Create an Exponential Basis
create.exponential.basis |
Language Reference for FDA Library
|
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)
OPTIONAL 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 exponential 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
.
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)