Extending an existing matrix

The goal

numpy.tile

numpy.tile(A, reps)

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 < 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 > 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.

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:

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)

Examples:

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)

Output:

[[1 2 3 4]
 [1 2 3 4]
 [1 2 3 4]
 [1 2 3 4]]

Be very careful if you haven’t newaxis-ed…

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)

Output:

[[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]]]

numpy.repeat

Don’t confuse tile() with repeat()!

numpy.repeat(a, repeats, axis=None)[source]

Repeat each element of an array after themselves

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,)

numpy.pad

numpy.pad(array, pad_width, mode='constant', **kwargs)

Pad an array.

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.

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.

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]

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]]))

Output:

[[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]]

Pad can do more complex padding patterns than just pad with constant values!

mode : str or function, optional

One of the following string values or a user supplied function.


‘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.
	Padding function, see Notes.

The source code is Open Source and can be found on GitHub.