bspline {hpa}

B-splines generation, estimation and combination

Description

Function bsplineGenerate generates a list of all basis splines with appropriate knots vector and degree. Function bsplineComb allows to get linear combinations of these b-splines with particular weights. Function bsplineEstimate estimates the spline at points x. The structure of this spline should be provided via m and knots arguments.

Usage

bsplineGenerate(knots, degree, is_names = TRUE)

bsplineEstimate(x, m, knots)

bsplineComb(splines, weights)

Arguments

knots

sorted in ascending order numeric vector representing knots of the spline.

degree

positive integer representing degree of the spline.

is_names

logical; if TRUE (default) then rows and columns of the spline matrices will have a names. Set it to FALSE in order to get notable speed boost.

x

numeric vector representing the points at which the spline should be estimated.

m

numeric matrix which rows correspond to spline intervals while columns represent variables powers. Therefore the element in i-th row and j-th column represents the coefficient associated with the variable that 1) belongs to the i-th interval i.e. between i-th and (i + 1)-th knots 2) raised to the power of (j - 1).

splines

list being returned by the bsplineGenerate function or a manually constructed list with b-splines knots and matrices entries.

weights

numeric vector of the same length as splines.

Details

In contrast to bs function bsplineGenerate generates a splines basis in a form of a list containing information concerning these b-splines structure. In order to evaluate one of these b-splines at particular points bsplineEstimate function should be applied.

Value

Function bsplineGenerate returns a list. Each element of this list is a list containing the following information concerning b-spline structure:

• knots - knots vector of the b-spline.

• m - matrix representing polynomial coefficients for each interval of the spline in the same manner as for m argument (see this argument description above).

• ind - index of the b-spline.

Function bsplineComb returns a list with the following arguments:

• knots - knots vector of the splines.

• m - linear combination of the splines matrices; coefficients of this linear combination are given via weights argument.

Function bsplineGenerate returns a numeric vector of values being calculated at points x via splines with knots vector and matrix m.

Examples

# Let's generate all b-splines of degree 3 with knots 
# vector (-2.1, 1.5, 1.5, 2.2, 3.7, 4.2, 5)
b <- bsplineGenerate(knots = c(-2.1, 1.5, 1.5, 2.2, 3.7, 4.2, 5), 
                     degree = 3)

# Get the first of these b-splines
b[[1]]

# Take a linear combination of these splines with 
# weights 1.6, -1.2 and 3.2.
b_comb <- bsplineComb(splines = b, weights = c(1.6, -1.2, 3.2))

# Estimate this spline value at points (-3, 0.7, 2.5, 3.8, 10)
b_values <- bsplineEstimate(x = c(-3, 0.7, 2.5, 3.8, 10),  
                            knots = b_comb$knots, 
                            m = b_comb$m)

# Visualize the spline
s <- seq(from = 0, to = 5, length = 1000)
b_values_s <- bsplineEstimate(x = s,  
                              knots = b_comb$knots, 
                              m = b_comb$m)
plot(s, b_values_s)