Coefficients of log of parts in a balance matrix, (+1) for numerator and (-1) for denominator, are transformed into the corresponding isometric log-ratio (ilr) coefficients
a (D-1 x D) balance matrix with cells +1, 0 or -1.
logical, if TRUE, balance names are attributed to ilr transforms; if FALSE (default) ilr transforms are numbered ilr1 to ilrD1, where D1=D-1 and D is the number of parts.
Two scalars multiplying positive and negative cells respectively are defined for each row of the matrix bal in such a way that the resulting matrix defines the ilr transformation to apply to the log of a compositional vector. The output transformation matrix is transposed for application to a compositional dataset where the compositions are the rows.
a D \times (D-1) matrix giving the coefficients of the ilr transforms
Pawlowsky-Glahn, V., J. J. Egozcue, and R. Tolosana-Delgado (2007). Lecture Notes on Compositional Data Analysis.
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