T3Tangent.weighted_norm

t3toolbox.manifold.T3Tangent.weighted_norm(weights)

def weighted_norm(self, weights: 'bvf.T3FrameWeights'):

The weighted (Grasedyck-Kramer) coordinate norm: absorb the metric weights into the variation cores (down->V, up/left/right->H) and take the coordinate norm. The frame stays orthonormal (untouched). Vectorized over the stack (returns shape K + C). The inserted diagonal is squared by the norm, so weights = 1/sigma penalises by 1/sigma^2. As with corewise_norm(), this is the coordinate metric (= HS on an orthonormal, gauged frame). weights is frame-like: its stack must equal the frame’s C (checked – check_fw_pair()), and it broadcasts over K. Backend twin: fv_weighted_norm().

Parameters:

weights (T3FrameWeights)