fda (version 1.2.3)

create.exponential.basis: 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 a

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

values

a list containing the basis functions and their derivatives evaluated at the quadrature points contained in the first column of quadvals.

Value

• a basis object with the type expon.

Details

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

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)