numpy.block

numpy.block(arrays)[source]

Assemble an nd-array from nested lists of blocks.

Blocks in the innermost lists are concatenated (see concatenate) along the last dimension (-1), then these are concatenated along the second-last dimension (-2), and so on until the outermost list is reached.

Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make block.ndim the same for all blocks. This is primarily useful for working with scalars, and means that code like np.block([v, 1]) is valid, where v.ndim == 1.

When the nested list is two levels deep, this allows block matrices to be constructed from their components.

Parameters:

arraysnested list of array_like or scalars (but not tuples)

If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied).

Elements shapes must match along the appropriate axes (without broadcasting), but leading 1s will be prepended to the shape as necessary to make the dimensions match.

Returns:

block_arrayndarray

The array assembled from the given blocks.

The dimensionality of the output is equal to the greatest of:

• the dimensionality of all the inputs
• the depth to which the input list is nested

Raises:

ValueError

• If list depths are mismatched - for instance, [[a, b], c] is illegal, and should be spelt [[a, b], [c]]
• If lists are empty - for instance, [[a, b], []]

See also

concatenate

Join a sequence of arrays along an existing axis.

stack

Join a sequence of arrays along a new axis.

vstack

Stack arrays in sequence vertically (row wise).

hstack

Stack arrays in sequence horizontally (column wise).

dstack

Stack arrays in sequence depth wise (along third axis).

column_stack

Stack 1-D arrays as columns into a 2-D array.

vsplit

Split an array into multiple sub-arrays vertically (row-wise).

unstack

Split an array into a tuple of sub-arrays along an axis.

Notes

When called with only scalars, np.block is equivalent to an ndarray call. So np.block([[1, 2], [3, 4]]) is equivalent to np.array([[1, 2], [3, 4]]).

This function does not enforce that the blocks lie on a fixed grid. np.block([[a, b], [c, d]]) is not restricted to arrays of the form:

AAAbb
AAAbb
cccDD

But is also allowed to produce, for some a, b, c, d:

AAAbb
AAAbb
cDDDD

Since concatenation happens along the last axis first, block is not capable of producing the following directly:

AAAbb
cccbb
cccDD

Matlab’s “square bracket stacking”, [A, B, ...; p, q, ...], is equivalent to np.block([[A, B, ...], [p, q, ...]]).

Examples

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The most common use of this function is to build a block matrix:

>>> import numpy as np
>>> A = np.eye(2) * 2
>>> B = np.eye(3) * 3
>>> np.block([
...     [A,               np.zeros((2, 3))],
...     [np.ones((3, 2)), B               ]
... ])
array([[2., 0., 0., 0., 0.],
       [0., 2., 0., 0., 0.],
       [1., 1., 3., 0., 0.],
       [1., 1., 0., 3., 0.],
       [1., 1., 0., 0., 3.]])

With a list of depth 1, block can be used as hstack:

>>> np.block([1, 2, 3])              # hstack([1, 2, 3])
array([1, 2, 3])

>>> a = np.array([1, 2, 3])
>>> b = np.array([4, 5, 6])
>>> np.block([a, b, 10])             # hstack([a, b, 10])
array([ 1,  2,  3,  4,  5,  6, 10])

>>> A = np.ones((2, 2), int)
>>> B = 2 * A
>>> np.block([A, B])                 # hstack([A, B])
array([[1, 1, 2, 2],
       [1, 1, 2, 2]])

With a list of depth 2, block can be used in place of vstack:

>>> a = np.array([1, 2, 3])
>>> b = np.array([4, 5, 6])
>>> np.block([[a], [b]])             # vstack([a, b])
array([[1, 2, 3],
       [4, 5, 6]])

>>> A = np.ones((2, 2), int)
>>> B = 2 * A
>>> np.block([[A], [B]])             # vstack([A, B])
array([[1, 1],
       [1, 1],
       [2, 2],
       [2, 2]])

It can also be used in place of atleast_1d and atleast_2d:

>>> a = np.array(0)
>>> b = np.array([1])
>>> np.block([a])                    # atleast_1d(a)
array([0])
>>> np.block([b])                    # atleast_1d(b)
array([1])

>>> np.block([[a]])                  # atleast_2d(a)
array([[0]])
>>> np.block([[b]])                  # atleast_2d(b)
array([[1]])

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