t3toolbox.backend.contractions.dMNa_dMaib_dMNb_to_dMNi

t3toolbox.backend.contractions.dMNa_dMaib_dMNb_to_dMNi(dMNa: t3toolbox.backend.common.NDArray, dMaib: t3toolbox.backend.common.NDArray, dMNb: t3toolbox.backend.common.NDArray, use_jax: bool = False) → t3toolbox.backend.common.NDArray

Computes contraction MNa,dMaib,MNb->dMNi.

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 dMNa_dMaib_dMNb_to_dMNi
>>> dMNa = np.random.randn(8, 2,3, 4,5,6, 10)
>>> dMaib = np.random.randn(8, 2,3, 10,11,12)
>>> dMNb = np.random.randn(8, 2,3, 4,5,6, 12)
>>> result = dMNa_dMaib_dMNb_to_dMNi(dMNa, dMaib, dMNb)
>>> result2 = np.einsum('duvxyza,duvaib,duvxyzb->duvxyzi', dMNa, dMaib, dMNb)
>>> 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 dMNa_dMaib_dMNb_to_dMNi
>>> dMNa = np.random.randn(8, 4,5,6, 10)
>>> dMaib = np.random.randn(8, 10,11,12)
>>> dMNb = np.random.randn(8, 4,5,6, 12)
>>> result = dMNa_dMaib_dMNb_to_dMNi(dMNa, dMaib, dMNb)
>>> result2 = np.einsum('dxyza,daib,dxyzb->dxyzi', dMNa, dMaib, dMNb)
>>> 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 dMNa_dMaib_dMNb_to_dMNi
>>> dMNa = np.random.randn(8, 2,3, 10)
>>> dMaib = np.random.randn(8, 2,3, 10,11,12)
>>> dMNb = np.random.randn(8, 2,3, 12)
>>> result = dMNa_dMaib_dMNb_to_dMNi(dMNa, dMaib, dMNb)
>>> result2 = np.einsum('duva,duvaib,duvb->duvi', dMNa, dMaib, dMNb)
>>> 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 dMNa_dMaib_dMNb_to_dMNi
>>> dMNa = np.random.randn(8, 10)
>>> dMaib = np.random.randn(8, 10,11,12)
>>> dMNb = np.random.randn(8, 12)
>>> result = dMNa_dMaib_dMNb_to_dMNi(dMNa, dMaib, dMNb)
>>> result2 = np.einsum('da,daib,db->di', dMNa, dMaib, dMNb)
>>> print(result.shape == result2.shape)
True
>>> print(np.linalg.norm(result - result2))
0.0