t3toolbox.backend.contractions.dMNa_dMaib_dMNb_to_dMNi
======================================================

.. py:function:: 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.

   .. rubric:: 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