# span: Calculate Span of Tangent Plane In curve: Dynamic Systems Estimation - Curvature Extensions

## Description

Calculate the dimension of the tangent space

## Usage

 ```1 2 3 4 5 6 7``` ``` 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

 ```1 2 3 4``` ```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)) ```

curve documentation built on May 31, 2017, 3:42 a.m.