High-contrast homogenization: Entry.Multiscale.Global.PartialChangeMetric #
Imported from the Apache-2.0 HighContrastHomogenization development at commit
7a13dbcd8d6609264a713373f5c69ceeac870472.
The metric part of a partial geometry change #
The projective-metric bookkeeping of a partial geometry change, serving p.global.selection:
the geometry update moves the current metric a distance exactly ε towards the target when the
target is not reached, and the residual distance to the target drops by ε.
p.global.selection: the metric part of a partial geometry change. m₊ = geometryUpdate ε m m⋆ with
m⋆ = m(𝐀_{n+2L,q}) not reached (d_pr([m],[m⋆]) > ε, so d_pr([m₊],[m⋆]) = d_pr([m],[m⋆]) - ε
by Geometry.projectiveDistance_geometryUpdate_eq_min), 𝐀_{n+2L,q} ≤ 𝐀_{k,q}
(explicitCanonicalMetric_projectiveDistance_le_logDet), and the bridge sandwich
e.global.selection.geometry.comparison
(explicitCanonicalMetric_projectiveDistance_le_of_deltaSandwich),
glued by projectiveDistance_triangle and the symmetry of projectiveDistance.