create.exponential.basis {fda}R Documentation

Create an Exponential Basis

Description

Create an exponential basis object defining a set of exponential functions with rate constants in argument ratevec.

Usage

create.exponential.basis(rangeval=c(0,1), nbasis=1,
                         ratevec=1, dropind=NULL,
                         quadvals=NULL, values=NULL)

Arguments

rangeval a vector of length 2 containing the initial and final values of the interval over which the functional data object can be evaluated.
nbasis the number of basis functions.
ratevec a vector of length nbasis of rate constants defining basis functions of the form exp(rate*x).
dropind a vector of integers specifiying the basis functions to be dropped, if any. For example, if it is required that a function be zero at the left boundary, this is achieved by dropping the first basis function, the only one that is nonzero at that point. Default value NULL.
quadvals a matrix with two columns and a number of rows equal to the number of argument values used to approximate an integral using Simpson's rule. The first column contains these argument values. A minimum of 5 values are required for each inter-knot interval, and that is often enough. These are equally spaced between two adjacent knots. The second column contains the weights used for Simpson's rule. These are proportional to 1, 4, 2, 4, ..., 2, 4, 1.
values a list containing the basis functions and their derivatives evaluated at the quadrature points contained in the first column of quadvals .

Details

Exponential functions are of the type $exp(bx)$ where $b$ is the rate constant. If $b = 0$, the constant function is defined.

Value

a basis object with the type expon.

See Also

basisfd, create.bspline.basis, create.constant.basis, create.fourier.basis, create.monomial.basis, create.polygonal.basis, create.polynomial.basis, create.power.basis

Examples


#  Create an exponential basis over interval [0,5]
#  with basis functions 1, exp(-t) and exp(-5t)
basisobj <- create.exponential.basis(c(0,5),3,c(0,-1,-5))
#  plot the basis
plot(basisobj)


[Package fda version 1.1.6 Index]