Purpose

The module EvaluateInterpolationPolynomial evaluates a multidimensional, scalar interpolation polynomial at a given point and shows additional information.

Usage

Connect the polynomial to be examined, enter the point at which to evaluate and watch the result.

Note that the polynomial might internally be stored as a sum of polynomials. This is in particular true for those polynomials created by the SmolyakInterpolationPolynomial module. In this case, some of the information shown applies to one summand only, and you can browse through the summands with the Select Summand Number field. Also, you can evaluate the summands individually by enabling the Evaluate one summand only field.

Windows

Default Panel

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

Input Fields

inputPolynomial

name: inputPolynomial, type: MLBase

Parameter Fields

Field Index

Bounding Box: String Number of Summands: Integer
Dimension of Summand: Integer Select Summand Number: Integer
Evaluate one summand only: Bool  
Evaluation Point: String  
Evaluation Value: Double  
Interpolation Nodes: String  
Is constant: Bool  
Newton Values: String  

Visible Fields

Evaluation Point

name: evalPoint, type: String

Sets the point at which the polynomial should be evaluated.

Separate components with comma. If the point does not match the dimension, it will internally be truncated or supplemented with zeros as required.

Evaluation Value

name: evalValue, type: Double, persistent: no

Shows the value of the polynomial at the given point.

If the Evaluate one summand only field is enabled, it displays the value of the current summand at the given point.

Number of Summands

name: countSummands, type: Integer, persistent: no

Shows the number of summands the polynomial consists of.

Select Summand Number

name: numSummand, type: Integer, default: 0

Sets the number of the summand (starting with 0) that should be examined.

This refers to all read-only fields that display properties of one summand only.

Dimension of Summand

name: dim, type: Integer, persistent: no

Shows the space dimension of the current summand.

Usually, the dimension is the same for all summands, but the data structure does not require it to be like this.

Also, if you create a polynomial with the SmolyakInterpolationPolynomial module, the summands will usually have different degrees, so that for certain derivatives (obtained using the DeriveInterpolationPolynomial module), some summands might be constant (and thus stored as a zero-dimensional polynomial) while others are not. See the example network for an example.

Evaluate one summand only

name: evalOneSummandOnly, type: Bool, default: FALSE

If checked, the behavior of Evaluation Value, Bounding Box, and Is constant is changed.

Interpolation Nodes

name: nodes, type: String, persistent: no

Shows some internal information about the current summand.

Newton Values

name: cValues, type: String, persistent: no

Shows some internal information about the current summand.

Bounding Box

name: bBox, type: String, persistent: no

Shows the polynomial's bounding box.

Each polynomial has a generic bounding box, determined by the way it was created with the TensorInterpolationPolynomial or the SmolyakInterpolationPolynomial module.

Usually, the bounding box is defined the way you would intuitively expect it to be. However, if you compute partial derivatives with the DeriveInterpolationPolynomial module, this will usually make the bounding box unexpectedly smaller.

If the Evaluate one summand only field is enabled, this field displays the bounding box of the current summand (instead of the whole polynomial).

Is constant

name: isConst, type: Bool, persistent: no

Shows whether the polynomial is by its representation a constant.

If it is true, this means that the polynomial takes exactly the same values at all points.

If it is false, the polynomial is very likely to be non-constant, but it may occur that the constantness cannot be detected from the representation. To be absolutely sure, use a SimplifyInterpolationPolynomial module before this.