make_constraint_matrix: Create Smoothing Spline Constraint Matrix

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Create Smoothing Spline Constraint Matrix

Description

Constructs constraint matrix \textbf{A} enforcing continuity and smoothness at knot boundaries by constraining function values, derivatives, and interactions between partitions.

Usage

make_constraint_matrix(
  p_expansions,
  CKnots,
  power1_cols,
  power2_cols,
  nonspline_cols,
  interaction_single_cols,
  interaction_quad_cols,
  triplet_cols,
  K,
  include_constrain_fitted,
  include_constrain_first_deriv,
  include_constrain_second_deriv,
  include_constrain_interactions,
  include_2way_interactions,
  include_3way_interactions,
  include_quadratic_interactions,
  colnm_expansions,
  expansion_scales,
  add_first_and_second_derivative_constraints = NULL
)

Arguments

p_expansions	Integer; number of columns in basis expansion per partition
CKnots	Matrix; basis expansions evaluated at knot points
power1_cols	Integer vector; indices of linear terms
power2_cols	Integer vector; indices of quadratic terms
nonspline_cols	Integer vector; indices of non-spline terms
interaction_single_cols	Integer vector; indices of linear interaction terms
interaction_quad_cols	Integer vector; indices of quadratic interaction terms
triplet_cols	Integer vector; indices of three-way interaction terms
K	Integer; number of interior knots (K+1 partitions)
include_constrain_fitted	Logical; constrain function values at knots
include_constrain_first_deriv	Logical; constrain first derivatives at knots
include_constrain_second_deriv	Logical; constrain second derivatives at knots
include_constrain_interactions	Logical; constrain interaction terms at knots
include_2way_interactions	Logical; include two-way interactions
include_3way_interactions	Logical; include three-way interactions
include_quadratic_interactions	Logical; include quadratic interactions
colnm_expansions	Character vector; column names for basis expansions
expansion_scales	Numeric vector; scaling factors for standardization
add_first_and_second_derivative_constraints	Logical or NULL; when both first- and second-derivative constraints are requested, combine the corresponding derivative rows before adding them to the smoothing constraint matrix. If NULL, this is done when more than one predictor is spline-expanded. If FALSE, first- and second-derivative constraints are imposed as separate equality rows.

Value

Matrix \textbf{A} of constraint coefficients. Columns correspond to constraints, rows to coefficients across all K+1 partitions.

lgspline documentation built on May 8, 2026, 5:07 p.m.