t3toolbox.backend.contractions.dMNi_dMio_to_dMNo

t3toolbox.backend.contractions.dMNi_dMio_to_dMNo(dMNi: t3toolbox.backend.common.NDArray, dMio: t3toolbox.backend.common.NDArray, use_jax: bool = False) → t3toolbox.backend.common.NDArray

Computes named contraction.

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 dMNi_dMio_to_dMNo
>>> dMNi = np.random.randn(8, 5,6, 2,3,4, 10)
>>> dMio = np.random.randn(8, 5,6, 10,13)
>>> result = dMNi_dMio_to_dMNo(dMNi, dMio)
>>> result2 = np.einsum('duvxyzi,duvio->duvxyzo', dMNi, dMio)
>>> 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 dMNi_dMio_to_dMNo
>>> dMNi = np.random.randn(8, 2,3,4, 10)
>>> dMio = np.random.randn(8, 10,13)
>>> result = dMNi_dMio_to_dMNo(dMNi, dMio)
>>> result2 = np.einsum('dxyzi,dio->dxyzo', dMNi, dMio)
>>> 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 dMNi_dMio_to_dMNo
>>> dMNi = np.random.randn(8, 5,6, 10)
>>> dMio = np.random.randn(8, 5,6, 10,13)
>>> result = dMNi_dMio_to_dMNo(dMNi, dMio)
>>> result2 = np.einsum('duvi,duvio->duvo', dMNi, dMio)
>>> 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 dMNi_dMio_to_dMNo
>>> dMNi = np.random.randn(8, 10)
>>> dMio = np.random.randn(8, 10,13)
>>> result = dMNi_dMio_to_dMNo(dMNi, dMio)
>>> result2 = np.einsum('di,dio->do', dMNi, dMio)
>>> print(result.shape == result2.shape)
True
>>> print(np.linalg.norm(result - result2))
0.0