t3toolbox.backend.contractions.MNa_Maib_No_Mio_to_MNb
=====================================================

.. py:function:: 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.

   .. rubric:: 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