The L1 estimator, or geometric median, is a multivariate generalization of the (univariate) median concept. This function performs a multivariate aggregation (via L1 estimator) according to a suite of ratio-scale soil properties. The L1 estimator is applied to soil profile data that have been sliced to a 1-depth-unit basis. Data should be well stratified by groups defined in `fm`

, otherwise the L1 median may not make any sense.

See the L1 Profiles Tutorial for additional examples.

```
L1_profiles(
x,
fm,
basis = 1,
method = c("regex", "simple", "constant"),
maxDepthRule = c("max", "min"),
maxDepthConstant = NULL
)
```

## Arguments

- x
`SoilProfileCollection`

object

- fm
formula, for example: `group ~ p1 + p2 + p3`

, where "group" is a site-level grouping variable, and "p1", "p2", and "p3" are horizon level variables

- basis
positive integer, aggregation basis (e.g. 1 for 1-depth-unit intervals). Values other than 1 are not currently supported.

- method
soil depth evaluation method: "regex" for regular expression, "simple", or "constant". See details.

- maxDepthRule
maximum depth rule: "max" or "min" See details.

- maxDepthConstant
positive integer, maximum depth when `maxDepthRule = 'constant'`

## Value

a `SoilProfileCollection`

object

## Details

See this related tutorial for additional examples. The `method`

, `maxDepthRule`

, and `maxDepthConstant`

arguments set the maximum depth (over the entire collection) of analysis used to build "L1 profiles". The following rules are available:

`method = 'regex'`

uses pattern matching on horizon designations (note that `hzdesgnname`

metadata must be set with `hzdesgnname(x) <- 'columnname'`

)

`method = 'simple'`

uses `min`

or `max`

as applied to `x`

, no accounting for non-soil horizons (e.g. Cr or R)

`method = 'constant'`

uses a fixed depth value supplied by `maxDepthConstant`

The `maxDepthRule`

argument sets depth calculation constraint, applied to soil depths computed according to `method`

(`min`

or `max`

).

## Note

This function requires the `Gmedian`

package.

## References

Cardot, H., Cenac, P. and Zitt, P-A. (2013). Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm. Bernoulli, 19, 18-43.