Array Stacking

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

| Function | Description | | :------------------ | :----------------------------------------- | | np.stack() | Stack along a new axis | | np.column_stack() | Stack 1D/2D arrays as columns (axis=1) | | np.vstack() | Stack vertically (new rows, axis=0 conceptually) | | np.hstack() | Stack horizontally (new columns, axis=1 conceptually) | | np.dstack() | Stack along depth (new axis at the end, axis=2 conceptually) |

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.

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