5.4.2. nvector.util.mdot¶

mdot(a, b)[source]¶

Returns multiple matrix multiplications of two arrays i.e. dot(a, b)[i,j,k] = sum(a[i,:,j] * b[:,j,k])

Parameters

aarray_like: First argument.
barray_like: Second argument.

See also

numpy.einsum

Notes

if a and b have the same shape this is the same as

np.concatenate([np.dot(a[…,i], b[…,i])[:, :, None] for i in range(n)], axis=2)

Examples

3 x 3 x 2 times 3 x 3 x 2 array -> 3 x 2 x 2 array

>>> import numpy as np
>>> import nvector as nv
>>> a = 1.0 * np.arange(18).reshape(3,3,2)
>>> b = - a
>>> t = np.concatenate([np.dot(a[...,i], b[...,i])[:, :, None]
...                    for i in range(2)], axis=2)
>>> tm = nv.mdot(a, b)
>>> tm.shape
(3, 3, 2)
>>> np.allclose(t, tm)
True

3 x 3 x 2 times 3 x 1 array -> 3 x 1 x 2 array

>>> t1 = np.concatenate([np.dot(a[...,i], b[:,0,0][:,None])[:,:,None]
...                    for i in range(2)], axis=2)

>>> tm1 = nv.mdot(a, b[:,0,0].reshape(-1,1))
>>> tm1.shape
(3, 1, 2)
>>> np.allclose(t1, tm1)
True

3 x 3 times 3 x 3 array -> 3 x 3 array

>>> tt0 = nv.mdot(a[...,0], b[...,0])
>>> tt0.shape
(3, 3)
>>> np.allclose(t[...,0], tt0)
True

3 x 3 times 3 x 1 array -> 3 x 1 array

>>> tt0 = nv.mdot(a[...,0], b[:,:1,0])
>>> tt0.shape
(3, 1)
>>> np.allclose(t[:,:1,0], tt0)
True

3 x 3 times 3 x 1 x 2 array -> 3 x 1 x 2 array

>>> tt0 = nv.mdot(a[..., 0], b[:, :2, 0][:, None])
>>> tt0.shape
(3, 1, 2)
>>> np.allclose(t[:,:2,0][:,None], tt0)
True