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kron(a, b)

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

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 ]]

Parameters

a, b : array_like

Returns

out : ndarray

Kronecker product of two arrays.

See Also

outer

The outer product

Examples

>>> np.kron([1,10,100], [5,6,7])
array([  5,   6,   7, ..., 500, 600, 700])
>>> np.kron([5,6,7], [1,10,100])
array([  5,  50, 500, ...,   7,  70, 700])
>>> np.kron(np.eye(2), np.ones((2,2)))
array([[1.,  1.,  0.,  0.],
       [1.,  1.,  0.,  0.],
       [0.,  0.,  1.,  1.],
       [0.,  0.,  1.,  1.]])
>>> a = np.arange(100).reshape((2,5,2,5))
... b = np.arange(24).reshape((2,3,4))
... c = np.kron(a,b)
... c.shape (2, 10, 6, 20)
>>> I = (1,3,0,2)
... J = (0,2,1)
... J1 = (0,) + J # extend to ndim=4
... S1 = (1,) + b.shape
... K = tuple(np.array(I) * np.array(S1) + np.array(J1))
... c[K] == a[I]*b[J] True
See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /numpy/lib/shape_base.py#1067
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