t3toolbox.backend.contractions.MNi_Mio_to_MNo

t3toolbox.backend.contractions.MNi_Mio_to_MNo(MNi: t3toolbox.backend.common.NDArray, Mio: t3toolbox.backend.common.NDArray, use_jax: bool = False) → t3toolbox.backend.common.NDArray

Computes contraction i,io->o.

N and M may be individual indices, groups of indices, or nonexistent.

Examples

Vectorize over both N and M:

>>> import numpy as np
>>> from t3toolbox.utils.contractions import MNi_Mio_to_MNo
>>> Ni = np.random.randn(2,3,4, 10)
>>> Mio = np.random.randn(5,6, 10,13)
>>> result = MNi_Mio_to_MNo(Ni, Mio)
>>> result2 = np.einsum('xyzi,uvio->uvxyzo', Ni, Mio)
>>> 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 MNi_Mio_to_MNo
>>> Ni = np.random.randn(2,3,4, 10)
>>> Mio = np.random.randn(10,13)
>>> result = MNi_Mio_to_MNo(Ni, Mio)
>>> result2 = np.einsum('xyzi,io->xyzo', Ni, Mio)
>>> 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 MNi_Mio_to_MNo
>>> Ni = np.random.randn(10)
>>> Mio = np.random.randn(5,6, 10,13)
>>> result = MNi_Mio_to_MNo(Ni, Mio)
>>> result2 = np.einsum('i,uvio->uvo', Ni, Mio)
>>> 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 MNi_Mio_to_MNo
>>> Ni = np.random.randn(10)
>>> Mio = np.random.randn(10,13)
>>> result = MNi_Mio_to_MNo(Ni, Mio)
>>> result2 = np.einsum('i,io->o', Ni, Mio)
>>> print(result.shape == result2.shape)
True
>>> print(np.linalg.norm(result - result2))
0.0