fv_operations#

Operations on raw (frame, variations) data: variation constructors, frame ops, residuals.

fv_variations_{zeros,randn,unit,from_vector} build variation tuples for a given frame; fv_frame_reverse and the fv_frame_*_residual checkers operate on the frame alone. The fv_*_weights functions are the weighted-layer tangent metric (absorb into the variation cores).

Functions#

fv_variations_from_vector(flat, variation_shapes[, ...])

Rebuild variation cores from a 1D vector (inverse of flattening the variation cores).

fv_variations_zeros(variation_shapes[, stack_shape, ...])

All-zero variation cores of the given variation shapes (and stack).

fv_variations_randn(variation_shapes[, stack_shape, ...])

I.i.d. standard-normal variation cores of the given variation shapes (and stack).

fv_variations_unit(variation_shapes, index[, ...])

Canonical unit variation: all-zero cores except a single entry set to 1.

fv_frame_reverse(frame)

Reverse the mode order of a T3 frame 4-tuple (up, down, left, right).

fv_frame_orthogonality_residual(frame)

Max deviation from orthogonality of the four frame core families, per stack element.

fv_frame_consistency_residual(frame)

Relative Frobenius mismatch between the left- and right-canonical reconstructions of the base

fv_absorb_weights(variations, weights)

Absorb the four-family metric weights into the VARIATION cores (the tangent metric on coordinates,

fv_weights_consistent(variations, weights)

True iff the four weight families (each len=d) can be absorbed into variations (non-raising).

fv_concatenate_weights(weights_A, weights_B)

Per-edge concatenation of two frame-weight 4-tuples (the '+' combine; ranks add). Last-axis.

fv_kronecker_weights(weights_A, weights_B)

Per-edge Kronecker product of two frame-weight 4-tuples (the Hadamard combine; ranks multiply).

fv_weights_from_t3_weights(t3_weights)

Build frame weights (a tangent metric) from base-point edge weights (tucker_weights, tt_weights).

fv_weighted_norm(variations, weights, n_stack)

Weighted (Grasedyck-Kramer) coordinate norm of a tangent's variations: the corewise stack-norm of

fv_weighted_inner(variations_A, variations_B, weights, ...)

Weighted coordinate inner product <absorb(W,A), absorb(W,B)> w.r.t. one metric weights --