Davrot at 16:33, 17 October 2025

2025-10-17T16:33:24Z

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	~~== The goal ==~~
	Matrices have dimensions. But how to add and remove extra dimensions (i.e. dimensions with length 1)?		Matrices have dimensions. But how to add and remove extra dimensions (i.e. dimensions with length 1)?

Davrot: Created page with "== The goal == Matrices have dimensions. But how to add and remove extra dimensions (i.e. dimensions with length 1)? Questions to [mailto:davrot@uni-bremen.de David Rotermund] == [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html numpy.ndarray.shape] == ndarray.shape
Tuple of array dimensions. The shape property is usually used to get the current shape of an array, but may also be used..."

2025-10-16T16:06:14Z

Created page with "== The goal == Matrices have dimensions. But how to add and remove extra dimensions (i.e. dimensions with length 1)? Questions to [mailto:davrot@uni-bremen.de David Rotermund] == [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html numpy.ndarray.shape] == <syntaxhighlight lang="python">ndarray.shape</syntaxhighlight><blockquote>Tuple of array dimensions. The shape property is usually used to get the current shape of an array, but may also be used..."

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== The goal ==
Matrices have dimensions. But how to add and remove extra dimensions (i.e. dimensions with length 1)?

Questions to [mailto:davrot@uni-bremen.de David Rotermund]

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html numpy.ndarray.shape] ==
<syntaxhighlight lang="python">ndarray.shape</syntaxhighlight><blockquote>Tuple of array dimensions.

The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with numpy.reshape, one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.</blockquote><syntaxhighlight lang="python">import numpy as np

data = np.zeros((2, 4, 2, 7, 2))
print(data.shape) # -> (2, 4, 2, 7, 2)</syntaxhighlight>

== Vanishing dimensions ==
<syntaxhighlight lang="python">import numpy as np

data = np.zeros((5, 3, 2))

# All the same dimensionwise
print(data.shape) # -> (5, 3, 2)
print(data[:].shape) # -> (5, 3, 2)
print(data[:, :, :].shape) # -> (5, 3, 2)
print(data[...].shape) # -> (5, 3, 2)

print(data[0, :, :].shape) # -> (3, 2)
print(data[:, 0, :].shape) # -> (5, 2)
print(data[:, :, 0].shape) # -> (5, 3)

print(data[:, 0, 0].shape) # -> (5,)
print(data[0, :, 0].shape) # -> (3,)
print(data[0, 0, :].shape) # -> (2,)

print(data[0, 0, 0].shape) # -> ()
print(type(data[0, 0, 0])) # -> <class 'numpy.float64'></syntaxhighlight>

=== keepdims ===
There are functions like<syntaxhighlight lang="python">ndarray.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)
ndarray.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)
ndarray.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)
ndarray.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
ndarray.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
ndarray.argmax(axis=None, out=None, *, keepdims=False)
ndarray.argmin(axis=None, out=None, *, keepdims=False)</syntaxhighlight>that normally make one dimension vanish. However, often this type of functions have an argument '''keepdims''' that keeps this dimension alive.<syntaxhighlight lang="python">import numpy as np

data = np.zeros((5, 3, 2))

# All the same dimensionwise
print(data.shape) # -> (5, 3, 2)
print(data.sum().shape) # -> ()
print(data.sum(axis=0).shape) # -> (3, 2)
print(data.sum(axis=1).shape) # -> (5, 2)
print(data.sum(axis=2).shape) # -> (5, 3)

# You can use keepdims:

print(data.sum(axis=0, keepdims=True).shape) # -> (1, 3, 2)
print(data.sum(axis=1, keepdims=True).shape) # -> (5, 1, 2)
print(data.sum(axis=2, keepdims=True).shape) # -> (5, 3, 1)</syntaxhighlight>As as reminder, shape is only availabe for np.ndarray and torch.Tensor matrices:<syntaxhighlight lang="python">z = int(7)
print(np.array(z).shape) # -> ()
print(type(np.array(z))) # -> <class 'numpy.ndarray'>
print(type(z)) # -> <class 'int'>
print(z.shape) # -> AttributeError: 'int' object has no attribute 'shape'</syntaxhighlight>

== Stop vanishing dimensions ==
One way to do stop vanishing dimensions is to use slices of thickness 1. If you want the nth element, then use '''n:n+1''':<syntaxhighlight lang="python">import numpy as np

data = np.zeros((5, 3, 2))

# All the same dimensionwise
print(data.shape) # -> (5, 3, 2)

print(data[0:1, :, :].shape) # -> (1, 3, 2)
print(data[:, 0:1, :].shape) # -> (5, 1, 2)
print(data[:, :, 0:1].shape) # -> (5, 3, 1)

print(data[:, 0:1, 0:1].shape) # -> (5, 1, 1)
print(data[0:1, :, 0:1].shape) # -> (1, 3, 1)
print(data[0:1, 0:1, :].shape) # -> (1, 1, 2)

print(data[0:1, 0:1, 0:1].shape) # -> (1, 1, 1)
print(type(data[0:1, 0:1, 0:1])) # -> <class 'numpy.ndarray'></syntaxhighlight>'''Please understand this creates a view which is connected to original data.''' If necessary make a '''copy()'''.

== Adding dimensions with [https://numpy.org/doc/stable/reference/constants.html#numpy.newaxis np.newaxis] ==
<syntaxhighlight lang="python">numpy.newaxis</syntaxhighlight><blockquote>A convenient alias for None, useful for indexing arrays.</blockquote><syntaxhighlight lang="python">import numpy as np

data = np.zeros((2))
print(data.shape) # -> (2,)
print(data[:, np.newaxis].shape) # -> (2, 1)
print(data[np.newaxis, :].shape) # -> (1, 2)

print(data[:, np.newaxis, np.newaxis].shape) # -> (2, 1, 1)
print(data[np.newaxis, :, np.newaxis].shape) # -> (1, 2, 1)
print(data[:, np.newaxis, np.newaxis].shape) # -> (2, 1, 1)</syntaxhighlight>

== Adding dimensions with [https://numpy.org/doc/stable/reference/generated/numpy.expand_dims.html numpy.expand_dims] ==
In the case you don’t like newaxis for adding a new dimension…<syntaxhighlight lang="python">numpy.expand_dims(a, axis)</syntaxhighlight><blockquote>Expand the shape of an array.

Insert a new axis that will appear at the axis position in the expanded array shape.</blockquote><syntaxhighlight lang="python">import numpy as np

data = np.zeros((2))
print(data.shape) # -> (2,)
print(np.expand_dims(data, axis=0).shape) # -> (1, 2)
print(np.expand_dims(data, axis=1).shape) # -> (2, 1)
print(np.expand_dims(data, axis=(1, 2, 3)).shape) # -> (2, 1, 1, 1)</syntaxhighlight>

== Removing dimensions with [https://numpy.org/doc/stable/reference/generated/numpy.squeeze.html numpy.squeeze] ==
<syntaxhighlight lang="python">numpy.squeeze(a, axis=None)</syntaxhighlight><blockquote>Remove axes of length one from a.</blockquote><syntaxhighlight lang="python">import numpy as np

data = np.zeros((1, 2, 1, 1))
print(data.shape) # -> (1, 2, 1, 1)
print(np.squeeze(data).shape) # -> (2,)
print(np.squeeze(data, axis=0).shape) # -> (2, 1, 1)
print(np.squeeze(data, axis=2).shape) # -> (1, 2, 1)
print(np.squeeze(data, axis=3).shape) # -> (1, 2, 1)

print(np.squeeze(data, axis=(0, -1)).shape) # -> (2, 1)

print(
np.squeeze(data, axis=1).shape
) # -> ValueError: cannot select an axis to squeeze out which has size not equal to one</syntaxhighlight>

Dimensions and shape - Revision history

Davrot at 16:33, 17 October 2025