Spectral initialization — the dim smallest non-trivial eigenvectors of the normalized graph Laplacian L = I - D^-1/2 A D^-1/2 (umap.spectral.spectral_layout).
Two paths, selected by graph size:
All array number-crunching is deftm; spectral-init is a thin orchestrator.
Spectral initialization — the dim smallest non-trivial eigenvectors of the
normalized graph Laplacian L = I - D^-1/2 A D^-1/2 (umap.spectral.spectral_layout).
Two paths, selected by graph size:
- tiny n (<= dense-cutoff): dense LAPACK eigh (exact, O(n^3) but n is small).
- large n: matrix-free Lanczos on the spectral-transformed operator
M = I + D^-1/2 A D^-1/2 (eigenvalues in [0,2])
The smallest eigenvectors of L are the LARGEST of M, and Lanczos converges
fastest to the largest end of the spectrum. We take the top dim+1 of M,
drop the trivial one (eigenvalue ~2, the all-ones-ish vector), and keep dim.
All array number-crunching is deftm; `spectral-init` is a thin orchestrator.(->affinity-meta-embedding!_m_doubles_doubles_long_long_Impl)Positional factory function for class umap.spectral.affinity-meta-embedding!_m_doubles_doubles_long_long_Impl.
Positional factory function for class umap.spectral.affinity-meta-embedding!_m_doubles_doubles_long_long_Impl.
(->build-norm-laplacian!_m_ints_ints_doubles_doubles_doubles_long_long_Impl)Positional factory function for class umap.spectral.build-norm-laplacian!_m_ints_ints_doubles_doubles_doubles_long_long_Impl.
Positional factory function for class umap.spectral.build-norm-laplacian!_m_ints_ints_doubles_doubles_doubles_long_long_Impl.
(->centroid-affinity!_m_doubles_doubles_long_long_Impl)Positional factory function for class umap.spectral.centroid-affinity!_m_doubles_doubles_long_long_Impl.
Positional factory function for class umap.spectral.centroid-affinity!_m_doubles_doubles_long_long_Impl.
(->component-centroids!_m_doubles_ints_doubles_doubles_long_long_long_Impl)Positional factory function for class umap.spectral.component-centroids!_m_doubles_ints_doubles_doubles_long_long_long_Impl.
Positional factory function for class umap.spectral.component-centroids!_m_doubles_ints_doubles_doubles_long_long_long_Impl.
(->connected-components!_m_ints_ints_ints_long_long_Impl)Positional factory function for class umap.spectral.connected-components!_m_ints_ints_ints_long_long_Impl.
Positional factory function for class umap.spectral.connected-components!_m_ints_ints_ints_long_long_Impl.
(->connected-spectral_m_ints_ints_doubles_long_long_Impl)Positional factory function for class umap.spectral.connected-spectral_m_ints_ints_doubles_long_long_Impl.
Positional factory function for class umap.spectral.connected-spectral_m_ints_ints_doubles_long_long_Impl.
(->degrees!_m_ints_doubles_doubles_long_Impl)Positional factory function for class umap.spectral.degrees!_m_ints_doubles_doubles_long_Impl.
Positional factory function for class umap.spectral.degrees!_m_ints_doubles_doubles_long_Impl.
(->dense-spectral_m_ints_ints_doubles_doubles_long_long_long_Impl)Positional factory function for class umap.spectral.dense-spectral_m_ints_ints_doubles_doubles_long_long_long_Impl.
Positional factory function for class umap.spectral.dense-spectral_m_ints_ints_doubles_doubles_long_long_long_Impl.
(->densify-labels!_m_ints_ints_ints_long_Impl)Positional factory function for class umap.spectral.densify-labels!_m_ints_ints_ints_long_Impl.
Positional factory function for class umap.spectral.densify-labels!_m_ints_ints_ints_long_Impl.
(->extract-eigvecs!_m_doubles_doubles_long_long_Impl)Positional factory function for class umap.spectral.extract-eigvecs!_m_doubles_doubles_long_long_Impl.
Positional factory function for class umap.spectral.extract-eigvecs!_m_doubles_doubles_long_long_Impl.
(->find-root_m_ints_long_Impl)Positional factory function for class umap.spectral.find-root_m_ints_long_Impl.
Positional factory function for class umap.spectral.find-root_m_ints_long_Impl.
(->inv-sqrt!_m_doubles_doubles_long_Impl)Positional factory function for class umap.spectral.inv-sqrt!_m_doubles_doubles_long_Impl.
Positional factory function for class umap.spectral.inv-sqrt!_m_doubles_doubles_long_Impl.
(->lanczos-spectral_m_ints_ints_doubles_doubles_long_long_long_Impl)Positional factory function for class umap.spectral.lanczos-spectral_m_ints_ints_doubles_doubles_long_long_long_Impl.
Positional factory function for class umap.spectral.lanczos-spectral_m_ints_ints_doubles_doubles_long_long_long_Impl.
(->meta-data-ranges!_m_doubles_doubles_long_long_Impl)Positional factory function for class umap.spectral.meta-data-ranges!_m_doubles_doubles_long_long_Impl.
Positional factory function for class umap.spectral.meta-data-ranges!_m_doubles_doubles_long_long_Impl.
(->meta-embedding!_m_doubles_long_long_Impl)Positional factory function for class umap.spectral.meta-embedding!_m_doubles_long_long_Impl.
Positional factory function for class umap.spectral.meta-embedding!_m_doubles_long_long_Impl.
(->norm-adj-matvec!_m_ints_ints_doubles_doubles_doubles_doubles_doubles_long_long_Impl)Positional factory function for class umap.spectral.norm-adj-matvec!_m_ints_ints_doubles_doubles_doubles_doubles_doubles_long_long_Impl.
Positional factory function for class umap.spectral.norm-adj-matvec!_m_ints_ints_doubles_doubles_doubles_doubles_doubles_long_long_Impl.
(->normalize-unit!_m_doubles_long_long_Impl)Positional factory function for class umap.spectral.normalize-unit!_m_doubles_long_long_Impl.
Positional factory function for class umap.spectral.normalize-unit!_m_doubles_long_long_Impl.
(->pack-eigvec-column!_m_doubles_doubles_long_long_long_Impl)Positional factory function for class umap.spectral.pack-eigvec-column!_m_doubles_doubles_long_long_long_Impl.
Positional factory function for class umap.spectral.pack-eigvec-column!_m_doubles_doubles_long_long_long_Impl.
(->place-small!_m_doubles_ints_doubles_long_long_long_double_Impl)Positional factory function for class umap.spectral.place-small!_m_doubles_ints_doubles_long_long_long_double_Impl.
Positional factory function for class umap.spectral.place-small!_m_doubles_ints_doubles_long_long_long_double_Impl.
(->scale-embedding!_m_doubles_double_Impl)Positional factory function for class umap.spectral.scale-embedding!_m_doubles_double_Impl.
Positional factory function for class umap.spectral.scale-embedding!_m_doubles_double_Impl.
(->scatter-component!_m_doubles_doubles_ints_doubles_long_long_long_double_Impl)Positional factory function for class umap.spectral.scatter-component!_m_doubles_doubles_ints_doubles_long_long_long_double_Impl.
Positional factory function for class umap.spectral.scatter-component!_m_doubles_doubles_ints_doubles_long_long_long_double_Impl.
(affinity-meta-embedding!_m_doubles_doubles_long_long & args__68167)(build-norm-laplacian!_m_ints_ints_doubles_doubles_doubles_long_long
&
args__67435)(centroid-affinity!_m_doubles_doubles_long_long & args__68115)(component-centroids!_m_doubles_ints_doubles_doubles_long_long_long &
args__68063)(connected-components!_m_ints_ints_ints_long_long & args__67903)(connected-spectral_m_ints_ints_doubles_long_long & args__67799)(dense-spectral_m_ints_ints_doubles_doubles_long_long_long & args__67695)(extract-eigvecs!_m_doubles_doubles_long_long & args__67487)(lanczos-spectral_m_ints_ints_doubles_doubles_long_long_long & args__67747)(meta-data-ranges!_m_doubles_doubles_long_long & args__68219)(norm-adj-matvec!_m_ints_ints_doubles_doubles_doubles_doubles_doubles_long_long
&
args__67539)(pack-eigvec-column!_m_doubles_doubles_long_long_long & args__67591)(place-small!_m_doubles_ints_doubles_long_long_long_double & args__68375)(scatter-component!_m_doubles_doubles_ints_doubles_long_long_long_double
&
args__68323)(spectral-init head tail weights n dim)(spectral-init head tail weights n dim X data-dim)Spectral embedding of a symmetric weighted graph (edge list head/tail/weights).
Returns the ndim row-major embedding. Single connected component -> direct
spectral solve; multiple components -> per-component spectral + meta-placement.
Pass X (data, ndata-dim) to enable data-centroid meta-placement (Tier C) for
highly-fragmented graphs (c > 2*dim); without it, ±eye placement is used.
Spectral embedding of a symmetric weighted graph (edge list head/tail/weights). Returns the n*dim row-major embedding. Single connected component -> direct spectral solve; multiple components -> per-component spectral + meta-placement. Pass `X` (data, n*data-dim) to enable data-centroid meta-placement (Tier C) for highly-fragmented graphs (c > 2*dim); without it, ±eye placement is used.
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