IntegrationInterpolationPolynomial¶

MLModule¶

author	`Tim Kroeger`
package	`FMEwork/Release`
dll	`MLStochasticCollocation`
definition	MLStochasticCollocation.def
see also	`TensorInterpolationPolynomial`, `SmolyakInterpolationPolynomial`, `EvaluateInterpolationPolynomial`, `HistogramInterpolationPolynomial`, `ScalePointInterpolationPolynomial`, `DeriveInterpolationPolynomial`, `SimplifyInterpolationPolynomial`, `MultiplyInterpolationPolynomial`, `IntegrateBoxInterpolationPolynomial`, `CovarianceMatrixInterpolationPolynomial`, `PartiallyEvaluateInterpolationPolynomial`, `Histogram3DInterpolationPolynomial`, `HistogramSphereInterpolationPolynomial`, `AddInterpolationPolynomial`, `SlightlySimplifyInterpolationPolynomial`, `TranslateInterpolationPolynomial`, `ImageListInterpolationPolynomial`, `GraphInterpolationPolynomial`, `InterpolatePolynomialToLinearFunction`, `FactorZeroInterpolationPolynomial`
keywords	`interpolation`, `polynomial`, `multivariate`, `integrate`, `anti-derivative`, `antiderivative`, `integral`, `integration`

Purpose¶

The module IntegrationInterpolationPolynomial computes a partial anti-derivative (of arbitrary order) of a multidimensional, scalar interpolation polynomial.

Tips¶

There is no way to specify any of the integration constants.

Note in particular that for multivariate polynomials, the integration “constant” is in fact a function of all variables except the one with respect to that is integrated.

Windows¶

Default Panel¶

../../../Modules/ML/MLStochasticCollocation/mhelp/Images/Screenshots/IntegrationInterpolationPolynomial._default.png

Input Fields¶

inputPolynomial¶

name: inputPolynomial, type: MLBase¶

Output Fields¶

outputPolynomial¶

name: outputPolynomial, type: MLBase¶

Parameter Fields¶

Visible Fields¶

List of Variables¶

name: variableList, type: String¶

Sets a comma-separated list of variable numbers with respect to which the polynomial has to be integrated.

The numbering starts with 0. The order of the indices should not matter (due to Schwarz’s theorem). Consistently, if the field is left empty, the polynomial will be left unchanged.

Auto apply¶

name: autoApply, type: Bool, default: FALSE¶: If checked, the module computes anew on any parameter or input change.

Apply¶

name: apply, type: Trigger¶: If pressed, the module computes anew.