pivotCoordInv

pivotCoordInv transforms back the output of pivotCoord

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Syntax

  • Xback=pivotCoordInv(Xilr)example
  • Xback=pivotCoordInv(Xilr,Name,Value)example

Description

The pivot coordinates represent one-to-one mapping and this function restores the original parts

example

Xback =pivotCoordInv(Xilr) call to CoordInv with all default options.

example

Xback =pivotCoordInv(Xilr, Name, Value) call to CoordInv with option norm.

Examples

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  • call to CoordInv with all default options.

    • X=rand(100,5);
X=X./sum(X,2);
Xilr=pivotCoord(X);
Xback=pivotCoordInv(Xilr);
assert(max(abs(X-Xback),[],'all')<1e-12)

  • call to CoordInv with option norm.

    • X=rand(100,5);
X=X./sum(X,2);
nor=false;
Xilr=pivotCoord(X,'norm',nor);
Xback=pivotCoordInv(Xilr,'norm',nor);

    Input Arguments

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    Xilr — Input data. Matrix or table.

    Matrix or table containing of size n-by-(D-1) contained units transformed into ilr coordinates

    Data Types: single| double

    Name-Value Pair Arguments

    Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

    Example: 'norm',false

    norm —the normalizing constant.boolean.

    If norm is true (default) sqrt((D-i)/(D-i+1)) is used else norm is set equal to 1.

    Example: 'norm',false

    Data Types: logical

    Output Arguments

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    Xback —The original data restored. Array or table

    X is a matrix (or table depending on the input) which is of size n-by-D. Note that the rows are rescaled in such a way that the sum of each row is 1.

    References

    Filzmoser, P., Hron, K. and Templ, M. (2018), "Applied Compositional Data Analysis". Springer, Cham.

    Atkinson, A.C., Riani,M., Corbellini,A., Perrotta D., and Todorov,V. (2024), Applied Robust Statistics through the Monitoring Approach, Heidelberg: Springer Nature.

    See Also

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