# ARTS built-in documentation server

## Workspace Method jacobianSetFuncTransformation

### Description

```Sets the functional transformation of the last element of
jacobian_quantities.

See below for a general description of how retrieval transformations
are defined. Transformations are not applied by methods such asyCalc.
activate the transformations.

The following transformations can be selected (by *transformation_func*):
log   : The natural logarithm
log10 : The base-10 logarithm
atanh : Area hyperbolic tangent
none  : No transformation at all

This method needs only to be called if a functional transformation
is wanted. Default is to make no such tranformation at all (i.e.
the option "none" exists only for reasons of flexibility).

The log-options are applied as log(z-z_min) and log10(z-z_min).
The default for *z_min* is zero, but by changing it the lower limit
for z can be changed. Note that *z_min* becomes the lower limit for
allowed values of z. The GIN *z_max* is here ignored.

For the atanh-option, also *z_max* is considered. This transformation
is applied as atanh((2(z-z_min)/(z_max-z_min))-1). As above,*z_min*
is lower limit for allowed values of z. On the other hand, *z_max*
eines the upper limit for z.

The GIN *transformation_func* is so far only used for atanh. The parameter
specifies the maximum allowed value allowed for u. That is, the valid
range for u becomes ]0,tfunc_parameter[. Note that log and log10
demands/ensures that u > 0, but implies no upper limit.

General handling of retrieval units and transformations:
---
Default is that quantities are retrieved as defined in ARTS, but
both some unit conversion and transformations are provided. These
operations are applied as:
x = A * ( f(u(z)) - b )
where
z is the quantity as defined ARTS
u represents the change of unit
f is the transformation function
A and b define together an affine transformation
x is the retrieved quantity
For example, this systen allows to retrive a principal component
representation (A and b) of the log (f) of relative humidity (u).

Change of unit is selected by the quantity specific jacobian-add
methods (so far only at hand for gas species).

Activating a transformation function is done by this method. Note
that the functions are defined as the transformation from z to x.
For more details on affine transformations, see
jacobianSetAffineTransformation.

```

Authors: Patrick Eriksson, Simon Pfreundschuh

### Synopsis

 jacobianSetFuncTransformation( jacobian_quantities, transformation_func, z_min, z_max )

### Variables

 OUT+IN jacobian_quantities (ArrayOfRetrievalQuantity) The retrieval quantities in the Jacobian matrix. GIN transformation_func (String) The transformation function. GIN z_min (Numeric, Default: 0) Lower limit of z. GIN z_max (Numeric, Default: -99e99) Upper limit of z.