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.ndimthe 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.
New in version 1.13.0.
- 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.
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
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], ]
Join a sequence of arrays along an existing axis.
Join a sequence of arrays along a new axis.
Stack arrays in sequence vertically (row wise).
Stack arrays in sequence horizontally (column wise).
Stack arrays in sequence depth wise (along third axis).
Stack 1-D arrays as columns into a 2-D array.
Split an array into multiple sub-arrays vertically (row-wise).
When called with only scalars,
np.blockis 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,
blockis _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, ...]]).
The most common use of this function is to build a block matrix
>>> 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,
blockcan be used as
>>> 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,
blockcan be used in place of
>>> 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 places of
>>> a = np.array(0) >>> b = np.array() >>> np.block([a]) # atleast_1d(a) array() >>> np.block([b]) # atleast_1d(b) array()
>>> np.block([[a]]) # atleast_2d(a) array([]) >>> np.block([[b]]) # atleast_2d(b) array([])