t3toolbox.backend.contractions.MNa_Maib_No_Mio_to_MNb

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

Computes vectorized einsum a,aib,o,io->b, with vectorization over a and i, or aib and io, 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 MNa_Maib_No_Mio_to_MNb
>>> uv_xyz_a = np.random.randn(5,6, 2,3,4, 10)
>>> uv_aib = np.random.randn(5,6, 10,11,12)
>>> xyz_o = np.random.randn(2,3,4, 13)
>>> uv_io = np.random.randn(5,6, 11,13)
>>> MNb = MNa_Maib_No_Mio_to_MNb(uv_xyz_a, uv_aib, xyz_o, uv_io)
>>> MNb_true = np.einsum('uvxyza,uvaib,xyzo,uvio->uvxyzb', uv_xyz_a, uv_aib, xyz_o, uv_io)
>>> print(MNb.shape == MNb_true.shape)
True
>>> print(np.linalg.norm(MNb - MNb_true))
1.4784891826885966e-12

Vectorize over N only

>>> import numpy as np
>>> from t3toolbox.utils.contractions import MNa_Maib_No_Mio_to_MNb
>>> xyz_a = np.random.randn(2,3,4, 10)
>>> aib = np.random.randn(10,11,12)
>>> xyz_o = np.random.randn(2,3,4, 13)
>>> io = np.random.randn(11,13)
>>> MNb = MNa_Maib_No_Mio_to_MNb(xyz_a, aib, xyz_o, io)
>>> MNb_true = np.einsum('xyza,aib,xyzo,io->xyzb', xyz_a, aib, xyz_o, io)
>>> print(MNb.shape == MNb_true.shape)
True
>>> print(np.linalg.norm(MNb - MNb_true))
4.083260418474411e-13

Vectorize over both M only:

>>> import numpy as np
>>> from t3toolbox.utils.contractions import MNa_Maib_No_Mio_to_MNb
>>> uv_a = np.random.randn(5,6, 10)
>>> uv_aib = np.random.randn(5,6, 10,11,12)
>>> o = np.random.randn(13)
>>> uv_io = np.random.randn(5,6, 11,13)
>>> MNb = MNa_Maib_No_Mio_to_MNb(uv_a, uv_aib, o, uv_io)
>>> MNb_true = np.einsum('uva,uvaib,o,uvio->uvb', uv_a, uv_aib, o, uv_io)
>>> print(MNb.shape == MNb_true.shape)
True
>>> print(np.linalg.norm(MNb - MNb_true))
2.859552860272838e-13

No vectorization:

>>> import numpy as np
>>> from t3toolbox.utils.contractions import MNa_Maib_No_Mio_to_MNb
>>> a = np.random.randn(10)
>>> aib = np.random.randn(10,11,12)
>>> o = np.random.randn(13)
>>> io = np.random.randn(11,13)
>>> MNb = MNa_Maib_No_Mio_to_MNb(a, aib, o, io)
>>> MNb_true = np.einsum('a,aib,o,io->b', a, aib, o, io)
>>> print(MNb.shape == MNb_true.shape)
True
>>> print(np.linalg.norm(MNb - MNb_true))
3.638551654418504e-14