Shape After Indexing

Indexing and slicing affect array dimensions differently.

Index vs Slice

Single index reduces dimensions; slice preserves them.

1. Single Index

import numpy as np

def main():
    a = np.zeros((8, 8, 8, 8))
    print(f"{a[1].shape = }")

if __name__ == "__main__":
    main()

Output:

a[1].shape = (8, 8, 8)

2. Slice of One

import numpy as np

def main():
    a = np.zeros((8, 8, 8, 8))
    print(f"{a[1:2].shape = }")

if __name__ == "__main__":
    main()

Output:

a[1:2].shape = (1, 8, 8, 8)

3. Key Difference

a[1] removes a dimension; a[1:2] keeps it with size 1.

Mixed Operations

Combining indices and slices on different axes.

1. Index Two Axes

import numpy as np

def main():
    a = np.zeros((8, 8, 8, 8))
    print(f"{a[1, :, 3, :].shape = }")

if __name__ == "__main__":
    main()

Output:

a[1, :, 3, :].shape = (8, 8)

2. Index and Slice

import numpy as np

def main():
    a = np.zeros((8, 8, 8, 8))
    print(f"{a[1:2, :, 3, :].shape = }")

if __name__ == "__main__":
    main()

Output:

a[1:2, :, 3, :].shape = (1, 8, 8)

3. All Slices

import numpy as np

def main():
    a = np.zeros((8, 8, 8, 8))
    print(f"{a[1:2, :, 3:4, :].shape = }")

if __name__ == "__main__":
    main()

Output:

a[1:2, :, 3:4, :].shape = (1, 8, 1, 8)

Complete Comparison

Side-by-side comparison of all cases.

1. Summary Table

import numpy as np

def main():
    a = np.zeros((8, 8, 8, 8))
    print(f"{a[1].shape = }")
    print(f"{a[1:2].shape = }")
    print(f"{a[1, :, 3, :].shape = }")
    print(f"{a[1:2, :, 3, :].shape = }")
    print(f"{a[1:2, :, 3:4, :].shape = }")

if __name__ == "__main__":
    main()

Output:

a[1].shape = (8, 8, 8)
a[1:2].shape = (1, 8, 8, 8)
a[1, :, 3, :].shape = (8, 8)
a[1:2, :, 3, :].shape = (1, 8, 8)
a[1:2, :, 3:4, :].shape = (1, 8, 1, 8)

2. Dimension Rule

Each integer index removes one dimension; each slice keeps it.

Practical Impact

Understanding shape changes is crucial for array operations.

1. Broadcasting

Shape mismatches cause broadcasting errors; use slices to preserve dimensions.

2. Neural Networks

Batch dimensions must be preserved; use [0:1] instead of [0].

3. Matrix Operations

Some operations require 2D arrays; slicing maintains dimensionality.