t3toolbox.backend.contractions.dMio_dNo_to_dMNi
===============================================

.. py:function:: t3toolbox.backend.contractions.dMio_dNo_to_dMNi(dMio: t3toolbox.backend.common.NDArray, dNo: t3toolbox.backend.common.NDArray, use_jax: bool = False) -> t3toolbox.backend.common.NDArray

   Computes contraction dMio,dNo->dMNi.

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