Package {BsplineQuantReg}

Type: Package
Title: 'Constrained Quantile Regression with B-Splines'
Version: 0.2.2
Date: 2026-07-26
Description: Quantile regression with B-splines under shape constraints. The initial version with cubic splines is now augmented with splines of degree 1 to 4. Constraints for degrees 3 (monotone) and 4 (monotone and convex) use the Karlin-Studden SOCP characterization for the sign of the polynomial, while other constraints applied at the knots are added as linear problems. The method for cubic splines is described in Abbes (2026) <doi:10.5281/zenodo.17427913>. Other formulations are simple consequences of the other given references. This R implementation is intended for demonstration and prototyping. All B-spline and polynomial functions have been rewritten for consistency. An equivalent Python package is available at https://pypi.org/project/BsplineQuantRegpy/.
License: GPL-3
URL: https://github.com/alexandreabbes/BsplineQuantReg
BugReports: https://github.com/alexandreabbes/BsplineQuantReg/issues
Depends: R (≥ 3.5.0)
Imports: CVXR
Suggests: clarabel, ECOSolveR, cobs, quantreg
Encoding: UTF-8
Config/roxygen2/version: 8.0.0
NeedsCompilation: no
Packaged: 2026-07-28 00:12:51 UTC; abbes
Author: Alexandre Abbes [aut, cre]
Maintainer: Alexandre Abbes <alexandre.abbes@proton.me>
Repository: CRAN
Date/Publication: 2026-07-28 13:20:15 UTC

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Usage

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Build B-spline basis in piecewise polynomial form Computes local polynomial coefficients for each B-spline basis function on each interval. Polynomials are expressed in the canonical basis Uses De Boor's recursion formula.

Description

Build B-spline basis in piecewise polynomial form Computes local polynomial coefficients for each B-spline basis function on each interval. Polynomials are expressed in the canonical basis Uses De Boor's recursion formula.

Usage

Bspline_base(sn, degree = 3, der = 0, verbose = FALSE)

Arguments

sn

Extended knot vector (including endpoint repetitions) This means if t0..tkn it the set of knot then sn should be given as a vector with "degree" times t_0 and t_kn at the beginning and the ends. its length is number of intervals+1+2*degree.

degree

'B-spline' degree (default = 3 for cubic)

der

Derivative order (0 = original basis)

verbose

boolean FALSE (default) or TRUE.

Value

A list containing:

base

Coefficients in the local bases, in the form of an 3-d array [j,nu,coeff], j : the number of the spline in the basis, nu: the number of the interval in the extended notation, coeff : the coefficients in decreasing order Decresing (matlab) convention on the local bases (t-s_nu)^l, l=3.2.1 base[j,,] is a matrix of piecewise polynomial function compatible with the pp-form.

base0

Coefficients in canonical basis (centered at 0) (1, t, t^2, t^3) centered at the interval origin.

ext_knot

Extended knot vector

knot

Effective knot partition including ends)

degree

Spline degree

n_splines

Number of basis functions

deriv_order

Applied derivative order

Examples

sn <- c(0,0,0,0,1,2,3,4,5,5,5,5)
basis <- Bspline_base(sn, degree=3)
x=(0:(5*100))/100
y=bs_direct(basis,x)
matplot(x,t(y))
#or simple:
#view_basis(basis)

Differentiate a B-spline basis

Description

Computes the basis of order der derivatives of a B-spline basis.

Usage

Bspline_base_deriv(Bsbasis, der = 1, verbose = FALSE)

Arguments

Bsbasis

Object returned by Bspline_base or an equivalent coherent list with enough parameters.

der

Derivative order

verbose

boolean FALSE (default) or TRUE.

Value

A list similar to Bspline_base for the derivative basis

Compute derivative coefficients of a B-spline

Description

Given a B-spline of given degree, coefficients, knots, compute the coefficients of the derivative of order 'der' in the B-spline basis of degree d-der. Uses the standard algorithm for differentiating bsplines

Usage

Bspline_deriv(bspline, der = 1, callable = NULL, verbose = FALSE)

Arguments

bspline

callable_spline or non_callable_spline class list or function, or list with variable names 'degree', 'knot' ,'coeff'.

der

Derivative order (default = 1)

callable

Boolean, if TRUE returns a callable Bspline. If not provided

verbose

Boolean gives output messages when TRUE return the same class as input : 'callable' or 'non_callable'

Value

Coefficients of the derivative B-spline (degree = degree - der)

Convert a B-spline to Piecewise Polynomial (PP) form

Description

Transforms a B-spline object (callable or non-callable) into a piecewise polynomial representation. The resulting PP object contains the polynomial coefficients for each interval between knots.

Usage

Bsplinetopp(Bspline, Bsbasis = NULL, callable = FALSE, verbose = FALSE)

Arguments

Bspline

A B-spline object (list, non_callable_spline, or callable_spline) containing at least 'coeff', 'degree', and 'knot'.

Bsbasis

Optional pre-computed B-spline basis object from Bspline_base(). If NULL, the basis is computed automatically.

callable

Logical; if TRUE, returns a callable function for evaluation. If FALSE (default), returns a non_callable_pp object. If a callable spline is given as input, then by default is return a callable pp.

verbose

Logical; if TRUE, print progress messages.

Value

A PP object (piecewise polynomial) with class: - "callable_pp" if callable = TRUE - "non_callable_pp" if callable = FALSE The object can be evaluated with evalpp() or directly if callable.

See Also

makpp, evalpp, Bspline_base

Examples

## Not run: 
# Create a B-spline
sn <- c(0,0,0,0,1,2,3,4,5,5,5,5)
basis <- Bspline_base(sn, degree = 3)
basis$coeff <- runif(basis$n_splines)

# Convert to PP (non-callable)
pp <- Bsplinetopp(basis, callable = FALSE)
y <- evalpp(pp, seq(0, 5, length.out = 100))

# Convert to PP (callable)
pp_call <- Bsplinetopp(basis, callable = TRUE)
y <- pp_call(seq(0, 5, length.out = 100))

## End(Not run)

Omega function for De Boor recursion

Description

Computes the affine element used in the recursive De Boor algorithm for B-spline construction. for a given extended knot partition s(1),.. Omega(j,l)(x)=(s(j-x))/(s(j+l-1)-s(j)\), with l: order of the spline

Usage

Omega(s, j, o)

Arguments

s

Extended knot vector

j

Knot index

o

Spline order (degree + 1)

Value

(Side function) A Vector of coefficients [alpha, beta] representing (alpha*t + beta)

Wrapper function for linear spline quantile regression

Description

This is a convenience wrapper for SplineLinearQuant.

Usage

SplineConstQuantRegBs1(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knots

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained

solver

CVXR solver to use (default = "OSQP")

weight

Observation weights (default = 1 for all)

verbose

logical; if TRUE, print progress messages

Value

Same as SplineLinearQuant

Wrapper function for quadratic spline quantile regression Previous version notation style This is a convenience wrapper for SplineQuadraticQuant.

Description

Wrapper function for quadratic spline quantile regression Previous version notation style This is a convenience wrapper for SplineQuadraticQuant.

Usage

SplineConstQuantRegBs2(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  convcons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knots

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained. Although constraints are set at knots; we apply them on each interval, at both extremities. kn+1 knots, kn constraints taken into account.

convcons

Convexity constraint vector per interval: 1 = convex, -1 = concave, 0 = unconstrained. kn constraints are considered for kn+1 knots.

solver

'CVXR' solver to use (default = 'CLARABEL')

weight

Observation weights (default = 1 for all)

verbose

logical; if TRUE, print progress messages

Value

Same as SplineQuadraticQuant

Wrapper function for Cubic spline quantile regression

Description

This is a convenience wrapper for SplineCubicQuant with convention of previous versions SplineConstQuantRegBs3.

Usage

SplineConstQuantRegBs3(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  convcons = 0,
  der3cons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knot (quantiles are then used)

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained. If scalar, repeated.

convcons

Convexity constraint vector per knot: 1 = convex, -1 = concave, 0 = unconstrained. If scalar, repeated.

der3cons

Constraint on the 3rd derivative (on esach intervall: -1: negative, 0: no constraint, 1: positive constraint

solver

'CVXR' solver to use (default = 'CLARABEL')

weight

Observation weights (default = 1 for all)

verbose

boolean FALSE (default) or TRUE.

Value

Same as SplineCubicQuant

Wrapper function for quartic spline quantile regression

Description

This is a convenience wrapper for SplineQuarticQuant that follows the same naming convention as SplineConstQuantRegBs3.

Usage

SplineConstQuantRegBs4(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  convcons = 0,
  der3cons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knot

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained

convcons

Convexity constraint vector per interval: 1 = convex, -1 = concave, 0 = unconstrained

der3cons

Third derivative constraint vector at knot: 1 = positive third derivative, -1 = negative, 0 = unconstrained

solver

'CVXR' solver to use (default = "OSQP")

weight

Observation weights (default = 1 for all)

verbose

Logical; if TRUE, print progress messages

Value

Same as SplineQuarticQuant

Constrained quantile regression with cubic splines

Description

Performs quantile regression using cubic B-splines, with optional monotonicity constraints (via Karlin-Studden) and convexity constraints.

Usage

SplineCubicQuant(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  convcons = 0,
  der3cons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knot (quantiles are then used)

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained. If scalar, repeated.

convcons

Convexity constraint vector per knot: 1 = convex, -1 = concave, 0 = unconstrained. If scalar, repeated.

der3cons

Constraint on the 3rd derivative (on esach intervall: -1: negative, 0: no constraint, 1: positive constraint

solver

'CVXR' solver to use (default = 'CLARABEL')

weight

Observation weights (default = 1 for all)

verbose

boolean FALSE (default) or TRUE.

Value

A list containing:

coefficients

B-spline coefficients (including y mean)

degree

Spline degree (always 3)

ext_knot

ext_knot vector used

int_knot

knot vector

References

See Also

Related 'R' packages:

Other implementations:

Examples

#optional set.seed(42)
x <- seq(0, 1, length=100)
y <- 2*x + sin(6*pi*x)/2 + rnorm(100, 0, 0.05)
knot <- quantile(x, probs=seq(0,1,length.out=10))

# Median quantile regression without constraints
fit <- SplineConstQuantRegBs3(x, y, knot, tau=0.5)

# With increasing monotonicity constraint
fit_monot <- SplineConstQuantRegBs3(x, y, knot, tau=0.5, monot=1)

# With convexity constraint
fit_convex <- SplineConstQuantRegBs3(x, y, knot, tau=0.5, convcons=1)

Quantile regression with linear splines and monotonicity constraints

Description

Performs quantile regression using linear B-splines with monotonicity constraints. For linear splines, the derivative is constant on each interval, so monotonicity is a simple linear constraint on the derivative.

Usage

SplineLinearQuant(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knots

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained

solver

CVXR solver to use (default = "OSQP")

weight

Observation weights (default = 1 for all)

verbose

logical; if TRUE, print progress messages

Value

A list containing coefficients, degree, and knots

Quantile regression with quadratic splines and shape constraints

Description

Performs quantile regression using quadratic B-splines with: - Monotonicity: Karlin-Studden constraints on the derivative (linear) - Convexity: Karlin-Studden constraints on the second derivative (constant)

Usage

SplineQuadraticQuant(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  convcons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knots

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained. Although constraints are set at knots; we apply them on each interval, at both extremities. kn+1 knots, kn constraints taken into account.

convcons

Convexity constraint vector per interval: 1 = convex, -1 = concave, 0 = unconstrained. kn constraints are considered for kn+1 knots.

solver

'CVXR' solver to use (default = 'CLARABEL')

weight

Observation weights (default = 1 for all)

verbose

logical; if TRUE, print progress messages

Value

A list containing coefficients, degree, and knots

Quantile regression with quartic splines and shape constraints

Description

Performs quantile regression using quartic (degree 4) B-splines with monotonicity (Karlin-Studden constraints on the cubic derivative), convexity (Karlin-Studden constraints on the quadratic second derivative), and third derivative constraints (linear at knot).

Usage

SplineQuarticQuant(
  xtab,
  ytab,
  knot,
  tau,
  monot = 0,
  convcons = 0,
  der3cons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knot

tau

Quantile (between 0 and 1)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained

convcons

Convexity constraint vector per interval: 1 = convex, -1 = concave, 0 = unconstrained

der3cons

Third derivative constraint vector at knot: 1 = positive third derivative, -1 = negative, 0 = unconstrained

solver

'CVXR' solver to use (default = "OSQP")

weight

Observation weights (default = 1 for all)

verbose

Logical; if TRUE, print progress messages

Value

A list containing coefficients, degree, and knot

Derivatives at knot of a B-spline

Description

Computes derivative values of a B-spline at knot (efficient because it directly uses polynomial coefficients).

Usage

Spline_der_knot(Bsbase, der = 1)

Arguments

Bsbase

Object returned by Bspline_base

der

Derivative order (default = 1)

Value

Matrix of derivative values (n_splines x n_knot)

Apply Karlin-Studden constraints for a cubic polynomial

Description

For a cubic polynomial p(u) = a*u^3 + b*u^2 + c*u + d on [0,1], this function applies the 'Karlin-Studden SOCP constraints' to ensure p(u) >= 0 or p(u) <= 0 on [0,1].

Usage

apply_karlin_cubic(p3, p2, p1, p0, z0, z1, sign = 1)

Arguments

p3

Coefficient of u^3

p2

Coefficient of u^2

p1

Coefficient of u

p0

Constant term

z0

Auxiliary SOCP variable for cubic

z1

Auxiliary SOCP variable for cubic

sign

Sign of the constraint (+1 for >= 0, -1 for <= 0)

Value

List of 'CVXR' constraints

Apply Karlin-Studden constraints for a quadratic polynomial

Description

For a quadratic polynomial p(u) = a*u^2 + b*u + c on [0,1], this function applies the Karlin-Studden SOCP constraints to ensure p(u) >= 0 or p(u) <= 0 on [0,1].

Usage

apply_karlin_quadratic(p2, p1, p0, z0, sign = 1)

Arguments

p2

Coefficient of u^2

p1

Coefficient of u

p0

Constant term

z0

Auxiliary SOCP variable

sign

Sign of the constraint (+1 for >= 0, -1 for <= 0)

Value

List of 'CVXR' constraints

Apply linear constraints at knot for the third derivative

Description

For a quartic spline, the third derivative is affine (linear) on each interval. This function applies sign constraints at the knot.

Usage

apply_linear_constraint(const_value, sign = 1)

Arguments

const_value

Value of the third derivative at a knot

sign

Sign of the constraint (+1 for >= 0, -1 for <= 0)

Value

List of 'CVXR' constraints

Direct evaluation of a B-spline basis

Description

Computes the values of all B-spline basis functions at given points.

Usage

bs_direct(Basis, x_values = NULL, verbose = FALSE)

Arguments

Basis

Object returned by Bspline_base

x_values

Vector of evaluation points

verbose

set to TRUE increases verbosity

Value

Matrix of basis function values (n_splines x length(x_values))

normalized first and second derivative coefficients on each interval. for a cubic B-spline basis

Description

normalized first and second derivative coefficients on each interval. for a cubic B-spline basis

Usage

bspline_to_deriv_coeffs_cubic(tn, degree = 3, x_values = 0, verbose = FALSE)

Arguments

tn

Knot vector (effective partition, not extended)

degree

Spline degree (default = 3)

x_values

Evaluation points for design matrix (0 = no evaluation)

verbose

boolean FALSE (default) or TRUE.

Value

A list containing (kn: Nb intervals, N=kn+3: Nb basis functions):

d0

Design matrix (if x_values provided)

d1

First derivative coefficients [a3, a2, a1] for each interval: (kn x N x 3) array

d2

Second derivative values at knot: ((kn+1) x N) matrix

d3

Third derivative values at knots: (kn x N) matrix

Derivative coefficients for linear B-spline to Computes normalized first derivative coefficients for linear B-splines. For linear splines, the derivative is constant on each interval.

Description

Derivative coefficients for linear B-spline to Computes normalized first derivative coefficients for linear B-splines. For linear splines, the derivative is constant on each interval.

Usage

bspline_to_deriv_coeffs_lin(tn, degree = 1, x_values = 0, verbose = FALSE)

Arguments

tn

Knot vector (effective partition)

degree

Spline degree (should be 1)

x_values

Evaluation points for design matrix (0 = no evaluation)

verbose

logical; if TRUE, print progress messages

Value

A list containing:

d0

Design matrix (if x_values provided)

d1

First derivative values (constant per interval)

quadratic B-spline derivative coefficients

Description

Computes normalized first and second derivative coefficients for quadratic B-splines on each interval.

Usage

bspline_to_deriv_coeffs_quad(tn, degree = 2, x_values = 0, verbose = FALSE)

Arguments

tn

Knot vector (effective partition)

degree

Spline degree (should be 2)

x_values

Evaluation points for design matrix (0 = no evaluation)

verbose

logical; if TRUE, print progress messages

Value

A list containing:

d0

Design matrix (if x_values provided)

d1

First derivative coefficients [a1, a0] for each interval

d2

Second derivative values (constant per interval)

Convert quartic B-spline to derivative coefficients

Description

Computes normalized first, second, and third derivative coefficients for quartic B-splines on each interval.

Usage

bspline_to_deriv_coeffs_quart(knot, degree = 4, x_values = 0)

Arguments

knot

Knot vector (effective partition)

degree

Spline degree (should be 4)

x_values

Evaluation points for design matrix

Value

A list containing:

d0

Design matrix (if x_values provided)

d1

First derivative coefficients [a3, a2, a1, a0] for each interval

d2

Second derivative coefficients [a2, a1, a0] for each interval

d3

Third derivative values at knot (linear constraints)

Change polynomial basis (Taylor expansion)

Description

Converts a polynomial expressed in the basis (t-a)^k to its representation in the basis (t-b)^k using Taylor's formula. P(t) = sum c_k (t-a)^k P(t) = sum c"_k (t-b)^k

Usage

change_polynomial_base_taylor(coeffs_a, a, b)

Arguments

coeffs_a

Coefficients in basis centered at a (decreasing powers)

a

Original expansion point

b

New expansion point

Value

Coefficients in basis centered at b

Evaluates a piecewise polynomial (PP form) function at given points.

Description

Evaluates a piecewise polynomial (PP form) function at given points.

Usage

evalpp(p, x_values)

Arguments

p

List with components ext_knot (ext_knot) and coeff

x_values

Vector of evaluation points

Value

Function values at the requested points

Get parameters from a callable spline or a callable pp object

Description

Get parameters from a callable spline or a callable pp object

Usage

get_parameters(x)

Arguments

x

A callable spline object

Value

A list with degree, knots, coefficients, and 'Bspline' object

Create a callable spline object

Description

Transforms a list container 'Bspline' that may result from any of the regression functions associated to 'quantile_spline' into a callable function that is the spline function with given knots and coefficients on the corresponding B-spline basis. It can be evaluated at any point of the knot range transfering the call to the 'spline_eval()' function, while preserving access to parameters. Outside the knots range, it extrapolates the side part of the spline.

Usage

make_spline(Bspline, verbose = FALSE, callable = TRUE)

Arguments

Bspline

A list containing at least (knot, coefficients, degree) like the one returned by quantile_spline or one of the degree-specific functions. If it already contains a 'spline' element, returns the object unchanged.

verbose

Boolean. If TRUE : output the attributes of the 'Bspline'

callable

is a Boolean flag that allows to return a simple spline list with class 'non_callable_spline'.

Value

Either a callable function can be called as 'Bspline(x)', with class ('callable_spline'), and all parameters as attributes or the list of parameters with an additional 'non_callable_spline' classe.

Build a piecewise polynomial (PP) form

Description

Creates a PP structure from polynomial coefficients and knots. If callable = TRUE, returns a function that evaluates the PP.

Usage

makpp(coefficients, tn, callable = FALSE, verbose = FALSE)

Arguments

coefficients

Coefficient matrix (kn x (degree+1))

tn

a Knot vector of length kn+1.

callable

Boolean; if TRUE, returns a callable function

verbose

Boolean

Value

A PP object or a callable function

Evaluate polynomial

Description

Evaluates a polynomial at one or more points.

Usage

poly_eval(p, xvalues)

Arguments

p

Coefficient vector (decreasing powers)

xvalues

vector at which to evaluate the polynomial

Value

Vector of same length as xvalues : polynomial values at the points xvalues

Examples

# P(x) = 1 + x + x^2
poly_eval(c(1, 1, 1), c(0, 1, 2)) # returns c(1, 3, 7)

Polynomial addition

Description

Adds two polynomials represented by coefficients in decreasing power order.

Usage

polyadd(p1, p2, verbose = FALSE)

Arguments

p1

First polynomial (coefficient vector)

p2

Second polynomial (coefficient vector)

verbose

boolean FALSE (default) or TRUE.

Value

Coefficient vector of the sum

Examples

polyadd(c(1, 1), c(1, -1)) # returns c(2, 0)

Polynomial derivative Computes the derivative of order der of a polynomial.

Description

Polynomial derivative Computes the derivative of order der of a polynomial.

Usage

polyderiv(p, der = 1)

Arguments

p

Coefficient vector (decreasing powers)

der

Derivative order (default = 1)

Value

Coefficients of the derivative polynomial

Examples

# P(x) = x^2 -> P'(x) = 2x
polyderiv(c(1, 0, 0), 1) # returns c(2, 0)

Polynomial multiplication

Description

Multiplies two polynomials represented by coefficients in decreasing power order.

Usage

polymul(p1, p2, ord = 0, verbose = FALSE)

Arguments

p1

First polynomial (coefficient vector, decreasing powers)

p2

Second polynomial (coefficient vector, decreasing powers)

ord

Unused (compatibility parameter)

verbose

boolean FALSE (default) or TRUE.

Value

Coefficient vector of the product polynomial (decreasing powers)

Examples

# (1 + x) * (1 + x) = 1 + 2x + x^2
polymul(c(1, 1), c(1, 1)) # returns c(1, 2, 1)

Print method for callable_pp objects

Description

Print method for callable_pp objects

Usage

## S3 method for class 'callable_pp'
print(x, ...)

Arguments

x

A callable_pp object

...

Additional arguments

Print method for callable spline

Description

Print method for callable spline

Usage

## S3 method for class 'callable_spline'
print(x, ...)

Arguments

x

A callable spline object

...

Additional arguments

Print method for non_callable_pp objects

Description

Print method for non_callable_pp objects

Usage

## S3 method for class 'non_callable_pp'
print(x, ...)

Arguments

x

A non_callable_pp object

...

Additional arguments

Print method for non_callable_spline results

Description

Print method for non_callable_spline results

Usage

## S3 method for class 'non_callable_spline'
print(x, ...)

Arguments

x

Result object from quantile_spline when callable=FALSE

...

Additional arguments

Unified Quantile Regression with B-Splines of Any Degree (1 to 4)

Description

This function provides a unified interface for quantile regression with B-splines of degrees 1 to 4, with shape constraints (monotonicity, convexity, third derivative).

Usage

quantile_spline(
  xtab,
  ytab,
  knot,
  tau = 0.5,
  degree = 3,
  monot = 0,
  convcons = 0,
  der3cons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE,
  callable = TRUE
)

Arguments

xtab

Predictor vector (x)

ytab

Response vector (y)

knot

Knot vector or number of knots (quantiles are then used)

tau

Quantile (between 0 and 1)

degree

Spline degree: 1 (linear), 2 (quadratic), 3 (cubic), or 4 (quartic)

monot

Monotonicity constraint vector per interval: 1 = increasing, -1 = decreasing, 0 = unconstrained. If scalar, repeated.

convcons

Convexity constraint vector: For degree 1: not available (ignored) For degree 2: per interval (1 = convex, -1 = concave) For degree 3: per knot (1 = convex, -1 = concave) For degree 4: per interval (1 = convex, -1 = concave)

der3cons

Third derivative constraint: For degree 1: not available (third derivative = 0) For degree 2: not available (third derivative = 0) For degree 3: per interval (1 = positive, -1 = negative) For degree 4: per knot (1 = positive, -1 = negative)

solver

'CVXR' solver to use (default = 'CLARABEL')

weight

Observation weights (default = 1 for all)

verbose

logical; if TRUE, print progress messages

callable

render the final container object callable: 'y=Bspline(x)' or 'y=Bspline(x,Bvalues)' for evaluation at x

Value

A list containing coefficients, degree, and knots

References

See Also

SplineLinearQuant, SplineQuadraticQuant, SplineCubicQuant, SplineQuarticQuant

Examples

# Generate data
set.seed(42)
x <- seq(0, 1, length.out = 100)
y <- 2*x + sin(6*pi*x)/2 + rnorm(100, 0, 0.05)
knot <- quantile(x, probs = seq(0, 1, length.out = 10))

# Linear spline (degree 1) with increasing constraint
fit_lin <- quantile_spline(x, y, knot, tau = 0.5, degree = 1, monot = 1)

# Quadratic spline (degree 2) with convexity constraint
fit_quad <- quantile_spline(x, y, knot, tau = 0.5, degree = 2, convcons = 1)

# Cubic spline (degree 3) with both constraints
fit_cubic <- quantile_spline(x, y, knot, tau = 0.5, degree = 3,
                             monot = 1, convcons = 1)

# Quartic spline (degree 4) with all constraints
fit_quart <- quantile_spline(x, y, knot, tau = 0.5, degree = 4,
                             monot = 1, convcons = 1, der3cons = 1)

Reduce polynomial

Description

Removes leading zeros from a polynomial coefficient vector.

Usage

reduce_pol(p, verbose = FALSE)

Arguments

p

Polynomial coefficient vector(coefficients are in decreasing order)

verbose

Boolean FALSE (default) or TRUE.

Value

Reduced vector (without leading zeros)

Examples

reduce_pol(c(0,0, 1, 1))

Evaluate a B-spline

Description

Evaluates a spline (linear combination of B-splines) at given points.

Usage

spline_eval(Bspline, x_values = NULL, der = 0, Bvalues = NULL, verbose = FALSE)

Arguments

Bspline

Spline object (list with coefficients on the 'Bspline' basis, degree, extended knot) A 'Bspline' can also be rendered callable witk 'make_spline(BSpline)'

x_values

Vector of evaluation points. By default, evaluation is calculated at the knots

der

integer 0 (defalut)...degree is the order of derivative

Bvalues

: the values of the 'Bspline' basis evaluated at the values x this increases the speed by avoiding re-doing the same calculations of the basis for each spline with the same knots.

verbose

boollean, if TRUE output more messages

Value

vector of same length as x_values, with Spline values at the requested points

Examples

{ # Create and evaluate a spline
# This function is also used when a 'Bspline' object is rendered callable as a function
# with make_spline()
tn<-c(0,1,2,3,4,5)
x_values<-seq(0,5,length=100)
Bspline=list(degree=3, knot=tn,coefficients=runif(length(tn)+3-1))
y <- spline_eval(Bspline, x_values)
#alternatively compute the base before to optimize if needed
sn <- c(0,0,0,0,1,2,3,4,5,5,5,5)
Bsbase <- Bspline_base(sn, degree=3)
Bvalues <-bs_direct(Bsbase,x_values)
y <- spline_eval(Bspline=Bspline,x_values=x_values, Bvalues=Bvalues )}

Comprehensive test function

Description

Runs quantile regression tests with and without constraints, and displays results. Demo function. This example also shows that solution may be evaluated (extrapolation) out of the knot range

Usage

test_karlin_simple(degree = 3, seed = NULL, verbose = FALSE)

Arguments

degree

1, 2, 3 or 4 (default 3). The degree of the regression spline.

seed

(default=NULL) value for the random generator.

verbose

boolean FALSE (default) or TRUE.

Visualize a B-spline functions basis

Description

Plots all functions of a B-spline basis.

Usage

view_basis(BB, x_values = 0)

Arguments

BB

Object returned by Bspline_base

x_values

Vector of evaluation points for plotting (by default 100 points are computed in the knot range)

Value

No return value, called for side effects (generates a plot)