ResampleLinearFunction

MLModule

author	Tim Kroeger
package	FMEwork/Release
dll	MLStochasticCollocation
definition	MLStochasticCollocation.def
see also	LoadLinearFunction, InterpolatePolynomialToLinearFunction, EvaluateLinearFunction, GraphLinearFunction, NodesLinearFunction, PartiallyEvaluateLinearFunction, IntegrateBoxLinearFunction, SelectLinearFunction, CovarianceMatrixLinearFunction, ThresholdLinearFunction, SaveLinearFunction, HistogramLinearFunction, AddLinearFunction, BoundingBoxLinearFunction, HistogramSphereLinearFunction
keywords	interpolation, function, multivariate, piecewise, multilinear, resample, refine, refinement

Purpose

The module ResampleLinearFunction creates a piecewise multi-linear function (or an array of such functions) out of another such function (or an array, respectively), using different refinement settings.

The new refinement settings must be less strict than the original settings that were used to create the input object, since otherwise additional evaluations of the originally approximated function would be required.

The use of this module is for convergence studies. Usually, you will approximate you function using piecewise multi-linear functions with increasing fineness and check for convergence (in whatsoever way). Since you would certainly minimize the total amount of function evaluations of your original function as well as the total amount of written code, it is a good idea to just run you code once with the finest refinement settings that you require and then feed the result into a ResampleLinearFunction module to simulate what would have happened if coarser settings would have been used.

Windows

Default Panel

Input Fields

inputFunctions

name: inputFunctions, type: MLBase

Output Fields

outputFunctions

name: outputFunctions, type: MLBase

Parameter Fields

Field Index

Apply: Trigger	Refinement Rule: Enum
Auto apply: Bool	Use unfinished: Bool
Balance Mode: Enum
Epsilon: String
Exponent: Double
Maximal Level: Integer
Maximal Level per Direction: String
Minimal Level: Integer

Visible Fields

Minimal Level

name: minLevel, type: Integer, default: 2, minimum: 0

Sets a value so that the sparse grid on which the function is interpolated is refined uniformly up to this level.

Maximal Level

name: maxLevel, type: Integer, default: 10, minimum: 0

Sets a value so that the sparse grid on which the function is interpolated is not refined more than to this level.

Maximal Level per Direction

name: maxLevelPerDirection, type: String

Sets a level value per direction.

Additionally to the Maximal Level field, it is possible to specify here maximal levels for each direction (separated by commas). This allows to do the following two things: First, use different maximal levels for different directions. Secondly, specify that the finest allowed grid is a uniform grid, which is often useful for discontinuous functions.

Refinement Rule

name: refinementRule, type: Enum, default: Default

Sets a refinement rule that is applied to values between Minimal Level and Maximal Level.

Values:

Title	Name	Description
Default	Default	This is what the MutlivarLinFuncCreator class does if no user-specified refinement rule is employed: Let ε be the value of the Epsilon, a the value of the Exponent field, n the current level, and x the surplus on a node of this level. Then, the node corresponding to x is refined if any only if x > ε2-na.
Distance And Angle	Distance And Angle	This mode assumes that the number of functions is an even number (typically 6) and that the first half of them denote position vectors in an n-dimensional space (typically n=3) and the second half of them denote direction vectors in the same dimension. Any node is refined if the Euclidean norm of the surplus of the position is larger than ε1 or the cosine of the angle between the refined and unrefined directions is smaller than 1-ε2. Here, the Epsilon should contain exactly two values; they correspond to ε1 and ε2.

Epsilon

name: eps, type: String, default: 1.0e-5

Sets a value for refinement.

These values are supposed to be parameters to the selected refinement rule. If the Default refinement rule is selected, the Epsilon field should contain as many values (separated by commas) as the function array has components. See rules for a detailed description of the meaning of these values. For the other refinement rules, see also the above description for the number of the expected parameters and their meanings. The Exponent field is only utilized for the Default rule.

Exponent

name: epsExponent, type: Double, default: 0

Sets a value for refinement.

See Epsilon for further information.

Balance Mode

name: balanceMode, type: Enum, default: Adaptive

Defines a balance mode.

For details about balancing see the paper Bungartz/Dirnstorfer: Computing 71, 89-114 (2003).

Values:

Title	Name
None	None
Full	Full
Adaptive	Adaptive

Use unfinished

name: useUnfinished, type: Bool, default: FALSE

If the module detects that the input function(s) do not provide all the information required to create the requested output function(s) (that means, the selected refinement settings would lead to a grid that is at least partially finer than the original one), this is indicated by invalidating the output completely. Usually, this means that you should recompute your input function with finer settings. If, for whatever reason, you like to get the (unfinished) result of the computation, please enable this field.

Auto apply

name: autoApply, type: Bool, default: FALSE

If checked, the module computes anew on any parameter or input changes.

Apply

name: apply, type: Trigger

If pressed, the module computes anew.