# gam.reparam: Finding stable orthogonal re-parameterization of the square... In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

 gam.reparam R Documentation

## Finding stable orthogonal re-parameterization of the square root penalty.

### Description

INTERNAL function for finding an orthogonal re-parameterization which avoids "dominant machine zero leakage" between components of the square root penalty.

### Usage

```gam.reparam(rS, lsp, deriv)
```

### Arguments

 `rS` list of the square root penalties: last entry is root of fixed penalty, if `fixed.penalty==TRUE` (i.e. `length(rS)>length(sp)`). The assumption here is that `rS[[i]]` are in a null space of total penalty already; see e.g. `totalPenaltySpace` and `mini.roots`. `lsp` vector of log smoothing parameters. `deriv` if `deriv==1` also the first derivative of the log-determinant of the penalty matrix is returned, if `deriv>1` also the second derivative is returned.

### Value

A list containing

• `S`: the total penalty matrix similarity transformed for stability.

• `rS`: the component square roots, transformed in the same way.

• `Qs`: the orthogonal transformation matrix `S = t(Qs)%*%S0%*%Qs`, where `S0` is the untransformed total penalty implied by `sp` and `rS` on input.

• `det`: log|S|.

• `det1`: dlog|S|/dlog(sp) if `deriv >0`.

• `det2`: hessian of log|S| wrt log(sp) if `deriv>1`.

### Author(s)

Simon N. Wood <simon.wood@r-project.org>.

mgcv documentation built on March 29, 2022, 5:06 p.m.