curvature: Curvature

In curve: Dynamic Systems Estimation - Curvature Extensions

Description

Curvature calculations and summary statistics as in Bates and Watts.

Usage

    curvature(func, ...)
    ## Default S3 method:
curvature(func, x, 
       method="Richardson", method.args=list(d=0.01, eps=1e-4, r=6, v=2),
        signif=0.05, show.details=FALSE, warn=TRUE, ...)
    ## S3 method for class 'Darray'
curvature(func, signif = 0.05,
      show.extra.details=FALSE, show.details=show.extra.details, warn=TRUE, ...)

Arguments

func	a function for the default method, a Darray object, or a object for which a specific method is defined (e.g. a TSestModel).
x	parameters to the function.
signif	The significance level for F test (passed to qf).
show.details	logical indicating if intermediate calculations should be printed.
show.extra.details	logical indicating if extra intermediate calculations should be printed.
warn	see effectiveCurvature.
method	string indicating the numerical approximation method.
method.args	list with arguments to method (see grad).
...	additional arguments passed to func.

Details

This function is generic. It can be called with a function and parameter x, in which case the Bates and Watts D matrix is calculated, or with a previously calculated D matrix. A function func should return a sample space vector at the parameter value x. The method for a Darray object works on the result from genD which has already done most of the calculations. The Darray has an element Dlist with the 3 elements as follows: D is a matrix of first(gradients) and second order partial derivatives organized in the same manner as Bates and Watts. (first p columns are the gradients and the next p(p-1)/2 columns are the lower triangle of the Hessian). p is the dimension of the parameter space=dim of the tangent space. f0 is the function value at the point where the matrix D was calculated. (The calculation should not/does not? depend on this value - but it should be the right dimension and 0's do not work.

Value

A list is returned (with invisible). Curvature summary statistics as in Bates and Watts are in the element stat. A representation of the Bates and Watts D matrix is in the element Dlist. The curvature array C as in Batts and Watts defn. (7.16) p242 and examples p244 & p245 is in the elements C.parameter and C.intrinsic.

Side Effects

Curvature summary statistics as in Bates and Watts are printed.

References

Bates and Watts(1983), 'Nonlinear Regression Analysis and Its Applications.'

See Also

genD curvature.TSestModel effectiveCurvature

Examples

    func <- function(x){c(x[1], x[1], x[2]^2)}
 #   curvature(func, c(2,2))

curve documentation built on May 2, 2019, 5:31 p.m.