functionnormalizationConstant

Calculate the normalization constant for a distribution given by a piecewise linear density function

Extends from ICON ((Weighted) geometric mean).

Information

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The output y is the area under a piecewise linear probability distribution function specified by a list of points p1, p2, ... pn.

Syntax

Functions.normalizationConstant({{x1,y1},{x2,y2}, ...});

Implementation


y := 0.0;
for i in 1:n - 1 loop
  y := y + areaLineSegment(plPDF[i], plPDF[i + 1]);
end for;

Examples


normalizationConstant({{1,1},{2,2}});    // 1.5
normalizationConstant({{0,1},{10,1}});   // 10.0

Inputs

TypeNameDefaultDescription
Realx (from geometricMean)Vector input
Realweights (from geometricMean)ones(size(x, 1))Vector of weights
RealplPDFPiecewise linear probability density function, i.e., { p1, p2, ... }

Outputs

TypeNameDefaultDescription
Realy (from geometricMean)

Revisions

  • Introduced in v2.1.0.

  • Robustified the implementation in v2.2.