a pattern
pattern = np.array([[1, 0], [0, 1]])
grid = np.tile(pattern, (2, 3))
print("Tiled pattern:\n", grid)
print("Shape:", grid.shape)

Output:

TEXT 📖 Display only

repeat: [1 1 1 2 2 2 3 3 3]
tile: [1 2 3 1 2 3 1 2 3]
Tiled pattern:
 [[1 0 1 0 1 0]
 [0 1 0 1 0 1]
 [1 0 1 0 1 0]
 [0 1 0 1 0 1]]
Shape: (4, 6)

❓ FAQ

Q What's the difference between concatenate and stack?

A concatenate joins existing arrays along an existing axis — no new dimensions. stack creates a new axis and joins along it, adding one dimension.

Q Can I concatenate arrays of different shapes?

A They must match in all dimensions except the join axis. For example, to concatenate along axis 0, the arrays must have the same number of columns.

Q What happens if I split an array into unequal parts?

A np.split requires equal divisions — it raises an error. Use np.array_split for unequal splits, which handles the remainder gracefully.

📖 Summary

concatenate joins along an existing axis; axes must match except the join axis
vstack / hstack are shortcuts for axis 0 and axis 1 concatenation
stack creates a new dimension, useful for building batches of data
split / vsplit / hsplit divide arrays into equal parts or at specific indices
repeat repeats elements; tile repeats the whole array

📝 Exercises

Beginner (Difficulty ⭐): Create two 3x4 arrays of random numbers. Concatenate them along axis 0, then along axis 1. Print the shapes of the results.
Intermediate (Difficulty ⭐⭐): Create three 1D arrays of length 5. Use stack to combine them into a 3x5 array. Then use vstack and compare the shapes.
Advanced (Difficulty ⭐⭐⭐): Create a 12x8 array. Split it into 3 equal parts, then split it at indices [3, 7]. Use np.tile to repeat a 2x2 pattern into an 8x8 grid.

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About Us

NumPy: Concatenation and Splitting

Concatenation and Splitting

1. What You'll Learn

2. A Developer's True Story

(1) The Problem

(2) The Solution

(3) The Payoff

3. Key Concepts

(1) np.concatenate — Join Along an Axis

(2) vstack and hstack

(3) stack — Join with a New Dimension

(4) split — Splitting Arrays

(5) repeat and tile

▶ Example

4. Comparison Tables

(1) Concatenation Methods

(2) repeat vs tile

▶ Example: Using array_split for uneven splits (Difficulty ⭐⭐)

▶ Example: repeat and tile for data expansion (Difficulty ⭐)

❓ FAQ

📖 Summary

📝 Exercises

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