Stacking Arrays in NumPy

Stacking in NumPy refers to combining multiple arrays along a new axis, thereby increasing the dimensionality of the resulting array. This is distinct from concatenation, which merges arrays along an existing axis.

NumPy offers several efficient functions for array stacking:

• numpy.stack()
• numpy.vstack()
• numpy.hstack()
• numpy.dstack()
• numpy.column_stack()

1. numpy.stack()

The numpy.stack() function creates a new array by stacking a sequence of input arrays along a new axis. This effectively increases the dimensionality of the output.

Syntax:

numpy.stack(arrays, axis=0)

• arrays: A sequence of array-like objects, all of which must have the same shape.
• axis: An integer specifying the index of the new axis in the dimensions of the resulting array.

Example: Stacking 1D Arrays (Axis 0)

When axis=0, the arrays are stacked along the first dimension.

import numpy as np

arr1 = np.array([10, 20, 30])
arr2 = np.array([40, 50, 60])
arr3 = np.array([70, 80, 90])

stacked = np.stack((arr1, arr2, arr3), axis=0)
print("Stacked along Axis 0:")
print(stacked)

Output:

Stacked along Axis 0:
[[10 20 30]
 [40 50 60]
 [70 80 90]]

Example: Stacking 1D Arrays (Axis 1)

When axis=1, the arrays are stacked along the second dimension.

import numpy as np

arr1 = np.array([10, 20, 30])
arr2 = np.array([40, 50, 60])
arr3 = np.array([70, 80, 90])

stacked = np.stack((arr1, arr2, arr3), axis=1)
print("Stacked along Axis 1:")
print(stacked)

Output:

Stacked along Axis 1:
[[10 40 70]
 [20 50 80]
 [30 60 90]]

Example: Stacking 2D Arrays

When stacking 2D arrays, axis=0 inserts the new axis as the first dimension, creating a 3D array.

import numpy as np

arr1 = np.array([[1, 3], [5, 7]])
arr2 = np.array([[9, 11], [13, 15]])

stacked = np.stack((arr1, arr2), axis=0)
print("Stacked 2D Arrays along Axis 0:")
print(stacked)

Output:

Stacked 2D Arrays along Axis 0:
[[[ 1  3]
  [ 5  7]]

 [[ 9 11]
  [13 15]]]

2. numpy.column_stack()

The numpy.column_stack() function treats 1D arrays as columns to be stacked into a 2D array. If 2D arrays are provided, they are stacked column-wise (along axis=1).

Syntax:

numpy.column_stack(tup)

• tup: A tuple of array-like objects.

Example: Stacking 1D Arrays as Columns

Each 1D array becomes a column in the resulting 2D array.

import numpy as np

arr1 = np.array([2, 4, 6])
arr2 = np.array([8, 10, 12])

stacked = np.column_stack((arr1, arr2))
print("1D Arrays Stacked as Columns:")
print(stacked)

Output:

1D Arrays Stacked as Columns:
[[ 2  8]
 [ 4 10]
 [ 6 12]]

Example: Column-wise Stacking of 2D Arrays

For 2D arrays, column_stack appends columns from the second array to the first.

import numpy as np

arr1 = np.array([[1, 3], [5, 7]])
arr2 = np.array([[9, 11], [13, 15]])

stacked = np.column_stack((arr1, arr2))
print("2D Arrays Stacked Column-wise:")
print(stacked)

Output:

2D Arrays Stacked Column-wise:
[[ 1  3  9 11]
 [ 5  7 13 15]]

3. numpy.vstack() (Vertical Stacking)

The numpy.vstack() function stacks arrays vertically, meaning it appends the arrays as new rows. This increases the number of rows in the resulting array.

Syntax:

numpy.vstack(tup)

• tup: A tuple of array-like objects. All arrays must have the same shape along axis=1.

Example: Vertical Stacking

The second array is placed below the first array.

import numpy as np

arr1 = np.array([[10, 20, 30], [40, 50, 60]])
arr2 = np.array([[70, 80, 90], [100, 110, 120]])

stacked = np.vstack((arr1, arr2))
print("Vertically Stacked Array:")
print(stacked)

Output:

Vertically Stacked Array:
[[ 10  20  30]
 [ 40  50  60]
 [ 70  80  90]
 [100 110 120]]

4. numpy.hstack() (Horizontal Stacking)

The numpy.hstack() function stacks arrays horizontally, meaning it appends the arrays as new columns. This increases the number of columns in the resulting array.

Syntax:

numpy.hstack(tup)

• tup: A tuple of array-like objects. For 1D arrays, they are concatenated. For 2D arrays, they are stacked column-wise.

Example: Horizontal Stacking

The second array's columns are appended to the first array's columns.

import numpy as np

arr1 = np.array([[5, 10], [15, 20]])
arr2 = np.array([[25, 30], [35, 40]])

stacked = np.hstack((arr1, arr2))
print("Horizontally Stacked Array:")
print(stacked)

Output:

Horizontally Stacked Array:
[[ 5 10 25 30]
 [15 20 35 40]]

5. numpy.dstack() (Depth Stacking)

The numpy.dstack() function stacks arrays along the third dimension (depth). This creates a 3D array where the new axis is the last dimension.

Syntax:

numpy.dstack(tup)

• tup: A tuple of array-like objects.

Example: Depth Stacking

Each pair of input arrays forms a "slice" along the new depth dimension.

import numpy as np

arr1 = np.array([[1, 2], [3, 4]])
arr2 = np.array([[5, 6], [7, 8]])

stacked = np.dstack((arr1, arr2))
print("Depth-wise Stacked Array:")
print(stacked)

Output:

Depth-wise Stacked Array:
[[[1 5]
  [2 6]]

 [[3 7]
  [4 8]]]

Summary of Stacking Functions

These stacking methods are invaluable for constructing complex data structures from simpler components, particularly in fields such as data science, image processing, machine learning, and matrix operations.

SEO Keywords: NumPy array stacking, NumPy stack function, NumPy vertical stacking, NumPy horizontal stacking, NumPy column stack, NumPy depth stacking, NumPy array manipulation, stacking vs concatenation NumPy.