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 using the normalrules. Instead, leading axes of size 1 are inserted, to makeblock.ndimthe same for all blocks. This is primarily useful for 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.

New in version 1.13.0.

Parameters:	arrays:nested 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_array:ndarray 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 together.

stack

Stack arrays in sequence along a new dimension.

hstack

Stack arrays in sequence horizontally (column wise).

vstack

Stack arrays in sequence vertically (row wise).

dstack

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

vsplit

Split array into a list of multiple sub-arrays vertically.

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 is _not_capable 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

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

>>>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 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]])