t3toolbox.backend.contractions.MNi_Mio_to_MNo
=============================================

.. py:function:: 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.

   .. rubric:: 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