Adding dimensions to numpy.arrays: newaxis v.s. reshape v.s. expand_dims

This post demonstrates 3 ways to add new dimensions to numpy.arrays using numpy.newaxis, reshape, or expand_dim. It covers these cases with examples:

• 1.1 From 0-D (scalar) to n-D
• 1.1.1 From 0-D to 1-D
• 1.1.2 From 0-D to 2-D
• 1.2 From 1-D to n-D (n>1)
• 1.2.1 From 1-D to 2-D
• 1.3 From 2-D to n-D (n>2)
• 1.3.1 2-D to 3-D
• 1.3.1.1 Case 1 : Add newaxis at the beginning
• 1.3.1.2 Case 2: Squeeze newaxis in the middle
• 1.3.1.3 Case 3: Add newaxis to the end

from numpy import array, newaxis, expand_dims

First define a display function.

def show_array(y):
print('array: \n', y)
print('array.ndim:', y.ndim)
print('array.shape:', y.shape)

1.1 From 0-D (scalar) to n-D

x = array(5)
show_array(x)
array: 
 5
array.ndim: 0
array.shape: ()

1.1.1 From 0-D to 1-D

y is the result of adding a new dimension to x, and the shape is no longer empty.

y = array(x)[newaxis]
show_array(y)
array: 
 [5]
array.ndim: 1
array.shape: (1,)

Equivalently,

y = expand_dims(x, axis=0)
show_array(y)
array: 
 [5]
array.ndim: 1
array.shape: (1,)

Any number >= 0 does the same as the above.

y = expand_dims(x, axis=123456)
show_array(y)
array: 
 [5]
array.ndim: 1
array.shape: (1,)
/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:1: DeprecationWarning: Both axis > a.ndim and axis < -a.ndim - 1 are deprecated and will raise an AxisError in the future.
  """Entry point for launching an IPython kernel.

Also equivalently,

y = x.reshape(-1,)
show_array(y)
array: 
 [5]
array.ndim: 1
array.shape: (1,)

1.1.2 From 0-D to 2-D

y = array(x)[newaxis, newaxis]
show_array(y)
array: 
 [[5]]
array.ndim: 2
array.shape: (1, 1)
y = expand_dims(x, axis=0)
z = expand_dims(y, axis=0)
show_array(z)
array: 
 [[5]]
array.ndim: 2
array.shape: (1, 1)
y = x.reshape(-1, 1)
show_array(y)
array: 
 [[5]]
array.ndim: 2
array.shape: (1, 1)

1.2 From 1-D to n-D (n>1)

x = array([5, 6, 7])
show_array(x)
array: 
 [5 6 7]
array.ndim: 1
array.shape: (3,)

1.2.1 From 1-D to 2-D

Vector to row matrix

Adding newaxis at the beginning changes the shape from (3,) to (1, 3).

y = array(x)[newaxis, :]
show_array(y)
array: 
 [[5 6 7]]
array.ndim: 2
array.shape: (1, 3)
y = array(x)[newaxis] # This is short hand of y = array(x)[newaxis, :]
show_array(y)
array: 
 [[5 6 7]]
array.ndim: 2
array.shape: (1, 3)
y = expand_dims(x, axis=0)
show_array(y)
array: 
 [[5 6 7]]
array.ndim: 2
array.shape: (1, 3)
y = x.reshape(1, -1)
show_array(y)
array: 
 [[5 6 7]]
array.ndim: 2
array.shape: (1, 3)

Vector to column matrix

Adding newaxis at the end changes the shape from (3,) to (3, 1).

y = array(x)[:, newaxis]
show_array(y)
array: 
 [[5]
 [6]
 [7]]
array.ndim: 2
array.shape: (3, 1)
y = expand_dims(x, axis=1)
show_array(y)
array: 
 [[5]
 [6]
 [7]]
array.ndim: 2
array.shape: (3, 1)

Equivalently,

y = expand_dims(x, axis=-1)
show_array(y)
array: 
 [[5]
 [6]
 [7]]
array.ndim: 2
array.shape: (3, 1)

Any number >= 1 does the same.

y = expand_dims(x, axis=123456)
show_array(y)
array: 
 [[5]
 [6]
 [7]]
array.ndim: 2
array.shape: (3, 1)
/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:1: DeprecationWarning: Both axis > a.ndim and axis < -a.ndim - 1 are deprecated and will raise an AxisError in the future.
  """Entry point for launching an IPython kernel.
y = x.reshape(-1, 1)
show_array(y)
array: 
 [[5]
 [6]
 [7]]
array.ndim: 2
array.shape: (3, 1)

1.3 From 2-D to n-D (n>2)

x = array([[1, 2, 3], [4, 5, 6]])
show_array(x)
array: 
 [[1 2 3]
 [4 5 6]]
array.ndim: 2
array.shape: (2, 3)

1.3.1 2-D to 3-D

1.3.1.1 Case 1 : Add newaxis at the beginning

y = array(x)[newaxis, :, :]
show_array(y)
array: 
 [[[1 2 3]
  [4 5 6]]]
array.ndim: 3
array.shape: (1, 2, 3)

Equivalently,

y = array(x)[newaxis, :]
show_array(y)
array: 
 [[[1 2 3]
  [4 5 6]]]
array.ndim: 3
array.shape: (1, 2, 3)

Equivalently,

y = array(x)[newaxis]
show_array(y)
array: 
 [[[1 2 3]
  [4 5 6]]]
array.ndim: 3
array.shape: (1, 2, 3)
y = expand_dims(x, axis=0)
show_array(y)
array: 
 [[[1 2 3]
  [4 5 6]]]
array.ndim: 3
array.shape: (1, 2, 3)
y = x.reshape(-1, 2, 3)
show_array(y)
array: 
 [[[1 2 3]
  [4 5 6]]]
array.ndim: 3
array.shape: (1, 2, 3)
y = x.reshape(-1, *x.shape)
show_array(y)
array: 
 [[[1 2 3]
  [4 5 6]]]
array.ndim: 3
array.shape: (1, 2, 3)

1.3.1.2 Case 2: Squeeze newaxis in the middle

y = array(x)[:, newaxis, :]
show_array(y)
array: 
 [[[1 2 3]]
 [[4 5 6]]]
array.ndim: 3
array.shape: (2, 1, 3)
y = array(x)[:, newaxis]
show_array(y)
array: 
 [[[1 2 3]]
 [[4 5 6]]]
array.ndim: 3
array.shape: (2, 1, 3)
y = expand_dims(x, axis=1)
show_array(y)
array: 
 [[[1 2 3]]
 [[4 5 6]]]
array.ndim: 3
array.shape: (2, 1, 3)
y = x.reshape(2, 1, 3)
show_array(y)
array: 
 [[[1 2 3]]
 [[4 5 6]]]
array.ndim: 3
array.shape: (2, 1, 3)
y = x.reshape(x.shape[0], -1, x.shape[1])
show_array(y)
array: 
 [[[1 2 3]]
 [[4 5 6]]]
array.ndim: 3
array.shape: (2, 1, 3)

1.3.1.3 Case 3: Add newaxis to the end

y = array(x)[:, :, newaxis]
show_array(y)
array: 
 [[[1]
  [2]
  [3]]
 [[4]
  [5]
  [6]]]
array.ndim: 3
array.shape: (2, 3, 1)
y = expand_dims(x, axis=2)
show_array(y)
array: 
 [[[1]
  [2]
  [3]]
 [[4]
  [5]
  [6]]]
array.ndim: 3
array.shape: (2, 3, 1)
y = expand_dims(x, axis=-1)
show_array(y)
array: 
 [[[1]
  [2]
  [3]]
 [[4]
  [5]
  [6]]]
array.ndim: 3
array.shape: (2, 3, 1)

Any number >= 2 does the same.

y = expand_dims(x, axis=123456)
show_array(y)
array: 
 [[[1]
  [2]
  [3]]
 [[4]
  [5]
  [6]]]
array.ndim: 3
array.shape: (2, 3, 1)
/opt/conda/lib/python3.6/site-packages/ipykernel_launcher.py:1: DeprecationWarning: Both axis > a.ndim and axis < -a.ndim - 1 are deprecated and will raise an AxisError in the future.
  """Entry point for launching an IPython kernel.
y = x.reshape(*x.shape, -1)
show_array(y)
array: 
 [[[1]
  [2]
  [3]]
 [[4]
  [5]
  [6]]]
array.ndim: 3
array.shape: (2, 3, 1)

Notebook is here: https://github.com/yang-zhang/yang-zhang.github.io/blob/master/ds_code/numpy_newaxis.ipynb