powerbasis function

Power Basis Function Values

Evaluates a set of power basis functions, or a derivative of these functions, at a set of arguments.

powerbasis(x, exponents, nderiv=0)

Arguments

• x: a vector of argument values at which the power basis functions are to evaluated. Since exponents may be negative, for example after differentiation, it is required that all argument values be positive.
• exponents: a vector of exponents defining the power basis functions. If $y$ is such a rate value, the corresponding basis function is $x$ to the power $y$. The number of basis functions is equal to the number of exponents.
• nderiv: the derivative to be evaluated. The derivative must not exceed the order. The default derivative is 0, meaning that the basis functions themselves are evaluated.

Returns

a matrix of function values. The number of rows equals the number of arguments, and the number of columns equals the number of basis functions.

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

create.power.basis, powerpen

Examples

#  set up a set of 10 positive argument values.
x <- seq(0.1,1,0.1)
#  compute values for three power basis functions
exponents <- c(0, 1, 2)
#  evaluate the basis matrix
basismat <- powerbasis(x, exponents)