ThresholdLinearFunction

MLModule

author	Tim Kroeger
package	FMEwork/Release
dll	MLStochasticCollocation
definition	MLStochasticCollocation.def
see also	LoadLinearFunction, InterpolatePolynomialToLinearFunction, EvaluateLinearFunction, GraphLinearFunction, NodesLinearFunction, PartiallyEvaluateLinearFunction, IntegrateBoxLinearFunction, SelectLinearFunction, CovarianceMatrixLinearFunction, HistogramLinearFunction, SaveLinearFunction, ResampleLinearFunction, AddLinearFunction, BoundingBoxLinearFunction, HistogramSphereLinearFunction
keywords	interpolation, function, multivariate, piecewise, multilinear, cumulative, distribution, function, threshold, cdf

Purpose

The module ThresholdLinearFunction computes the measure of the subset of points (in the bounding box) on which the value of a piecewise multi-linear function is above a given threshold.

More precisely, it computes the measure of the set on which the function is greater than or equal to the threshold.

Multiple thresholds can be specified, resulting in multiple results.

The module internally approximates the function by a piecewise linear (rather than multi-linear) function, where the pieces are d-simplices (d being the dimension). The bounding box is covered by 2^{d*l`*d! simplices (l being the level supplied in the :field:`level} field), on each of which the corresponding measure is computed exactly. This usually gives a much better result than just evaluating the function on a uniform grid and counting the values that lie above the threshold.

Windows

Default Panel

Input Fields

inputFunction

name: inputFunction, type: MLBase

Parameter Fields

Field Index

Apply: Trigger

Auto apply: Bool

Divide by box size: Bool

Level: Integer

Recommended Level: Integer

Results: String

Thresholds: String

Visible Fields

Recommended Level

name: recommLevel, type: Integer, persistent: no

Sets a recommended level value.

The error that the algorithm makes (besides the fact that the function itself is usually only an approximation of the function you actually want to examine) consists of (a) errors due to leaving out some details of the function, (b) errors due to the approximation by a piecewise linear function, and (c) round-off errors. If you choose the level to be at least the value displayed here, the (a) part of the error is guaranteed to vanish. You should, however, not take this value too seriously.

Level

name: level, type: Integer, default: 1, minimum: 1

Sets the level value.

The higher this value is chosen, the more precise the result is. The number of points at which the function is evaluated is given by (2^l + 1)^d , but the algorithm will evaluate some points more than once, and the number of function evaluations is therefore larger and given by (3 * 2^l-1)^d.

The level must be at least 1. (You will find the reason for this yourself if you compute the number of function evaluations for l=0.)

Divide by box size

name: divideByBoxSize, type: Bool, default: TRUE

If checked, the resulting measures are divided by the size of the bounding box, thus scaled to the interval [0,1].

Thresholds

name: thresh, type: String

Sets the thresholds (separated by commas) that you want to examine.

Results

name: result, type: String

Shows the resulting measures.

Auto apply

name: autoApply, type: Bool, default: FALSE

If checked, the module computes anew on any parameter change.

Apply

name: apply, type: Trigger

If pressed, the module computes anew.