`scipy._lib.array_api_extra._lib._funcs:kron`

source: /scipy/_lib/array_api_extra/_lib/_funcs.py :409

Signature

   def     kron (    a  :  Array | complex    ,    b  :  Array | complex    ,  / ,     xp  :  ModuleType | None    =  None     )   →  Array

Summary

Kronecker product of two arrays.

Extended Summary

Computes the Kronecker product, a composite array made of blocks of the second array scaled by the first.

Equivalent to numpy.kron for NumPy arrays.

Parameters

a, b : Array | int | float | complex: Input arrays or scalars. At least one must be an array.
xp : array_namespace, optional: The standard-compatible namespace for a and b. Default: infer.

Returns

: array: The Kronecker product of a and b.

Notes

The function assumes that the number of dimensions of a and b are the same, if necessary prepending the smallest with ones. If a.shape = (r0,r1,..,rN) and b.shape = (s0,s1,...,sN), the Kronecker product has shape (r0*s0, r1*s1, ..., rN*SN). The elements are products of elements from a and b, organized explicitly by

kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]

where

kt = it * st + jt,  t = 0,...,N

In the common 2-D case (N=1), the block structure can be visualized

[[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
 [  ...                              ...   ],
 [ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]

Examples

import array_api_strict as xp
import array_api_extra as xpx
xpx.kron(xp.asarray([1, 10, 100]), xp.asarray([5, 6, 7]), xp=xp)

⚠

xpx.kron(xp.asarray([5, 6, 7]), xp.asarray([1, 10, 100]), xp=xp)

⚠

xpx.kron(xp.eye(2), xp.ones((2, 2)), xp=xp)

⚠

a = xp.reshape(xp.arange(100), (2, 5, 2, 5))
b = xp.reshape(xp.arange(24), (2, 3, 4))
c = xpx.kron(a, b, xp=xp)
c.shape

⚠

I = (1, 3, 0, 2)
J = (0, 2, 1)
J1 = (0,) + J             # extend to ndim=4

✓

S1 = (1,) + b.shape
K = tuple(xp.asarray(I) * xp.asarray(S1) + xp.asarray(J1))
c[K] == a[I]*b[J]

⚠

Aliases

scipy.differentiate.xpx.kron