Package 'geosmooth'

A "metric.graph.lowpass.basis" object.

Numeric response vector or matrix with one row per graph vertex.

Numeric filter-parameter grid.

Spectral low-pass filter family.

Optional number of response columns processed together.

Positive tolerance smaller than one used to classify truncated-basis candidates as spectrally resolved.

Action when a truncated-basis candidate exceeds truncation.tol: "warn", "error", or "allow".

Logical. For heat filtering, return the input exactly at eta = 0. This avoids treating a truncated spectral projection as the identity.

A synthetic_dataset.

Optional row names.

Ignored.

Ignored.

A "malps" object from fit.malps or refit.malps.

Number of successful bootstrap replicates requested.

Bootstrap weight generator, one of "bayesian" or "multinomial".

Optional response vector. Defaults to object$y.

Optional nonnegative sampling probabilities for weight.type = "multinomial".

Pointwise interval level used in the returned summary.

Optional integer seed for reproducible bootstrap weights.

Maximum failed refit attempts allowed before stopping.

Logical; store the generated bootstrap weights in the returned object.

Logical; emit progress messages every ten successful replicates.

Reserved for future extensions.

Synthetic datasets.

Absolute-plus-relative comparison tolerance.

A synthetic_quadform_geometry.

Matching endpoint matrices with one segment per row.

Positive integration tolerance.

A synthetic geometry component.

Latent coordinates in rows.

Optional realized orthonormal frame.

Numeric matrix with one row per source/support point.

Numeric response or mass vector of length nrow(X).

Optional numeric matrix of evaluation points. Defaults to X.

Number of source points in each local support.

Kernel name. Supported values are "gaussian", "tricube", "epanechnikov", and "triangular".

Positive multiplier applied to the local support radius.

Optional integer candidate neighborhood sizes. If supplied, or if foldid is supplied, the function performs row-wise cross-validation and refits the selected candidate on all rows.

Optional kernel candidates for cross-validation.

Optional bandwidth-multiplier candidates for cross-validation.

Optional positive integer vector assigning source rows to cross-validation folds.

Number of folds used when foldid is not supplied.

Random seed used to generate folds when foldid is not supplied.

Local coordinate method. "coordinates" uses centered ambient coordinates. "local.pca" projects centered support points onto a local PCA basis.

Local PCA dimension when coordinate.method = "local.pca". If NULL, the dimension is min(ncol(X), support.size - 1). The deployable input-only policies "auto" and "local.auto" use the same local-PCA dimension diagnostics as fit.lps; "auto" resolves one global chart dimension, while "local.auto" resolves one dimension per evaluation anchor.

Optional candidate chart dimensions for experimental row-wise cross-validation. Numeric grids can be evaluated with selection.strategy = "sparse_kd".

Candidate-selection strategy. "grid" evaluates the requested candidate grid. "sparse_kd" evaluates a sparse support-size by chart-dimension skeleton when chart.dim.grid is supplied. "plateau_kd" uses the same geometry-only support-size and chart-dimension plateau rule as fit.lps.

Optional explicit maximum chart dimension for the sparse coupled candidate family.

Nonnegative integer subtracted from the local-PCA rank cap min(ncol(X), support.size - 1). The default zero applies only the Nadaraya–Watson chart-geometry requirement; this is not a local polynomial design margin.

Support system used by chart.dim = "auto" or "local.auto". Chart-kernel smoothers currently use coordinate supports for both coordinate and operator diagnostics.

Which auto chart-dimension diagnostic to use when both coordinate and operator summaries are requested.

Optional positive reference-measure weights q_i. Defaults to unit weights.

Positive floor used when the local denominator is numerically zero.

Logical; if TRUE, keep per-evaluation diagnostics.

Numeric matrix with one row per support point.

Optional nonnegative mass/count vector of length nrow(X). Required by count-based density methods.

Density method identifier.

Optional precomputed graph object.

List of graph-method controls.

List controlling clipping, normalization, and accounting checks. Recognized entries are mass.tol, neg.tol, clip.negative, and renormalize.

Logical; if TRUE, keep diagnostic details in the result.

Additional method-specific arguments.

List of integer neighbor vectors using 1-based vertex indices. The graph must be undirected: every edge must appear in both endpoint adjacency lists.

Optional list of positive edge weights parallel to adj.list. For operator.family = "graph.laplacian.recursive", weights are graph trend-filtering weights or conductances. For operator.family = "path.divided.difference", weights are metric edge lengths used to define path coordinates. If NULL, all values are one.

Numeric response vector of length length(adj.list).

Integer trend-filtering order. Supported values are 0L, 1L, and 2L.

Optional non-negative lambda grid. For lambda.selection = "fixed", this must contain exactly one value. For lambda.selection = "cv", NULL builds a default grid from the fitted full-data solution path.

"cv" for vertex K-fold cross-validation or "fixed" for a supplied fixed lambda.

Character scalar. "conductance" uses weight.list directly as $\omega_e$; "sqrt.conductance" uses $\sqrt{w_e}$; "unit" ignores weight.list. This applies to operator.family = "graph.laplacian.recursive".

Character scalar selecting the penalty operator family. The default "graph.laplacian.recursive" preserves the existing graph trend-filtering semantics. "path.divided.difference" uses local pathwise finite differences and is designed to reproduce classical one-dimensional trend filtering on path graphs.

Character scalar used for operator.family = "path.divided.difference". "branch.continuation" keeps paths whose internal vertices do not pass through branch points. "all.simple" keeps all simple paths of the required length.

Character scalar used for operator.family = "path.divided.difference". "unit" assigns every canonical path row weight one. "anchor.mean" divides rows by the number of retained canonical paths sharing the same canonical start vertex.

Number of default lambda candidates when lambda.grid = NULL and lambda.selection = "cv".

Number of CV folds.

Optional integer fold assignments of length length(y).

Maximum number of path steps passed to genlasso.

Minimum lambda passed to genlasso.

Logical; passed to genlasso.

Numerical controls passed to genlasso.

Logical. If TRUE, pass verbose output to genlasso.

Numeric matrix with one row per source/support point.

Numeric response vector. For likelihood.family = "density", this must be a nonnegative mass/intensity vector with positive total mass. For "bernoulli", values must lie in [0, 1].

Optional numeric matrix of evaluation points. Defaults to X.

Local likelihood family.

Number of source points in each local support.

Local chart feature degree. Supported values are 0, 1, and 2. The density branch omits an intercept because the intercept is not identifiable in the normalized local density likelihood. The Bernoulli branch includes an intercept in its internal logistic feature map.

Kernel name. Supported values are "gaussian", "tricube", "epanechnikov", and "triangular".

Positive multiplier applied to the local support radius.

Optional integer candidate neighborhood sizes for cross-validation. CV selection is currently implemented for likelihood.family = "bernoulli".

Optional local polynomial degree candidates for Bernoulli cross-validation.

Optional kernel candidates for Bernoulli cross-validation.

Optional bandwidth-multiplier candidates for Bernoulli cross-validation.

Optional ridge-penalty candidates for Bernoulli cross-validation.

Optional positive integer vector assigning source rows to cross-validation folds.

Number of folds used when foldid is not supplied.

Random seed used to generate folds when foldid is not supplied.

Local coordinate method. "coordinates" uses centered ambient coordinates. "local.pca" projects centered support points onto a local PCA basis.

Local PCA dimension when coordinate.method = "local.pca". If NULL, the dimension is min(ncol(X), support.size - 1). The deployable input-only policies "auto" and "local.auto" use the same local-PCA dimension diagnostics as fit.lps; "auto" resolves one global chart dimension, while "local.auto" resolves one dimension per evaluation anchor.

Optional candidate chart dimensions for experimental cross-validation. Numeric grids can be evaluated with selection.strategy = "sparse_kd".

Candidate-selection strategy. "grid" evaluates the requested candidate grid. "sparse_kd" evaluates a sparse support-size by chart-dimension skeleton when chart.dim.grid is supplied. "plateau_kd" uses the same geometry-only support-size and chart-dimension plateau rule as fit.lps.

Optional explicit maximum chart dimension for the sparse coupled candidate family.

Nonnegative integer feasibility margin used to screen local polynomial design size before candidate evaluation.

Support system used by chart.dim = "auto" or "local.auto". Local-likelihood smoothers currently use coordinate supports for both coordinate and operator diagnostics.

Which auto chart-dimension diagnostic to use when both coordinate and operator summaries are requested.

Optional positive reference-measure weights. Defaults to unit weights.

Nonnegative ridge penalty on identifiable coefficients.

Minimum local kernel-weighted mass needed before attempting a higher-degree density fit. For Bernoulli fits this is used only as diagnostic telemetry.

Minimum number of locally weighted positive-mass source points needed before attempting a higher-degree local fit.

Fallback policy for underidentified or failed higher-degree local fits. Zero local mass always uses "zero".

Optimizer for nonzero-degree density fits. "newton" is implemented; "optim" is accepted and delegates to BFGS.

Maximum optimizer iterations.

Convergence tolerance for gradient norm and step norm.

Logical; if TRUE, keep per-evaluation diagnostics.

Optional coordinate matrix used to build lpl.tf.operator when operator is NULL.

Numeric response vector.

Optional "lpl_tf_operator" object.

Optional graph inputs passed to lpl.tf.operator when operator is NULL.

Polynomial degree passed to lpl.tf.operator when operator is NULL.

Optional nonnegative lambda grid.

Optional fixed lambda shortcut. If supplied, it is used as the single fixed lambda and lambda.selection must be "fixed".

"cv" or "fixed". Phase 2 requires an explicit lambda.grid for CV so the candidate grid is not generated from the full response vector before fold scoring.

Optional Phase-3 operator candidate grid. Supply a data frame with one row per candidate or a list of named lists. Candidate fields may include operator-construction arguments such as degree, support.type, support.size, min.support, support.buffer, kernel, row.normalize, and local.solver.

Optional deterministic fold assignments for CV.

Number of generated folds when foldid = NULL.

Cross-validation loss, "mse", "rmse", or "mae". "rmse" uses the same lambda ordering as MSE and reports square-rooted fold errors.

Reserved for reproducible generated folds. Phase 2 generated folds are deterministic even when this is NULL.

Phase 2 supports only one CV repeat.

Phase 2 supports only "genlasso".

Lambda selection rule, "min" or "one.se".

Number of generated lambdas when a genlasso path is used and lambda.grid = NULL.

Genlasso controls.

Logical.

Additional arguments passed to lpl.tf.operator when the operator is built internally.

Numeric design/coordinate matrix with one observation per row.

Numeric response vector with length nrow(X).

Optional positive integer vector assigning rows to CV folds.

Integer candidate neighborhood sizes.

Integer polynomial degrees. Currently degrees 0, 1, and 2 are supported.

Candidate kernels. Supported kernels are "gaussian", "tricube", "epanechnikov", and "triangular".

Number of folds used when foldid is not supplied.

Random seed used to generate folds when foldid is not supplied.

Optional matrix of prediction locations. Defaults to X.

Local coordinate system. "coordinates" uses centered ambient coordinates. "local.pca" uses a local PCA chart.

Chart dimension for coordinate.method = "local.pca". If NULL, defaults to ncol(X). The special value "auto" estimates one global chart dimension from observed X only. The experimental special value "local.auto" estimates a local chart dimension separately for each prediction anchor in the ordinary local-PCA R backend.

Optional candidate chart dimensions for experimental coupled support-size by chart-dimension selection. When supplied, coordinate.method must be "local.pca" and the evaluated candidates use scalar numeric chart dimensions after feasibility filtering. The default NULL preserves the historical single-chart.dim behavior.

Local chart constructor used when coordinate.method = "local.pca". "pca" preserves the ordinary local-PCA chart path. "second.order.svd" uses an experimental curvature-corrected second-order local SVD chart and records compact chart fallback diagnostics. This option is opt-in and does not affect ambient coordinate fits.

Support system used when chart.dim = "auto" or "local.auto". Included for consistency with LPL-TF and S-LPL-TF; because this smoother uses coordinate supports, "operator" is equivalent to "coordinates".

Which auto chart-dimension diagnostic to select when both diagnostics are requested.

Computation backend. "auto" uses the C++ backend for coordinate.method = "coordinates" and the R reference backend for coordinate.method = "local.pca". "R" always uses the reference implementation. "cpp" requires ambient coordinates. "cpp.local.pca" is an opt-in prototype backend for coordinate.method = "local.pca" with local.chart.method = "pca".

Local polynomial design backend. "monomial" uses the ordinary raw monomial design. "weighted.qr" solves the same design using an explicit weighted-QR numerical path. "weighted.qr.drop" first drops numerically dependent local design columns by weighted QR before solving. "orthogonal.polynomial.drop" replaces the local monomial design by a weighted-orthogonal basis spanning its estimable polynomial directions, dropping numerically rank-deficient directions first.

Relative QR tolerance used by design.basis = "weighted.qr.drop" or design.basis = "orthogonal.polynomial.drop".

Nonnegative scale-relative ridge multipliers tried by the R local-solve backend. The smallest multiplier whose penalized local normal equations pass ridge.condition.max is used.

Maximum allowed condition number for the penalized local normal equations. Use Inf to disable this guard.

Action when no local solve passes the rank and condition guards. "mean" preserves the historical weighted-mean fallback. "na" returns NA, causing CV candidates with unstable predictions to be avoided.

Response family. "gaussian" preserves the ordinary numeric-response LPS behavior. "bernoulli" treats 0/1 responses as numeric conditional-expectation targets for $\Pr(Y=1\mid X)$, keeps the same local least-squares fitting core, clips reported response-scale probabilities to [0,1], selects candidates by the observed CV Brier score of the clipped predictions (E2.12: the selection score is the deployed metric, which requires per-point CV predictions, so "bernoulli" – like "binomial" – always uses the R backend: backend = "auto" resolves to "R" and an explicit C++ backend is an error), and records Brier/log-loss probability diagnostics. "binomial" uses local weighted logistic polynomial fits, selects candidates by observed CV log loss with the log-loss probability truncation pinned at 1e-6 (E2.12) and with any candidate having a non-finite CV prediction scored Inf – unselectable, the same rule as the gaussian/bernoulli selection scores (E2.15) – and reports probability diagnostics on the fitted probabilities. The local logistic IRLS uses deviance step-halving (E2.14): a Newton update is accepted only if the weighted binomial deviance does not increase by more than 1e-8; otherwise the step is halved toward the current iterate (at most 30 times, after which the solve is declared non-convergent). The deviance is evaluated on the same [-35, 35] clamped linear predictor the IRLS update uses, so it is finite for every finite iterate. A solve that does not converge within the iteration cap (including under exact separation, where the unpenalized logistic MLE does not exist) falls back deterministically to the local weighted event rate under unstable.action = "mean" or to NA under unstable.action = "na"; every fallback is counted in logistic.diagnostics (fallback.path, event.rate.fallback, na.failure).

Nonnegative bandwidth multipliers added to the CV candidate grid. For a candidate with multiplier $b$, the local kernel bandwidth becomes $h = b \cdot d_{(K)}$ where $d_{(K)}$ is the distance to the $K$-th nearest support neighbor, decoupling the kernel scale from the support size. The default 1 reproduces the historical behavior exactly (the bandwidth equals the support radius). Any grid other than exactly 1 requires the R reference backend: backend = "auto" then resolves to "R", and explicit backend = "cpp" or "cpp.local.pca" is an error. The selected multiplier is returned in $selected$bandwidth.multiplier and as a bandwidth.multiplier column of cv.table.

Logical; if TRUE, the returned object additionally carries cv.predictions, the matrix of out-of-fold CV predictions with one column per cv.table row, so selection scores can be recomputed from the actual CV predictions (E2.12). NULL on the C++ CV paths (reachable only for outcome.family = "gaussian"), which do not materialize per-point predictions. Default FALSE leaves the returned object exactly as before.

Shrinkage target of the local ridge penalty in the least-squares solve (E2.13). The default "zero" preserves the historical behavior bit-for-bit: in the orthogonal design bases the penalty acts on every transformed direction, including the constant, so a large ridge multiplier shrinks the local prediction toward 0. "local.mean" – the statistically recommended setting – leaves the constant direction unpenalized via a weighted-centering reparametrization, so a large ridge shrinks the prediction toward the local weighted mean instead, and rho = 0 remains the unpenalized weighted least-squares solve. The two settings coincide for the non-orthogonal design bases ("monomial", "weighted.qr", "weighted.qr.drop"), whose constant column is already unpenalized, and at rho = 0. The setting applies to the least-squares solve (outcome.family "gaussian" / "bernoulli"); it has no effect on the "binomial" local logistic solver, whose ridge keeps the historical structure (a warning is issued if combined).

Candidate-selection strategy. "grid" preserves the full Cartesian candidate grid. The experimental "sparse_kd" strategy evaluates a sparse coupled support-size by chart-dimension skeleton when chart.dim.grid is supplied. "plateau_kd" is a geometry-only selector: from observed X only, it estimates the local PCA variance dimension over the supplied support grid, finds the initial support-size plateau where that dimension is stable from the smallest support size, aggregates plateau endpoints across representative anchors, and evaluates the resulting single (support.size, chart.dim) candidate.

Optional sparse-response chart activation rule. "none" preserves the ordinary LPS behavior. "subject.od" is intended for subject-occupation density workflows: a local chart whose support contains too little subject occupation mass, too few positive subject-visited points, or only fringe occupation receives fitted value zero without constructing the local polynomial fit.

Optional nonnegative response used only by chart.activation = "subject.od" to decide whether a chart is active. When omitted, y is used.

List controlling sparse chart activation. Supported fields are mass.min, n.positive.min, positive.tol, core.weight.rule, core.weight.quantile, and core.weight.min. The OD default is two positive support points and a chart-specific 0.25 weight quantile.

Optional explicit maximum chart dimension for the experimental coupled selector.

Nonnegative prefit margin used to mark coupled (support.size, chart.dim) candidates infeasible when the full local polynomial design would be underdetermined.

Numeric coordinate matrix with one row per observation.

Numeric response vector with length nrow(X).

Optional supported dgraphs graph object, for example from dgraphs::create.rknn.graph(). When support.metric = "graph.geodesic" or "auto" with a graph supplied, weighted shortest-path distances from this graph are used for support construction.

Optional 1-based undirected adjacency list. Must be supplied together with weight.list when using a supplied graph payload.

Optional positive edge-length list parallel to adj.list. Edge weights are interpreted as graph lengths.

Graph lifecycle stage used when graph is a dgraphs graph object. Supported stages include "final", "raw", and "pruned" when those payloads are available on the supplied graph.

Optional integer vector of observed rows used as local model anchors. Defaults to all rows when anchor.coordinates is NULL.

Optional numeric coordinate matrix of off-sample local model anchors with the same number of columns as X. This option is currently supported only with coordinate support distances, not with support.metric = "graph.geodesic".

Local polynomial degree, one of 0L, 1L, or 2L.

Optional degree grid used when support.selection is "cv" or "gcv".

Support construction rule. "knn" uses exactly support.size nearest observations including the anchor itself for full-data local fitting supports. Prediction supports are then rebuilt from the induced local radius, so tied targets at the kNN boundary can be covered even when they were not part of the exact-size fitting support. "adaptive.radius" uses a radius large enough to include at least min.support observations. "fixed.radius" uses the supplied radius.

Number of nearest observations for support.type = "knn". If NULL, defaults to min.support.

Optional kNN support-size grid used when support.selection is "cv" or "gcv".

Radius for support.type = "fixed.radius" and optional base radius for support.type = "adaptive.radius".

Optional radius grid used when support.selection is "cv" or "gcv".

Minimum positive-weight support size. If NULL, defaults to the local polynomial design size plus support.buffer.

Optional minimum-support grid used when support.selection is "cv" or "gcv".

Nonnegative integer added to the local design size when deriving the default min.support.

Kernel used for local fitting and model averaging.

Optional kernel grid used when support.selection is "cv" or "gcv".

Optional per-anchor model-quality multiplier applied to the ordinary kernel averaging weights. "none" preserves the kernel-only averaging from earlier phases. "condition" downweights poorly conditioned local designs with $q_u^{\mathrm{cond}}=1/\max(\kappa_u,1)$. "support" upweights anchors with larger positive fitting supports using support size divided by the maximum support size. "boundary" downweights asymmetric boundary-like supports with $q_u^{\mathrm{bdry}}=1/(1+b_u)$. "quality" multiplies these three component weights. For every non-"none" rule, diagnostics$model.weight.raw stores the selected unnormalized rule multiplier, while model.weights and diagnostics$model.weight store the final multipliers after median-one normalization over positive raw values. Raw zero or non-finite multipliers are retained diagnostically but are replaced by a tiny positive final floor before prediction averaging, so model-quality rules reweight existing prediction support rather than removing anchors from support membership. These weights affect prediction averaging only; they do not change local supports or local coefficient estimation.

How duplicate coordinate rows should be handled. "keep" allows duplicates, records duplicate diagnostics, and preserves observed-anchor self-inclusion. "error" rejects duplicate rows. Jittering duplicates is deliberately not implemented in Phase 1.

Coordinate system used for each local polynomial design. "coordinates" uses supplied coordinates centered at the anchor. "local.pca" uses a deterministic local PCA chart estimated from the anchor support.

Local chart dimension for coordinate.method = "local.pca". If NULL, defaults to ncol(X). The special value "auto" estimates a single observed-data local PCA dimension without using responses, truth values, latent coordinates, or labels. For coordinate.method = "coordinates", chart.dim must be NULL.

Distance system used for support construction. "coordinates" uses Euclidean distances in X. "graph.geodesic" uses weighted shortest-path distances from graph or adj.list/weight.list. "auto" uses graph geodesic distances when graph input is supplied and coordinate distances otherwise.

Support system used when chart.dim = "auto". "coordinates" uses Euclidean coordinate neighborhoods, "operator" uses the resolved MALPS support metric, and "both" computes both diagnostics side by side.

Which auto chart-dimension diagnostic to use for the fitted MALPS model when both diagnostics are available. The default "coordinates" preserves historical behavior.

"fixed" for a single support profile, "cv" to tune support parameters by cross-validation, or "gcv" to tune support parameters by exact dense generalized cross-validation. The GCV path is cached across candidates and is exact for fixed-weight linear MALPS fits; it rejects robust residual reweighting.

Optional integer fold assignments. If supplied, cv.repeats is forced to one.

Number of folds generated when foldid = NULL.

Cross-validation loss.

Number of independent fold assignments generated when foldid = NULL.

Optional seed for generated folds.

Logical; use a one-standard-error rule for support selection.

Maximum number of observations allowed for exact dense GCV support selection. Larger datasets should use "cv" until a sparse or trace-estimated GCV path is implemented.

Local weighted least-squares solver. "auto" uses normal equations only for full-rank, well-conditioned local designs and otherwise falls back to SVD.

Maximum local design condition number for normal equations under local.solver = "auto".

Number of Cleveland-style robust residual reweighting iterations applied inside each local polynomial fit. The default 0L preserves ordinary MALPS. Positive values multiply the geometric fitting weights by Tukey bisquare residual weights recomputed from the local fit.

Positive bisquare tuning constant. The default 6 matches the usual LOWESS convention in which residuals are scaled by 6 * median(abs(residuals)).

Logical; reserved for future progress messages.

Reserved for future extensions. Supplying unused arguments is an error.

List of integer neighbor vectors using 1-based vertex indices.

List of positive metric edge lengths parallel to adj.list. These are interpreted as edge lengths, not conductances.

Numeric response vector of length length(adj.list).

Character scalar. One of "inverse.length.power", "exp.length", "exp.length.squared", or "self.tuned.gaussian".

Positive numeric regularizer used by inverse-power conductances and as a local-scale floor.

Positive numeric exponent for "inverse.length.power".

Optional positive global scale for exponential rules. If NULL, it is selected by conductance.sigma.rule.

Rule for selecting a global scale when needed.

Quantile used when conductance.sigma.rule = "edge.quantile".

Positive integer local incident-edge order statistic for "self.tuned.gaussian".

Laplacian operator. "unnormalized" uses the weighted graph Laplacian $L = D - C$. "symmetric.normalized" uses $L_{\mathrm{sym}} = I - D^{-1/2} C D^{-1/2}$.

Positive integer number of eigenpairs to compute.

Spectral low-pass filter family.

Optional numeric eta grid. Values must be positive except for filter.type = "heat_kernel", where eta = 0 is allowed and gives the identity/no-smoothing limit. If NULL, the existing package helper generate.eta.grid() is used.

Number of eta candidates when eta.grid = NULL.

"auto", "sparse", or "dense". "auto" uses dense decomposition only for n <= dense.eigen.threshold, then sparse-first.

Exact dense threshold for auto mode. Default 200L, intended for small reference/testing problems.

Maximum graph size for emergency dense fallback when sparse decomposition fails and fallback is allowed.

"auto", "never", or "always".

Logical. Reserved for future diagnostic messages.

Heat-time search controller. "fixed" evaluates the supplied or generated grid once. "guarded.gcv" is available only for filter.type = "heat_kernel" and proposes one lower positive time whenever GCV selects the current lower endpoint.

Geometric divisor used by guarded GCV lower-time expansion.

Maximum number of guarded GCV lower-time extensions.

Smallest allowed departure from the identity at the largest retained graph-Laplacian eigenvalue.

Omitted-mode attenuation tolerance used to certify guarded proposals for a truncated basis.

Numeric covariate matrix.

Numeric response vector.

Optional integer cross-validation fold assignment.

Optional single neighborhood size for the fixed local setup path. Use support.grid for CV selection over neighborhood sizes.

Single local polynomial degree for the fixed local setup path. Use degree.grid for CV selection over degrees.

Single kernel name for the fixed local setup path. Use kernel.grid for CV selection over kernels.

Chart dimension for the local PCA charts. A scalar fixes one dimension for all anchors; an integer vector supplies one local chart dimension per anchor. The special value "auto" estimates one global chart dimension from observed X only. The experimental special value "local.auto" estimates one local chart dimension per anchor, using the same local-PCA dimension rule as fit.lps.

Candidate neighborhood sizes. When supplied, PS-LPS selects over support size, degree, kernel, and synchronization strength by materialized-fold CV. If both support.size and support.grid are absent, defaults to c(10L, 15L, 20L), matching fit.lps.

Candidate local polynomial degrees for grid selection. Defaults to the scalar degree.

Candidate kernels for grid selection. Defaults to the scalar kernel.

Support system used when chart.dim = "auto" or "local.auto". Because PS-LPS uses coordinate supports, "operator" is equivalent to "coordinates".

Which auto chart-dimension diagnostic to select when both diagnostics are requested.

Optional candidate chart dimensions for experimental local-candidate selection. Numeric grids can be evaluated with selection.strategy = "sparse_kd".

Candidate-selection strategy. "grid" evaluates the requested candidate grid. "sparse_kd" evaluates a sparse support-size by chart-dimension skeleton when chart.dim.grid is supplied. "plateau_kd" uses the same geometry-only support-size and chart-dimension plateau rule as fit.lps.

Optional explicit maximum chart dimension for the sparse coupled candidate family.

Nonnegative integer feasibility margin used to screen local polynomial design size before candidate evaluation.

Candidate synchronization strengths.

Lambda-search policy. "grid" evaluates the supplied grid exactly. "guarded" uses an experimental guarded coarse-to-refine search with boundary expansion.

Lambda-selection mode. "cv" performs the usual internal fold-weighted lambda selection. "fixed" treats the single value in lambda.sync.grid as preselected and skips internal lambda CV; this is intended for outer selection loops that already score scalar candidates.

Local-candidate search policy when support.grid, degree.grid, or kernel.grid contains more than one candidate. "screened" is the routine default: it first ranks candidates by ordinary LPS materialized-fold CV, then runs PS-LPS only on a screened subset plus guard candidates. "full" evaluates PS-LPS lambda search for every local candidate and is the exact audit/reference path. "subgrid" skips the ordinary-LPS screening pass and evaluates only a deterministic support/kernel guard subgrid; this is intended for high-dimensional preflight runs where the screening pass is itself too expensive.

Optional list controlling screened local-candidate search. Supported fields are top.n (default 8), max.candidates (default 12), neighbor.radius (default 1), and guard.support.quantiles (default c(0, 0.5, 1)).

Optional list controlling guarded search. Supported fields are coarse.size (default 5), refine.radius (default 2), rel.tol (default 0.002), boundary.guard.rel.tol (default 0.01), boundary.expand (default TRUE), boundary.factor (default 3), max.boundary.expansions (default 2), and max.candidates (default 25). Boundary expansion may evaluate positive candidates outside the supplied lambda.sync.grid. max.candidates is a global cap on distinct evaluated candidates; a very small cap can prevent local refinement or boundary expansion.

Lambda-diagnostic evaluation policy. "all" computes synchronization-energy and local-GCV diagnostics for every evaluated lambda and is the audit/reference mode. "selected" computes those diagnostics only for the selected lambda, which is faster for routine selection.

Nonnegative scale-relative ridge used in the chart coefficient solve. Use 0 for the unregularized least-squares model.

Local polynomial design backend. See fit.lps. In PS-LPS, "weighted.qr.drop" drops numerically dependent columns separately in each anchor chart before the synchronized system is assembled, and "orthogonal.polynomial.drop" builds each synchronized chart in a weighted-orthogonal polynomial basis.

Relative QR tolerance used by design.basis = "weighted.qr.drop" or design.basis = "orthogonal.polynomial.drop".

Optional nonnegative ridge multipliers for adaptive scale-relative ridge selection. When supplied, the solver uses the smallest multiplier whose penalized normal equations pass ridge.condition.max. If NULL, lambda.ridge is used as the single multiplier for backward compatibility.

Maximum allowed condition number for adaptive ridge selection. Use Inf to disable the condition-number guard.

Number of nearby anchor pairs considered for synchronization from each anchor support.

Overlap weighting rule.

Optional sparse-response chart activation rule. "none" preserves ordinary PS-LPS. "subject.od" is intended for subject-occupation density workflows and deactivates local charts with no subject mass, too few positive subject-visited support points, or only fringe occupation.

Optional nonnegative vector used only for chart.activation = "subject.od" to decide whether each chart is active. When omitted, y is used.

List controlling sparse chart activation; see fit.lps.

Optional precomputed geometry cache used by occupation-density cross-validation. This is an implementation detail; ordinary callers should leave it as NULL.

Optional precomputed local-PCA supports used when activation-specific frames must be rebuilt. This is an implementation detail; ordinary callers should leave it as NULL.

Number of folds when foldid is absent.

Fold seed when foldid is absent.

Optional "pttf_geometry" object. Used only when operator is NULL.

Optional "pttf_operator" object. Supplying an operator is recommended for validation so geometry/operator construction is separated from fitting.

Optional data matrix used to build pttf.geometry when both geometry and operator are NULL.

Numeric response vector.

Integer derivative order passed to pttf.operator when an operator must be built.

"l1" for generalized-lasso style fitting or "l2" for the quadratic energy fit.

Optional lambda grid. Required for lambda.selection = "fixed".

"cv" or "fixed".

Number of lambdas in a generated grid.

Number of folds used only when foldid = NULL.

Optional integer fold assignments. Validation lanes should pass a materialized foldid; otherwise folds are generated by R's current RNG state.

Cross-validation loss, "mse" or "mae".

Lambda selection rule, "min" or "one.se".

Currently recorded as metadata. Phase 3 implements no new extension heuristic.

L1 solver backend.

Which operator rows to use for fitting.

Vertex order for 1-D boundary-row policies.

Number of endpoint ranks to drop for operator.row.policy = "drop.line.boundary". Defaults to derivative.order.

Passed to pttf.operator when this function builds an operator. row.normalize is also used as the L1 solver row scaling for the supplied fit operator.

Optional nonnegative observation weights.

Genlasso controls for L1 fits.

ADMM controls used when the L1 backend is "admm" or falls back to ADMM.

Logical.

Additional arguments passed to pttf.geometry or pttf.operator when those objects are built internally.

Optional coordinate matrix used to build slpl.tf.operator when operator is NULL.

Numeric response vector.

Optional "slpl_tf_operator" object.

Fixed LPL-TF $\ell_1$ penalty, or a shortcut for lambda1.grid when lambda.selection = "cv".

Fixed quadratic synchronization penalty, or a shortcut for lambda2.grid when lambda.selection = "cv".

Optional nonnegative $\lambda_1$ grid for CV.

Optional nonnegative $\lambda_2$ grid for CV.

"fixed" or "cv". CV uses materialized folds and a deterministic Cartesian grid over lambda1.grid and lambda2.grid.

Optional Phase-S3 operator candidate grid. Supply a data frame with one row per candidate or a list of named lists.

Optional deterministic fold assignments for CV.

Number of generated folds when foldid = NULL.

Cross-validation loss, "mse", "rmse", or "mae".

Optional seed for reproducible generated folds.

Phase S3 supports only one CV repeat.

Current implementation supports only "genlasso".

Selection rule, "min" or "one.se". For the two-parameter one-standard-error rule, the most regularized eligible pair is chosen by decreasing lambda1 and then decreasing lambda2.

Genlasso controls.

Logical.

Additional arguments passed to slpl.tf.operator when the operator is built internally.

Numeric matrix with one observation per row. Distances for the default neighborhood search are Euclidean distances in these coordinates.

Numeric response vector of length nrow(X). Matrix responses are not yet supported for the $\ell_1$ path.

Integer number of nearest neighbors per point, including the point itself, used when neighborhood.type = "knn". This follows the SSRHE Matlab convention. For adaptive-radius neighborhoods, k may be omitted when adaptive.k.scale is supplied.

Integer tangent dimension used for the local PCA chart. Required when tangent.dim.rule = "fixed". If NULL and tangent.dim.rule = "eigen.cumulative", the dimension is selected locally from the PCA variance ratio.

Optional nonnegative lambda grid. For lambda.selection = "fixed", this must contain exactly one value. For lambda.selection = "cv", NULL builds a default grid from the fitted full-data generalized-lasso path.

"cv" for observed-label K-fold cross-validation or "fixed" for a supplied fixed lambda.

Optional nonnegative observation weights. Missing responses automatically receive zero weight.

Number of default lambda candidates when lambda.grid = NULL and lambda.selection = "cv".

Number of validation folds over observed positive-weight labels. Ignored when fold.id is supplied.

Optional integer fold assignments of length nrow(X).

Validation loss, currently "mse" or "mae".

Selection rule. "min" chooses the smallest mean validation loss. "one.se" chooses the largest lambda within one standard error of the minimum.

Optional integer matrix of neighbor indices, with nrow(X) rows and k columns. Each row must contain its center vertex. If NULL, Euclidean k-NN including self is computed in C++.

Local support rule. "knn" uses the original rectangular self-including kNN neighborhoods. "adaptive.radius" builds variable-size supports from dgraphs::create.rknn.graph(). "supplied" uses support.index directly.

Optional list of integer vectors, one per row of X. Each element gives a variable-size local support and must contain its center vertex.

Integer local-scale k used by dgraphs::create.rknn.graph() when neighborhood.type = "adaptive.radius".

Adaptive-radius graph parameters passed to dgraphs::create.rknn.graph().

Optional minimum local support size for adaptive-radius supports. Defaults to the local quadratic design size plus support.buffer, clamped to nrow(X).

Optional maximum local support size. Oversized adaptive supports are trimmed to the closest max.support vertices while keeping the center vertex.

Nonnegative integer added to the local quadratic design size when choosing the default min.support.

How undersized adaptive-radius supports are enlarged. "nearest" appends ambient nearest neighbors. "none" leaves supports unchanged and lets the C++ operator reject undersized supports.

Either "fixed" or "eigen.cumulative".

Cumulative local PCA variance threshold used when tangent.dim.rule = "eigen.cumulative" and tangent.dim = NULL.

Integer derivative order of the local SSRHE-style operator. 2L is the original local Hessian energy. 3L is an experimental third-derivative energy whose rows estimate unique symmetric third-derivative tensor components with factorial and tensor-multiplicity scaling.

Nonnegative tolerance multiplier for local pseudoinverses.

Local least-squares backend used to map local function values to derivative coefficients. "auto" is the default: it uses normal equations when the local design is full rank and has condition number no larger than normal.equations.max.condition, and otherwise falls back to SVD. "normal.equations" requests the normal-equation solve for full-rank local designs and falls back only on hard numerical failures. "svd" is the most stable reference path. "qr" uses pivoted QR and falls back to SVD for rank-deficient local designs.

Positive condition-number guard used by local.solver = "auto" before accepting the normal-equation backend. The default is deliberately conservative because normal-equation solves square the effective condition number and order-3 near-minimum local supports can be numerically fragile.

Solver backend. "genlasso" uses the generalized-lasso path backend. "admm" uses a fixed-lambda ADMM solver for each lambda value. "auto" tries "genlasso" first and falls back to ADMM when path extraction produces an error or non-finite fitted values.

Optional row scaling for the penalty matrix before solving. "l2" scales nonzero rows of $A$ to unit Euclidean norm.

ADMM controls used when solver = "admm" or when solver = "auto" falls back to ADMM.

Controls passed to genlasso.

Support-profile selection rule. "rule" uses the supplied adaptive.k.scale, min.support, and max.support. "cv" is currently supported for neighborhood.type = "adaptive.radius" with lambda.selection = "cv" and chooses among rows of support.grid by an outer response cross-validation loop.

Optional data frame of support profiles with columns adaptive.k.scale, min.support, and optional max.support. If NULL, ssrhe.support.grid builds a compact default grid.

Maximum number of support profiles to try when support.selection = "cv".

Logical. If TRUE, compute additional R-side local chart diagnostics such as chart distortion and boundary asymmetry. These diagnostics are useful for operator audits, but can be skipped in fitting and cross-validation paths for speed.

Logical. If TRUE, attach a phase-level elapsed time table to the returned operator. The timings separate R-side validation, neighborhood/support construction, native local operator construction, optional local diagnostics, sparse matrix assembly, and output finalization. For adaptive-radius neighborhoods, subphase timings are also attached in neighborhoods$timing.

Numeric matrix with one observation per row. Distances for the default neighborhood search are Euclidean distances in these coordinates.

Numeric response vector of length nrow(X) or numeric matrix with nrow(X) rows. Matrix columns are fit as separate responses. NA values are allowed and are treated as unobserved by setting the corresponding observation weight to zero.

Integer number of nearest neighbors per point, including the point itself, used when neighborhood.type = "knn". This follows the SSRHE Matlab convention. For adaptive-radius neighborhoods, k may be omitted when adaptive.k.scale is supplied.

Integer tangent dimension used for the local PCA chart. Required when tangent.dim.rule = "fixed". If NULL and tangent.dim.rule = "eigen.cumulative", the dimension is selected locally from the PCA variance ratio.

Nonnegative Hessian-energy penalty multiplier for $f^\top B f = \|Af\|_2^2$.

Nonnegative supplemental-stabilizer multiplier for $f^\top B_S f$. If positive, stabilizer must be TRUE. Currently supported only for derivative.order = 2L.

Optional nonnegative observation weights. May be NULL, a vector of length nrow(X), or a matrix with the same dimensions as y.

Optional integer matrix of neighbor indices, with nrow(X) rows and k columns. Each row must contain its center vertex. If NULL, Euclidean k-NN including self is computed in C++.

Local support rule. "knn" uses the original rectangular self-including kNN neighborhoods. "adaptive.radius" builds variable-size supports from dgraphs::create.rknn.graph(). "supplied" uses support.index directly.

Optional list of integer vectors, one per row of X. Each element gives a variable-size local support and must contain its center vertex.

Integer local-scale k used by dgraphs::create.rknn.graph() when neighborhood.type = "adaptive.radius".

Adaptive-radius graph parameters passed to dgraphs::create.rknn.graph().

Optional minimum local support size for adaptive-radius supports. Defaults to the local quadratic design size plus support.buffer, clamped to nrow(X).

Optional maximum local support size. Oversized adaptive supports are trimmed to the closest max.support vertices while keeping the center vertex.

Nonnegative integer added to the local quadratic design size when choosing the default min.support.

How undersized adaptive-radius supports are enlarged. "nearest" appends ambient nearest neighbors. "none" leaves supports unchanged and lets the C++ operator reject undersized supports.

Either "fixed" or "eigen.cumulative".

Cumulative local PCA variance threshold used when tangent.dim.rule = "eigen.cumulative" and tangent.dim = NULL.

Integer derivative order of the local SSRHE-style operator. 2L is the original local Hessian energy. 3L is an experimental third-derivative energy whose rows estimate unique symmetric third-derivative tensor components with factorial and tensor-multiplicity scaling.

Logical. If TRUE, also construct the supplemental stabilizer matrix described in the SSRHE supplement. Currently supported only for derivative.order = 2L.

Nonnegative tolerance multiplier for local pseudoinverses.

Local least-squares backend used to map local function values to derivative coefficients. "auto" is the default: it uses normal equations when the local design is full rank and has condition number no larger than normal.equations.max.condition, and otherwise falls back to SVD. "normal.equations" requests the normal-equation solve for full-rank local designs and falls back only on hard numerical failures. "svd" is the most stable reference path. "qr" uses pivoted QR and falls back to SVD for rank-deficient local designs.

Positive condition-number guard used by local.solver = "auto" before accepting the normal-equation backend. The default is deliberately conservative because normal-equation solves square the effective condition number and order-3 near-minimum local supports can be numerically fragile.

Nonnegative diagonal ridge added to the linear system for numerical stabilization.

Logical. If TRUE, return $A$ as a sparse matrix.

Logical. If TRUE, compute additional R-side local chart diagnostics such as chart distortion and boundary asymmetry. These diagnostics are useful for operator audits, but can be skipped in fitting and cross-validation paths for speed.

Logical. If TRUE, attach a phase-level elapsed time table to the returned operator. The timings separate R-side validation, neighborhood/support construction, native local operator construction, optional local diagnostics, sparse matrix assembly, and output finalization. For adaptive-radius neighborhoods, subphase timings are also attached in neighborhoods$timing.

Logical. If TRUE, print a short native construction message.

Numeric matrix with one observation per row. Distances for the default neighborhood search are Euclidean distances in these coordinates.

Numeric response vector of length nrow(X) or numeric matrix with nrow(X) rows. Matrix columns are fit as separate responses. NA values are allowed and are treated as unobserved by setting the corresponding observation weight to zero.

Integer number of nearest neighbors per point, including the point itself, used when neighborhood.type = "knn". This follows the SSRHE Matlab convention. For adaptive-radius neighborhoods, k may be omitted when adaptive.k.scale is supplied.

Integer tangent dimension used for the local PCA chart. Required when tangent.dim.rule = "fixed". If NULL and tangent.dim.rule = "eigen.cumulative", the dimension is selected locally from the PCA variance ratio.

Nonnegative numeric vector of Hessian-energy penalty candidates.

Nonnegative numeric vector of supplemental-stabilizer penalty candidates. Use 0 to omit the supplemental stabilizer from selection.

Optional nonnegative observation weights. May be NULL, a vector of length nrow(X), or a matrix with the same dimensions as y.

Number of validation folds over observed positive-weight labels. Ignored when fold.id is supplied.

Optional integer vector of length nrow(X) assigning observed positive-weight labels to validation folds. Nonpositive or NA entries are ignored.

Validation loss, currently "mse" or "mae".

Selection rule. "min" chooses the smallest mean validation loss. "one.se" chooses the largest total penalty among candidates within one standard error of the minimum.

Optional integer matrix of neighbor indices, with nrow(X) rows and k columns. Each row must contain its center vertex. If NULL, Euclidean k-NN including self is computed in C++.

Local support rule. "knn" uses the original rectangular self-including kNN neighborhoods. "adaptive.radius" builds variable-size supports from dgraphs::create.rknn.graph(). "supplied" uses support.index directly.

Optional list of integer vectors, one per row of X. Each element gives a variable-size local support and must contain its center vertex.

Integer local-scale k used by dgraphs::create.rknn.graph() when neighborhood.type = "adaptive.radius".

Adaptive-radius graph parameters passed to dgraphs::create.rknn.graph().

Optional minimum local support size for adaptive-radius supports. Defaults to the local quadratic design size plus support.buffer, clamped to nrow(X).

Optional maximum local support size. Oversized adaptive supports are trimmed to the closest max.support vertices while keeping the center vertex.

Nonnegative integer added to the local quadratic design size when choosing the default min.support.

How undersized adaptive-radius supports are enlarged. "nearest" appends ambient nearest neighbors. "none" leaves supports unchanged and lets the C++ operator reject undersized supports.

Either "fixed" or "eigen.cumulative".

Cumulative local PCA variance threshold used when tangent.dim.rule = "eigen.cumulative" and tangent.dim = NULL.

Integer derivative order of the local SSRHE-style operator. 2L is the original local Hessian energy. 3L is an experimental third-derivative energy whose rows estimate unique symmetric third-derivative tensor components with factorial and tensor-multiplicity scaling.

Logical. If TRUE, also construct the supplemental stabilizer matrix described in the SSRHE supplement. Currently supported only for derivative.order = 2L.

Nonnegative tolerance multiplier for local pseudoinverses.

Local least-squares backend used to map local function values to derivative coefficients. "auto" is the default: it uses normal equations when the local design is full rank and has condition number no larger than normal.equations.max.condition, and otherwise falls back to SVD. "normal.equations" requests the normal-equation solve for full-rank local designs and falls back only on hard numerical failures. "svd" is the most stable reference path. "qr" uses pivoted QR and falls back to SVD for rank-deficient local designs.

Positive condition-number guard used by local.solver = "auto" before accepting the normal-equation backend. The default is deliberately conservative because normal-equation solves square the effective condition number and order-3 near-minimum local supports can be numerically fragile.

Nonnegative diagonal ridge added to the linear system for numerical stabilization.

Logical. If TRUE, return $A$ as a sparse matrix.

Logical. If TRUE, compute additional R-side local chart diagnostics such as chart distortion and boundary asymmetry. These diagnostics are useful for operator audits, but can be skipped in fitting and cross-validation paths for speed.

Logical. If TRUE, attach a phase-level elapsed time table to the returned operator. The timings separate R-side validation, neighborhood/support construction, native local operator construction, optional local diagnostics, sparse matrix assembly, and output finalization. For adaptive-radius neighborhoods, subphase timings are also attached in neighborhoods$timing.

Support-profile selection rule. "rule" uses the supplied adaptive.k.scale, min.support, and max.support. "cv" is currently supported for neighborhood.type = "adaptive.radius" and chooses among rows of support.grid by outer response cross-validation.

Optional data frame of support profiles with columns adaptive.k.scale, min.support, and optional max.support. If NULL, ssrhe.support.grid builds a compact default grid.

Maximum number of support profiles to try when support.selection = "cv".

Logical. If TRUE, print a short native construction message.

Numeric matrix with one observation per row. Distances for the default neighborhood search are Euclidean distances in these coordinates.

Numeric response vector of length nrow(X) or numeric matrix with nrow(X) rows. Matrix columns are fit as separate responses. NA values are allowed and are treated as unobserved by setting the corresponding observation weight to zero.

Integer number of nearest neighbors per point, including the point itself, used when neighborhood.type = "knn". This follows the SSRHE Matlab convention. For adaptive-radius neighborhoods, k may be omitted when adaptive.k.scale is supplied.

Integer tangent dimension used for the local PCA chart. Required when tangent.dim.rule = "fixed". If NULL and tangent.dim.rule = "eigen.cumulative", the dimension is selected locally from the PCA variance ratio.

Nonnegative numeric vector of Hessian-energy penalty candidates.

Nonnegative numeric vector of supplemental-stabilizer penalty candidates. Use 0 to omit the supplemental stabilizer from selection.

Optional nonnegative observation weights. May be NULL, a vector of length nrow(X), or a matrix with the same dimensions as y.

Optional integer matrix of neighbor indices, with nrow(X) rows and k columns. Each row must contain its center vertex. If NULL, Euclidean k-NN including self is computed in C++.

Local support rule. "knn" uses the original rectangular self-including kNN neighborhoods. "adaptive.radius" builds variable-size supports from dgraphs::create.rknn.graph(). "supplied" uses support.index directly.

Optional list of integer vectors, one per row of X. Each element gives a variable-size local support and must contain its center vertex.

Integer local-scale k used by dgraphs::create.rknn.graph() when neighborhood.type = "adaptive.radius".

Adaptive-radius graph parameters passed to dgraphs::create.rknn.graph().

Optional minimum local support size for adaptive-radius supports. Defaults to the local quadratic design size plus support.buffer, clamped to nrow(X).

Optional maximum local support size. Oversized adaptive supports are trimmed to the closest max.support vertices while keeping the center vertex.

Nonnegative integer added to the local quadratic design size when choosing the default min.support.

How undersized adaptive-radius supports are enlarged. "nearest" appends ambient nearest neighbors. "none" leaves supports unchanged and lets the C++ operator reject undersized supports.

Either "fixed" or "eigen.cumulative".

Cumulative local PCA variance threshold used when tangent.dim.rule = "eigen.cumulative" and tangent.dim = NULL.

Integer derivative order of the local SSRHE-style operator. 2L is the original local Hessian energy. 3L is an experimental third-derivative energy whose rows estimate unique symmetric third-derivative tensor components with factorial and tensor-multiplicity scaling.

Logical. If TRUE, also construct the supplemental stabilizer matrix described in the SSRHE supplement. Currently supported only for derivative.order = 2L.

Nonnegative tolerance multiplier for local pseudoinverses.

Local least-squares backend used to map local function values to derivative coefficients. "auto" is the default: it uses normal equations when the local design is full rank and has condition number no larger than normal.equations.max.condition, and otherwise falls back to SVD. "normal.equations" requests the normal-equation solve for full-rank local designs and falls back only on hard numerical failures. "svd" is the most stable reference path. "qr" uses pivoted QR and falls back to SVD for rank-deficient local designs.

Positive condition-number guard used by local.solver = "auto" before accepting the normal-equation backend. The default is deliberately conservative because normal-equation solves square the effective condition number and order-3 near-minimum local supports can be numerically fragile.

Nonnegative diagonal ridge added to the linear system for numerical stabilization.

Logical. If TRUE, return $A$ as a sparse matrix.

Logical. If TRUE, compute additional R-side local chart diagnostics such as chart distortion and boundary asymmetry. These diagnostics are useful for operator audits, but can be skipped in fitting and cross-validation paths for speed.

Logical. If TRUE, attach a phase-level elapsed time table to the returned operator. The timings separate R-side validation, neighborhood/support construction, native local operator construction, optional local diagnostics, sparse matrix assembly, and output finalization. For adaptive-radius neighborhoods, subphase timings are also attached in neighborhoods$timing.

Support-profile selection rule. "rule" uses the supplied adaptive.k.scale, min.support, and max.support. "gcv" is currently supported for neighborhood.type = "adaptive.radius" and chooses among rows of support.grid by outer GCV.

Optional data frame of support profiles with columns adaptive.k.scale, min.support, and optional max.support. If NULL, ssrhe.support.grid builds a compact default grid.

Maximum number of support profiles to try when support.selection = "gcv".

Method used to compute the smoother trace in the GCV score. "exact" solves against the full diagonal weight matrix. "hutchinson" estimates the trace with Rademacher probe vectors.

Number of Hutchinson probe vectors to use when gcv.trace.method = "hutchinson".

Optional integer seed for reproducible Hutchinson trace estimates.

Logical. If TRUE, print a short native construction message.