t3toolbox.backend.contractions.MNa_Maib_MNb_to_MNi
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.. py:function:: t3toolbox.backend.contractions.MNa_Maib_MNb_to_MNi(MNa: t3toolbox.backend.common.NDArray, Maib: t3toolbox.backend.common.NDArray, MNb: t3toolbox.backend.common.NDArray, use_jax: bool = False) -> t3toolbox.backend.common.NDArray

   Computes contraction MNa,Maib,MNb->MNi.

   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 MNa_Maib_MNb_to_MNi
   >>> MNa = np.random.randn(2,3, 4,5,6, 10)
   >>> Maib = np.random.randn(2,3, 10,11,12)
   >>> MNb = np.random.randn(2,3, 4,5,6, 12)
   >>> result = MNa_Maib_MNb_to_MNi(MNa, Maib, MNb)
   >>> result2 = np.einsum('uvxyza,uvaib,uvxyzb->uvxyzi', MNa, Maib, MNb)
   >>> 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 MNa_Maib_MNb_to_MNi
   >>> MNa = np.random.randn(4,5,6, 10)
   >>> Maib = np.random.randn(10,11,12)
   >>> MNb = np.random.randn(4,5,6, 12)
   >>> result = MNa_Maib_MNb_to_MNi(MNa, Maib, MNb)
   >>> result2 = np.einsum('xyza,aib,xyzb->xyzi', MNa, Maib, MNb)
   >>> 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 MNa_Maib_MNb_to_MNi
   >>> MNa = np.random.randn(2,3, 10)
   >>> Maib = np.random.randn(2,3, 10,11,12)
   >>> MNb = np.random.randn(2,3, 12)
   >>> result = MNa_Maib_MNb_to_MNi(MNa, Maib, MNb)
   >>> result2 = np.einsum('uva,uvaib,uvb->uvi', MNa, Maib, MNb)
   >>> 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 MNa_Maib_MNb_to_MNi
   >>> MNa = np.random.randn(10)
   >>> Maib = np.random.randn(10,11,12)
   >>> MNb = np.random.randn(12)
   >>> result = MNa_Maib_MNb_to_MNi(MNa, Maib, MNb)
   >>> result2 = np.einsum('a,aib,b->i', MNa, Maib, MNb)
   >>> print(result.shape == result2.shape)
   True
   >>> print(np.linalg.norm(result - result2))
   0.0