base_lr_transforms.Rdglr is generic log-ratio transform, code used by other
transforms, can be called directly.
glr(x, V) glrInv(y, V) create_alr_base(D, d, inv = FALSE) alr(x, d = NULL) alrInv(y, d = NULL) create_default_ilr_base(D) ilr(x, V = NULL) ilrInv(y, V = NULL) create_clr_base(D, inv = FALSE) clr(x) clrInv(y)
| x | vector or matrix (rows are samples, parts are columns) of data in simplex |
|---|---|
| V | transformation matrix (defines transform) |
| y | matrix (rows are samples, coords are columns) of transformed data |
| D | the number of parts (e.g., number of columns in untransformed data) |
| d | for ALR, which component (integer position) to take as reference (default is ncol(x)) for alrInv corresponds to column position in untransformed matrix. |
| inv | for ALR and CLR, transformation matrix is different forward and inverse |
matrix (converts vectors to row matricies)
The implementation of the ILR transform here relies on the fact that
all the standard log-ratio transforms can be written in the following form
$$y=\log(x)V$$ with inverse transform given by
$$x=\mathcal{C}[exp(yV^t)]$$ where \(\mathcal{C}[\cdot]\) is the closure operator (miniclo). Note however that if \(V\) does not represent an orthonormal
basis in the Aitchison geometry then the \(V\) used for the log-ratio transform may be different
than the one used for the reverse transform (this is the case for the ALR and CLR transforms).
Default ILR base formed by Gram-Schmidt orthogonalization of an ALR basis.
#ALR Transform x <- matrix(runif(30), 10, 3) x <- miniclo(x) x.alr <- alr(x, 2) x <- alrInv(x.alr, 2) # ILR x.ilr <- ilr(x) x <- ilrInv(x.ilr) # CLR x.clr <- clr(x) x <- clrInv(x.clr) # CUSTOM - Be careful if your custom matrix is not # orthogonal the inverse transform may not be given by just the transpose! # For example, this is the case for the ALR V <- matrix(c(1, 1, -1), 3, 1) x.custom <- glr(x, V)