Calculate Span of Tangent Plane

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Description

Calculate the dimension of the tangent space

Usage

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    span(func, x, 
         method="Richardson", method.args=list(d=0.01, eps=1e-4, r=6, v=2),
         show.details=FALSE, ...)
    ## Default S3 method:
span(func, x, 
         method="Richardson", method.args=list(d=0.01, eps=1e-4, r=6, v=2),
         show.details=FALSE, ...)

Arguments

func

a function which returns the residual vector for a given parameter vector.

x

parameter vector first argument to function func indicating the point with respect to which the derivative is calculated.

show.details

logical indicating if detailed calculations should be shown.

method

string indicating the numerical approximation method.

method.args

list with arguments to method (see grad).

...

additional arguments passed to func.

Details

The first argument of a function must be a vector. span performs a svd of the tangent vectors at the point x. This can be used to calculate the dimension of the tangent space (ie. by over specifying the model and counting the number of significant singular values). This function uses Richardson extrapolation (for more details see the functions grad and genD) to get a numerical approximation of the tangent vectors to the parameter manifold. SVD is then used to calculate their span.

Value

The singular values of the matrix of tangent vectors are returned.

Side Effects

If show.details is T then intermediate calculations are printed.

See Also

span.TSestModel, grad, genD

Examples

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func <- function(x){c(x[1], x[1], x[2]^2)}
span(func, c(2,2))
span(func, c(2,5))
span(func, c(2,2,5))