numpy.block#

numpy.block(arrays)[source]#

Assemble an nd-array from nested lists of blocks.

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

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

When the nested list is two levels deep, this allows block matrices to beconstructed 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), thisis returned unmodified (and not copied).

Elements shapes must match along the appropriate axes (withoutbroadcasting), but leading 1s will be prepended to the shape asnecessary 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] isillegal, 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 ndarraycall. Sonp.block([[1,2],[3,4]]) is equivalent tonp.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:

AAAbbAAAbbcccDD

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

AAAbbAAAbbcDDDD

Since concatenation happens along the last axis first,block isnotcapable of producing the following directly:

AAAbbcccbbcccDD

Matlab’s “square bracket stacking”,[A,B,...;p,q,...], isequivalent tonp.block([[A,B,...],[p,q,...]]).

Examples

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

>>>importnumpyasnp>>>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 ashstack:

>>>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 ofvstack:

>>>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 ofatleast_1d andatleast_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]])
On this page