Shape and ndim¶

Every NumPy array has shape and ndim attributes that describe its structure.

The shape Attribute¶

The shape attribute returns a tuple indicating the size along each dimension.

1. 1D Array Shape¶

```python import numpy as np

def main(): x = np.array([7, 2, 9, 10]) print(f"{x.shape = }")

if name == "main": main() ```

Output:

x.shape = (4,)

2. 2D Array Shape¶

```python import numpy as np

def main(): y = np.array([[5.2, 3.0, 4.5], [9.1, 0.1, 0.3]]) print(f"{y.shape = }")

if name == "main": main() ```

Output:

y.shape = (2, 3)

3. 3D Array Shape¶

```python import numpy as np

def main(): z = np.zeros((4, 3, 2)) print(f"{z.shape = }, {z.dtype = }")

if name == "main": main() ```

Output:

z.shape = (4, 3, 2), z.dtype = dtype('float64')

The ndim Attribute¶

The ndim attribute returns the number of dimensions (axes) of the array.

1. 1D Array ndim¶

```python import numpy as np

def main(): x = np.array([7, 2, 9, 10]) print(f"{x.ndim = }")

if name == "main": main() ```

Output:

x.ndim = 1

2. 2D Array ndim¶

```python import numpy as np

def main(): y = np.array([[5.2, 3.0, 4.5], [9.1, 0.1, 0.3]]) print(f"{y.ndim = }")

if name == "main": main() ```

Output:

y.ndim = 2

3. 3D Array ndim¶

```python import numpy as np

def main(): z = np.zeros((4, 3, 2)) print(f"{z.ndim = }")

if name == "main": main() ```

Output:

z.ndim = 3

Relationship¶

The ndim equals the length of the shape tuple.

1. Mathematical Link¶

```python import numpy as np

x = np.zeros((4, 3, 2)) assert x.ndim == len(x.shape) ```

2. Practical Use¶

Use ndim to check dimensionality before operations that require specific dimensions.

Shape Debugging Checklist¶

When an operation fails with a shape mismatch:

1. Print shapes: print(a.shape, b.shape) — the single most useful debugging step.
2. Check ndim: is one array 1D when it should be 2D? Use np.expand_dims or reshape.
3. Check broadcasting: shapes must be equal or one must be 1 in each trailing dimension.
4. Check after slicing: indexing with a scalar reduces ndim by 1 (e.g., a[0] turns (3, 4) into (4,)). Use a[0:1] to keep the dimension.

```python import numpy as np

a = np.zeros((3, 4)) print(a[0].shape) # (4,) — scalar index drops dimension print(a[0:1].shape) # (1, 4) — slice preserves dimension ```

Exercises¶

Exercise 1. Create arrays with 0, 1, 2, and 3 dimensions: a scalar np.array(42), a 1D array np.array([1, 2, 3]), a 2D array np.zeros((2, 3)), and a 3D array np.ones((2, 3, 4)). Print the ndim and shape of each. Verify that ndim equals len(shape) for every array.

import numpy as np

arrays = [
    np.array(42),
    np.array([1, 2, 3]),
    np.zeros((2, 3)),
    np.ones((2, 3, 4)),
]

for arr in arrays:
    print(f"ndim={arr.ndim}, shape={arr.shape}, len(shape)={len(arr.shape)}")
    assert arr.ndim == len(arr.shape)

Exercise 2. Given a = np.arange(60).reshape(3, 4, 5), print its shape and use the shape tuple to compute the total number of elements. Verify your answer against a.size.

import numpy as np

a = np.arange(60).reshape(3, 4, 5)
print(a.shape)  # (3, 4, 5)

total = 1
for dim in a.shape:
    total *= dim
print(f"Computed total: {total}")  # 60
print(f"a.size: {a.size}")          # 60
print(total == a.size)              # True

Exercise 3. Create a 1D array a = np.array([10, 20, 30]) and check its ndim. Then use a.reshape(1, -1) and a.reshape(-1, 1) to produce 2D arrays. Print the ndim and shape of each reshaped array.

import numpy as np

a = np.array([10, 20, 30])
print(f"Original: ndim={a.ndim}, shape={a.shape}")  # ndim=1, shape=(3,)

row = a.reshape(1, -1)
print(f"Row vector: ndim={row.ndim}, shape={row.shape}")  # ndim=2, shape=(1, 3)

col = a.reshape(-1, 1)
print(f"Col vector: ndim={col.ndim}, shape={col.shape}")  # ndim=2, shape=(3, 1)