Add Tensorization functions to the Functional API.

[hello-fri-end]

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• Linear Algebra Functions:

  These should be implemented inside: ivy/functional/ivy/experimental/linear\_algebra.py

  • [x] #22026
  • [x] #22091
  • [x] #22254 general_inner_product
  • [ ] #22139 randomized_range_finder
  • [ ] #23068
  • [ ] #23109
  • [ ] #22049
  • [ ] tt_vonneumann_entropy -- TT class needs to be implemented first.
  • [ ] cp_vonneumann_entropy --CP class needs to be implemented first
  • [ ] #26434 congruence_coefficient
  • [ ] #22136 correlation_index
  • [x] #22732

  The following linear algebra functions should be supersetted:

  • [ ] #23703

• Factorized Classes:

  These should be implemented inside: ivy/data\_classes/FactorizedTensor -- See ivy/data\_classes/FactorizedTensor/Tucker\_Tensor.py for an example.

  • [x] #21986
  • [x] #23212
  • [x] #22092
  • [ ] #23129
  • [x] #22188

• Creation Functions:

  These should be implemented inside: ivy/functional/ivy/experimental/creation.py -- See ivy.random\_tucker for an example Note: The respective classes should already be implemented before implementing these.

  • [x] #23744
  • [x] #21998
  • [x] #23180
  • [x] #23181
  • [x] #22184

• Sparse Tensor Operations: These functions should be implemented inside: ivy/functional/ivy/experimental/elementwise.py

  • [x] #22020

• Decomposition Methods:

  These should also be implemented inside: ivy/functional/ivy/experimental/linear\_algebra.py -- See ivy.Tucker for an example Note: The respective classes should already be implemented before implementing some of these. Refer to the source-code.

  • [ ] Tucker Decomposition

  • non_negative_tucker

  • non_negative_tucker_hals

  • [ ] #26260

  • initialize_cp

  • error_calc -- This should be implemented as a private function.

  • parafac

  • sample_khatri_rao Should be implemented as a private function.

  • randomized_parafac

  • [ ] #23208

  • initialize_parafac2

  • _compute_projections - private function

  • _project_tensor_slices - private function

  • _parafac2_recontruction_error - private function

  • parafac2

  • [ ] #26583

  • tensor_train

  • tensor_train_matrix

  • [ ] #27030

  • tensor_ring

  • tensor_ring_als

  • [ ] CPPower

  • power_iteration

  • parafac_power_iteration

  • [ ] Non Negative CP

  • non_negative_parafac

  • non_negative_parafac_hals

  • [ ] Constrained CP

    • initialize_constrained_parafac
    • constrained_parafac

  • [ ] Symmetric CP Decomposition

  • symmetric_power_iteration

  • symmetric_parafac_power_iteration

  • [ ] Coupled Matrix Tensor 3D Factorization

  • coupled_matrix_tensor_3d_factorization

  • [ ] #22696

  • robust_pca

[Mr-Niraj-Kulkarni]

• [ ] #22694