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T3Toolbox 2026.0.0 documentation

  • Getting started
  • User guide
  • Design notes
  • Contributor guide
  • API reference
  • Getting started
  • User guide
  • Design notes
  • Contributor guide
  • API reference

Section Navigation

  • t3toolbox
    • backend
      • apply
        • t3_apply
        • t3_apply_ambient_transpose
        • tv_apply
        • tv_apply_transpose
        • tv_precompute_apply_frame_sweep
        • tv_apply_jacobian_from_sweep
        • tv_apply_transpose_from_sweep
        • t3_apply_corewise_transpose
      • common
        • ValueHashedMasks
        • is_boolean_ndarray
        • ragged_scan
        • numpy_scan
        • ragged_map
        • numpy_map
        • get_backend
        • xwhile
        • xcat
        • xappend
        • xprepend
        • randn
        • tree_contains_jax
        • tree_to_jax
        • items_are_uniform
        • save_core_families
        • load_core_families
        • require_concrete_masks
        • prefix_mask
      • contractions
        • contract
      • entries
        • t3_entries
        • t3_entries_ambient_transpose
        • tv_entries
        • tv_entries_transpose
        • tv_precompute_entries_frame_sweep
        • tv_entries_jacobian_from_sweep
        • tv_entries_transpose_from_sweep
        • t3_entries_corewise_transpose
      • fitting
        • SamplingKind
        • sumsq_over_samples
        • sumsq_over_probes
        • block_sumsq_over_samples
        • block_sumsq_over_probes
        • probe_kind
        • apply_derivatives_kind
        • entries_derivatives_kind
        • probe_derivatives_kind
      • fv_conversions
        • fv_to_t3
        • t3_orthogonal_representations
      • fv_operations
        • fv_variations_from_vector
        • fv_variations_zeros
        • fv_variations_randn
        • fv_variations_unit
        • fv_frame_reverse
        • fv_frame_orthogonality_residual
        • fv_frame_consistency_residual
        • fv_absorb_weights
        • fv_weights_consistent
        • fv_concatenate_weights
        • fv_kronecker_weights
        • fv_weights_from_t3_weights
        • fv_weighted_norm
        • fv_weighted_inner
      • linalg
        • pad_or_truncate
        • truncated_svd
        • left_svd
        • right_svd
        • up_svd
        • left_svd_pair
        • right_svd_pair
        • up_svd_pair
        • down_svd_pair
      • optimizer_display
        • relative_errors
        • format_newton_iter
        • make_newton_display
      • optimizers
        • GeometryOps
        • LocalModel
        • Problem
        • NewtonInfo
        • least_squares_problem
        • flat_draw
        • gradient_descent
        • mc_sgd
        • adam
        • newton_cg
      • probing
        • t3_probe
        • compute_xi
        • compute_mu
        • compute_nu
        • compute_eta
        • assemble_z
        • compute_dxi
        • compute_sigma
        • compute_tau
        • compute_deta
        • assemble_tangent_z
        • tv_probe_jacobian_from_sweep
        • tv_probe
        • tv_precompute_probe_frame_sweep
        • compute_sigma_hat
        • compute_deta_tilde
        • compute_tau_tilde
        • compute_sigma_tilde
        • compute_dxi_tilde
        • assemble_tucker_variations
        • assemble_tt_variations
        • tv_probe_transpose_from_sweep
        • tv_probe_transpose
        • t3_probe_ambient_transpose
        • t3_probe_corewise_transpose
        • dense_probe
      • ranks
        • normalize_max_ranks
        • compute_minimal_ranks
        • edge_condition_numbers
        • compute_continuation_ranks
        • compute_raw_sweep_ranks
        • compute_orthogonal_representation_ranks
        • compute_manifold_dim
        • frame_has_minimal_ranks
      • regularization
        • Regularizer
        • IdentityRegularizer
      • sampling_derivatives
        • t3_probe_derivatives
        • check_perturbation_vectors
        • check_perturbation_index
        • binomial_combine_tensor
        • build_input_jets
        • compute_mu_jets_trs
        • compute_mu_jets
        • compute_nu_jets_trs
        • compute_nu_jets
        • compute_eta_jets_trs
        • compute_eta_jets
        • assemble_z_jets
        • tv_precompute_apply_frame_sweep_jets
        • tv_precompute_entries_frame_sweep_jets
        • tv_precompute_probe_frame_sweep_jets
        • compute_sigma_jets_trs
        • compute_tau_jets_trs
        • compute_deta_jets_trs
        • compute_deta_jets
        • compute_sigma_jets
        • compute_tau_jets
        • assemble_tangent_z_jets
        • tv_probe_jacobian_derivatives_from_sweep
        • tv_probe_derivatives
        • t3_apply_derivatives
        • tv_apply_jacobian_derivatives_from_sweep
        • tv_apply_derivatives
        • t3_entries_derivatives
        • tv_entries_jacobian_derivatives_from_sweep
        • tv_entries_derivatives
        • compute_deta_tilde_jets
        • compute_tau_tilde_jets_trs
        • compute_sigma_tilde_jets_trs
        • compute_tau_tilde_jets
        • compute_sigma_tilde_jets
        • compute_dxi_tilde_jets
        • assemble_tucker_variation_jets_trs
        • assemble_tucker_variation_jets
        • assemble_tt_variation_jets_trs
        • assemble_tt_variation_jets
        • estimate_chunk_size
        • max_chunk_size_within
        • tv_probe_transpose_derivatives_from_sweep
        • tv_probe_derivatives_transpose
        • compute_sigma_hat_jets
        • tv_apply_transpose_derivatives_from_sweep
        • tv_apply_derivatives_transpose
        • tv_entries_transpose_derivatives_from_sweep
        • tv_entries_derivatives_transpose
        • t3_probe_corewise_derivatives_transpose
        • t3_apply_corewise_derivatives_transpose
        • t3_entries_corewise_derivatives_transpose
        • dense_probe_derivatives
        • dense_apply_derivatives
        • dense_entries_derivatives
      • stacking
        • tree_depth
        • get_first_leaf
        • trees_have_same_structure
        • apply_func_to_leaf_subtrees
        • stack
        • unstack
        • sum_leafs_along_axes
        • basic_ragged_unstack
        • basic_ragged_stack
        • basic_uniform_unstack
        • basic_uniform_stack
        • tree_zip
      • t3_constructors
        • t3_zeros
        • t3_ones
        • t3_corewise_randn
      • t3_conversions
        • t3_to_dense
        • t3_to_dense_chain
        • t3_to_vector
        • t3_from_vector
        • t3_to_tensor_train
        • t3_from_tensor_train
        • t3_from_canonical
      • t3_linalg
        • t3_add
        • t3_sum_stack
        • t3_scale
        • t3_inner_product
        • t3_norm
        • t3_mult
        • t3m_form_then_round
        • t3m_inplace_fused
        • t3m_swap
        • t3_plus_scalar
        • t3_weighted_norm
        • t3_weighted_inner
      • t3_operations
        • t3_broadcast_to_common_stack
        • t3_absorb_tucker_into_tt
        • t3_squash_tails
        • t3_segment
        • t3_concatenate
        • tucker_change_core_shapes
        • t3_stack
        • t3_unstack
        • t3_core_shapes
        • t3_sum
        • t3_absorb_weights
        • t3_weights_consistent
        • t3_concatenate_weights
        • t3_kronecker_weights
      • t3_orthogonalization
        • t3_orthogonality_residual
        • t3_left_orthogonalize
        • t3_right_orthogonalize
        • t3_up_orthogonalize_tt_cores
        • t3_down_orthogonalize_tucker_cores
        • t3_down_svd_tucker_core
        • t3_left_svd_tt_core
        • t3_right_svd_tt_core
        • t3_down_svd_tt_core
        • t3_up_svd_tt_core
        • t3_orthogonalize_relative_to_tucker_core
        • t3_orthogonalize_relative_to_tt_core
      • t3_svd
        • t3svd
        • t3_rank_adjustment_sweep
        • dense_tucker_svd
        • dense_ttsvd
        • dense_t3svd
      • tt_operations
        • tt_reverse
        • tt_squash_tails
        • tt_change_core_shapes
        • tt_zipper_left_to_right
        • tt_zipper_right_to_left
      • tt_orthogonalization
        • tt_left_orthogonalize
        • tt_right_orthogonalize
      • tv_operations
        • tv_to_dense
        • tv_orthogonal_gauge_projection
        • tv_oblique_gauge_projection
        • tv_to_t3
        • tv_project_t3_onto_tangent_space
        • tv_project_dense_onto_tangent_space
        • tv_unstack_tangent_stack
        • tv_stack_tangent_stack
        • tv_unstack_frame_stack
        • tv_stack_frame_stack
        • tv_gauge_residual
        • tv_retract
      • ufv_conversions
        • ut3_orthogonal_representations
        • ut3frame_to_t3frame
        • t3frame_to_ut3frame
        • ut3variations_to_t3variations
        • t3variations_to_ut3variations
        • t3frameweights_to_ut3frameweights
        • ut3frameweights_to_t3frameweights
      • ufv_masking
        • ufv_make_frame_masks
        • ufv_apply_frame_masks
        • ufv_apply_variations_masks
      • ufv_operations
        • ufv_leaf_structure
        • ufv_unstack_axes
        • ufv_stack_axes
        • ufv_unstack
        • ufv_stack
        • ufv_variations_sum_stack
        • ufv_frame_reverse
        • ufv_variations_reverse
        • ufv_save
        • ufv_load
        • ufv_frame_orthogonality_residual
        • ufv_absorb_weights
        • ufv_weights_consistent
        • ufv_weights_from_ut3_weights
        • ufv_reciprocal_weights
        • ufv_sqrt_weights
        • ufv_concatenate_weights
        • ufv_kronecker_weights
      • uniform_fitting
        • uniform_manifold_ops
        • uniform_corewise_ops
        • uniform_geometry_ops
        • uniform_apply_kind
        • uniform_entries_kind
        • uniform_probe_kind
        • uniform_sampling_kind
        • uniform_apply_derivatives_kind
        • uniform_entries_derivatives_kind
        • uniform_probe_derivatives_kind
        • uniform_derivatives_kind
        • pack_sample
        • pack_data
        • uniform_minimal
        • uniform_least_squares_problem
      • ut3_constructors
        • ut3_zeros
        • ut3_ones
        • ut3_corewise_randn
        • ut3_save
        • ut3_load
      • ut3_conversions
        • t3_to_ut3
        • ut3_to_dense
        • ut3_to_t3
        • t3weights_to_ut3weights
        • ut3weights_to_t3weights
      • ut3_linalg
        • ut3_scale
        • ut3_add
        • ut3_sum_stack
        • ut3_inner_product
        • ut3_norm_orthogonalized
        • ut3_weighted_norm
        • ut3_weighted_inner
      • ut3_masking
        • ut3_make_masks
        • ut3_apply_masks
      • ut3_operations
        • ut3_leaf_structure
        • ut3_squash_tails
        • ut3_reverse
        • pack_vectors
        • unpack_vectors
        • is_packed
        • pack_if_ragged
        • ut3_unstack
        • ut3_stack
        • ut3_absorb_weights
        • ut3_weights_consistent
        • ut3_reciprocal_weights
        • ut3_sqrt_weights
        • ut3_concatenate_weights
        • ut3_kronecker_weights
      • ut3_orthogonalization
        • ut3_orthogonality_residual
        • down_orthogonalize_tucker_supercores
        • ut3_down_orthogonalize_tucker_cores
        • up_orthogonalize_tt_supercores
        • ut3_up_orthogonalize_tt_cores
        • ut3_left_orthogonalize_tt_cores
        • ut3_right_orthogonalize_tt_cores
      • ut3_sampling
        • ut3_entries
        • ut3_apply
        • ut3_probe
        • ut3_full_sum
        • ut3_apply_corewise_transpose
        • ut3_entries_corewise_transpose
        • ut3_probe_corewise_transpose
        • ut3_probe_derivatives
        • ut3_apply_derivatives
        • ut3_entries_derivatives
        • ut3_apply_corewise_derivatives_transpose
        • ut3_entries_corewise_derivatives_transpose
        • ut3_probe_corewise_derivatives_transpose
      • ut3_svd
        • ut3svd
        • ut3_rank_adjustment_sweep
        • ut3svd_supercores
      • utv_operations
        • utv_unstack_tangent_stack
        • utv_stack_tangent_stack
        • utv_unstack_frame_stack
        • utv_stack_frame_stack
        • utv_sum_tangent_stack
        • utv_to_ut3
        • utv_retract
        • utv_corewise_retract
        • utv_corewise_inner
        • utv_orthogonal_gauge_projection
        • utv_oblique_gauge_projection
        • utv_gauge_residual
        • utv_project_ut3_onto_tangent_space
        • utv_weighted_norm
        • utv_weighted_inner
      • utv_sampling
        • utv_probe
        • utv_apply
        • utv_entries
        • utv_precompute_apply_frame_sweep
        • utv_precompute_probe_frame_sweep
        • utv_precompute_entries_frame_sweep
        • utv_apply_jacobian_from_sweep
        • utv_probe_jacobian_from_sweep
        • utv_entries_jacobian_from_sweep
        • utv_apply_transpose_from_sweep
        • utv_probe_transpose_from_sweep
        • utv_entries_transpose_from_sweep
        • utv_precompute_apply_frame_sweep_jets
        • utv_precompute_probe_frame_sweep_jets
        • utv_precompute_entries_frame_sweep_jets
        • utv_apply_jacobian_derivatives_from_sweep
        • utv_probe_jacobian_derivatives_from_sweep
        • utv_entries_jacobian_derivatives_from_sweep
        • utv_apply_transpose_derivatives_from_sweep
        • utv_probe_transpose_derivatives_from_sweep
        • utv_entries_transpose_derivatives_from_sweep
        • utv_probe_derivatives
        • utv_apply_derivatives
        • utv_entries_derivatives
        • utv_probe_transpose
        • utv_apply_transpose
        • utv_entries_transpose
        • utv_probe_derivatives_transpose
        • utv_apply_derivatives_transpose
        • utv_entries_derivatives_transpose
    • corewise
      • corewise_add
      • corewise_sub
      • corewise_scale
      • corewise_zeros_like
      • corewise_map
      • corewise_neg
      • corewise_sum
      • corewise_dot
      • corewise_stack_dot
      • corewise_stack_scale
      • corewise_stack_sum
      • corewise_norm
      • corewise_stack_norm
      • corewise_err
      • corewise_relerr
      • corewise_logical_not
    • fitting
      • GaussNewtonModel
        • GaussNewtonModel.objective_value
        • GaussNewtonModel.gradient
        • GaussNewtonModel.jacobian
        • GaussNewtonModel.gn_quadratic
        • GaussNewtonModel.gn_hessian
        • GaussNewtonModel.evaluate
      • UniformGaussNewtonModel
        • UniformGaussNewtonModel.kind
        • UniformGaussNewtonModel.objective_value
        • UniformGaussNewtonModel.gradient
        • UniformGaussNewtonModel.jacobian
        • UniformGaussNewtonModel.gn_quadratic
        • UniformGaussNewtonModel.gn_hessian
        • UniformGaussNewtonModel.evaluate
      • apply_model
      • entries_model
      • probe_model
      • apply_derivatives_model
      • entries_derivatives_model
      • probe_derivatives_model
    • frame_variations_format
      • T3Frame
        • T3Frame.d
        • T3Frame.shape
        • T3Frame.up_ranks
        • T3Frame.down_ranks
        • T3Frame.left_ranks
        • T3Frame.right_ranks
        • T3Frame.stack_shape
        • T3Frame.structure
        • T3Frame.variation_shapes
        • T3Frame.data
        • T3Frame.to_jax
        • T3Frame.to_numpy
        • T3Frame.copy
        • T3Frame.contains_jax
        • T3Frame.size
        • T3Frame.data_size
        • T3Frame.__repr__
        • T3Frame.orthogonality_residual
        • T3Frame.is_orthogonal
        • T3Frame.minimal_ranks
        • T3Frame.has_minimal_ranks
        • T3Frame.has_numerically_minimal_ranks
        • T3Frame.validate
        • T3Frame.__post_init__
        • T3Frame.unstack
        • T3Frame.stack
        • T3Frame.from_t3
        • T3Frame.random_orthogonal
        • T3Frame.random_orthogonal_like
        • T3Frame.save
        • T3Frame.load
        • T3Frame.reverse
        • T3Frame.to_t3
        • T3Frame.to_dense
        • T3Frame.orthogonalize
        • T3Frame.is_consistent
        • T3Frame.allclose
      • T3Variations
        • T3Variations.d
        • T3Variations.shape
        • T3Variations.stack_shape
        • T3Variations.variation_shapes
        • T3Variations.data
        • T3Variations.to_jax
        • T3Variations.to_numpy
        • T3Variations.copy
        • T3Variations.contains_jax
        • T3Variations.size
        • T3Variations.data_size
        • T3Variations.__repr__
        • T3Variations.validate
        • T3Variations.__post_init__
        • T3Variations.unstack
        • T3Variations.stack
        • T3Variations.zeros
        • T3Variations.randn
        • T3Variations.unit
        • T3Variations.zeros_like
        • T3Variations.randn_like
        • T3Variations.to_vector
        • T3Variations.from_vector
        • T3Variations.save
        • T3Variations.load
        • T3Variations.reverse
        • T3Variations.sum_stack
        • T3Variations.__add__
        • T3Variations.__sub__
        • T3Variations.__mul__
        • T3Variations.__neg__
        • T3Variations.allclose
      • T3FrameWeights
        • T3FrameWeights.data
        • T3FrameWeights.d
        • T3FrameWeights.up_ranks
        • T3FrameWeights.down_ranks
        • T3FrameWeights.left_ranks
        • T3FrameWeights.right_ranks
        • T3FrameWeights.stack_shape
        • T3FrameWeights.validate
        • T3FrameWeights.__post_init__
        • T3FrameWeights.is_consistent_with
        • T3FrameWeights.reciprocal
        • T3FrameWeights.sqrt
        • T3FrameWeights.reverse
        • T3FrameWeights.concatenate
        • T3FrameWeights.kronecker
        • T3FrameWeights.unstack
        • T3FrameWeights.stack
        • T3FrameWeights.from_t3weights
      • fv_to_t3
      • t3_orthogonal_representations
      • fv_absorb_weights
    • manifold
      • T3Tangent
        • T3Tangent.__post_init__
        • T3Tangent.validate
        • T3Tangent.__repr__
        • T3Tangent.d
        • T3Tangent.shape
        • T3Tangent.frame_stack_shape
        • T3Tangent.tangent_stack_shape
        • T3Tangent.stack_shape
        • T3Tangent.structure
        • T3Tangent.data
        • T3Tangent.to_jax
        • T3Tangent.to_numpy
        • T3Tangent.copy
        • T3Tangent.contains_jax
        • T3Tangent.size
        • T3Tangent.data_size
        • T3Tangent.to_dense
        • T3Tangent.to_t3
        • T3Tangent.to_vector
        • T3Tangent.from_vector
        • T3Tangent.save
        • T3Tangent.load
        • T3Tangent.reverse
        • T3Tangent.sum_tangents
        • T3Tangent.zeros
        • T3Tangent.unit
        • T3Tangent.zeros_like
        • T3Tangent.__add__
        • T3Tangent.__sub__
        • T3Tangent.__mul__
        • T3Tangent.__neg__
        • T3Tangent.corewise_inner
        • T3Tangent.corewise_norm
        • T3Tangent.absorb_weights
        • T3Tangent.weighted_norm
        • T3Tangent.weighted_inner
        • T3Tangent.normalized
        • T3Tangent.allclose
        • T3Tangent.minimal_ranks
        • T3Tangent.tangent_space_dimension
        • T3Tangent.has_minimal_ranks
        • T3Tangent.has_numerically_minimal_ranks
        • T3Tangent.is_orthogonal
        • T3Tangent.gauge_residual
        • T3Tangent.is_gauged
        • T3Tangent.probe
        • T3Tangent.probe_transpose
        • T3Tangent.apply
        • T3Tangent.entries
        • T3Tangent.apply_transpose
        • T3Tangent.entries_transpose
        • T3Tangent.probe_derivatives
        • T3Tangent.apply_derivatives
        • T3Tangent.entries_derivatives
        • T3Tangent.probe_derivatives_transpose
        • T3Tangent.apply_derivatives_transpose
        • T3Tangent.entries_derivatives_transpose
        • T3Tangent.unstack_tangents
        • T3Tangent.unstack_frame
        • T3Tangent.stack_tangents
        • T3Tangent.stack_frame
      • ManifoldGeometry
        • ManifoldGeometry.frame
        • ManifoldGeometry.randn
        • ManifoldGeometry.random_orthogonal
        • ManifoldGeometry.randn_like
        • ManifoldGeometry.project
        • ManifoldGeometry.project_oblique
        • ManifoldGeometry.inner
        • ManifoldGeometry.norm
        • ManifoldGeometry.retract
        • ManifoldGeometry.project_ambient
        • ManifoldGeometry.transport
      • CorewiseGeometry
        • CorewiseGeometry.frame
        • CorewiseGeometry.randn
        • CorewiseGeometry.randn_like
        • CorewiseGeometry.project
        • CorewiseGeometry.inner
        • CorewiseGeometry.norm
        • CorewiseGeometry.retract
      • manifold_dim
    • optimizers
      • gradient_descent
      • mc_sgd
      • adam
      • newton_cg
    • safety
      • SafetyTolerances
      • current_safety
      • set_default_safety
      • safe
      • unsafe
      • effective_rtol
      • is_tracing
      • checks_active
      • require
      • frames_equal
      • frames_equal_or_skip
    • tucker_tensor_train
      • TuckerTensorTrain
        • TuckerTensorTrain.__repr__
        • TuckerTensorTrain.get_core_shapes
        • TuckerTensorTrain.get_minimal_ranks
        • TuckerTensorTrain.has_numerically_minimal_ranks
        • TuckerTensorTrain.is_left_orthogonal
        • TuckerTensorTrain.is_right_orthogonal
        • TuckerTensorTrain.validate
        • TuckerTensorTrain.__post_init__
        • TuckerTensorTrain.to_dense
        • TuckerTensorTrain.segment
        • TuckerTensorTrain.concatenate
        • TuckerTensorTrain.squash_tails
        • TuckerTensorTrain.reverse
        • TuckerTensorTrain.resize
        • TuckerTensorTrain.to_jax
        • TuckerTensorTrain.to_numpy
        • TuckerTensorTrain.copy
        • TuckerTensorTrain.unstack
        • TuckerTensorTrain.stack
        • TuckerTensorTrain.zeros
        • TuckerTensorTrain.ones
        • TuckerTensorTrain.randn
        • TuckerTensorTrain.from_canonical
        • TuckerTensorTrain.from_tensor_train
        • TuckerTensorTrain.to_tensor_train
        • TuckerTensorTrain.to_vector
        • TuckerTensorTrain.from_vector
        • TuckerTensorTrain.save
        • TuckerTensorTrain.load
        • TuckerTensorTrain.__add__
        • TuckerTensorTrain.__mul__
        • TuckerTensorTrain.t3m
        • TuckerTensorTrain.__neg__
        • TuckerTensorTrain.__sub__
        • TuckerTensorTrain.inner
        • TuckerTensorTrain.norm
        • TuckerTensorTrain.sum
        • TuckerTensorTrain.sum_stack
        • TuckerTensorTrain.sum_stack_corewise
        • TuckerTensorTrain.down_svd_tucker_core
        • TuckerTensorTrain.left_svd_tt_core
        • TuckerTensorTrain.right_svd_tt_core
        • TuckerTensorTrain.up_svd_tt_core
        • TuckerTensorTrain.orthogonalize_relative_to_tucker_core
        • TuckerTensorTrain.orthogonalize_relative_to_tt_core
        • TuckerTensorTrain.down_orthogonalize_tucker_cores
        • TuckerTensorTrain.up_orthogonalize_tt_cores
        • TuckerTensorTrain.left_orthogonalize_tt_cores
        • TuckerTensorTrain.right_orthogonalize_tt_cores
        • TuckerTensorTrain.entries
        • TuckerTensorTrain.apply
        • TuckerTensorTrain.probe
        • TuckerTensorTrain.probe_ambient_transpose
        • TuckerTensorTrain.probe_corewise_transpose
        • TuckerTensorTrain.apply_ambient_transpose
        • TuckerTensorTrain.entries_ambient_transpose
        • TuckerTensorTrain.apply_corewise_transpose
        • TuckerTensorTrain.entries_corewise_transpose
        • TuckerTensorTrain.probe_derivatives
        • TuckerTensorTrain.apply_derivatives
        • TuckerTensorTrain.entries_derivatives
        • TuckerTensorTrain.probe_corewise_derivatives_transpose
        • TuckerTensorTrain.apply_corewise_derivatives_transpose
        • TuckerTensorTrain.entries_corewise_derivatives_transpose
        • TuckerTensorTrain.t3svd
        • TuckerTensorTrain.continuation_ranks
        • TuckerTensorTrain.rank_adjustment_sweep
        • TuckerTensorTrain.t3svd_dense
      • T3Weights
        • T3Weights.validate
        • T3Weights.__post_init__
        • T3Weights.is_consistent_with
        • T3Weights.reciprocal
        • T3Weights.sqrt
        • T3Weights.reverse
        • T3Weights.concatenate
        • T3Weights.kronecker
        • T3Weights.unstack
        • T3Weights.stack
        • T3Weights.from_t3svd
      • t3_absorb_weights
      • t3_weighted_norm
      • t3_weighted_inner
    • uniform_frame_variations_format
      • UT3Frame
        • UT3Frame.data
        • UT3Frame.d
        • UT3Frame.N
        • UT3Frame.nU
        • UT3Frame.nD
        • UT3Frame.rL
        • UT3Frame.rR
        • UT3Frame.stack_shape
        • UT3Frame.uniform_structure
        • UT3Frame.uniform_variation_shapes
        • UT3Frame.up_ranks
        • UT3Frame.down_ranks
        • UT3Frame.left_ranks
        • UT3Frame.right_ranks
        • UT3Frame.structure
        • UT3Frame.apply_masks
        • UT3Frame.orthogonality_residual
        • UT3Frame.is_orthogonal
        • UT3Frame.minimal_ranks
        • UT3Frame.has_minimal_ranks
        • UT3Frame.has_numerically_minimal_ranks
        • UT3Frame.is_consistent
        • UT3Frame.allclose
        • UT3Frame.from_t3frame
        • UT3Frame.to_t3frame
        • UT3Frame.from_ut3
        • UT3Frame.to_ut3
        • UT3Frame.to_dense
        • UT3Frame.reverse
        • UT3Frame.orthogonalize
        • UT3Frame.random_orthogonal
        • UT3Frame.random_orthogonal_like
        • UT3Frame.save
        • UT3Frame.load
        • UT3Frame.supercores
        • UT3Frame.contains_jax
        • UT3Frame.to_jax
        • UT3Frame.to_numpy
        • UT3Frame.copy
        • UT3Frame.__repr__
        • UT3Frame.validate
        • UT3Frame.__post_init__
        • UT3Frame.unstack
        • UT3Frame.stack
      • UT3Variations
        • UT3Variations.d
        • UT3Variations.N
        • UT3Variations.nU
        • UT3Variations.nD
        • UT3Variations.rL
        • UT3Variations.rR
        • UT3Variations.stack_shape
        • UT3Variations.uniform_structure
        • UT3Variations.uniform_variation_shapes
        • UT3Variations.up_ranks
        • UT3Variations.down_ranks
        • UT3Variations.variation_left_ranks
        • UT3Variations.variation_right_ranks
        • UT3Variations.structure
        • UT3Variations.data
        • UT3Variations.apply_masks
        • UT3Variations.from_t3variations
        • UT3Variations.to_t3variations
        • UT3Variations.supercores
        • UT3Variations.contains_jax
        • UT3Variations.to_jax
        • UT3Variations.to_numpy
        • UT3Variations.copy
        • UT3Variations.__repr__
        • UT3Variations.validate
        • UT3Variations.__post_init__
        • UT3Variations.unstack
        • UT3Variations.stack
        • UT3Variations.__add__
        • UT3Variations.__sub__
        • UT3Variations.__mul__
        • UT3Variations.__neg__
        • UT3Variations.reverse
        • UT3Variations.save
        • UT3Variations.load
        • UT3Variations.sum_stack
        • UT3Variations.allclose
        • UT3Variations.zeros
        • UT3Variations.randn
        • UT3Variations.unit
        • UT3Variations.zeros_like
        • UT3Variations.randn_like
      • UT3FrameWeights
        • UT3FrameWeights.supercores
        • UT3FrameWeights.data
        • UT3FrameWeights.d
        • UT3FrameWeights.nU
        • UT3FrameWeights.nD
        • UT3FrameWeights.rL
        • UT3FrameWeights.rR
        • UT3FrameWeights.stack_shape
        • UT3FrameWeights.up_ranks
        • UT3FrameWeights.down_ranks
        • UT3FrameWeights.left_ranks
        • UT3FrameWeights.right_ranks
        • UT3FrameWeights.validate
        • UT3FrameWeights.__post_init__
        • UT3FrameWeights.__repr__
        • UT3FrameWeights.is_consistent_with
        • UT3FrameWeights.reciprocal
        • UT3FrameWeights.sqrt
        • UT3FrameWeights.concatenate
        • UT3FrameWeights.kronecker
        • UT3FrameWeights.from_ut3weights
        • UT3FrameWeights.from_t3frameweights
        • UT3FrameWeights.to_t3frameweights
      • ut3_orthogonal_representations
      • check_ufw_pair
      • ufv_absorb_weights
    • uniform_manifold
      • UT3Tangent
        • UT3Tangent.__post_init__
        • UT3Tangent.validate
        • UT3Tangent.__repr__
        • UT3Tangent.d
        • UT3Tangent.shape
        • UT3Tangent.frame_stack_shape
        • UT3Tangent.tangent_stack_shape
        • UT3Tangent.stack_shape
        • UT3Tangent.structure
        • UT3Tangent.data
        • UT3Tangent.to_jax
        • UT3Tangent.to_numpy
        • UT3Tangent.copy
        • UT3Tangent.contains_jax
        • UT3Tangent.__add__
        • UT3Tangent.__sub__
        • UT3Tangent.__mul__
        • UT3Tangent.__neg__
        • UT3Tangent.corewise_inner
        • UT3Tangent.corewise_norm
        • UT3Tangent.absorb_weights
        • UT3Tangent.weighted_norm
        • UT3Tangent.weighted_inner
        • UT3Tangent.normalized
        • UT3Tangent.allclose
        • UT3Tangent.minimal_ranks
        • UT3Tangent.tangent_space_dimension
        • UT3Tangent.has_minimal_ranks
        • UT3Tangent.has_numerically_minimal_ranks
        • UT3Tangent.is_orthogonal
        • UT3Tangent.gauge_residual
        • UT3Tangent.is_gauged
        • UT3Tangent.to_ut3
        • UT3Tangent.to_dense
        • UT3Tangent.to_t3tangent
        • UT3Tangent.from_t3tangent
        • UT3Tangent.reverse
        • UT3Tangent.probe
        • UT3Tangent.apply
        • UT3Tangent.entries
        • UT3Tangent.probe_derivatives
        • UT3Tangent.apply_derivatives
        • UT3Tangent.entries_derivatives
        • UT3Tangent.probe_transpose
        • UT3Tangent.apply_transpose
        • UT3Tangent.entries_transpose
        • UT3Tangent.probe_derivatives_transpose
        • UT3Tangent.apply_derivatives_transpose
        • UT3Tangent.entries_derivatives_transpose
        • UT3Tangent.sum_tangents
        • UT3Tangent.zeros
        • UT3Tangent.unit
        • UT3Tangent.zeros_like
        • UT3Tangent.unstack_tangents
        • UT3Tangent.unstack_frame
        • UT3Tangent.stack_tangents
        • UT3Tangent.stack_frame
      • UniformManifoldGeometry
        • UniformManifoldGeometry.frame
        • UniformManifoldGeometry.randn
        • UniformManifoldGeometry.random_orthogonal
        • UniformManifoldGeometry.randn_like
        • UniformManifoldGeometry.project
        • UniformManifoldGeometry.project_oblique
        • UniformManifoldGeometry.inner
        • UniformManifoldGeometry.norm
        • UniformManifoldGeometry.retract
        • UniformManifoldGeometry.project_ambient
        • UniformManifoldGeometry.transport
      • UniformCorewiseGeometry
        • UniformCorewiseGeometry.frame
        • UniformCorewiseGeometry.randn
        • UniformCorewiseGeometry.randn_like
        • UniformCorewiseGeometry.project
        • UniformCorewiseGeometry.inner
        • UniformCorewiseGeometry.norm
        • UniformCorewiseGeometry.retract
    • uniform_tucker_tensor_train
      • UT3Masks
      • UniformTuckerTensorTrain
        • UniformTuckerTensorTrain.validate
        • UniformTuckerTensorTrain.__post_init__
        • UniformTuckerTensorTrain.__repr__
        • UniformTuckerTensorTrain.apply_masks
        • UniformTuckerTensorTrain.to_dense
        • UniformTuckerTensorTrain.from_t3
        • UniformTuckerTensorTrain.to_t3
        • UniformTuckerTensorTrain.reverse
        • UniformTuckerTensorTrain.squash_tails
        • UniformTuckerTensorTrain.__mul__
        • UniformTuckerTensorTrain.__neg__
        • UniformTuckerTensorTrain.__add__
        • UniformTuckerTensorTrain.__sub__
        • UniformTuckerTensorTrain.sum_stack
        • UniformTuckerTensorTrain.inner
        • UniformTuckerTensorTrain.norm
        • UniformTuckerTensorTrain.entries
        • UniformTuckerTensorTrain.apply
        • UniformTuckerTensorTrain.probe
        • UniformTuckerTensorTrain.probe_derivatives
        • UniformTuckerTensorTrain.apply_derivatives
        • UniformTuckerTensorTrain.entries_derivatives
        • UniformTuckerTensorTrain.apply_corewise_transpose
        • UniformTuckerTensorTrain.entries_corewise_transpose
        • UniformTuckerTensorTrain.probe_corewise_transpose
        • UniformTuckerTensorTrain.apply_corewise_derivatives_transpose
        • UniformTuckerTensorTrain.entries_corewise_derivatives_transpose
        • UniformTuckerTensorTrain.probe_corewise_derivatives_transpose
        • UniformTuckerTensorTrain.sum
        • UniformTuckerTensorTrain.down_orthogonalize_tucker_cores
        • UniformTuckerTensorTrain.up_orthogonalize_tt_cores
        • UniformTuckerTensorTrain.left_orthogonalize_tt_cores
        • UniformTuckerTensorTrain.right_orthogonalize_tt_cores
        • UniformTuckerTensorTrain.is_left_orthogonal
        • UniformTuckerTensorTrain.is_right_orthogonal
        • UniformTuckerTensorTrain.t3svd
        • UniformTuckerTensorTrain.rank_adjustment_sweep
        • UniformTuckerTensorTrain.unstack
        • UniformTuckerTensorTrain.stack
        • UniformTuckerTensorTrain.to_jax
        • UniformTuckerTensorTrain.to_numpy
        • UniformTuckerTensorTrain.copy
        • UniformTuckerTensorTrain.zeros
        • UniformTuckerTensorTrain.ones
        • UniformTuckerTensorTrain.randn
        • UniformTuckerTensorTrain.save
        • UniformTuckerTensorTrain.load
      • UT3Weights
        • UT3Weights.validate
        • UT3Weights.__post_init__
        • UT3Weights.__repr__
        • UT3Weights.is_consistent_with
        • UT3Weights.reciprocal
        • UT3Weights.sqrt
        • UT3Weights.concatenate
        • UT3Weights.kronecker
        • UT3Weights.from_ut3svd
        • UT3Weights.from_t3weights
        • UT3Weights.to_t3weights
      • ut3_absorb_weights
      • ut3_weighted_norm
      • ut3_weighted_inner
  • API reference
  • t3toolbox
  • tucker_tensor_train
  • t3_absorb_weights

t3_absorb_weights#

t3toolbox.tucker_tensor_train.t3_absorb_weights(x, weights)#
def t3_absorb_weights(x: 'TuckerTensorTrain', weights: T3Weights) -> 'TuckerTensorTrain':

Contract diagonal edge weights into x’s cores (shape-preserving): the returned TuckerTensorTrain represents the fully-weighted network. See t3toolbox.backend.t3_operations.t3_absorb_weights() for the side-conventions.

Parameters:
  • x (TuckerTensorTrain)

  • weights (T3Weights)

Return type:

TuckerTensorTrain

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