View source for Extending an existing matrix: tile, repeat, pad

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

== [https://numpy.org/doc/stable/reference/generated/numpy.tile.html numpy.tile] ==
<syntaxhighlight lang="python">numpy.tile(A, reps)</syntaxhighlight><blockquote>Construct an array by repeating A the number of times given by reps.

If reps has length d, the result will have dimension of max(d, A.ndim).

If A.ndim &#x3C; d, A is promoted to be d-dimensional by prepending new axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication, or shape (1, 1, 3) for 3-D replication. If this is not the desired behavior, promote A to d-dimensions manually before calling this function.

If A.ndim &#x3E; d, reps is promoted to A.ndim by pre-pending 1’s to it. Thus for an A of shape (2, 3, 4, 5), a reps of (2, 2) is treated as (1, 1, 2, 2).

Note: Although tile may be used for broadcasting, it is strongly recommended to use numpy’s broadcasting operations and functions.</blockquote>'''You might want to first use numpy.newaxis to create the required additional axis and then use tile.'''

Adding a new dimension makes a copy:<syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 5)

print(a)  # -> [1 2 3 4]
print(a.shape)  # -> (4,)

b = a[np.newaxis, :]
print(b.shape)  # -> (1, 4)
print(np.may_share_memory(a, b))  # -> True (View)

c = np.tile(a, (1, 1))
print(c.shape)  # -> (1, 4)
print(np.may_share_memory(a, c))  # -> False (Copy)</syntaxhighlight>Examples:<syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 5)[np.newaxis, :]

print(a)  # -> [[1 2 3 4]]
print(a.shape)  # -> (1, 4)

c = np.tile(a, (1, 1))
print(c)  # -> [[1 2 3 4]]
print(c.shape)  # -> (1, 4)

c = np.tile(a, (4, 1))
print(c)
print(c.shape)  # -> (4, 4)

c = np.tile(a, (1, 4))
print(c)  # -> [[1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4]]
print(c.shape)  # -> (1, 16)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[1 2 3 4]
 [1 2 3 4]
 [1 2 3 4]
 [1 2 3 4]]</syntaxhighlight>Be very careful if you haven’t newaxis-ed…<syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 5)

print(a)  # -> [1 2 3 4]
print(a.shape)  # -> (4,)

c = np.tile(a, (4))
print(c)  # -> [1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4]
print(c.shape)  # -> (16,)

c = np.tile(a, (1, 4))
print(c)  # -> [[1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4]]
print(c.shape)  # -> (1, 16)

c = np.tile(a, (4, 1))
print(c)
print(c.shape)  # -> (4, 4)
print()

c = np.tile(a, (4, 1, 1))
print(c) 
print(c.shape)  # -> (4, 1, 4)
print()

c = np.tile(a, (1, 4, 1))
print(c) 
print(c.shape)  # -> (1, 4, 4)
print()

c = np.tile(a, (1, 1, 4))
print(c)  # -> [[[1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4]]]
print(c.shape)  # -> (1, 1, 16)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[1 2 3 4]
 [1 2 3 4]
 [1 2 3 4]
 [1 2 3 4]]

[[[1 2 3 4]]

 [[1 2 3 4]]

 [[1 2 3 4]]

 [[1 2 3 4]]]

[[[1 2 3 4]
  [1 2 3 4]
  [1 2 3 4]
  [1 2 3 4]]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.repeat.html#numpy-repeat numpy.repeat] ==
'''Don’t confuse tile() with repeat()!'''<syntaxhighlight lang="python">numpy.repeat(a, repeats, axis=None)[source]</syntaxhighlight><blockquote>Repeat each element of an array after themselves</blockquote><syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 5)
print(a)  # -> [1 2 3 4]
print(a.shape)  # -> (4,)

b = np.repeat(a, (4))
print(b)  # -> [1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4]
print(b.shape)  # -> (16,)</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.pad.html numpy.pad] ==
<syntaxhighlight lang="python">numpy.pad(array, pad_width, mode='constant', **kwargs)</syntaxhighlight><blockquote>Pad an array.</blockquote><blockquote>'''pad_width''': {sequence, array_like, int}

Number of values padded to the edges of each axis. ((before_1, after_1), … (before_N, after_N)) unique pad widths for each axis. (before, after) or ((before, after),) yields same before and after pad for each axis. (pad,) or int is a shortcut for before = after = pad width for all axes.</blockquote><blockquote>'''constant_values''': sequence or scalar, optional

Used in ‘constant’. The values to set the padded values for each axis.

((before_1, after_1), … (before_N, after_N)) unique pad constants for each axis.

(before, after) or ((before, after),) yields same before and after constants for each axis.

(constant,) or constant is a shortcut for before = after = constant for all axes.

Default is 0.</blockquote><syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 5)
print(a)  # -> [1 2 3 4]
print(a.shape)  # -> (4,)


print(np.pad(a, 2))  # -> [0 0 1 2 3 4 0 0]
print(np.pad(a, [2, 3]))  # -> [0 0 1 2 3 4 0 0 0]
print(np.pad(a, [2, 3], constant_values=-1))  # -> [-1 -1  1  2  3  4 -1 -1 -1]</syntaxhighlight><syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 5).reshape((1, 4))
print(a)  # -> [[1 2 3 4]]
print(a.shape)  # -> (1, 4)


print(np.pad(a, [[2, 3], [1, 1]]))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 1 2 3 4 0]
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]]</syntaxhighlight>

=== Pad can do more complex padding patterns than just pad with constant values! ===
<blockquote>'''mode''': str or function, optional

One of the following string values or a user supplied function.</blockquote>
{| class="wikitable"
|‘constant’ (default)
|Pads with a constant value.
|-
|‘edge’
|Pads with the edge values of array.
|-
|‘linear_ramp’
|Pads with the linear ramp between end_value and the array edge value.
|-
|‘maximum’
|Pads with the maximum value of all or part of the vector along each axis.
|-
|‘mean’
|Pads with the mean value of all or part of the vector along each axis.
|-
|‘median’
|Pads with the median value of all or part of the vector along each axis.
|-
|‘minimum’
|Pads with the minimum value of all or part of the vector along each axis.
|-
|‘reflect’
|Pads with the reflection of the vector mirrored on the first and last values of the vector along each axis.
|-
|‘symmetric’
|Pads with the reflection of the vector mirrored along the edge of the array.
|-
|‘wrap’
|Pads with the wrap of the vector along the axis. The first values are used to pad the end and the end values are used to pad the beginning.
|-
|‘empty’
|Pads with undefined values.
|-
|<function>
|Padding function, see Notes.
|}