Using splines2 with Rcpp

Constructors

There are mainly three constructors in addition to the default constructor: BSpline().

The first non-default constructor is called when internal knots are explicitly specified.

// 1. specified internal_knots
BSpline(const vec& x,
        const vec& internal_knots,
        const unsigned int degree = 3,
        const vec& boundary_knots = vec())

The second non-default constructor is called when an unsigned integer representing the degree of freedom of the complete spline basis (different with df in the R interface) is specified. Then the number of internal knots is computed as spline_df - degree - 1 and the placement of internal knots uses quantiles of specified x.

// 2. specified spline degree of freedom (df)
BSpline(const vec& x,
        const unsigned int spline_df,
        const unsigned int degree = 3,
        const vec& boundary_knots = vec())

The third non-default constructor is explicit and takes a pointer to a base class object. It can be useful when we want to create a new object using the same specification (degree, internal_knots, boundary_knots, etc.) of an existing object.

// 3. create a new object from a base class pointer
BSpline(const SplineBase* pSplineBase)

Function Members

The main methods are

• basis() for spline basis matrix
• derivative() for derivatives of spline bases
• integral() for integrals of spline bases

The specific function signatures are as follows:

mat basis(const bool complete_basis = true)
mat derivative(const unsigned int derivs = 1,
               const bool complete_basis = true)
mat integral(const bool complete_basis = true)

In addition, we may set and get the spline specifications through the following setter and getter functions, respectively.

// setter functions
set_x(const vec&)
set_x(const double)
set_internal_knots(const vec&)
set_boundary_knots(const vec&)
set_degree(const unsigned int)
set_order(const unsigned int)

// getter functions
get_x()
get_internal_knots()
get_boundary_knots()
get_degree()
get_order()
get_spline_df()

The setter function returns a pointer to the current object so that the specification can be chained for convenience. For example,

vec x { arma::regspace(0, 0.1, 1) }; // 0, 0.1, ..., 1
BSpline obj { x, 5 };                // degree = 3 dy default
// change degree to 2 and get basis
mat basis_mat { obj.set_degree(2)->basis() };

Constructors

The main non-default constructor is as follows:

BernsteinPoly(const vec& x,
              const unsigned int degree,
              const vec& boundary_knots = vec())

Function Members

Same with BSpline, the main methods are

• basis() for basis matrix
• derivative() for derivatives of bases
• integral() for integrals of bases

The specific function signatures are as follows:

mat basis(const bool complete_basis = true)
mat derivative(const unsigned int derivs = 1,
               const bool complete_basis = true)
mat integral(const bool complete_basis = true)

In addition, we may similarly set and get the specifications through the following setter and getter functions, respectively.

// setter functions
set_x(const vec&)
set_x(const double)
set_degree(const unsigned int)
set_order(const unsigned int)
set_boundary_knots(const vec&)

// getter functions
get_x()
get_degree()
get_order()
get_boundary_knots()

The setter function also returns a pointer to the current object.