t3toolbox.backend.contractions.Mio_No_to_MNi

t3toolbox.backend.contractions.Mio_No_to_MNi(Mio: t3toolbox.backend.common.NDArray, No: t3toolbox.backend.common.NDArray, use_jax: bool = False) → t3toolbox.backend.common.NDArray

Computes vectorized einsum io,o->i, with vectorization over io, o, or both

N and M are the vectorization indices, which may be groups of indices.

Examples

Vectorize over both N and M:

>>> import numpy as np
>>> from t3toolbox.utils.contractions import Mio_No_to_MNi
>>> Mio = np.random.randn(5,6, 10,13)
>>> No = np.random.randn(2,3,4, 13)
>>> result = Mio_No_to_MNi(Mio, No)
>>> result2 = np.einsum('uvio,xyzo->uvxyzi', Mio, No)
>>> print(result.shape == result2.shape)
True
>>> print(np.linalg.norm(result - result2))
0.0

Vectorize over N only

>>> import numpy as np
>>> from t3toolbox.utils.contractions import Mio_No_to_MNi
>>> Mio = np.random.randn(10,13)
>>> No = np.random.randn(2,3,4, 13)
>>> result = Mio_No_to_MNi(Mio, No)
>>> result2 = np.einsum('io,xyzo->xyzi', Mio, No)
>>> print(result.shape == result2.shape)
True
>>> print(np.linalg.norm(result - result2))
0.0

Vectorize over both M only:

>>> import numpy as np
>>> from t3toolbox.utils.contractions import Mio_No_to_MNi
>>> Mio = np.random.randn(5,6, 10,13)
>>> No = np.random.randn(13)
>>> result = Mio_No_to_MNi(Mio, No)
>>> result2 = np.einsum('uvio,o->uvi', Mio, No)
>>> print(result.shape == result2.shape)
True
>>> print(np.linalg.norm(result - result2))
0.0

No vectorization:

>>> import numpy as np
>>> from t3toolbox.utils.contractions import Mio_No_to_MNi
>>> Mio = np.random.randn(10,13)
>>> No = np.random.randn(13)
>>> result = Mio_No_to_MNi(Mio, No)
>>> result2 = np.einsum('io,o->i', Mio, No)
>>> print(result.shape == result2.shape)
True
>>> print(np.linalg.norm(result - result2))
0.0