T3FrameWeights#

class t3toolbox.frame_variations_format.T3FrameWeights#

Diagonal weights defining a metric on the tangent coordinates – a Grasedyck-Kramer-style reweighting of the d variation directions (penalise poorly-informed ones with e.g. 1/sigma).

Four families, each len=d (one per variation core, Approach-1 / metric-on-variations): up (on H’s nU leg), down (on V’s nD leg), left (H’s rL), right (H’s rR). T3Tangent.weighted_norm() / weighted_inner() absorb these into the variation cores and take the coordinate norm/inner – the frame stays orthonormal and untouched.

Batching: a weight is FRAME-like (it is absorbed into the variations, but it batches with the frame – do not conflate the two). Every vector is stack_shape + (rank,), and that stack is the frame stack C, like T3Frame – not the variations’ K + C: a weight is one metric per base point, shared by all K tangent vectors at that frame, and it broadcasts over K for free (C is innermost). Pairing with variations alone follows the same trailing-stack rule as check_fv_pair() (the weight’s stack is the trailing/inner part of the variation stack); at the tangent level, where the frame is present too, check_fw_pair() enforces the exact weights.stack_shape == frame.stack_shape.

up_weights: t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]#

down_weights: t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]#

left_weights: t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]#

right_weights: t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]#

Methods#

`data`()
`d`()
`up_ranks`()
`down_ranks`()
`left_ranks`()
`right_ranks`()
`stack_shape`()
`validate`()	Structural: four families each of length d, and one uniform stack_shape on every vector.
`__post_init__`()
`is_consistent_with`(tangent)	True iff these weights match the variation ranks + stack of a `T3Tangent` (or `T3Variations`).
`reciprocal`()	Elementwise `1/w` on every family (e.g. inverse-singular-value weights).
`sqrt`()	Elementwise `sqrt` on every family.
`reverse`()	Reverse the mode order, swapping left``<->``right (mirrors `T3Frame.reverse()`).
`concatenate`(other)	Per-edge concatenation (the `+` combine; ranks add).
`kronecker`(other)	Per-edge Kronecker product (the Hadamard combine; ranks multiply).
`unstack`()	Unstack a stack of frame-weights into an array-like tree (mirrors `T3Variations.unstack`).
`stack`(xx)	Stack an array-like tree of frame-weights into one (mirrors `T3Variations.stack`).
`from_t3weights`(t3_weights)	Build a tangent metric from base-point edge weights (e.g. `T3Weights.from_t3svd(x)`):