directional_deriv {hmer}

Derivative inner product

Description

Find the (uncertainty modified) inner product between the derivative at a point x and a proposed direction v.

Usage

directional_deriv(em, x, v, sd = NULL, ...)

Arguments

em

The emulator in question

x

The point in input space to evaluate at

v

The direction to assess

sd

How many standard deviations to consider.

...

Additional arguments to pass through (eg local.var to the emulator functions)

Details

Given a point x and a direction v, we find the overlap between E[f'(x)] and v. The emulated derivative has uncertainty associated with it: the variance is taken into account using v^{T} Var[f'(x)] v.

If sd == NULL, then only the (normed) overlap between the derivative and the direction vector is returned. Otherwise a pair of values are returned: these are the normed overlap plus or minus sd times the uncertainty.

This function is concerned with ascertaining whether a direction is oriented in the direction of the emulator gradient, subject to the uncertainty around the estimate of the derivative. It allows for a consideration of "emulated gradient descent".

Value

Either a single numeric or a pair of numerics (see description)

Examples

 directional_deriv(SIREmulators$ems[[1]], SIRSample$validation[1,], c(1,1,1))